PHYS1002_Physics I (Foundamentals)_2013 Semester 1_module2_mechanics_mechanics09

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Defect Inspection in Low-Contrast LCD Images

136IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 7, NO. 1, FEBRUARY 2011Defect Inspection in Low-Contrast LCD Images Using Hough Transform-Based Nonstationary Line DetectionWei-Chen Li and Du-Ming Tsai, Member, IEEEAbstract—In this paper, we propose a Hough transform-based method to identify low-contrast defects in unevenly illuminated images, and especially focus on the inspection of mura defects in liquid crystal display (LCD) panels. The proposed method works on 1-D gray-level proﬁles in the horizontal and vertical directions of the surface image. A point distinctly deviated from the ideal line of a proﬁle can be identiﬁed as a defect one. A 1-D gray-level proﬁle in the unevenly illuminated image results in a nonstationary line signal. The most commonly used technique for straight line detection in a noisy image is Hough transform (HT). The standard HT requires a sufﬁcient number of points lie exactly on the same straight line at a given parameter resolution so that the accumulator will show a distinct peak in the parameter space. It fails to detect a line in a nonstationary signal. In the proposed HT scheme, the points that contribute to the vote do not have to lie on a line. Instead, a distance tolerance to the line sought is ﬁrst given. Any point with the distance to the line falls within the tolerance will be accumulated by taking the distance as the voting weight. A fast search procedure to tighten the possible ranges of line parameters is also proposed for mura detection in LCD images. Experimental results have shown that the proposed method can effectively detect various mura defects including spot-, line-, and region-mura. It performs well for the test images containing nontextured and structurally textured patterns in the unevenly illuminated surfaces. Index Terms—Defect detection, Hough transform (HT), liquid crystal display, mura, surface inspection.Fig. 1. Low-contrast surface images in macroview and microview of LCD panels: (a1), (a2) faultless LCD surface images under macroview (lower resolution) and microview (higher-resolution), respectively; (b1), (b2) respective enhanced images of (a1), (a2); (a3), (a4) defective LCD surface images under macro and microview, respectively; (b3), (b4) respective enhanced images of (a3), (a4).I. INTRODUCTIONIN AUTOMATED surface inspection, defects in uniform or nontextured surfaces can be easily identiﬁed if the local anomalies have distinct contrasts from their regular surrounding neighborhood. However, a defect in the low-contrast image is extremely difﬁcult to detect when the defect shows no clear edges from its surroundings and the background presents uneven illumination. In this paper, we consider the task of automated visual inspection of low-contrast defects and, especially, aim at the mura defects in liquid crystal display (LCD) panels, where the material surfaces require uneven lighting to intensify the hardly visible defects.“Mura” is one large category of defects found in LCD manufacturing. It is derived from the Japanese word for blemish. Mura is a local brightness nonuniformity that causes an unpleasant sensation to human vision [1]. According to the size and shape, the types of mura can be roughly classiﬁed as line-mura, spot-mura, and region-mura. A line-mura is a narrow straight of brightness different from its surrounding neighborhood. A spot-mura is a small circular-shaped area defect. Region-mura is one of the most difﬁcult defects to detect in terms of the automated surface inspection algorithms since the region-mura possesses a large area of a LCD image and shows smooth changes of brightness from its uneven-lighting, low-contrast neighborhood. Fig. 1(a1) and (a2) demonstrate two surface images of a defect-free LCD panel, in which Fig. 1(a1) and (a2) are, respectively, the macroview (lower image resolution) and microview (higher image resolution) of the panel. Fig. 1(b1) and (b2) illustrate the respective enhanced images of Fig. 1(a1) and (a2) by linearly stretching the original gray levels between 0 and 255 for 8-bit displays. The enhancement equation is given byManuscript received March 21, 2009; revised August 18, 2009; accepted October 12, 2009. First published November 24, 2009; current version published February 04, 2011. Paper no. TII-09-03-0041. The authors are with the Department of Industrial Engineering and Management, Yuan-Ze University, Chung-Li 32003, Taiwan, China (e-mail: s958909@.tw; iedmtsai@.tw). Color versions of one or more of the ﬁgures in this paper are available online at . Digital Object Identiﬁer 10.1109/TII.2009.2034844where is the gray level at image coordinates and and are respectively the minimum and maximum gray levels in the image. It can be seen from Fig. 1(a2) that the microview of LCD panel presents a textured background. It comprises horizontal gate lines and vertical data lines in the1551-3203/$26.00 © 2010 IEEELI AND TSAI: DEFECT INSPECTION IN LOW-CONTRAST LCD IMAGES USING HT-BASED NONSTATIONARY LINE DETECTION137surface, and makes the sensed image a class of structural texture. Fig. 1(a3) and (a4) present two defective LCD images that contain, respectively, a line-mura and a spot-mura on the surfaces. Fig. 1(b3) and (b4) are the corresponding enhanced defect images of Fig. 1(a3) and (a4). The enhanced images of both defect-free and defective surfaces show that the surface images are unevenly illuminated and the defects present only smooth edge transition and low intensity contrast from the surrounding background. All these surface properties in images make the automated defect inspection task extremely difﬁcult. This section ﬁrst reviews the previous work on surface defect detection. It then describes the properties of the low-contrast mura in LCD images and the core of the proposed method to tackle the defect detection problem. A. Review of Related Work The requirement of defect detection in uniform surfaces has arisen in glass plates [2], [3], sheet steel [4], aluminum strips [5], and web materials [6]. Defects in these uniform images can be effectively identiﬁed with simple statistical measures such as the mean and variance of gray levels. They can also be easily detected using simple thresholding or edge-detection techniques. The main target surfaces in the present paper involves low-contrast anomalies in an uneven lighting background, which invalidates the use of ﬁrst-order statistics and thresholding and gradient methods to segment the defects. The currently available surface inspection techniques for defect detection in low-contrast images are either only applicable for speciﬁc types of small mura defects such as line-mura and spot-mura, or very computationally intensive for large regionmura. Saitoh [7] presented a machine vision scheme for the inspection of brightness unevenness in LCD panel surfaces. An edge detection algorithm was used to identify discontinuous points ﬁrst. Then, a genetic algorithm was applied to extract the boundary of anomalous brightness region. Kim et al. [8] studied the detection of spot-type defects in LCD panel surfaces. An adaptive multiple-level thresholding method based on the statistical characteristics of the local block is applied to segment the macroview defect from the background surface. Oh et al. [9] studied the detection of line-type defects in TFT-LCD panels. In a low-resolution image, a directional ﬁlter bank (DFB) that ﬁnds directional information is used to identify horizontal or vertical line-shaped abnormal regions. In a high resolution image, an adaptive multilevel thresholding technique is employed to detect abnormal line defects that are brighter or darker than the surrounding pixels. Zhang and Zhang [10] presented a fuzzy expert system to detect point defects, line defects and region defects in TFT-LCD panels. The defects are measured by the features of intensity contrast, area, location, direction and shape. The choice of proper defect features and design of fuzzy rules are time consuming, and highly rely on the types and characteristics of defects in question. Lee and Yoo [11] proposed a surface ﬁtting approach to identify low-contrast region-mura in LCD panels. For each data pixel, they ﬁrst used the modiﬁed regression diagnostics to roughly estimate the background region. The background region was further approximated by a low-order polynomial to generate a background surface. The estimated background surface was then subtracted from the original image to remove the inﬂuence of nonuniform backgroundand transform the segmentation problem into a simple thresholding one. This approach showed good detection results in the experiment. However, it is rather computationally intensive for background surface estimation. By observing the horizontal or vertical scan lines of an unevenly illuminated LCD image, the gray-level proﬁle of a scan line shows the trend of a straight line. Due to the effect of uneven illumination in the surface image, the proﬁle will not present a well-structured line. Rather, the gray-level proﬁle can be considered as a nonstationary signal that shows an upward, downward or ﬂat variation in direction. In this paper, we propose a Hough transform (HT)-based one-dimensional surface inspection scheme that can detect both small- and large-sized mura defects of varying shapes in LCD panel surfaces. Finding a line segment in a noisy nonstationary signal is a nontrivial problem. The most commonly used technique for straight line detection in a noisy image is the HT [12]. The HT for line detection in an image is based on a voting procedure which accumulates the number of points that lie on the same line of speciﬁc parameter values. For straight-line detection, the best straight line is estimated by the maximum counts of accumulator which corresponds to a pair of speciﬁc line parameters. The merit of HT that converts the difﬁcult shape detection in the Cartesian space into simple peak detection in the parameter space will not be beneﬁcial for nonstationary signals. The points deviated from a speciﬁc line, even with a minor distance to the line, will not be accumulated and the resulting peak is low and scattering. In this study, the standard HT is not suitable to detect the linear trend of nonstationary gray-level proﬁles in low-contrast images. The standard HT has been popularly applied to straight line detection since Duda and Hart [13] proposed the parameterspace transform method. It converts the Cartesian coordinate to parameter space for a line equation system with in the range of and . The transform creates the corresponding line equations, which intersect in . The accumulators count the number the parameter space of intersection points and ﬁnd a peak to decide a pair of speciﬁc parameter with respect to the line equation. The HT is a very costly algorithm in terms of computation time. The space complexity of the standard algorithm is determined by the number of accumulators in the parameter space, and the time complexity is determined by the total number of increments of parameter values. A number of speed-up algorithms for straight-line detection were developed to overcome the high computation load of the standard HT. Bergen and Shvaytser [14] described an efﬁcient probabilistic algorithm with Monte Carlo approximation to the HT. The complexity of the proposed algorithm is independent of the input size. The proposed probabilistic steps involve randomly choosing small subsets of points, and have shown that the complexity can be further reduced by sampling small subsets of points that jointly vote for likely patterns. Rau and Chen [15] used the principal axis analysis method to accelerate the extraction of straight lines and increase the accuracy of the detected lines. Duquenoy and TalebAhmed [16] proposed two HT acceleration techniques, spatial under-sampling and anticipated maxima detection. The undersampling technique was presented to ﬁnd the best criterion derived from the observed stability of the peak position in the138IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 7, NO. 1, FEBRUARY 2011parameter space to stop the transform calculation. The anticipated maxima detection adaptively detects the maximum peak of accumulation in the parameter space to improve the estimated accuracy of peak detection. Furthermore, many a modiﬁed HT methods were also proposed to improve the accuracy of line parameter estimation based on the coarse-to-ﬁne technique [17]–[20]. Niblack and Petkovic [21] alternatively used ﬁltering techniques in the Hough space to improve the estimation accuracy of line parameter values. Costa and Sandler [22] presented a normalized parameter space to reduce the effect of noise points so that the accuracy of peak detection can be improved. B. Surface Properties of LCD Images and Overview of the Method In physics, the energy from a light source that reaches a given part of a surface falls off as the inverse square of the distance that the light travels from the source to the surface [23]. Given the distance from the light source to one end of the image plane and the adding distance to the opposite end of the image plane. Generally, the light source distance is signiﬁcantly larger than ). If the the width of the sensed surface (roughly equal to can be distance is normalized as one unit, then if the term is approximately given by close to zero. Therefore, the intensity is linearly decreased from one end to the opposite end in the image plane if the light source distance is distinctly larger than the sensed surface width. By scanning the sensed 2-D surface image horizontally or vertically, the 1-D gray-level proﬁles crossing over faultless and defective surface regions will all have a global representation of straight line. Given a nonstationary gray-level proﬁle with the trend of a straight line, the defect points on the gray-level proﬁle can be detected by calculating the distance of each point to the best ﬁtting line of the proﬁle. If the distance of a point on the proﬁle is distinctly far away from the ﬁtting line, the point can then be declared as a defect one. The currently available HT methods focused on either improving accuracy of parameter values or accelerating computation time. The standard HT may perform poorly for nonstationary gray-level proﬁles in a low-contrast, unevenly illuminated image. Fig. 2(a) demonstrates a textured LCD image, in which the dark mura defect is in the central bottom area. Fig. 2(b) shows the gray-level proﬁles of two horizontal scan lines across defect-free (scan line 1) and mura (scan line 2) regions. Fig. 2(c) shows the detection results of the standard HT for the defective gray-level proﬁle (scan line 2), in which the detected straight-line with the largest accumulation peak is depicted in the ﬁgure. Fig. 2(d) presents an ideal straight line which makes the mura defect segment far away from the ﬁtting line. The demonstration sample reveals that the standard voting procedure of the HT is invalidated to ﬁnd the line segment in a nonstationary gray-level proﬁle. In this study, a revised version of the HT is proposed for line detection in nonstationary gray-level proﬁles. The standard HT requires a sufﬁcient number of points lie exactly on the same straight line at a given parameter resolution so that the accumulator will show a distinct peak in the parameter space to indicate the presence of a straight line. It fails to detect a line that has numerous points distributed around the vicinity of the lineFig. 2. Two-dimensional and one-dimensional LCD images: (a) original LCD image containing a mura defect in the central bottom area; (b) gray-level proﬁles crossing over defect-free and mura regions; (c) straight line detected by the HT for the scan line 2 in (b); and (d) expected straight line for the scan line 2 in (b).in a nonstationary signal. In the proposed HT-based scheme, the distance tolerance of a point to the line sought is ﬁrst given. Any point with the distance to the line falls within the tolerance will be accumulated as a function of the distance to the line sought. This approach allows the nonstationary points contribute to the accumulator in the voting processing. The proposed HT with adaptive voting weight under a given distance tolerance can well detect the most possible line equation in a nonstationary gray-level proﬁle. Any points on the gray-level proﬁle that are distinctly far away from the ﬁtting line can then be identiﬁed as defective ones. A fast search procedure that can tighten the possible ranges of the line parameters is also proposed by ﬁnding the global dominant line segment of all gray-level proﬁles in each scan direction. By recursively applying the proposed HT method to all individual row and column gray-level proﬁles, the actual region of a mura defect can be presented in the 2-D inspection image. II. NONSTATIONARY LINE SEARCH This section presents the proposed HT scheme for line detection in nonstationary gray-level proﬁles. The standard HT is ﬁrst introduced in Section II-A. The proposed HT-based scheme is then described in Sections II-B and II-C. A. Overview of Hough Transform (HT) In the standard HT algorithm for straight-line detection, the equation used to describe a line in two-dimensional (2-D) space is given by the parameters and in the normal form (1) where is the perpendicular distance of the line to the origin, and is the angle between the normal to the line and the posi-LI AND TSAI: DEFECT INSPECTION IN LOW-CONTRAST LCD IMAGES USING HT-BASED NONSTATIONARY LINE DETECTION139tive axis. To apply the HT with this form, each point is parameter mapped to all possible parameter values in the despace. A two-dimensional (2-D) voting accumulator notes the number of points falling on the line with parameter values and . The largest peak of the accumulator determines and , i.e., the speciﬁc pair ofwhere and denote the most possible parameter values of the straight line sought in the Cartesian space. The standard HT algorithm can well detect a strict line segment in a complicated, noisy image. For a given parameter values and , it basically accumulates for only those points line with a given parameter that lie exactly on the resolution. The points in a nonstationary proﬁle will be treated as the noisy ones, even they are in a distant neighborhood of line. The detection of local peaks in the vicinity the of maximum accumulator value, or an iterative coarse-to-ﬁne search [17]–[20], cannot take into account those points. Therefore, the standard HT may perform poorly for a nonstationary gray-level proﬁle, where only a small segment shows the trend of a straight line. B. Proposed HT Scheme In the proposed HT scheme, the points that contribute to the vote do not have to lie exactly on a line. Instead, the distance tolerance of a point to the line sought is ﬁrst given. Any point with the distance to the line falls within the tolerance will be accumulated as a function of the distance. Conversely, any point with the distance beyond the tolerance is discarded in the voting process. Highly nonstationary gray-level proﬁles require a larger distance tolerance , while more stable gray-level proﬁles use a smaller distance tolerance for detecting the line equation. be of size . For Let the inspection image , the a given horizontal scan line Y, , row gray-level proﬁle is denoted by . The coordinates of a point on the gray-level is then given by , for proﬁle Y of length . To simplify the notation, the gray-level is represented by , i.e., the point on a gray-level proﬁle is denoted by . To calculate the distance between a point and a straight line, we can rewrite (1) from the normal . That is form to the slop-intercept form (2) is the slop , and where . Therefore, the distance from a point proﬁle to the line with parameter values is the intercept in the gray-level is calculated by (3) The distance of a point is used to derive the voting weight in the accumulator, which is given by (4)where is the exponent and is used to adjust the signiﬁcance of a small change in distance . It is set at 3 in this study. Note is in the range between 0 and 1. A that the weight line has a maximum weight of point lying exactly on the 1, whereas the weight is dramatically reduced to 0 as the point is far away from the line. In order to accommodate the nonstationary nature of the graywith distance less level proﬁle, a point than a predetermined distance tolerance is considered as a point on the line with the voting weight deﬁned in (4). HenceThe accumulator then adds the voting weight as (5) At the end of the voting process, the ﬁnal line equation of the gray-level proﬁle is, therefore, given by the maximum value of , i.e.,To demonstrate the effectiveness of the proposed HT and the effect of changes in tolerance , four synthetic 1-D linear signals , , 2, 3, 4, with varying degrees of random noise are are given by created to verify the performance. The signals the following linear equation, which arewhere is a Gaussian noise with zero mean and standard , , , and . is a straight deviation to are the same straight lines line containing no noise, and and direction with added Gaussian noise. The distance of the ideal straight line are . Fig. 3(a)–(d) show the results of line detection for signals , , and from the proposed method. The distance tolerance is given by 2, 5, and 10 to test the ﬁtting results. Table I lists all the estimated and values with varying values. It can be observed that the proposed method can well detect nonfor line stationary lines even under the severe noise signal . The detected parameter values are very close to the true parameter values (159, 84). The peaks of the accumulator are directly proportional to the value of and the detection results are not sensitive to the changes in value. A synthetic gray-level proﬁle is also generated to demonstrate the effectiveness of the proposed HT that uses the distance as the adaptive weight to ﬁnd a straight line within a given distance tolerance. Fig. 4(a) shows the line detection result from the standard HT for the synthetic nonstationary proﬁle. The result indicates the linear trend of the proﬁle cannot be precisely detected. In contrast, Fig. 4(b) shows the line detection result from the proposed method. It well performs the detection of linear trend, regardless of the variation along the line. In defect detection, the proposed HT scheme is used to identify best ﬁtting lines of the oscillated, nonstationary gray-level proﬁles in a low-contrast image. During the scanning procedure140IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 7, NO. 1, FEBRUARY 2011Fig. 3. Four nonstationary line signals and their detected lines from the proposed method: (a) a synthetic line signal L without noise; (b)–(d) three synthetic line signals L L with different Gaussian noises of , , respectively. (a) L ; (b) L and ; (c) L ; and . (d) L ( = 10)=6=8= 10( = 0)( = 6)( = 8)TABLE I FITTING RESULTS OF THE PROPOSED METHOD FOR THE LINE SIGNALS IN Fig. 3The expected distance and direction of the line signal: = 159, = 84.Fig. 4. (a) Detected straight line from the standard HT for a nonstationary proﬁle. (b) Detected straight line from the proposed HT method. (a) ; ; . ; . (b) ; (68 83)() = (63 88)()=of an inspection image, each column (vertical) and row (horizontal) gray-level proﬁles are individually evaluated. Any point deviated distinctly from the ﬁtting line is marked as a defect one. , we have to estimate gray-level For an image of size proﬁles of horizontal rows and gray-level proﬁles of vertical columns in the image. The voting procedure of the proposed HT scheme for the points on the gray-level proﬁle is based on thedistance tolerance , i.e., the points need not lie exactly on the line sought. The standard HT needs only to evaluate all possible values of in a small ﬁnite range, and then can be calculated by using (1). For the proposed HT method, the line (1) cannot be and used to calculate the value for given coordinates values. Therefore, the proposed HT method must evaluate all possible combinations of both and . This should result in a huge computational burden if all possible combinations of must be evaluated for every point on the gray-level proﬁle. In order to make the proposed HT applicable to defect detection in a manufacturing process, we present a fast selection process that ﬁnds the most possible ranges of and in the line equation. For a given inspection image, all row gray-level proﬁles in the image should have the similar trend of a straight-line shape with or without defects on the surface. It is also true for all column gray-level proﬁles in the image. The core idea for the constraints of and values is to evaluate the ranges from a proﬁle map. The proﬁle map is constructed by overlapping all row gray-level plane (or the proﬁles (or column proﬁles) in the plane). The most possible ranges of and will be extracted from this proﬁle map. The detailed process for searching the ranges of line parameters and in the proﬁle map is discussed in the following section. C. Constraints on the Line Parameters andThe gray-level proﬁles of the same scan direction in a lowcontrast image have approximately the same trend of a line slop. We can therefore plot all gray-level proﬁles of the same scan direction on a map which has the gray-level (from 0 to 255 forLI AND TSAI: DEFECT INSPECTION IN LOW-CONTRAST LCD IMAGES USING HT-BASED NONSTATIONARY LINE DETECTION141Fig. 5. Construction procedure for the row and column proﬁle maps. Fig. 6. High-pass Haar wavelet decomposition: (a) horizontal proﬁle map ^ (x) of (a); and (c) wavelet detail signal R(x; f (x)); (b) upper contour R ^ (x) of (b). The dash-line in (c) represents the control limit 2 d .an 8-bit display) in the vertical axis and the proﬁle point number in the row and in the column) in ( the horizontal axis. Each row (or column) scan image will be (or ) plane to form a proﬁle map. overlapped in the Fig. 5 illustrates an image of size . It therefore involves row proﬁles and column proﬁles. The row proﬁle plane is given by map in theLikewise, the column proﬁle map in the structed asplane is recon-row gray proﬁles has similar trend of a line slop, the upper contour and lower contour in the ﬁltered proﬁle map are basically identical in shape. In a given inspection image, the defect-free region is generally distinctly larger than the defective region. Therefore, the defect-free line segwill be longer than any of the ment in the upper contour defective segments. We need only to identify the defect-free line and the possible range can be easily desegment from termined from such a segment. In this study, we use the fast Haar wavelet decomposition to of detect the longest line segment in the upper contour the ﬁltered proﬁle map. The range search procedure is proin the ﬁltered proceeded as follows. The upper contour ﬁle map is given byRange of : In the proﬁle map, a point of gray-level proﬁles is marked by 0 (black intensity), and the remaining empty space is marked by 1 (white intensity). Once the maps of row and column gray-level proﬁles are separately constructed, we can easily ﬁnd the ranges of and from the maps. The transform representation in the map shows a principal direction of the gray-level proﬁles. Thus, we can easily restrict the search range of within a once the principal direction in the proﬁle map small interval is determined. In the proposed search scheme of parameter ranges, the ranges of will be separately estimated from the row and , column proﬁle maps. For the row proﬁle map the morphological closing operation is ﬁrst implemented to eliminate the noisy points ﬁrst, i.e.,The upper contour is then decomposed into its detailed part using the Haar wavelet frame. Thuswhere and denote, respectively, the dilation and erosion 3 structuring element. The binary operation, and B is a 3 closing operation smoothes the contour and removes isolated (extreme) points in the proﬁle map. Since the majority of thewhere are the high-pass coefﬁcients of the Haar basis [24], and are given by and . is the decomposed detail version of , which entails only the ﬁne detail of the upper contour. Note that has the because same full length of the original upper contour the ﬁltered 1-D signal is not subsampled. Fig. 6(a) illustrates the ﬁltered horizontal proﬁle map of an image, and Fig. 6(b) presents its upper contour. Fig. 6(c) shows the detailed version in the wavelet decomposition. In order to extract the of dominant line segment that shows signiﬁcantly linear trend in , a simple statistical process control limit is used to set up the threshold. This threshold can effectively detect the transition。

PID技术

The Study of MovingTarget Tracking Based on Kalman-CamShift in the VideoWANG Xiangyu Henan University of Technology Zhengzhou, China Wangxiangyu0602@LI XiujuanHenan University of Technology Zhengzhou, ChinaLee_xiujuan@Abstract—I n the process of target tracking, the direction and velocity information of the target is not used in CamShift algorithm so that the tracking is always failed when the target is covered or rotated, while Kalman filter can predict velocity and position of target accurately. For this reason, the paper proposed a novel approach combining CamShift algorithm with Kalman filter for moving target tracking. Firstly, use Kalman filter to predict the possible position of the target in the next frame, and then search and match the target in the corresponding areas using CamShift algorithm. The approach reduces the calculation work greatly because of the smaller searching area. It has a reliable tracking. When the target is rotated or covered, we can also get a well tracking result and the tracking is reliable. The experiment shows that the approach is effective and accurate. Keywords--Kalman filter; CamShift; tacking targetI.I NTRODUCTIONIn recent years, target tracking of video surveillance system has become the most active research areas in computer vision field. The moving target tracking is realized mainly through analyzing of video sequences, predicting the position of target and generating trajectories of the target, it has an important and broad application in the industry, transportation, medicine, military, aerospace and other fields.CamShift algorithm proposed by Bradski is a target tracking method based on color histogram [1]. It has a better tracking result in the simple background. But in the process of target tracking, the space direction and velocity information of the target is not used. So the tracking is always failed when there is serious interference. Kalman filter is a linear recursive filter, and can make optimal estimate to the next state based on the previous state, resulting in an unbiased, stable and optimal state prediction to the image sequence. So we propose an approach combining Kalman filter with CamShift algorithm for moving target tracking. The approach is effective and accurate when the target is rotated or covered.II.C AMSHIFT ALGORITHM ON THE COLOR HISTOGRAMThe principle of CamShift is described as follows. According to the color histogram of target, convert the image to color probability distribution and then initialize the size and the position of the search window. Adjust the window with the obtained result from previous frame adaptively and we can locate the center of the target in the current image.A.The calculating of Back projectiionFirstly calculate the color histogram of the target. The RGB color space has weakness in representing shading effects or rapid illumination changing [2]. To solve this problem, we consider converting from the RGB to HSV color space. In a variety of color spaces, only H channel in HSV color space can express the color information, so we extract it to make histogram. The calculation of H channel is as (1).2cos(2)/[2()()()]H arc R G B R G R B G B=−−−+−−(1)Then calculate its 1D histogram. According to the color histogram of H channel, the original image is converted to color probability distribution. This above process is called Back Projection. In this paper, we make the tracking to the selected target. The original image and color probability distribution are shown in Fig.1. Figure 2 shows the color histogram of H channel, where S and V channels have beeneliminated.Figure 1.The original image and color probability distributionFigure 2. The color histogram of H channelB. Mean shift of alogrithmMean Shift algorithm is a non-parametric estimation method based on gradient of density function which is proposed by Funkunag and applied to Pattern Recognition firstly [3-5]. To locate the target, it uses iterative search to find the extreme value of the probability distribution. The algorithm process is as follows [9]. Select a search window which size S in the probability distribution. The pixel position in the searching window is point (x,y) and I(x,y) is pixel value of point(x,y) in the probability distribution .Then calculate zeroth moment 00M .00(,)M I x y x y=∑∑ (2)Then calculate first moment M01 of x01(,)M yI x y x y=∑∑ (3)Then calculate first moment M10 of y10(,)x yM xI x y =∑∑ (4)Then calculate centric of the search window10000100(,)(//)c c x y M M M M =， (5) Reset the size of the windows = (6)Now we can get t he size of the search window from (6). Move the center of the window to the centroid. If the moving distance is larger than preset-threshold, recalculate the centroid of the adjusted search window by (5). Adjust theposition and size of the window until moving distance is less than preset-threshold. Repeat the before-mentioned steps in the next frame.When tracking the given target using Camshift algorithm, we only need to calculate the color probability distribution of the pixel in a larger region than the current window. Because we need not calculate probability distribution of all the pixelsin every frame image, it reduces the computation and savesthe searching time. C. Camshift algorithm Extending the mentioned Mean Shift to a continuous video sequence, we get CamShift algorithm [6]. The principle is to make Mean Shift algorithm apply to all the frame of the video sequence, and then regard the center and the size of thewindow obtained from the previous frame as the initial value of the search window in the next frame. Iterate this process, and we can succeed in the target tracking. The concrete steps as follows.1) Initialize the search window.2) Calculate the back projection to obtain the color probability distribution of the search window.3) Run Mean Shift algorithm to get the size and position of the new search window.4) In the next frame of the video, re-initialize the size and position of the search window with value of c), and then jump to b)III. CAMSHIFT ALGORITHM COMBINE WITH KALAM FILTER Kalman filter is an estimate algorithm of the minimum variance for status switch in the dynamic system [7]. It can predict the position and velocity of the target accurately. Thus, we adopt Kalman filter to estimate the parameters of the moving target. The state equation of the system is (7), and observation equation is (8).1k k k k X A X W +=+ (7)k k k k Y H X V =+ (8) Where k A is state transition matrix. k Y is measurement state of system. k H is observation matrix. k W is dynamic noise corresponding to state vector, and k V is measurement noise corresponding to observation vector. And Q and R are covariance matrixes of kW andkV respectively.()T k k k k k X x y x y = is state vector of the system, and()T kkk Y x y =is observation vector of the system. Thepredict vector is '''''()T k k k k k X x y xy = , where k x ,k y ,k x ,k y are the position and velocity of target in the x-axis and y-axis. k x ',k y ',k x ' ,k y ' are the position and velocity of target predicted by Kalman filter. According to (7) and (8), we can obtain state transitionmatrix A and the observation matrix H respectively. 10001000100001dt dt A =⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦，10010000H =⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦Kalman filter is divided into two stages: prediction and correction. At first, initialize the covariance matrix Q of dynamic noise, the covariance matrix R of measurementnoise and the state vector 0X . In software OpenCV, we create a random number generator, which is use to initialize above-mentioned parameters to reasonable numbers in the vicinity of zero. Then set the center position of search window in Camshift algorithm through k x 'and k y 'of the predictingvector 'k X , and regard the position of centroid calculated by Camshift algorithm as observation value k Y to revise state vector 'k X , and finally we can obtain 1k X +. Flow chat ofthe algorithm is shown in Fig.3.Figure 3.The flow chart of the proposed algorithmThe process can be summarized as follows. Firstly, initialize a search window, and then estimate the appearing position of target in the next moment by Kalman filter. Finally, search the target using CamShift algorithm in the estimated range to locate the final position of target. If the search is successful, the tracking result will be regarded as observed value of Kalman filter to estimate where target is in the next moment. Otherwise, the predictive value is directly used to estimate the position of target in the next moment.IV. E XPERIMENT AND RESULT ANALYSIS In accordance with the proposed approach, we carry out target track test in a number of video sequences by OpenCV. The experimental result as follows. Figure 4 shows the track result of CamShift algorithm and Figure 5 shows the track result of approach proposed. Through comparing and analyzing the experimental results, we can get a conclusion that both methods can complete tracking. But when the target is rotated or covered, the proposed approach in this paper increases the reliability of prediction result and has a better tracking performance. At the same time, there is no case oflost target or diverged track region.Figure 4.The experimental result of Camshift algorithmFigure 5.The result of CamShift combination Kalman filterV. CONCLUSIONSFollowing a brief introduction to Kalman filter and CamShift algorithm, we proposed a novel tracking approachfor moving target, which combined CamShift algorithm with Kalman filter. The new approach solves the problem of losing target tracking in CamShift algorithm when the target is rotated or covered. In this paper, we reasonably use Kalman filter which can predict the position and velocity of target in the process of CamShift algorithm and we realize target tracking by visual library of OpenCV in the Microsoft Visual C++ [8]. The experimental result demonstrated the efficiency and reliability of this algorithm proposed. A CKNOWLEDGMENT The authors would like to thank all the students, staff, and faculty of the Henan University of Technology, China, whomade themselves available for the experiments reported in this paper. The insightful comments of the anonymous reviewers and editors are also greatly appreciated. This work is supported by National Technology R&D program in the Eleventh Five-year plan of China (2008BADA8B04-2-1) and the School Research Fund of Henan University of Technology (09XZZ001).R EFERENCES[1]G. Eason, B. Noble, and I. N. Sneddon, “On certain integrals ofLipschitz-Hankel type involving products of Bessel functions,” Phil.Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955.(references) G. R.Bradski,“Real Time Face and Object Tracking as aComponent of a Perceptual User Interface,”IEEE workshop on Applications of Computer Vision, Princeton, pp. 214-219,October 1998. [2]P.Perez, C.Hue,J,Vermaak,M.Gangnet, “Color-Based ProbabilisticTracking,”Lecture Notes in Computer Science, Computer Vision,Vol.2305,pp.661-675,Spring Berlin,Heidelberg,2002 [3] D. COMANICIU，P. MEER. Mean shift analysis and application [J].Proceedings of the Seventh IEEE International Conference Computer Vision，1999，2：1197-1203.[4] D. COMANICIU，P. MEER. Mean shift: a robust application towardfeature space analysis [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence，2002，24(5)：603-619.[5]K Fukunaga,L D Hostetler. The estimation of the gradient of a densityfunction with application in pattern recognition [ J ]. IEEE Trans Information Theory, 1975, 21(1):32-40[6]Boyle M. The Effects of Capture Conditions on the CAMSHIFT FaceTracker[R]. Alberta, Canada: Department of Computer Sci-ence, University of Calgary, 2001[7]Jang Dae-Sik, Kim Gye-Young, ChoiHyung-Il. Kalman filterincorporated model updating for real-time tracking [C ]. P roc.1996 IEEE TENCON ,Digital Signal P rocessing App lications,1996: 878-882.[8]YU Shiqi,于LIU Ruizhen. Learing OpenCV .Publishing House ofTsingHua University ,2007.[9] D Comaniciu, V Ramesh, P Meer. Real time tracking ofnon rigid objectsusing mean shift [ J ]. IEEE Conference on Computer Vision and Pattern Recognition, 2000, 2:142 - 149。

报错解决——精选推荐

报错解决V ASP⾃旋轨道耦合计算错误汇总静态计算时，报错：VERY BAD NEWS! Internal内部error in subroutine⼦程序IBZKPT:Reciprocal倒数的lattice and k-lattice belong to different class of lattices. Often results are still useful (48)INCAR参数设置：对策：根据所⽤集群，修改INCAR中NPAR。

将NPAR=4变成NPAR=1，已解决！错误：sub space matrix类错误报错：静态和能带计算中出现警告：W ARNING: Sub-Space-Matrix is not hermitian共轭in DA V结构优化出现错误：WARNING: Sub-Space-Matrix is not hermitian in DA V 4 -4.681828688433112E-002对策：通过将默认AMIX=0.4，修改成AMIX=0.2（或0.3），问题得以解决。

以下是类似的错误：WARNING: Sub-Space-Matrix is not hermitian in rmm -3.00000000000000RMM: 22 -0.167633596124E+02 -0.57393E+00 -0.44312E-01 1326 0.221E+00BRMIX:very serious problems the old and the new charge density differ old charge density: 28.00003 new 28.06093 0.111E+00错误：WARNING: Sub-Space-Matrix is not hermitian in rmm -42.5000000000000ERROR FEXCP: supplied Exchange-correletion table is too small, maximal index : 4794错误：结构优化Bi2Te3时，log⽂件：WARNING in EDDIAG: sub space matrix is not hermitian 1 -0.199E+01RMM: 200 0.179366581305E+01 -0.10588E-01 -0.14220E+00 718 0.261E-01BRMIX: very serious problems the old and the new charge density differ old charge density: 56.00230 new 124.70394 66 F= 0.17936658E+01 E0= 0.18295246E+01 d E =0.557217E-02curvature: 0.00 expect dE= 0.000E+00 dE for cont linesearch 0.000E+00ZBRENT: fatal error in bracketingplease rerun with smaller EDIFF, or copy CONTCAR to POSCAR and continue但是，将CONTCAR拷贝成POSCAR，接着算静态没有报错，这样算出来的结果有问题吗？对策1：⽤这个CONTCAR拷贝成POSCAR重新做⼀次结构优化，看是否达到优化精度！对策2：⽤这个CONTCAR拷贝成POSCAR，并且修改EDIFF（⽬前参数EDIFF=1E-6）,默认为10-4错误：WARNING: Sub-Space-Matrix is not hermitian in DA V 1 -7.626640664998020E-003⽹上参考解决⽅案：对策1：减⼩POTIM: IBRION=0，标准分⼦动⼒学模拟。

Some recent developments in wave buoy measurement technology(波浪浮标研究进展)

Ž.Coastal Engineering 371999309–329 r locate r coastalengSome recent developments in wave buoymeasurement technologyHarald E.Krogstada,),Stephen F.Barstow b,1,Svein Erik Aasen b ,Ignacio Rodriguez c,2a Department of Mathematical Sciences,Norwegian Uni Õersity for Science and Technology,Trondheim,Norway b Oceanor,Trondheim,Norway c Puertos del Estado,Madrid,SpainAbstractŽ.Two new wave sensors,the Motion Reference Unit MRU and the differential Global Ž.Positioning System GPS technology used in the new Smart-800buoy are described and the results of a series of sea trials and intercomparisons with conventional wave measuring buoys using Datawell sensors are given.The results have shown that the directional spectra derived from Ž.the MRU are practically indistinguishable from the Datawell Heave r Pitch r Roll Hippy sensor.The Smart-800directional wave data are also shown to be of good quality.Both sensors have no moving parts and are,therefore,more robust than the conventional accelerometer based wave sensors which have dominated the market for the last 30years.In addition,of importance in particular to coastal applications and transportation in the high latitudes,neither sensor is sensitive to extremes of temperature.Both sensors have also low mass making for lighter buoys,easier deployment and transportation.q 1999Elsevier Science B.V.All rights reserved.Keywords:Wave buoys;GPS;Motion Reference Unit;Wave direction;Smart-800;SeawatchCorresponding author.Fax:q 47-73-59-3524;E-mail:harald.krogstad@math.ntnu.no1E-mail:sbarstow@oceanor.no.2E-mail:ignacio@puertos.es.0378-3839r 99r $-see front matter q 1999Elsevier Science B.V.All rights reserved.Ž.PII:S 0378-38399900031-9()310H.E.Krogstad et al.r Coastal Engineering371999309–3291.IntroductionThe collection of ocean wave data at sea away from man-made structures has,over the last30years or so,been served more or less exclusively by moored wave buoys of various types,based on the measurement of buoy motions by accelerometer and tilt sensors.The most successful commercial wave buoys have been Datawell’s Waverider Ž.used widely since the late1960s.Datawell’s original directional buoy,the Wavec,Ž.replaced later by the Directional Waverider since the early1990s,together with theŽ.Ž.two multi-sensor buoys Wavescan since the mid-1980s and Seawatch1990s mainly for deep water deployments and for multi-parameter environmental and metocean data collection.Both buoys have also until recently used Datawell sensors for wave data collection.In1996,the Smart-800buoy was launched,representing a novel approach to operational open-sea wave measurement technology.The Smart-800measures oceanŽ. waves using the Norwegian Seatex’s differential GPS Global Positioning System software.The buoy contains a GPS receiver,which measures the velocity of the buoy in the north,east and vertical directions at1Hz sampling rate.The raw data are transferred to a shore station via a UHF radio link where a PC carries out pre-processing,directional wave analysis,presentation,storage and data dissemination,making it ideal for coastal Ž.wave monitoring Krogstad et al.,1997.The second new arrival on the commercial market is the Motion Reference Unit Ž.MRU.The MRU,which is also manufactured by Seatex,can be set up to provide timeŽseries both for directional measurements in the Wavescan buoy i.e.,heave,pitch and .Ž.roll and in the Seawatch buoy heave and displacement.This sensor has a number of practical advantages including small size,low weight and the fact that it is not sensitive to rapid rotation under transport or to low temperatures,unlike the Datawell sensors.Following a short initial intercomparison in February1995of the Smart buoy against a Wavescan,which gave promising results,four different directional buoys,including the Smart-800,were deployed in late April1996.An intercomparison of the Smart buoy and a Directional Waverider during this period confirmed the quality of the GPS-based data.During winter1997–1998,a more comprehensive test to obtain data in higher wave conditions was carried out against a reference Directional Waverider on the exposed coast of mid-Norway.A shallow water test in the southern North Sea has also recently been completed.The deep water validation results will be presented in this paper.One of the other buoys in the April1996campaign was a Wavescan which was equipped with both a Datawell heave,pitch,roll sensor and an MRU-6from which absolutely synchronous measurements were obtained.These allowed a direct validation of the capabilities of the MRU sensor at measuring directional spectra as dynamic buoy effects will be equal with both systems.The synchronous measurements also made it possible to compare the raw time series on a wave-by-wave basis.Excellent agreement was found in the data from the two sensor systems apart from the directional spreading which was consistently lower from the MRU-6.Experience and validation of the MRU sensor in a Seawatch buoy is also discussed.In Section2,we discuss these new buoy r sensor systems which are now routinely used world-wide in the Norwegian Oceanor’s survey work and also sold commercially.We then describe,in Section3,()H.E.Krogstad et al.r Coastal Engineering371999309–329311 differences and similarities in the data processing between these systems,and in Section 4,the various field trials designed to validate the different buoy r sensor combinations.2.Directional buoys and wave sensorsŽ.Since the release of Datawell’s Directional Waverider DWR in1989and itsŽ.successful validation Barstow and Kollstad,1991,Oceanor have been using three different types of buoy for directional wave measurements around the world,according to actual customer data needs and the local metocean conditions.DWRs have been commonly used in coastal areas and deep water low current conditions,in projects where only wave measurements were called for.The DWR works on the heave–dis-placement principle,measuring time series of wave elevation and displacement in two orthogonal directions,and relies on the buoy moving closely with the orbital motion of a free-floating particle predicted by linear wave theory.For deep water locations,where also other meteorological,oceanographic or environ-mental parameters are required,Oceanor has preferred to use the Seawatch buoy,at least since1994following the comparison between the Seawatch buoy,equipped with a standard DWR sensor,and a stand-alone DWR showed that the directional wave spectraŽ.were almost identical Barstow et al.,1994.In fact,the results suggested that the Seawatch r DWR combination provides slightly narrower directional spread,possibly due to better surface following ability.For deep water and high current conditions,and otherwise when meteorological measurements are also required,the Wavescan buoy Ž.Barstow et al.,1991has most often been used.This buoy is a heave–pitch–roll buoy, measuring time series of the wave elevation together with the slope of the surface in two orthogonal directions.The arrival on the market of the GPS based Smart-800buoy and the MRU wave sensor,both developed by the Norwegian Seatex,led to a re-appraisal of the wave sensors used.2.1.The Seatex Motion Reference UnitŽ.The Seatex Motion Reference Unit6MRU-6is a compact sensor for directional wave measurements incorporating solid state linear accelerometers,angular rate sensors and servo flux gate compasses for all three axes together with a powerful microproces-sor for signal processing.Both heave–displacement data and heave–pitch–roll data are available from the sensor allowing for application in different types of wave buoy.The angular rate sensors are based on the Coriolis force vibrating angular rate principle.This principle is,in many respects,superior to traditional gyros and has no moving parts.The magnetometer is based on the servo fluxgate principle.This means that a local three-axisŽ.coil system cancels the external magnetic field i.e.,the field to be measured.This type of sensor has a much better linearity and stability than traditional fluxgate sensors based on direct voltage output from the fluxgate itself without the use of a zero field.Ž.The unit over-samples the sensor signals at800Hz and uses advanced digital signal processing algorithms for calculation of the wave motions.A variable gain12state Kalman filter is part of the sensor error estimator.This filter is tuned during operation to()312H.E.Krogstad et al.r Coastal Engineering371999309–329suppress horizontal acceleration noise on the orientation.As this noise is unknown during start-up,a warm-up period of at least20min has to be used with the MRU-6 sensor.The MRU-6is configurable to different applications and its dynamic response can be programmed.Linear motions are calculated by a limited double integration of accelera-tion.The lower cut-off frequency and damping of this filter can be set in the softwareŽ.for use on different platforms from buoys to large rigs.For the Seawatch and Wavescan buoys,a cut-off frequency of0.025Hz is used.Above this frequency,the dynamic frequency response is unity,except for frequencies near the cut-off frequency where the response is given and corrected for by the software in the buoy.This sensor has a number of advantages of importance compared to traditional sensors used in wave buoys including:Ž.ØSmall size cylinder of roughly10cm diameter and20cm length.Ž.ØLow weight 2.5kg.ØCan easily be transported and handled and is not sensitive to rapid rotation.ØNot sensitive to low or high temperatures.2.2.The Smart-800The Smart-800is a‘‘hybrid’’buoy which,although essentially an in-situ instrument,Ž.relies on the well known GPS Global Positioning System satellites to make waveŽ.measurements using differential GPS DGPS technology.The Smart-800system mea-sures,in fact,buoy velocities in both north,east and vertical directions once each second,using differential GPS measurements of the Doppler shifts,the most robust and accurate of the differential techniques for measuring relative motion.The raw data are transferred to a shore or platform based station via a UHF radio link where a PC carries out all pre-processing,directional wave analysis,data presentation,storage and dissemi-nation.The lack of active wave sensors in the buoy gives many advantages making the buoy more robust,enhancing reliability and providing for low maintenance.Its small size and low weight also makes it easy to transport,deploy and operate.The global positioning system consists of24satellites orbiting at an altitude of 20,200km.The Smart-800relies on the Doppler measurements from the GPS receiver on the buoy.The radial velocity of the satellite with respect to the receiver is computedŽ.from the ephemerides the reference orbit for each satellite which are transmitted via the satellite message.The difference between the velocity derived from the Doppler shift and the computed radial velocity is caused by the motion of the buoy,in addition to various error sources.Given the radial velocity of the buoy with respect to all theŽ.tracked GPS satellites at least four are required at any one time,the velocity of the buoy in latitude,longitude and the vertical may be computed.In order to obtain more precise Doppler shifts,and hence,more precise measure-Žments,GPS corrections obtained either from a local reference station,satellite or by .other means are used in order to remove most of the error sources on the GPS data Ž.DGPS mode.The GPS data are transmitted from the buoy by way of a UHF link Ž.430–450MHz.The Doppler measurements are,in particular,affected by the rate ofŽ. change of these errors,the main contribution to which is the Selective Availability SA, which is the‘‘noise’’added by the operators of the GPS system.SA affects the satellite()H.E.Krogstad et al.r Coastal Engineering371999309–329313Ž.clock frequency and the transmitted navigation message the ephemerides leading toŽ.degraded satellite coordinates position and velocity.The Smart-800system then utilises the time series of measured velocities in the three directions to compute theŽ.wave spectrum and associated wave parameters see Section3.The Doppler shift,which gives a basic accuracy on velocity of about3–5cm r s,is used because it is both more robust and has at least as good accuracy as the alternative, which is utilising the phase information,when computing relative motion.This alterna-tive GPS technique,which was considered during the development,uses the code phase to compute the position of the buoy rather than the velocity,and is reliant on a local GPS reference station no more than about7–10km distance for the best accuracy. Although the Smart-800needs to be within range of a receiver station for radio transmissions,it can also be used far from coasts in support of,say,an offshore operation from a boat,production ship,semi-submersible or other moving or fixed installation.In this case,the UHF receiver station and presentation software may be on the vessel whilst the GPS corrections are supplied by satellite.The robustness of the Smart-800system is due again to its measurement technique,which is much less sensitive to loss of lock,which may occur,for example,as a result of wave splash in high seas.For the Doppler Smart measurements,this is a relatively minor problem. Using the phases,it would take much longer before measurements could recommence, often an unacceptable situation when monitoring operations in high seas.Ž.Normally,the three velocities are sampled at1Hz each for17min1024samples,a sampling scheme used commonly for Waverider buoy measurements for many years. The logging interval of the time series is,however,flexible and can easily be set to anything between half-hourly and daily.Fig.1.The Smart-800buoy hardware.()H.E.Krogstad et al.r Coastal Engineering 371999309–329314The full Smart-800system consists of the buoy and its mooring,the shore station,in addition to the Smart-800Windows wave processing software.The buoy has a spheri-Ž.Ž.cally shaped hull,with a diameter of 80cm hence,the 800in the name Fig.1.The Žbuoy contains no moving parts.The main components are the battery package optional .alkaline or lithium batteries ,allowing a deployment of 1year if 3hourly data transmission and alkaline batteries are chosen,and the electronic housing which contains the UHF modem,the CPU and the GPS receiver,in addition to the GPS antenna,UHF antenna and a beacon light.The buoy weighs only 80kg.The shore station consists of a UHF modem,a CPU and the optional GPS receiver,which may be used,depending on the application,as the DGPS reference station.The Windows based real time presentation software gives a graphical presentation of both directional wave spectra and wave parameters.3.Data processingŽ.All three buoys Wavescan,Smart-800and the DWR are basically single point triplet devices measuring three linearly independent properties of the wave field.The Ž.analysis for both the DWR also as used in the Seawatch Buoy and the Smart-800is Žquite similar to the methods used for traditional heave–pitch–roll buoys see,e.g.,.Ž.Tucker,1991.One assumes Linear Wave Theory LWT with the directional wave Ž.Ž.Ž.Ž.spectrum E f ,u written as E f ,u s S f D u ,f ,where S is the frequency spectrum,and D the frequency dependent directional distribution,`1D u ,f s 1q 2a f cos n u q b f sin n u .1Ä4Ž.Ž.Ž.Ž.Ž.Ž.Ýn n 2p n s 12Ž.2Ž.Moreover,the dispersion relation is v s 2p f s gk tanh kh where v is the angular frequency,k the wavenumber,g the acceleration due to gravity,and h the Table 1Definitions of the main wave parametersNameSymbol Definition 1r 2a w Ž.x Significant wave heightH H s 4H S f d f m0m021r 2a w Ž.Ž.x Mean zero-upcrossing periodT T s H S f d f r H f S f d f m02m02Ž.Maximum spectral densitySf Sf s S f p p p Ž.Ž.Peak periodT T s 1r f ,max S f s S f p p p f p Ž.ŽŽ.Ž..Mean wave directionM M f s a tan2b f ,a f d1d1111r 2222Ž.ŽŽ..Ž.Ž.Directional spreadSpr Spr f s 21y r ,r s a f q b f 1111Ž.Direction at the spectral peakThT ThT s M f s 1r T p p d1p Main wave directionM Spectral weighted mean wave direction dir Low frequency significantH Significant wave height calculated with m0lf wave heightintegration limits 0.05–0.07Hz inclusive.Low frequency wave directionThL Mean direction in frequency band 0.05–0.07Hz f High frequency wave directionThH Mean direction in frequency band 0.40–0.44Hz f Ž.Spread at the spectral peakSprT SprT s Spr f s 1r T p p 1p a Integration limits 0.04–0.44Hz inclusive.()H.E.Krogstad et al.r Coastal Engineering 371999309–329315water depth.An overview of directional and non-directional sea state parameters,used in this paper,and their definitions from the directional wave spectrum is given in Table 1.Ž.The recorded time series data are heave,slope north and east Wavescan ,heave,Ž.displacement north and east Seawatch and the DWR and time series of the three Ž.velocity components in a fixed coordinate system vertical,longitude and latitude for the Smart-800.The cross spectrum between any two of these time series,i and j ,has the form 2p U S f ,u s S f T k f ,u T k f ,u D u ,f d u ,2Ž.Ž.Ž.Ž.Ž.Ž.Ž.Ž.H i j i j u s 0Ž.where T and T are appropriate transfer functions Allender et al.,1989.It turns out i j that the directional dependence in the transfer function is identical for slope,horizontal displacement and horizontal velocity.Therefore,the expressions for the directional Fourier coefficients which are obtained from the cross spectra will be identical to the Ž.Ž.relations for the heave–pitch–roll buoy Tucker,1991.Allsystems thus provide S f ,Ž.Ž.Ž.Ž.a f ,a f ,b f and b f .For the Smart-800measurements,the wave elevation 1212spectrum is obtained by dividing the vertical velocity spectrum by v 2.For a heave–pitch–roll buoy,such as Wavescan,the so-called check ratio is the ratio between the estimated root-mean-square wavenumber and the LWT wavenumber for each frequency,and is defined as follows S f q S f Ž.Ž.x x y y R f s r k ,3Ž.Ž.hpr (S f Ž.where S and S are the slope spectra in the x and y directions,respectively.x x y y A similar ratio may also be defined for Smart-800.S f q S f x x y y 2R f s tanh kh ,4Ž.Ž.Ž.(S f Ž.z z In this case S ,S and S denote the corresponding velocity spectra,and the ratio x x y y z z should be one in a linear wave field.4.ValidationThe MRU wave sensor has been tested both in its heave–pitch–roll configuration in a Wavescan buoy and also in its heave–displacement configuration in a Seawatch buoy.The Smart-800buoy has undergone a number of tests both in deep and shallow water.This system verification work is described in the following.4.1.MRU4.1.1.The Wa Õescan testIn April 1996,Seatex deployed a Wavescan buoy for about 5weeks on the exposed western coast of Norway close to the island Frøya.The buoy was instrumented with dual()316H.E.Krogstad et al.r Coastal Engineering371999309–329MRU-6and Hippy-120wave sensors which were set up to sample the buoy heave, pitch,roll and heading synchronously at2Hz for a17min interval each3h.Thus,both sensors sample exactly the same waves,and observed differences should be predomi-nantly due to instrument errors.The standard directional data analysis was identical for the two sensor data sets apart from the electronic transfer functions,which were compensated for in the frequency plane as specified by the manufacturers.Wavescan’sŽ.nominal dynamic transfer functions see Barstow and Krogstad,1984,which compen-sates for the buoy’s pitch r roll resonance at about2.4s,was applied to both sensor Ž. spectra equally the dynamic response was not checked specifically for this deployment. The initial intercomparison of wave parameters between the two sensors showed a ratherŽ.unexpected result.First,the significant wave height H was found to be systemati-m0cally5%lower from the MRU sensor.However,strangely,for the majority of recordsŽ.the maximum wave height H,determined from a zero-crossing analysis on the timemaxseries corrected for the electronic transfer functions,showed almost perfect agreement, but with a number of outliers,up to50cm in error.The inconsistency can be explained by examining the simultaneous time series from the two sensors.Fig.2shows the difference in elevation from the two sensors shown as a time series.From about5min into the series,the error drops to a very low level.The reason for the discrepancy at the beginning of the file was found to be due to the operational set up of the MRU sensor. In order to save power,the sensor is switched on some minutes before measurements commence.What we see for the first minutes of the actual time series is the sensor still ‘‘warming up’’.In practice,this is the time for the Kalman filter to stabilise.During thisFig.2.Time series of the difference in wave elevation at2Hz between the MRU and the Hippy,showing clearly the lack of agreement for the first5min or so of the record.()H.E.Krogstad et al.r Coastal Engineering371999309–329317 initialisation period the measurements are phase and amplitude shifted from the final theoretical electronic response.The cure for this problem has been simply to increase the ‘‘warm-up’’time for the sensor.Following the discovery of the reason for the discrepancy,the intercomparison was repeated based on a directional analysis of the second uncorrupted part of the time seriesparison of the wave parameters derived from the MRU and the Hippy sensor for the duration of Ž.Ž.Ž.Ž.Ž.Ž.the field trial;a H;b H;c T;d ThT;e SprT;and f Sf.See Table1for definitions.m0max p p p p()318H.E.Krogstad et al.r Coastal Engineering371999309–329Ž.Ž.Ž.parison of mean wave spectra from the MRU triangles and the Hippy squares;a all records Ž.and b H)3m.The spectra are indistinguishable apart from the very low frequencies.m0Ž.1024samples.During the measurement period,a good range of wave conditions were Ž.experienced for the time of the year.H reaches4m in two storms,a good mixturem0of wave directions were measured,and both local wind seas and the occasional longAtlantic swell occurred,reaching a peak period of close to15s in four events.Fig.3 shows scatter plots of selected wave parameters between the two sensors for the durationof the experiment.Both H and H now show close to perfect agreement with lessm0maxŽ.than1cm mean difference.The peak wave period T similarly shows little differencepŽ.one large outlier occurs in a strongly bimodal wave spectrum.The maximum spectral density also shows perfect agreement.The main differences are found for the directional parameters.There is somewhat larger scatter for the wave direction at the spectral peakŽ.Ž. parisons of mean spread as a function of frequency from a all simultaneous records and b forŽ.Ž.the30wave records where H)0.5m;for the MRU triangles and the Hippy squares.m0lfŽ.ThT although the overall features are similar and in agreement with the predominant pŽ. weather conditions.The directional spread at the spectral peak period SprT is,p however,systematically higher from the Hippy sensor by as much as22%on average.Ž. We next look at the average wave spectra constructed from all wave records Fig.4.parison of directional spectra,displayed as contour plots,for one of the most energetic long period swells;June1st,1200UTC.The left hand side shows the directional distribution calculated maximum entropy Ž.method Lygre and Krogstad,1986and on the right is shown the wave spectrum;above:Hippy and below: MRU.Notice the very close agreement of the form of the directional wave spectrum,but the somewhatŽ. broader directional distribution from the Hippy.For this example the spread at the spectral peak is408Hippy Ž.and268MRU and H is about2.7m.m0Ž.ŽBoth average spectra for all records N s299as well as storm spectra alone H)3m0 .m;N s7are shown.Apart from at the very low frequencies where the MRU seems to give slightly higher spectral levels compared to the Hippy,these average spectra are indistinguishable,even down to an apparent kink in the high frequency tail at about0.4 Hz which is probably related to the buoy’s pitch r roll eigenfrequency.ŽThe average directional spread calculated by averaging the wave spread at each.frequency over all simultaneous wave spectra for the two systems is shown in Fig.5, first for all records,and second,only for records where there is significant swell energy Žpresent H)0.5m;N s30;where H is the significant wave height calculated m0lf m0lf.over the frequency band from0.05to0.07Hz inclusive.We see again the significant difference in the wave spread estimates at the most energetic frequencies.At frequencies above0.3Hz,both systems give about the same result.For the swell spectra,we see an even bigger difference between the MRU and the Hippy.See,for example,Fig.6which shows simultaneous directional spectra contour plots for the two sensors during an Ž.energetic swell event on June1st emanating from a very deep unseasonal low between Iceland and Scotland.The reason for the difference in the spread estimates was found by looking at the time series of pitch,roll and buoy heading.For wave elevation,both sensors give almostŽ. identical measurements of pitch and roll.However,the buoy heading compass series Ž.Žare quite different Fig.7.The MRU heading time series from a three-axis fluxgate .compass is noticeably smoother than the data from the compass used with the Hippy sensor,which is a gymballed two-axis fluxgate Silva compass.In addition,inspection of several time series shows that spikes are not infrequent on the Silva compass time series. By removing the spikes and smoothing the compass time series,the directional spreadŽ.drops to about the same level as that derived from the MRU sensor Fig.8.The check ratio for the Wavescan buoy was described in Section3.The mean checkŽratio is presented for the same two classes of data as for wave spread all records and .swell events in Fig.9.This shows typical behaviour for the Wavescan buoy,with,forŽ.Ž. Fig.7.Typical time series of buoy heading from the MRU compass solid line and the Hippy dashed line.parison of left directional spread at the spectral peak and right wave direction at the spectral peak from the Wavescan Hippy sensor time series with the compass time series uncorrected against the smoothed de-spiked compass series.Ž.the lower frequencies closer agreement with the theory i.e.,unity for the swell events as we might expect.Interestingly,the agreement in the check ratio between the Hippy and the MRU sensors is almost perfect over all frequencies,which indicates that the departure from unity is due to real buoy effects caused by imperfect surface following, current effects,etc.A small increase close to the pitch r roll resonant frequency can also be seen,which is probably related to slightly non-optimal pitch–roll transfer functions Žthe transfer functions were not optimised specially for this buoy;see Barstow and.Krogstad,1984for more details about the pitch–roll transfer functions.4.1.2.The Seawatch buoy testA short test of a Seawatch buoy,equipped with an MRU-6wave sensor configured toprovide heave and displacement time series,was performed next to a DWR buoy at theparison of mean check ratio as a function of frequency,from left all simultaneous records and Ž.Ž.Ž. right for the30wave records where H)0.5m;for the MRU triangles and the Hippy squares.Them0lfcheck ratio is indistinguishable from the two sensors apart from the lowest frequencies.。

Singularity of the density of states in the two-dimensional Hubbard model from finite size

a r X i v :c o n d -m a t /9503139v 1 27 M a r 1995Singularity of the density of states in the two-dimensional Hubbard model from ﬁnitesize scaling of Yang-Lee zerosE.Abraham 1,I.M.Barbour 2,P.H.Cullen 1,E.G.Klepﬁsh 3,E.R.Pike 3and Sarben Sarkar 31Department of Physics,Heriot-Watt University,Edinburgh EH144AS,UK 2Department of Physics,University of Glasgow,Glasgow G128QQ,UK 3Department of Physics,King’s College London,London WC2R 2LS,UK(February 6,2008)A ﬁnite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane.The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential.Our analysis points to a second-order phase transition with critical exponent 12±1transition controlled by the chemical potential.As in order-disorder transitions,one would expect a symmetry breaking signalled by an order parameter.In this model,the particle-hole symmetry is broken by introducing an “external ﬁeld”which causes the particle density to be-come non-zero.Furthermore,the possibility of the free energy having a singularity at some ﬁnite value of the chemical potential is not excluded:in fact it can be a transition indicated by a divergence of the correlation length.A singularity of the free energy at ﬁnite “exter-nal ﬁeld”was found in ﬁnite-temperature lattice QCD by using theYang-Leeanalysisforthechiral phase tran-sition [14].A possible scenario for such a transition at ﬁnite chemical potential,is one in which the particle den-sity consists of two components derived from the regular and singular parts of the free energy.Since we are dealing with a grand canonical ensemble,the particle number can be calculated for a given chem-ical potential as opposed to constraining the chemical potential by a ﬁxed particle number.Hence the chem-ical potential can be thought of as an external ﬁeld for exploring the behaviour of the free energy.From the mi-croscopic point of view,the critical values of the chemical potential are associated with singularities of the density of states.Transitions related to the singularity of the density of states are known as Lifshitz transitions [15].In metals these transitions only take place at zero tem-perature,while at ﬁnite temperatures the singularities are rounded.However,for a small ratio of temperature to the deviation from the critical values of the chemical potential,the singularity can be traced even at ﬁnite tem-perature.Lifshitz transitions may result from topological changes of the Fermi surface,and may occur inside the Brillouin zone as well as on its boundaries [16].In the case of strongly correlated electron systems the shape of the Fermi surface is indeed aﬀected,which in turn may lead to an extension of the Lifshitz-type singularities into the ﬁnite-temperature regime.In relating the macroscopic quantity of the carrier den-sity to the density of quasiparticle states,we assumed the validity of a single particle excitation picture.Whether strong correlations completely distort this description is beyond the scope of the current study.However,the iden-tiﬁcation of the criticality using the Yang-Lee analysis,remains valid even if collective excitations prevail.The paper is organised as follows.In Section 2we out-line the essentials of the computational technique used to simulate the grand canonical partition function and present its expansion as a polynomial in the fugacity vari-able.In Section 3we present the Yang-Lee zeros of the partition function calculated on 62–102lattices and high-light their qualitative diﬀerences from the 42lattice.In Section 4we analyse the ﬁnite size scaling of the Yang-Lee zeros and compare it to the real-space renormaliza-tion group prediction for a second-order phase transition.Finally,in Section 5we present a summary of our resultsand an outlook for future work.II.SIMULATION ALGORITHM AND FUGACITY EXPANSION OF THE GRAND CANONICALPARTITION FUNCTIONThe model we are studying in this work is a two-dimensional single-band Hubbard HamiltonianˆH=−t <i,j>,σc †i,σc j,σ+U i n i +−12 −µi(n i ++n i −)(1)where the i,j denote the nearest neighbour spatial lat-tice sites,σis the spin degree of freedom and n iσis theelectron number operator c †iσc iσ.The constants t and U correspond to the hopping parameter and the on-site Coulomb repulsion respectively.The chemical potential µis introduced such that µ=0corresponds to half-ﬁlling,i.e.the actual chemical potential is shifted from µto µ−U412.(5)This transformation enables one to integrate out the fermionic degrees of freedom and the resulting partition function is written as an ensemble average of a product of two determinantsZ ={s i,l =±1}˜z = {s i,l =±1}det(M +)det(M −)(6)such thatM ±=I +P ± =I +n τ l =1B ±l(7)where the matrices B ±l are deﬁned asB ±l =e −(±dtV )e −dtK e dtµ(8)with V ij =δij s i,l and K ij =1if i,j are nearestneigh-boursand Kij=0otherwise.The matrices in (7)and (8)are of size (n x n y )×(n x n y ),corresponding to the spatial size of the lattice.The expectation value of a physical observable at chemical potential µ,<O >µ,is given by<O >µ=O ˜z (µ){s i,l =±1}˜z (µ,{s i,l })(9)where the sum over the conﬁgurations of Ising ﬁelds isdenoted by an integral.Since ˜z (µ)is not positive deﬁnite for Re(µ)=0we weight the ensemble of conﬁgurations by the absolute value of ˜z (µ)at some µ=µ0.Thus<O >µ= O ˜z (µ)˜z (µ)|˜z (µ0)|µ0|˜z (µ0)|µ0(10)The partition function Z (µ)is given byZ (µ)∝˜z (µ)N c˜z (µ0)|˜z (µ0)|×e µβ+e −µβ−e µ0β−e −µ0βn (16)When the average sign is near unity,it is safe to as-sume that the lattice conﬁgurations reﬂect accurately thequantum degrees of freedom.Following Blankenbecler et al.[1]the diagonal matrix elements of the equal-time Green’s operator G ±=(I +P ±)−1accurately describe the fermion density on a given conﬁguration.In this regime the adiabatic approximation,which is the basis of the ﬁnite-temperature algorithm,is valid.The situa-tion diﬀers strongly when the average sign becomes small.We are in this case sampling positive and negative ˜z (µ0)conﬁgurations with almost equal probability since the ac-ceptance criterion depends only on the absolute value of ˜z (µ0).In the simulations of the HSﬁelds the situation is dif-ferent from the case of fermions interacting with dynam-ical bosonﬁelds presented in Ref.[1].The auxilary HS ﬁelds do not have a kinetic energy term in the bosonic action which would suppress their rapidﬂuctuations and hence recover the adiabaticity.From the previous sim-ulations on a42lattice[3]we know that avoiding the sign problem,by updating at half-ﬁlling,results in high uncontrolledﬂuctuations of the expansion coeﬃcients for the statistical weight,thus severely limiting the range of validity of the expansion.It is therefore important to obtain the partition function for the widest range ofµ0 and observe the persistence of the hierarchy of the ex-pansion coeﬃcients of Z.An error analysis is required to establish the Gaussian distribution of the simulated observables.We present in the following section results of the bootstrap analysis[17]performed on our data for several values ofµ0.III.TEMPERATURE AND LATTICE-SIZEDEPENDENCE OF THE YANG-LEE ZEROS The simulations were performed in the intermediate on-site repulsion regime U=4t forβ=5,6,7.5on lat-tices42,62,82and forβ=5,6on a102lattice.The ex-pansion coeﬃcients given by eqn.(14)are obtained with relatively small errors and exhibit clear Gaussian distri-bution over the ensemble.This behaviour was recorded for a wide range ofµ0which makes our simulations reli-able in spite of the sign problem.In Fig.1(a-c)we present typical distributions of theﬁrst coeﬃcients correspond-ing to n=1−7in eqn.(14)(normalized with respect to the zeroth power coeﬃcient)forβ=5−7.5for diﬀer-entµ0.The coeﬃcients are obtained using the bootstrap method on over10000conﬁgurations forβ=5increasing to over30000forβ=7.5.In spite of diﬀerent values of the average sign in these simulations,the coeﬃcients of the expansion(16)indicate good correspondence between coeﬃcients obtained with diﬀerent values of the update chemical potentialµ0:the normalized coeﬃcients taken from diﬀerentµ0values and equal power of the expansion variable correspond within the statistical error estimated using the bootstrap analysis.(To compare these coeﬃ-cients we had to shift the expansion by2coshµ0β.)We also performed a bootstrap analysis of the zeros in theµplane which shows clear Gaussian distribution of their real and imaginary parts(see Fig.2).In addition, we observe overlapping results(i.e.same zeros)obtained with diﬀerent values ofµ0.The distribution of Yang-Lee zeros in the complexµ-plane is presented in Fig.3(a-c)for the zeros nearest to the real axis.We observe a gradual decrease of the imaginary part as the lattice size increases.The quantitative analysis of this behaviour is discussed in the next section.The critical domain can be identiﬁed by the behaviour of the density of Yang-Lee zeros’in the positive half-plane of the fugacity.We expect toﬁnd that this density is tem-perature and volume dependent as the system approaches the phase transition.If the temperature is much higher than the critical temperature,the zeros stay far from the positive real axis as it happens in the high-temperature limit of the one-dimensional Ising model(T c=0)in which,forβ=0,the points of singularity of the free energy lie at fugacity value−1.As the temperature de-creases we expect the zeros to migrate to the positive half-plane with their density,in this region,increasing with the system’s volume.Figures4(a-c)show the number N(θ)of zeros in the sector(0,θ)as a function of the angleθ.The zeros shown in theseﬁgures are those presented in Fig.3(a-c)in the chemical potential plane with other zeros lying further from the positive real half-axis added in.We included only the zeros having absolute value less than one which we are able to do because if y i is a zero in the fugacity plane,so is1/y i.The errors are shown where they were estimated using the bootstrap analysis(see Fig.2).Forβ=5,even for the largest simulated lattice102, all the zeros are in the negative half-plane.We notice a gradual movement of the pattern of the zeros towards the smallerθvalues with an increasing density of the zeros nearθ=πIV.FINITE SIZE SCALING AND THESINGULARITY OF THE DENSITY OF STATESAs a starting point for theﬁnite size analysis of theYang-Lee singularities we recall the scaling hypothesis forthe partition function singularities in the critical domain[11].Following this hypothesis,for a change of scale ofthe linear dimension LLL→−1),˜µ=(1−µT cδ(23)Following the real-space renormalization group treatmentof Ref.[11]and assuming that the change of scaleλisa continuous parameter,the exponentαθis related tothe critical exponentνof the correlation length asαθ=1ξ(θλ)=ξ(θ)αθwe obtain ξ∼|θ|−1|θ|ναµ)(26)where θλhas been scaled to ±1and ˜µλexpressed in terms of ˜µand θ.Diﬀerentiating this equation with respect to ˜µyields:<n >sing =(−θ)ν(d −αµ)∂F sing (X,Y )ν(d −αµ)singinto the ar-gument Y =˜µαµ(28)which deﬁnes the critical exponent 1αµin terms of the scaling exponent αµof the Yang-Lee zeros.Fig.5presents the scaling of the imaginary part of the µzeros for diﬀerent values of the temperature.The linear regression slope of the logarithm of the imaginary part of the zeros plotted against the logarithm of the inverse lin-ear dimension of the simulation volume,increases when the temperature decreases from β=5to β=6.The re-sults of β=7.5correspond to αµ=1.3within the errors of the zeros as the simulation volume increases from 62to 82.As it is seen from Fig.3,we can trace zeros with similar real part (Re (µ1)≈0.7which is also consistentwith the critical value of the chemical potential given in Ref.[22])as the lattice size increases,which allows us to examine only the scaling of the imaginary part.Table 1presents the values of αµand 1αµδ0.5±0.0560.5±0.21.3±0.3∂µ,as a function ofthe chemical potential on an 82lattice.The location of the peaks of the susceptibility,rounded by the ﬁnite size eﬀects,is in good agreement with the distribution of the real part of the Yang-Lee zeros in the complex µ-plane (see Fig.3)which is particularly evident in the β=7.5simulations (Fig.4(c)).The contribution of each zero to the susceptibility can be singled out by expressing the free energy as:F =2n x n yi =1(y −y i )(29)where y is the fugacity variable and y i is the correspond-ing zero of the partition function.The dotted lines on these plots correspond to the contribution of the nearby zeros while the full polynomial contribution is given by the solid lines.We see that the developing singularities are indeed governed by the zeros closest to the real axis.The sharpening of the singularity as the temperature de-creases is also in accordance with the dependence of the distribution of the zeros on the temperature.The singularities of the free energy and its derivative with respect to the chemical potential,can be related to the quasiparticle density of states.To do this we assume that single particle excitations accurately represent the spectrum of the system.The relationship between the average particle density and the density of states ρ(ω)is given by<n >=∞dω1dµ=ρsing (µ)∝1δ−1(32)and hence the rate of divergence of the density of states.As in the case of Lifshitz transitions the singularity of the particle number is rounded at ﬁnite temperature.However,for suﬃciently low temperatures,the singular-ity of the density of states remains manifest in the free energy,the average particle density,and particle suscep-tibility [15].The regular part of the density of states does not contribute to the criticality,so we can concentrate on the singular part only.Consider a behaviour of the typedensity of states diverging as the−1ρsing(ω)∝(ω−µc)1δ.(33)with the valueδfor the particle number governed by thedivergence of the density of states(at low temperatures)in spite of theﬁnite-temperature rounding of the singu-larity itself.This rounding of the singularity is indeedreﬂected in the diﬀerence between the values ofαµatβ=5andβ=6.V.DISCUSSION AND OUTLOOKWe note that in ourﬁnite size scaling analysis we donot include logarithmic corrections.In particular,thesecorrections may prove signiﬁcant when taking into ac-count the fact that we are dealing with a two-dimensionalsystem in which the pattern of the phase transition islikely to be of Kosterlitz-Thouless type[23].The loga-rithmic corrections to the scaling laws have been provenessential in a recent work of Kenna and Irving[24].In-clusion of these corrections would allow us to obtain thecritical exponents with higher accuracy.However,suchanalysis would require simulations on even larger lattices.The linearﬁts for the logarithmic scaling and the criti-cal exponents obtained,are to be viewed as approximatevalues reﬂecting the general behaviour of the Yang-Leezeros as the temperature and lattice size are varied.Al-though the bootstrap analysis provided us with accurateestimates of the statistical error on the values of the ex-pansion coeﬃcients and the Yang-Lee zeros,the smallnumber of zeros obtained with suﬃcient accuracy doesnot allow us to claim higher precision for the critical ex-ponents on the basis of more elaborateﬁttings of the scal-ing behaviour.Theﬁnite-size eﬀects may still be signiﬁ-cant,especially as the simulation temperature decreases,thus aﬀecting the scaling of the Yang-Lee zeros with thesystem rger lattice simulations will therefore berequired for an accurate evaluation of the critical expo-nent for the particle density and the density of states.Nevertheless,the onset of a singularity atﬁnite temper-ature,and its persistence as the lattice size increases,areevident.The estimate of the critical exponent for the diver-gence rate of the density of states of the quasiparticleexcitation spectrum is particularly relevant to the highT c superconductivity scenario based on the van Hove sin-gularities[25],[26],[27].It is emphasized in Ref.[25]thatthe logarithmic singularity of a two-dimensional electrongas can,due to electronic correlations,turn into a power-law divergence resulting in an extended saddle point atthe lattice momenta(π,0)and(0,π).In the case of the14.I.M.Barbour,A.J.Bell and E.G.Klepﬁsh,Nucl.Phys.B389,285(1993).15.I.M.Lifshitz,JETP38,1569(1960).16.A.A.Abrikosov,Fundamentals of the Theory ofMetals North-Holland(1988).17.P.Hall,The Bootstrap and Edgeworth expansion,Springer(1992).18.S.R.White et al.,Phys.Rev.B40,506(1989).19.J.E.Hirsch,Phys.Rev.B28,4059(1983).20.M.Suzuki,Prog.Theor.Phys.56,1454(1976).21.A.Moreo, D.Scalapino and E.Dagotto,Phys.Rev.B43,11442(1991).22.N.Furukawa and M.Imada,J.Phys.Soc.Japan61,3331(1992).23.J.Kosterlitz and D.Thouless,J.Phys.C6,1181(1973);J.Kosterlitz,J.Phys.C7,1046(1974).24.R.Kenna and A.C.Irving,unpublished.25.K.Gofron et al.,Phys.Rev.Lett.73,3302(1994).26.D.M.Newns,P.C.Pattnaik and C.C.Tsuei,Phys.Rev.B43,3075(1991);D.M.Newns et al.,Phys.Rev.Lett.24,1264(1992);D.M.Newns et al.,Phys.Rev.Lett.73,1264(1994).27.E.Dagotto,A.Nazarenko and A.Moreo,Phys.Rev.Lett.74,310(1995).28.A.A.Abrikosov,J.C.Campuzano and K.Gofron,Physica(Amsterdam)214C,73(1993).29.D.S.Dessau et al.,Phys.Rev.Lett.71,2781(1993);D.M.King et al.,Phys.Rev.Lett.73,3298(1994);P.Aebi et al.,Phys.Rev.Lett.72,2757(1994).30.E.Dagotto, A.Nazarenko and M.Boninsegni,Phys.Rev.Lett.73,728(1994).31.N.Bulut,D.J.Scalapino and S.R.White,Phys.Rev.Lett.73,748(1994).32.S.R.White,Phys.Rev.B44,4670(1991);M.Veki´c and S.R.White,Phys.Rev.B47,1160 (1993).33.C.E.Creﬃeld,E.G.Klepﬁsh,E.R.Pike and SarbenSarkar,unpublished.Figure CaptionsFigure1Bootstrap distribution of normalized coeﬃcients for ex-pansion(14)at diﬀerent update chemical potentialµ0for an82lattice.The corresponding power of expansion is indicated in the topﬁgure.(a)β=5,(b)β=6,(c)β=7.5.Figure2Bootstrap distributions for the Yang-Lee zeros in the complexµplane closest to the real axis.(a)102lat-tice atβ=5,(b)102lattice atβ=6,(c)82lattice at β=7.5.Figure3Yang-Lee zeros in the complexµplane closest to the real axis.(a)β=5,(b)β=6,(c)β=7.5.The correspond-ing lattice size is shown in the top right-hand corner. Figure4Angular distribution of the Yang-Lee zeros in the com-plex fugacity plane Error bars are drawn where esti-mated.(a)β=5,(b)β=6,(c)β=7.5.Figure5Scaling of the imaginary part ofµ1(Re(µ1)≈=0.7)as a function of lattice size.αm u indicates the theﬁt of the logarithmic scaling.Figure6Electronic susceptibility as a function of chemical poten-tial for an82lattice.The solid line represents the con-tribution of all the2n x n y zeros and the dotted line the contribution of the six zeros nearest to the real-µaxis.(a)β=5,(b)β=6,(c)β=7.5.。

西格玛泰克说明书

C-DIAS PROCESSOR MODULECCP 521C-DIAS Processor ModuleThe CCP 521 processor module runs the control program and thereby represents an essential component of an automation system. The internal DC/DC converter powers all modules on a C-DIAS module carrier. The VARAN bus, the CAN bus, an Ethernet interface or the USB device (Mini USB) can be used as the online interface connection. A 7-segment display and 2 status LEDs provide information on the actual status of the CPU. For program updates, the integrated USB Host interface can be used (USB stick, keyboard). With help from the exchangeable SD card, the entire control program can be easily exchanged. The CCP 521 processor module is designed to be mounted in the control cabinet.CCP 521Compatibility Completely PC-compatible. The CCP 521 works with standard PC BIOS and therefore no SIGMATEK-specific BIOS is needed; the LASAL operating system in provided.26.05.2010Page 1CCP 521C-DIAS PROCESSOR MODULETechnical DataPerformance dataProcessor Addressable I/O/P modules EDGE-Technology X86 compatible VARAN bus: 65,280 CAN bus: 32 C-DIAS bus: 8 No 32-kbyte L1 Cache 256-kbyte L2 Cache AMI 64 Mbytes 512 Kbytes 1-Gbyte micro SD card 1 x USB Host 2.0 (full speed 12 Mbit/s) 1 x USB Device 1.1 1 x Ethernet 1 x CAN 1 x VARAN 1 x C-DIAS Yes Yes Yes Yes (buffering approximately 10 days)Internal I/O Internal cache BIOS Internal program and data memory (DDR2 RAM) Internal remnant data memory Internal storage device (IDE) Interface connectionsData buffer Status display Status LEDs Real-time clockPage 2 a26.05.2010C-DIAS PROCESSOR MODULE Electrical requirementsSupply voltage Current consumption of (+24 V) power supply Starting current Power supply on the C-DIAS bus Current load on C-DIAS bus (power supply for I/O/P modules). Typically 150 mA +18 –30 V DCCCP 521Maximum 500 mAFor a very short time (~20 ms) : 30 A Supplied by the CCP 521 Maximum 1.2 AStandard configurationEthernet 1 CAN bus IP: 10.10.150.1 Station: 00 Subnet-Mask:255.0.0.0 Baud rate: 01 = 500 kBaudProblems can arise if a control is connected to an IP network, which contains modules that do not contain a SIGMATEK operating system. With such devices, Ethernet packets could be sent to the control with such a high frequency (i.e. broadcasts), that the high interrupt load could cause a real-time runtime error. By configuring the packet filter (Firewall or Router) accordingly however, it is possible to connect a network with SIGMATEK hardware to a third party network without triggering the error mentioned above.26.05.2010Page 3CCP 521 MiscellaneousArticle number Hardware version Project back-up StandardC-DIAS PROCESSOR MODULE12-104-521 1.x Internally on the micro SD card UL in preparationEnvironmental conditionsStorage temperature Operating temperature Humidity EMV stabilityShock resistance Protection Type -10 –+85 °C 0 –+50 °C 10 - 90 %, uncondensed According to EN 61000-6-2 (industrial area) EN 60068-2-27 EN 60529 150 m/s? IP 20Page 426.05.2010C-DIAS PROCESSOR MODULECCP 521Mechanical Dimensions104.10 (dimensioning incl. covers)109.212924.9026.05.2010Page 5CCP 521C-DIAS PROCESSOR MODULEConnector LayoutPC通讯底层通讯电源Page 626.05.2010C-DIAS PROCESSOR MODULE X1: USB Device 1.1CCP 521Pin 1 2 3 4 5Assignment +5 V DD+ GNDX2: USB Host 2.0Pin 1 2 3 4 Assignment +5 V DD+ GNDIt should be noted that many USB devices on the market do not comply with the relevant EMC standards for industrial environments. Connecting such a device can lead to malfunctions.X3: EthernetPin 1 2 3 4-5 6 7-8 Assignment TX+ TXRX+ RX-X4: VARANPin 1 2 3 4-5 6 7-8 Assignment TX+ / RX+ TX- / RXRX+ / TX+ RX- / TX-26.05.2010Page 7CCP 521 X5: CAN-BusC-DIAS PROCESSOR MODULE12Pin 1 2 3 4 5 6Assignment CAN A (CAN LOW) CAN B (High) CAN A (CAN LOW) CAN B (High) GND -56X6: Power plug1Pin 1 2Assignment +24 V supply GNDX7: micro SD card Sandisk SDSDQ-1024-KPage 826.05.2010C-DIAS PROCESSOR MODULE Exchanging the micro SD cardCCP 521The micro SD card is located under the LED cover.To exchange the micro SD card, carefully lift the LED cover.The micro SD card is located on the left side and can be disengaged by lightly pressing on the card itself.Remove the micro SD card.26.05.2010Page 9CCP 521C-DIAS PROCESSOR MODULEApplicable connectors USB Device: USB Host: Ethernet: VARAN: CAN-Bus: Supply: 5-pin, type mini B 4-pin, type A 8-pin, RJ45 8-pin, RJ45 6-pin Weidmüller plug, B2L3, 5/6 2-pin Phoenix plug with screw terminal technology MC1, 5/2-ST-3,5 2-pin Phoenix plug with spring terminal FK-MCP1, 5/2-ST-3Page 10 a26.05.2010C-DIAS PROCESSOR MODULECCP 521Status DisplaysEthernet LED Active Link Color Yellow Green Description Lights when data is exchanged over Ethernet Lights when the connection betweenthe two PHYs is established VARAN LED Active Link Color Yellow Green Description Lights when data is exchanged over the VARAN bus Lights when the connection between the two PHYs is established Control LED ERROR DCOK Color Red Green Description Lights when an error occurs (defective USV) Lights when the power supply is OK26.05.2010Page 11CCP 521C-DIAS PROCESSOR MODULEDisplayThe CCP 521 processor module has a 2-digit decimal display (7 segment display) for the following functions:- When configuring the processor module, the parameters are shown in the display. - If an error occurs while running the program or no valid user program is found, the displayshows an error message. Thereby, "Er" (error) and the error code aredisplayed alternatingly. The same error code is also shown in the LASAL status line.- While running the program, the display can be used to show digits using the system vari-able _cpuDisplay. Valid values are 0 to 255; values over 99, however, are not shown and the display remains dark.Page 1226.05.2010C-DIAS PROCESSOR MODULECCP 521CAN Bus SetupThis section explains how to configure a CAN bus correctly. The following parameters must first be set: Station number and data transfer rate. CAN bus station number Each CAN bus station is assigned its own station number. With this station number, data can be exchanged with other stations connected to the bus. Up to 31 stations can be installed in a CANbus system. However, each station number can only be assigned once. CAN bus data transfer rate The data transfer rate (baud rate) for the CAN bus can be set. However, the longer the length of the bus, the smaller the transfer rate that must be selected.Value 00 01 02 03 04 05 06 07Baud rate 615 kBit/s 500 kbit/s 250 kBit/s 125 kBit/s 100 kBit/s 50 kBit/s 20 kBit/s 1 Mbit / sMaximum length 60 m 80 m 160 m 320 m 400 m 800 m 1200 m 30 mThese values are valid for the following cable: 120 ?, Twisted Pair. NOTE: the following is valid for the CAN bus protocol: 1 kBit/s = 1 kBaud.26.05.2010Page 13CCP 521C-DIAS PROCESSOR MODULEConfiguration of the Process ModulePage 1426.05.2010C-DIAS PROCESSOR MODULECCP 521To enter the mode for setting changes, press and hold the SETbutton while the C-IPC is booting. When the following appears in the display:the SET button can be released. After releasing the SET button, the first menu appears in the display.With several short presses of the SET button, it is possible to switch through the various menu points. By pressing the SET button for approximately 1.5 s, the menu is accessed and the setting can be changed with short presses. Once the desired changes are made, press the SET button for about 5 seconds to end the process. If the changes areto be discarded, press the RESET button to restart the C-IPC. The settings for the IP address, subnet mask and gateway are hexadecimal, whereas in the left and right digits, 0 - F must be entered separately. The switch occurs when the SET button is pressed for about 1.5 s. The values from AUTOEXEC.LSL are used as the standard settings; changes are written back to this file. Before this, the original content of the file is written to AUTOEXEC.BAK.26.05.2010Page 15 aCCP 521C-DIAS PROCESSOR MODULEC1 ... CAN PLC station 00 –30 ... Station numberC2 ... CAN PLC baud rate 00 ... 615.000 01 …500.000 02 …250.000 03 …125.000 04 …100.000 05 …50.000 06 …20.000 07 …1.000.000 I1, I2, I3, I4 IP address I1.I2.I3.I4, Hexadecimal 00 –FF respectivelyS1,S2,S3,S4 Subnet Mask S1.S2.S3.S4, hexadecimal 00 –FFrespectivelyG1,G2,G3,G4 Gateway G1,G2.G3.G4, hexadecimal 00 –FF respectivelyPage 16 a26.05.2010C-DIAS PROCESSOR MODULECCP 521CAN Bus TerminationIn a CAN bus system, both end modules must be terminated. This is necessary to avoid transmission errors caused by reflections in the line.Device 1e.g. CPU DCP 080 CAN-Bustermination on terminal moduleDevice 2e.g. Terminal ET 081Device 3Device ne.g. Terminal ET 805 D-SUB-plug with terminating resistorsCAN-Bus-ConnectionsIf the CCP 521 processor module is an end module, it can be terminated by placing a 150Ohm resistor between CAN-A (Low) and CAN-B (High).1 x 150-Ohm resistor26.05.2010Page 17CCP 521C-DIAS PROCESSOR MODULEWiring and Mounting InstructionsEarth ConnectionThe CCP 521 must be connected to earth over the mounting on the back wall of the control cabinet or over the earth terminal provided (C-DIAS module carrier). It is important to create a low-ohm earth connection, only then can error-free operation be guaranteed. The earth connection should have the maximum cross section and the largest electrical surface possible. Any noise signals that reach the CCP 521 over external cables must be filtered out over the earth connection. With a large (electrical) surface, high frequency noise can also be well dissipated.Page 1826.05.2010C-DIAS PROCESSOR MODULECCP 521ShieldingThe wiring for the CAN bus, Ethernet and VARAN bus must be shielded. The low-ohm shielding is either connected at the entry to the control cabinet or directly before the CCP 521 processor module over a large surface (cable grommets, grounding clamps)! Noise signals can thereforebe prohibited from reaching the electronics and affecting the function.ESD ProtectionBefore any device is connected to or disconnected from the CCP 521, the potential with ground should be equalized (by touching the control cabinet or earth terminal). Static electricity (from clothing, footwear) can therefore be reduced.26.05.2010Page 19CCP 521C-DIAS PROCESSOR MODULEProcess DiagramMain voltage onOnline with Lasal Software?noyes Output of a reset of the peripheral modules Output of a reset of the peripheral modulesDeletion of specific data areasDeletion of specific data areasStatus RESETProgram in external memory module functional?noyes Copy program into application program memory Program in internal memory module functional? noyes Status RUN ROM Copy program into application program memory Status CHKSUM or POINTERCall of application programStatus RUN ROMCall of application programPage 2026.05.2010C-DIAS PROCESSOR MODULECCP 521Status and Error MessagesStatus and error messages are shown in the status test of the Lasal Class software. If the CPU has a status display, the status or error number is also show here as well. POINTER or CHKSUM messages can also be shown on the terminal screen.Number 00 Message RUN RAM Definition The user program is currently running in RAM. The display is not affected. 01 RUN ROM The user program in the program memory module was loaded into the RAM and is currently being run. The display is not affected. 02 RUNTIME The total duration of all cyclic objects exceeds the maximum time; the time can beconfigured using 2 system variables: -Runtime: time remaining -SWRuntime: pre-selected value for the runtime counter 03 POINTER Incorrect program pointers were detected before running the user program Possible Causes: Cause/solution- The program memory module ismissing, not programmed or defect.- The program in the user programmemory (RAM) is not executable.- The user program is overwriting asoftware error Solution:- Reprogram the memory module, if theerror reoccurs exchange the module.- Correct programming error04 CHKSUM An invalid checksum was detected before running the user program. Cause/solution: s. POINTER26.05.2010Page 21CCP 52105C-DIAS PROCESSOR MODULEWatchdog The program was interrupted through the watchdog logic. Possible Causes:- User program interrupts blockedover a longer period of time (STI command forgotten)- Programming error in a hardwareinterrupt.- INB, OUTB, INW, OUTW instructions used incorrectly.- The processor is defect.Solution:- Correct programming error.- Exchange CPU. 06 07 GENERAL ERROR PROM DEFECT General error An error has occurred while programming the memory module. Cause:- The program memory module isdefect.- The user program is too large. - The program memory module is missing. Solution:- Exchange the program memorymodule 08 Reset The CPU has received the reset signal and is waiting for further instructions. The user program is not processed. 09 WD DEFEKT The hardware monitoring circuit (watchdog logic) is defect. After power-up, the CPU checks the watchdog logic function. If an error occurs during this test, the CPU deliberately enters an infinite loop from which no further instructions are accepted. 10 11 12 13 14 STOP PROG BUSYS PROGRAM LENGTH PROG END PROG MEMO The memory module was successfully completed. The CPU is currently programming the memory module. Solution: Exchange CPU.Page 2226.05.2010C-DIAS PROCESSOR MODULE15 16 17 STOP BRKPT CPU STOP INT ERROR The CPU was stopped by a breakpoint in the program. The CPU was stopped by the PG software (F6 HALT in status test). The CPU has triggered a false interrupt and stopped the user program or has encountered an unknown instruction while running the program. Cause:CCP 521- A nonexistent operating system wasused.- Stack error (uneven number of PUSHand POP instructions).- The user program was interrupted bya software error. Solution: - Correct programming error. 18 19 2021 22 SINGLE STEP Ready LOAD UNZUL. Modul MEMORY FULL The CPU is insingle step mode and is waiting for further instructions. A module or project has been sent to the CPU and it is ready to run the program. Theprogram has stopped and is receiving a module or project. The CPU has received a module, which does not belong to the project. The operating system memory /Heap) is too small. No more memory could be reserved, when an internal or interface function was called from theapplication. When starting the CPU, a missing module or a module that does not belong to the project was detected. A division error has occurred. Possible Causes:23NOT LINKED24DIV BY 0- Division by 0. - The result of a division does not fit inthe result register. Solution: - Correct programming error.26.05.2010Page 23CCP 52125C-DIAS PROCESSOR MODULEDIAS ERROR An error has occurred accessing a DIAS module. while Possible Causes:- An attempt is made to accessa nonexistent DIAS module.- DIAS bus error.Solution:- Check the DIAS bus - Check the termination resistors. 26 27 28 29 30 WAIT OP PROG OP INSTALLED OS TOO LONG NO OPERATING SYSTEM The CPU is busy. The operating system is currently being reprogrammed. The operating system has been reinstalled. The operating system cannot be loaded; too little memory. Boot loader message. No operating system found in RAM. 31 32 33 34 SEARCH FOR OS NO DEVICE UNUSED CODE MEM ERROR The operating system loaded does not match the hardware configuration. The boot loader is searching for the operating system inRAM.35 36 37MAX IO MODULE LOAD ERROR GENERELLER BS-FEHLER The LASAL Module or project cannot be loaded. A general error has occurred while loading the operating system. An error has occurred in the application memory (user heap).38 39 40 41APPLMEM ERROR OFFLINE APPL LOAD APPL SAVEPage 2426.05.2010C-DIAS PROCESSOR MODULE46 47 50 APPL-LOAD-ERROR APPL-SAVE-ERROR ACCESS-EXCEPTIONERROR BOUND EXCEEDED PRIVILEDGED INSTRUCTION An error has occurred loading the application. whileCCP 521An error has occurred while attempting to save the application. Read or write access of a restricted memory area. (I.e. writing to the NULL pointer). An exception error caused by exceeding the memory limits An unauthorized instruction for the current CPU level was given. For example, setting the segment register. An error has occurred during a floating-point operation. Error from ASMaster. the Intelligent DIRestart; report error to Sigmatek.51 5253 60 64 65 66 67FLOATING POINT ERROR DIAS-RISC-ERROR INTERNAL ERROR FILE ERROR DEBUG ASSERTION FAILED REALTIME RUNTIMEAn internal error has occurred, all applications are stopped. An error has occurred during a file operation. Internal error. The total duration of all real-time objects exceeds the maximum time; the time cannot be configured. 2 ms for 386 CPUs 1 ms for all other CPUsRestart; report error to Sigmatek. Starting from Version 1.1.768BACKGROUND RUNTIMEThe total time for all background objects exceed the maximum time; the time can be configured using two system variables: -BTRuntime: time remaining -SWBTRuntime: pre-selected value for the runtime counter95 96 97 98USER DEFINED 0 USER DEFINED 1 USER DEFINED 2 USER DEFINED 3User-definable code. User-definable code. User-definable code.User-definable code.26.05.2010Page 25CCP 52199 100 101 102 103 104 105 106C-DIAS PROCESSOR MODULEUSER DEFINED 4 C_INIT C_RUNRAM C_RUNROM C_RUNTIME C_READY C_OKC_UNKNOWN_CID The CPU is ready for operation. The CPU is ready for operation. An unknown class from a standalong or embedded object: unknown base class. The operating system class cannot be created; the operating system is probably wrong. Reference to an unknown object in an interpreter program, creation of more than one DCC080 object. The hardware module number is greater than 60. No connection to the required channels. Wrong server attribute. No specific error, recompile all and reload project components. An attempt was made to open an unknown table.Memory allocation error Memory allocation error User-definable code. Initialization start; the configuration is run. The LASAL project was successfully started from RAM. The LASAL project was successfullystarted from ROM.107C_UNKNOWN_CONSTR108C_UNKNOWN_OBJECT109 110 111 112 113 114 115C_UNKNOWN_CHNL C_WRONG_CONNECT C_WRONG_ATTR C_SYNTAX_ERRORC_NO_FILE_OPEN C_OUTOF_NEAR C_OUT OF_FARPage 2626.05.2010C-DIAS PROCESSOR MODULE116 117 224 225 C_INCOMAPTIBLE C_COMPATIBLE LINKING LINKING ERROR An object with the same name exists but has another class. An object with the same name and class exists but must be updated. The application is currently linking. An error has occurred while linking. An error messaged is generated in the LASAL status window. Linking is complete. The operating system is currently being burned into the Flash memory. An error has occurred while burning the operating system. The operatingsystem is currently being installed. The power supply was disconnected; the UPS is active. The operating system is restarted.CCP 521226 230 231 232 240 241 242 243 252 253 254 255LINKING DONE OP BURN OP BURN FAIL OP INSTALL USV-WAIT Reboot LSL SAVE LSL LOAD CONTINUE PRERUN PRERESET CONNECTION BREAKThe application is started. The application is ended.26.05.2010Page 27CCP 521C-DIAS PROCESSOR MODULEApplication exceptionsSRAM and IRQ routines Writing remnant data during interruptroutines is not allowed and leads to a system crash. SRAM and consistency of changed data If more than 32 different sectors are changed (512 byteseach) shortly before shutting down the voltage supply while the user program is writing to the micro SD card, this can sometimes lead to partial loss of remnant data. The file system does not support safe writing through SRAM If files are stored, modified or written on the micro SD card from the user program, these files must always be storedwith a fixed maximum size. Since changes in size and the simultaneous shutdown of the voltage supply can corrupt the file system, a later change in the file size is not allowed. Data Breakpoint This CPU does not support the data breakpoint is a feature.Page 2826.05.2010C-DIAS PROCESSOR MODULECCP 521Recommended Shielding for VARANThe real-time VARAN Ethernet bus system exhibits very robust characteristics in industrial environments. Through the use of IEEE 802.3 standard Ethernet physics, the potentials between an Ethernet line andsending/receiving components are separated. Messages to a bus participant are immediately repeated by the VARAN Manager in the event of an error. The shielding described below is principally recommended. For applications in which the bus is run outside the control cabinet, the correct shielding is required. Especially when for structural reasons, the bus line must be placed next to strong electromagnetic interference. It is recommended to avoid placing Varan bus linesparallel to power cables whenever possible. SIGMATEK recommends the use of CAT5e industrial Ethernet bus cables. For the shielding, an S-FTP cable should be used. An S-FTP bus is a symmetric, multi-wire cable withunshielded pairs. For the total shielding, a combination of foil and braiding is used. A non-laminated variant is recommended.The VARAN cable must be secured at a distance of 20 cm from the connector for protection against vibration!26.05.2010Page 29CCP 521C-DIAS PROCESSOR MODULE1. Wiring from the Control Cabinet to an External VARAN ComponentIf the Ethernet lines are connected from a VARAN component to a VARAN node located outside the control cabinet, the shielding should be placed at the entry point to the control cabinet housing. All noise can then be dissipated before reaching the electronic components.Page 3026.05.2010C-DIAS PROCESSOR MODULECCP 5212. Wiring Outside of the Control CabinetIf a VARAN bus cable must be placed outside of the control cabinet, additional shielding is not required. Outside of the control cabinet,IP67 modules and connectors are used exclusively. These components are very robust and noise resistant. The shielding for all sockets in IP67modules is electrically connected internally or over the housing, whereby voltage spikes are not deflected through the electronics.26.05.2010Page 31CCP 521C-DIAS PROCESSOR MODULE3. Shielding for Wiring Within the Control CabinetSources of strong electromagnetic noise located within the control cabinet (drives, Transformers, etc.) can induce interference in a VARAN bus line. Voltage spikes are dissipated over the metallic housing of aRJ45 connector. Noise is conducted over the control cabinet without additional measures needed on the circuit board of electronic components. To avoid error sources with data exchange, it is recommended that shielding be placed before any electronic components in the control cabinet.Page 3226.05.2010C-DIAS PROCESSOR MODULECCP 5214. Connecting Noise-Generating Components.When connecting power lines to the bus that generate strong electromagnetic noise, the correct shielding is also important. The shielding should be placed before a power element (or group of power elements).26.05.2010Page 33CCP 521C-DIAS PROCESSOR MODULE5. Shielding Between Two Control CabinetsIf two control cabinets must be connected over a VARAN bus, it is recommended that the shielding be located at the entry points of each cabinet. Noise is therefore prevented from reaching the electronic components in both cabinets.Page 3426.05.2010。

ETS-EMCO产品说明书

Information presented is subject to change as product enhancements are made. Contact ETS Sales Department for current specifications.2/00 - 2k S © 2000 ETS-EMCO REV BUSA:Tel +1.512.835.4684Fax +1.512.835.4729FINLAND:Tel +358.2.8383.300Fax +358.2.8651.233ONLINE:****************1Positioning Controller Test Site HardwareFeatures:l Control for 2 Primary and4 Auxiliary Devicesl SEEK & SCAN Functionsl Automatic Target Overrun Correctionl Element Saving Limit Settingl Fiber Optic Control Linesl IEEE-488.2 I/O Portl Speed Control Model 2090 Positioning ControllerETS-EMCO’s Model 2090 Positioning Controller allows you to synchronize simultaneous movement of two primary ETS-EMCO devices (towers or turn-tables), and on/off operation of up to four auxiliary devices (LISNs, EUTs, etc.).Independent operation of primary devices can be performed manually, by either of the two front panel controls, or remotely, by a separate GPIB address for each device. Fiber optic control lines eliminate RF interference that can be conducted through traditional wire cables.The Model 2090 is designed to maximize the features of ETS-EMCO antenna towers and turntables. See page 4 for information about retrofits to earlier ETS-EMCO models and non-ETS products.Functions The front panel design of the Model 2090features a user-friendly interface which simplifies device control and clearly communicates primary device movement to the operator. T wo separate sets of controls (Device One and Device Two),each with identical displays and functions,are included. Other front panel features include four auxiliary control switches and the Model 2090 power switch.Model 2090A number of useful primary device commands can be performed by the operator. The SEEK function enables the user to reposition a device to a newtarget location and the SCAN command initiates cyclic movement of a device.The CONFIG and LIMIT functions enable the user to program operational parameters and upper/lower or clock-wise/counterclockwise limits for each device. The POSITION and STEP functions work together to control towercross boom and/or turntable positioning.Expanded details of these functions are offered below.SEEK & SC SEEK & SCAN AN SEEK allows a target location to be entered to redirect the device from its current location. Target locations can be automatically incremented/decremented by a given value. The SEEK command is available only through the GPIB. All otherfunctions can be performed from both the GPIB and the front panel. The SCAN key initiates cyclic movement of a device between pre-programmed limits. A cycle is defined as movement from the lower/counterclockwise limit to the upper/clockwise limit and back to the lower/counterclockwise limit. The total numberof cycles is programmable from 1 to 999or an entry of “000” causes the device to scan continuously.C ONFIG & LIMITThe CONFIG (Configuration of Param-eters) and LIMIT keys work together for system set up. The CONFIG function enables the operator to select six operational parameters for both primary devices.The LIMIT keys allow the operator to set upper and lower, or clockwise and counterclockwise limits. The user simplysets the limit by pressing the INCRM orDECRM keys until the desired limit is shown on the display and then selects the ENTER key. T o verify or set thecurrent position of a device undercontrol, the user can press the CURRENT POSITION key.POSITION & STEPThe POSITION and STEP functions work together to manually position the tower cross boom and/or turntable. Four POSITION keys and two STEP keys areavailable to achieve this control. 1981Information presented is subject to change as product enhancements are made. Contact ETS Sales Department for current specifications.2/00 - 2k S © 2000 ETS-EMCO REV BUSA:Tel +1.512.835.4684Fax +1.512.835.4729FINLAND:Tel +358.2.8383.300Fax +358.2.8651.233ONLINE:****************2Front Panel Illustration – Model 2090 Positioning ControllerPOSITION K POSITION Ke e y sl UP / CW UP moves the tower cross boom upward.CW moves the turntable clockwise.l DOWN / CCWDOWN moves the tower cross boom W moves the turntable counterclockwise.l STOP STOP ceases movement of device.l POLARIZATION / FLOTATION/SPEED HOR / UP/ FAST VERT / DN / SLOW On a tower, pressing this button will toggle the tower cross boom between HORIZONTAL and VERTICAL polarization.On an air flotation turntable, pressing this button will toggle the UP (inflation) and DOWN (deflation) of the turntable top. On a two-speed turntable, pressing this button will toggle the speed of the turntablebetween FAST and SLOW. On a variable speed turntable, pressing this button will cycle the SPEED between four presets. The indicator lights will illuminate in a binaryfashion to indicate the current preset speed selection i.e. first preset OFF-OFF, second preset ON-OFF, third preset OFF-ON, fourth preset ON-ON.STEP K STEP Ke e y s l INCINC moves the device up or clockwise.l DEC DEC moves the device down orcounterclockwise.The controller will move the device in the desired direction as long as the key is pressed. The device will stop when thekey is released.L OC OCAL/REMO AL/REMO AL/REMOTE OPER TE OPER TE OPERA A TION The Model 2090 can be operatedmanually from the front panel or remotely via the GPIB port. When the Model 2090 is addressed via the GPIBport, the RMT indicator light will illuminate and the ADDR indicator will flash to show bus activity. Pressing the LOCAL function key allows you to exit the remote mode. When the optionalHand Control Unit (see Options, page 3)is used, all position changes will berecorded and displayed by the Model 2090 Controller.A UXILIAR UXILIARY C Y C Y CONTR ONTR ONTROL OL Four front panel keys are available to control auxiliary devices. While in manual mode, you can activate an auxiliary device by pressing the AUX CONTROL key that corresponds to the auxiliary device port. In remote mode,auxiliary devices can be activated by using the appropriate GPIB command. Thecontrol lines are on/off output only . In order to use these four auxiliary lines, an interface box that will perform a custom function and accept a fiber optic input, is needed. Contact ETS-EMCO Sales for details.FeaturesAutomatic Target Overrun Correction The Model 2090 constantly monitors inertia-induced target overrun. Ifoverrun on turntables or towers occurs, itis identified and tracked. Utilizing a special algorithm, the Model 2090continually adjusts subsequent positionings to minimize overrun,allowing for proper device positioning during tests.Element Saving Limit Setting To prevent damage to antenna elements which may accidentally rotate into the ground plane or ceiling during polariza-tion, the Model 2090 allows you to program two upper and two lower limit settings. These settings allow you to safely maximize antenna scan height ineither horizontal or vertical polarization – especially useful with BiConiLogs TM ,biconicals, log periodics, and otherantennas with protruding elements.Fiber Optic Input/Output LinesThe 2090 features fiber optic controllines to eliminate conducted noise. Eachprimary device cable contains two fiberInformation presented is subject to change as product enhancements are made. Contact ETS Sales Department for current specifications.2/00 - 2k S © 2000 ETS-EMCO REV BUSA:Tel +1.512.835.4684Fax +1.512.835.4729FINLAND:Tel +358.2.8383.300Fax +358.2.8651.233ONLINE:****************2090115/230 VAC 1 2 A 250 VAC Time Delay 8 fiber optic connectors.50/60 Hz IEEE-488.2 connector.IEC 320 power inlet.Fuse holder.MODEL WIDTH DEPTH 2HEIGHT WEIGHT Physical SpecificationsElectrical SpecificationsMODEL POWER FUSE BACK PANEL I/032090 43.8cm 34.3cm 13.3cm 4.5kg 17.3in 13.5in 5.3in 10.0lb 2 Excluding handlesoptic lines (transmit/receive). Auxiliary device lines are output only. Reliable and easy-to-use ST connectors are standard.GPIB The General Purpose Interface Bus (GPIB) complies with IEEE 488.1/488.2standards. All front panel functions can be exercised using GPIB commands while in the remote mode. GPIB com-mands are backward compatible with ETS-EMCO Model 1050, 1060 and 1090Controllers, simplifying upgrades to the new model. Model 1050 and 1060commands are compatible with Hewlett Packard's Model HP 85876A Commercial Radiated EMI Measurement Software and Rohde & Schwarz Model ES-KI EMI Measurement & Evaluation Software.S p eed C eed Con on ontr tr trol ol Users whose test facilities include a two-speed turntable will find the Model 2090positioning controller well suited to their needs. The unit ’s SLOW control activates the turntable ’s lower speed drive. The FAST control activates the turntable ’s higher speed drive. The controller can be used for speed-control with ETS-EMCO turntables that feature dual speeds andother brands of two-speed turntables.Memory All settings in the Model 2090 are savedwhen the unit is turned off, allowing for easy set-up when testing is interrupted and returned to later.Precise Resolution Display accuracy on the Model 2090 is highly precise. The unit offers position readout increments of 1 mm for towersand 0.1 degree for turntables.Universal Power SupplyThe positioning controller has a conve-nient built-in auto ranging feature that automatically senses supply voltage. Any AC power source input within the range of 115/230 V AC, 50/60 Hz can be used.Rack Mounting For convenience, the Model 2090 is standard rack width and 3U rack size.Standard Configuration l Controller assembly l IEC 320 power cord l Manual OptionsHand Control Unit The Hand Control Unit is designed to manually operate ETS-EMCO antenna towers and turntables. Lightweight and easy to operate, this convenient unit plugs into the motor base of the tower orturntable and enables you to perform simple manual movement of these devices. It works in tandem with ETS-EMCO ’s Model 2090 Controller. Changes in position location made by the HandControl Unit will be recorded and displayed by the Model 2090 Controller.T o order, specify part number 105136.Auxiliary Control UnitThe Auxiliary Control Unit provides a means to remotely open and close contacts via fiber optic cable. These contacts can be used to remotely control power relays or other devices to automate EMC testing. Simplex fiber optic cable connects the output of the Model 2090Aux Control to the input of the Auxiliary Control Unit. The Auxiliary Control Unit is powered by a wall-mount power supply (user-specified 115 V AC or 230V AC at time of order).Additional Fiber Optic CableStandard fiber optic cable length is 10meters. Custom lengths are available.To order, specify part number 708029-m (10 m increments).Fiber Optic FeedthroughBulkhead feedthrough consisting of a wave-guide cutoff for fiber optic cable.To order, specify part number 105120.Rack Mount RailsA rack mount kit can be purchased for mounting the Model 2090 in a rack.To order, specify part number 540037.1 AutoselectInformation presented is subject to change as product enhancements are made. Contact ETS Sales Department for current specifications.2/00 - 2k S © 2000 ETS-EMCO REV BUSA:Tel +1.512.835.4684Fax +1.512.835.4729FINLAND:Tel +358.2.8383.300Fax +358.2.8651.233ONLINE:****************Positioning Controller Upgrade Kits Now your older ETS-EMCO tower and turntable can operate with all of the new command features available with our Model 2090 Positioning Controller. All you need is our Retrofit-Kit and a Model2090 Controller to replace your existing EMCO Model 1050, 1060, 1060C or 1090Controller. Y ou'll be able to control two devices (tower or turntable) and four auxiliary devices at once, plus access theSEEK, SCAN, target overrun, and multiple limit functions. For a thorough description of all Model 2090 features and functions please turn to page one.Note: Bore Sight functions are only available with Model 2071 towers.T o install the Retrofit-Kit, the included interface box is placed in line between the tower/ turntable motor box andcontroller. Existing cables are used between the tower/turntable motor box and the Retrofit-Kit's interface box. Fiber optic cables are connected between the interface box and the new Model 2090Positioning Controller.Retrofit-Kit to replaceModel 1050 or 1060 ControllersPN # 105637Retrofit-Kit to replace Model 1090 ControllerPN # 105797Retrofit-Kit for non-EMCOtowers/turntablesCALL FOR QUOTEAll kits consist of an interface box withpower cord and a 10 meter fiber opticcable.Specifications4OptionslCustom length fiber optic cable l Custom length wire cable l Hand Control Unit(SELECTABLE)Retrofit-Kit 35.6 cm 30.5cm 16.5cm 11.4 kg 115/23050/60for 1050, 106014.0 in12.0in 6.5in 25.2lbMODEL PHYSICAL ELECTRICALWIDTH DEPTH HEIGHT WEIGHT VOLTAGE HzExisting (pre Model 2090)Tower / Turntable Motor BoxExisting Cables (one cable on 1090 kit)New Interface Box New Fiber Optic CableModel 2090 Controller。

withanemphasison

directory – You are ready to go!
MSU NSCL DAQ School—Notre Dame 2006
More to Read
• MSU NSCL DAQ:
– Everything: /daq/index.php
– Software project: /projects/nscldaq
– Tree parameter GUI for powerful manipulation of the definition of parameters, spectra, variables, and gates
– Xamine for easy display and operations of histograms – Tcl/Tk for user-tailorable control GUI and easy extension of
SpectroDaq Data Server
SpecTcl Xamine
Scalers
Scaler Configuration
offline analysis
MSU NSCL DAQ School—Notre Dame 2006
Disk
Hardware Setup
¾ Caen v785, 32-ch ADC ¾ Caen v775, 32-ch TDC ¾ Caen v830, 32-ch Scaler ¾ Trigger to be upgraded
• SpecTcl
– Home: /daq/spectcl/ – Project: /projects/nsclspectcl – Tree Parameters:
/daq/spectcl/treeparam/TreeParameter.html – Tcl/Tk: /

MPI TITAN RF Probe Selection Guide

MPI Probe Selection GuideWith a critical understanding of the numerous measurement challenges associated with today’s RF ap-plications, MPI Corporation has developed TITAN™ RF Probes, a product series specifically optimized for these complex applications centered upon the requirements of advanced RF customers.TITAN™ Probes provide the latest in technology and manufacturing advancements within the field of RF testing. They are derived from the technology transfer that accompanied the acquisition of Allstron, then significantly enhanced by MPI’s highly experienced RF testing team and subsequently produced utilizing MPI’s world class MEMS technology. Precisely manufactured, the TITAN™ Probes include matched 50 Ohm MEMS contact tips with improved probe electrical characteristics which allow the realization of unmat -ched calibration results over a wide frequency range. The patented protrusion tip design enables small passivation window bond pad probing, while significantly reducing probe skate thus providing the out -standing contact repeatability required in today’s extreme measurement environments. TITAN TM Probes with all their features are accompanied by a truly affordable price.The TITAN™ Probe series are available in single-ended and dual tip configurations, with pitch range from 50 micron to 1250 micron and frequencies from 26 GHz to 110 GHz. TITAN™ RF Probes are the ideal choice for on-wafer S-parameter measurements of RF, mm-wave devices and circuits up to 110 GHz as well as for the characterization of RF power devices requiring up to 10 Watts of continuous power. Finally, customers can benefit from both long product life and unbeatable cost of ownership which they have desired foryears.Unique design of the MEMS coplanar contacttip of the TITAN™ probe series.DC-needle-alike visibility of the contact point and the minimal paddamage due to the unique design of the tipAC2-2 Thru S11 Repeatability. Semi-Automated System.-100-80-60-40-200 S 11 E r r o r M a g n i t u d e (d B )Frequency (GHz)Another advantage of the TITAN™ probe is its superior contact repeatability, which is comparable with the entire system trace noise when measured on the semi-automated system and on gold contact pads.CROSSTALKCrosstalk of TITAN™ probes on the short and the bare ceramic open standard of 150 micron spacing compared to conventional 110 GHz probe technologies. Results are corrected by the multiline TRL calibration. All probes are of GSG configuration and 100 micron pitch.-80-60-40-200Crosstalk on Open. Multiline TRL Calibration.M a g (S21) (d B )Frequency (GHz)-80-60-40-200Crosstalk on Short. Multiline TRL Calibration.M a g (S21) (d B )Frequency (GHz)The maximal probe c ontac t repeatability error of the c alibrate S11-parameter of the AC2-2 thru standard by T110 probes. Semi-automated system. Ten contact circles.Cantilever needle material Ni alloy Body materialAl alloy Contact pressure @2 mils overtravel 20 g Lifetime, touchdowns> 1,000,000Ground and signal alignment error [1]± 3 µm [1]Planarity error [1] ± 3 µm [1]Contact footprint width < 30 µm Contact resistance on Au < 3 mΩThermal range-60 to 175 °CMechanical CharacteristicsAC2-2 Thru S21 Repeatability. Manual TS50 System.-100-80-60-40-200S 21 E r r o r M a g n i t u d e (d B )Frequency (GHz)MECHANICAL CHARACTERISTICSThe maximal probe c ontac t repeatability error of the c alibrate S21-parameter of the AC2-2 thru standard by T50 probes. Manual probe system TS50.26 GHZ PROBES FOR WIRELESS APPLICATIONSUnderstanding customer needs to reduce the cost of development and product testing for the high competitive wireless application market, MPI offers low-cost yet high-performance RF probes. The specifically developed SMA connector and its outstanding transmission of electro-magnetic waves through the probe design make these probes suitable for applications frequencies up to 26 GHz. The available pitch range is from 50 micron to 1250 micron with GS/SG and GSG probe tip configurations. TITAN™ 26 GHz probes are the ideal choice for measurement needs when developing components for WiFi, Bluetooth, and 3G/4G commercial wireless applications as well as for student education.Characteristic Impedance 50 ΩFrequency rangeDC to 26 GHz Insertion loss (GSG configuration)1< 0.4 dB Return loss (GSG configuration)1> 16 dB DC current ≤ 1 A DC voltage ≤ 100 V RF power, @10 GHz≤ 5 WTypical Electrical Characteristics26 GHz Probe Model: T26Connector SMAPitch range50 µm to 1250 µm Standard pitch step from 50 µm to 450 µm from 500 µm to 1250 µm25 µm step 50 µm stepAvailable for 90 µm pitch Tip configurations GSG, GS, SG Connector angleV-Style: 90-degree A-Style: 45-degreeMechanical CharacteristicsT26 probe, A-Style of the connectorTypical Electrical Characteristics: 26 GHz GSG probe, 250 micron pitchPROBES FOR DEVICE AND IC CHARACTERIZATION UP TO 110 GHZTITAN™ probes realize a unique combination of the micro-coaxial cable based probe technology and MEMS fabricated probe tip. A perfectly matched characteristic impedance of the coplanar probe tips and optimized signal transmission across the entire probe down to the pads of the device under test (DUT) result in excellent probe electrical characteristics. At the same time, the unique design of the probe tip provides minimal probe forward skate on any type of pad metallization material, therefo -re achieving accurate and repeatable measurement up to 110 GHz. TITAN™ probes are suitable for probing on small pads with long probe lifetime and low cost of ownership.The TITAN™ probe family contains dual probes for engineering and design debug of RF and mm-wave IC’s as well as high-end mm-wave range probes for S-parameter characterization up to 110 GHz for modeling of high-performance microwave devices.Characteristic Impedance 50 ΩFrequency rangeDC to 40 GHz Insertion loss (GSG configuration)1< 0.6 dB Return loss (GSG configuration)1> 18 dB DC current ≤ 1 A DC voltage ≤ 100 V RF power, @10 GHz≤ 5 WTypical Electrical Characteristics40 GHz Probe Model: T40Connector K (2.92 mm)Pitch range50 µm to 500 µmStandard pitch step For GSG configuration:from 50 µm to 450 µm from 500 µm to 800 µmFor GS/SG configuration:from 50 µm to 450 µm 25 µm step 50 µm stepAvailable for 90 µm pitch25 µm stepAvailable for 90/500 µm pitch Tip configurations GSG, GS, SG Connector angleV-Style: 90-degree A-Style: 45-degreeMechanical CharacteristicsTypical Electrical Characteristics: 40 GHz GSG probe, 150 micron pitchT40 probe, A-Style of the connectorCharacteristic Impedance50 ΩFrequency range DC to 50 GHz Insertion loss (GSG configuration)1< 0.6 dB Return loss (GSG configuration)1> 17 dBDC current≤ 1 ADC voltage≤ 100 VRF power, @10 GHz≤ 5 W Typical Electrical Characteristics Connector Q (2.4 mm)Pitch range50 µm to 250 µm Standard pitch stepFor GSG configuration: from 50 µm to 450 µm For GS/SG configuration: from 50 µm to 450 µm 25 µm stepAvailable for 90/500/550 µm pitch 25 µm stepAvailable for 90/500 µm pitchTip configurations GSG, GS, SG Connector angle V-Style: 90-degreeA-Style: 45-degreeMechanical CharacteristicsT50 probe, A-Style of the connectorTypical Electrical Characteristics: 50 GHz GSG probe, 150 micron pitchCharacteristic Impedance50 ΩFrequency range DC to 67 GHz Insertion loss (GSG configuration)1< 0.8 dB Return loss (GSG configuration)1> 16 dBDC current≤ 1 ADC voltage≤ 100 VRF power, @10 GHz≤ 5 W Typical Electrical Characteristics Connector V (1.85 mm)Pitch range50 µm to 250 µm Standard pitch stepFor GSG configuration: from 50 µm to 400 µm For GS/SG configuration: from 50 µm to 250 µm 25 µm step Available for 90 µm pitch25 µm step Available for 90 µm pitchTip configurations GSG Connector angle V-Style: 90-degreeA-Style: 45-degreeMechanical CharacteristicsT67 probe, A-Style of the connectorTypical Electrical Characteristics: 67 GHz GSG probe, 100 micron pitchCharacteristic Impedance 50 ΩFrequency rangeDC to 110 GHz Insertion loss (GSG configuration)1< 1.2 dB Return loss (GSG configuration)1> 14 dB DC current ≤ 1 A DC voltage ≤ 100 V RF power, @10 GHz≤ 5 WTypical Electrical CharacteristicsMechanical CharacteristicsTypical Electrical Characteristics: 110 GHz GSG probe, 100 micron pitchT110 probe, A-Style of the connectorCharacteristic impedance50 ΩFrequency range DC to 220 GHz Insertion loss (GSG configuration)1< 5 dB Connector end return loss(GSG configuration)1> 9 dBTip end return loss(GSG configuration)1> 13 dBDC current≤ 1.5 ADC voltage≤ 50 V Typical Electrical CharacteristicsConnector Broadband interface Pitch range50/75/90/100/125 µm Temperature range -40 ~ 150 ºC Contact width15 µmquadrant compatible(allowing corner pads)Yes recommended pad size20 µm x 20 µm recommended OT (overtravel)15 µmcontact resistance(on Al at 20 ºC using 15 µm OT)< 45 mΩlifetime touchdowns(on Al at 20 ºC using 15 µm OT)> 200,000Mechanical CharacteristicsT220 probe, broadband interface Typical Performance (at 20 ºC for 100 µm pitch)BODY DIMENSIONS PROBES Single-Ended V-StyleT220 GHz Probe1.161.1628.328437.455.6512.5527.73Single-Ended A-StyleCALIBRATION SUBSTRATESAC-series of calibration standard substrates offers up to 26 standard sets for wafer-level SOL T, LRM probe-tip cali -bration for GS/SG and GSG probes. Five coplanar lines provide the broadband reference multiline TRL calibration as well as accurate verification of conventional methods. Right-angled reciprocal elements are added to support the SOLR calibration of the system with the right-angled configuration of RF probes. A calibration substrate for wide-pitch probes is also available.Material Alumina Elements designCoplanarSupported calibration methods SOLT, LRM, SOLR, TRL and multiline TRL Thickness 635 µmSizeAC2-2 : 16.5 x 12.5 mm AC3 : 16.5 x 12.5 mm AC5 : 22.5 x 15 mm Effective velocity factor @20 GHz0.45Nominal line characteristic impedance @20 GHz 50 ΩNominal resistance of the load 50 ΩTypical load trimming accuracy error ± 0.3 %Open standardAu pads on substrate Calibration verification elements Yes Ruler scale 0 to 3 mm Ruler step size100 µmCalibration substrate AC2-2Probe Configuration GSGSupported probe pitch100 to 250 µm Number of SOL T standard groups 26Number of verification and calibration lines5Calibration substrate AC-3Probe Configuration GS/SG Supported probe pitch50 to 250 µm Number of SOL T standard groups 26Number of verification and calibration lines5Calibration substrate AC-5Probe Configuration GSG, GS/SG Supported probe pitch250 to 1250 µm Number of SOL T standard groups GSG : 7GS : 7SG : 7Open standardOn bare ceramic Number of verification and calibration linesGSG : 2GS : 1Typical characteristics of the coplanar line standard of AC2-2 calibration substrate measured using T110-GSG100 probes, and methods recommended by the National Institute of Standard and Technologies [2, 3].2468(d B /c m )F requency (G Hz)α-6-4-202I m a g (Z 0) ()F requency (G Hz)AC2-2 W#006 and T110A-GSG100Ω2.202.222.242.262.282.30 (u n i t l e s s )F requency (G Hz)β/βо4045505560R e a l (Z 0) ()F requency (G Hz)ΩTypical Electrical CharacteristicsMPI QAlibria® RF CALIBRATION SOFTWAREMPI QAlibria® RF calibration software has been designed to simplify complex and tedious RF system calibration tasks. By implementing a progressive disclosure methodology and realizing intuitive touch operation, QAlibria® provides crisp and clear guidance to the RF calibration process, minimizing con-figuration mistakes and helping to obtain accurate calibration results in fastest time. In addition, its concept of multiple GUI’s offers full access to all configuration settings and tweaks for advanced users. QAlibria® offers industry standard and advanced calibration methods. Furthermore, QAlibria® is integrated with the NIST StatistiCal™ calibration packages, ensuring easy access to the NIST mul-tiline TRL metrology-level calibration and uncertainty analysis.MPI Qalibria® supports a multi-language GUI, eliminating any evitable operation risks and inconvenience.SpecificationsRF AND MICROWAVE CABLESMPI offers an excellent selection of flexible cables and acces-sories for RF and mm-wave measurement applications forcomplete RF probe system integration.CablesHigh-quality cable assemblies with SMA and 3.5 mm connectorsprovide the best value for money, completing the entry-level RFsystems for measurement applications up to 26 GHz. Phase stab-le high-end flexible cable assemblies with high-precision 2.92, 2.4, 1.85 and 1 mm connectors guarantee high stability, accuracy and repeatability of the calibration and measurement for DC applications up to 110 GHz.MPI offers these cable assemblies in two standard lengths of 120 and 80 cm, matching the probe system’s footprint and the location of the VNA.Cables Ordering InformationMRC-18SMA-MF-80018 GHz SMA flex cable SMA (male) - SMA (female), 80 cmMRC-18SMA-MF-120018 GHz SMA flex cable SMA (male) - SMA (female), 120 cmMRC-26SMA-MF-80026 GHz SMA flex cable SMA (male) - SMA (female), 80 cmMRC-26SMA-MF-120026 GHz SMA flex cable SMA (male) - SMA (female), 120 cmMRC-40K-MF-80040 GHz flex cable 2.92 mm (K) connector, male-female, 80 cm longMRC-40K-MF-120040 GHz flex cable 2.92 mm (K) connector, male-female, 120 cm longMRC-50Q-MF-80050 GHz flex cable 2.4 mm (Q) connector, male-female , 80 cm longMRC-50Q-MF-120050 GHz flex cable 2.4 mm (Q) connector, male-female , 120 cm longMRC-67V-MF-80067 GHz flex cable 1.85 mm (V) connector, male-female, 80 cm longMRC-67V-MF-120067 GHz flex cable 1.85 mm (V) connector, male-female, 120 cm longMMC-40K-MF-80040 GHz precision flex cable 2.92 mm (K) connector, male-female, 80 cm long MMC-40K-MF-120040 GHz precision flex cable 2.92 mm (K) connector, male-female, 120 cm long MMC-50Q-MF-80050 GHz precision flex cable 2.4 mm (Q) connector, male-female , 80 cm long MMC-50Q-MF-120050 GHz precision flex cable 2.4 mm (Q) connector, male-female , 120 cm long MMC-67V-MF-80067 GHz precision flex cable 1.85 mm (V) connector, male-female, 80 cm long MMC-67V-MF-120067 GHz precision flex cable 1.85 mm (V) connector, male-female, 120 cm long MMC-110A-MF-250110 GHz precision flex cable 1 mm (A) connector, male-female, 25 cm longMPI Global PresenceDirect contact:Asia region: ****************************EMEA region: ******************************America region: ********************************MPI global presence: for your local support, please find the right contact here:/ast/support/local-support-worldwide© 2023 Copyright MPI Corporation. All rights reserved.[1] [2][3] REFERENCESParameter may vary depending upon tip configuration and pitch.R. B. Marks and D. F. Williams, "Characteristic impedance determination using propagation constant measu -rement," IEEE Microwave and Guided Wave Letters, vol. 1, pp. 141-143, June 1991.D. F. Williams and R. B. Marks, "Transmission line capacitance measurement," Microwave and Guided WaveLetters, IEEE, vol. 1, pp. 243-245, 1991.AdaptersHigh-In addition, high-quality RF and high-end mm-wave range adapters are offered to address challenges ofregular system reconfiguration and integration with different type of test instrumentation. MRA-NM-350F RF 11 GHz adapter N(male) - 3.5 (male), straight MRA-NM-350M RF 11 GHz adapter N(male) - 3.5 (female), straightMPA-350M-350F Precision 26 GHz adapter 3.5 mm (male) - 3.5 mm (female), straight MPA-350F-350F Precision 26 GHz adapter 3.5 mm (female) - 3.5 mm (female), straight MPA-350M-350M Precision 26 GHz adapter 3.5 mm (male) - 3.5 mm (male), straight MPA-292M-240F Precision 40 GHz adapter 2.92 mm (male) - 2.4 mm (female), straight MPA-292F-240M Precision 40 GHz adapter 2.92 mm (female) - 2.4 mm (male), straight MPA-292M-292F Precision 40 GHz adapter 2.92 mm (male) - 2.92 mm (female), straight MPA-292F-292F Precision 40 GHz adapter 2.92 mm (female) - 2.92 mm (female), straight MPA-292M-292M Precision 40 GHz adapter 2.92 mm (male) - 2.92 mm (male), straight MPA-240M-240F Precision 50 GHz adapter 2.4 mm (male) - 2.4 mm (female), straight MPA-240F-240F Precision 50 GHz adapter 2.4 mm (female) - 2.4 mm (female), straight MPA-240M-240M Precision 50 GHz adapter 2.4 mm (male) - 2.4 mm (male), straight MPA-185M-185F Precision 67 GHz adapter 1.85 mm (male) -1.85 mm (female), straight MPA-185F-185F Precision 67 GHz adapter 1.85 mm (female) -1.85 mm (female), straight MPA-185M-185M Precision 67 GHz adapter 1.85 mm (male) -1.85 mm (male), straight MPA-185M-100FPrecision 67 GHz adapter 1.85 mm (male) -1.00 mm (female), straightDisclaimer: TITAN Probe, QAlibria are trademarks of MPI Corporation, Taiwan. StatistiCal is a trademark of National Institute of Standards and Technology (NIST), USA. All other trademarks are the property of their respective owners. Data subject to change without notice.。

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

article
info
abstract
In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control. © 2011 Elsevier Ltd. All rights reserved.

高斯状态

centered at the origin with width determined by d. Thus this state represents a particle
“localized” near the origin within a statistical uncertainty speciﬁed by d.
We deﬁne this state by giving its components in the position basis, i.e., its wave
function:
1
x2
ψ(x) = x|ψ =
√ π1/4 d
exp ikx − 2d2
.
You can check as a good excercise that this wave function is normalized:
Combining systems in quantum mechanics
In our generalization from a particle moving in 1-d to a particle moving in 3-d we tacitly took advantage of a general quantum mechanical scheme for combining systems to make composite systems. In particular, we viewed a particle moving in 3-d as essentially 3 copies of a particle moving in 1-d. We do this sort of thing all the time in physics. For example, if we have a satisfactory kinematic model of a particle and we want to consider a kinematic model for 2 particles, we naturally try to use two copies of the model that we used for one particle. As another example, we have presented a model of a spin 1/2 system, what if we want to describe 2 spin 1/2 systems? Or what if we want to describe a particle with spin 1/2? All these situations require us to know how to combine quantum mechanical models to make composite models. Here we outline the scheme using our generalization from a 1-d particle to a 3-d particle as illustration. Later we will have occasion to use this construction again.

smp_phy_controlsulogin --- LINUX FEDORA命令

NAMEsmp_phy_control − invoke PHY CONTROL SMP functionSYNOPSISsmp_phy_control[−−attached=ADN][−−expected=EX][−−help][−−hex][−−interface=PARAMS] [−−max=MA][−−min=MI][−−op=OP][−−phy=ID][−−pptv=TI][−−raw][−−sa=SAS_ADDR] [−−verbose][−−version]SMP_DEVICE[,N]DESCRIPTIONSends a SAS Management Protocol (SMP) PHY CONTROL request function to a SMP target. The SMP target is identiﬁed by the SMP_DEVICE and the SAS_ADDR.Depending on the interface, the SAS_ADDR may be deduced from the SMP_DEVICE.With one interface there is one SMP_DEVICE per machine so the SMP_DEVICE,N syntax is needed to differentiate between HBAs if there are multiple present.The PHY CONTROL function is used to change the state of a phy within a SMP target. SMP targets are typically SAS expanders which have multiple phys. Certain operation values (e.g. ’lr’ (link reset) and ’hr’(hard reset)) change the state of the attached phy. Sending such operation values to the phy in the SMP tar-get that is attached to the originator (i.e. the SMP initiator) may lead to a bad response.Invoking this utility with no arguments (other than SMP_DEVICE which might be in an environment vari-able and−−sa=SAS_ADDR which might be in an environment variable or not needed) is harmless. In other words a phy’s state is only changed when either−−max=MA,−−min=MI,−−op=OP or−−pptv=TI is given with a non default value.OPTIONSMandatory arguments to long options are mandatory for short options as well.−a,−−attached=ADNspeciﬁes the attached device name (ADN). The default value is 0 .The ADN is in decimal but islikely to be a SAS address which is typically shown in hexadecimal. To specify a number in hex-adecimal either preﬁx it with ’0x’ or put a trailing ’h’ on it.−E,−−expected=EXset the ’expected expander change count’ ﬁeld in the SMP request.The value EX is from 0 to65535 inclusive with 0 being the default value. When EX is greater than zero then if the valuedoesn’t match the expander change count of the SMP target (i.e. the expander) when the requestarrives then the target ignores the request and sets a function result of "invalid expander changecount" in the response.−h,−−helpoutput the usage message then exit.−H,−−hexoutput the response in hexadecimal.−I,−−interface=PARAMSinterface speciﬁc parameters. In this case "interface" refers to the path through the operating sys-tem to the SMP initiator.See the smp_utils man page for more information.−M,−−max=MApermits the programmed maximum physical link rate to be changed on the gven phy. Permittedvalues are: 0 −> no change, 8 −> 1.5 Gbps, 9 −> 3 Gbps, 10 −> 6 Gbps. Default value is 0.−m,−−min=MIpermits the programmed minimum physical link rate to be changed on the given phy.Permittedvalues are: 0 −> no change, 8 −> 1.5 Gbps, 9 −> 3 Gbps, 10 −> 6 Gbps. Default value is 0.−o,−−op=OPspeciﬁes the operation to be performed on the given phy.The OP argument can be either numericor a string. If a number is given, it is put into the ’phy operation’ ﬁeld of the request. Allowablestrings are abbreviations of which only the ﬁrst two characters need to match. The supportedstrings are: ’nop’ (no operation), ’lr’ (link reset), ’hr’ (hard reset), ’dis’ (disable phy), ’cel’ (clearerror log), ’ca’ (clear afﬁliation), ’tspss’ (transmit SATA port selection signal), ’citnl’ (clear STPI_T nexus loss (bit)), and ’sadn’ (set attached device name).The default value is 0 (no operation).−p,−−phy=IDphy identiﬁer.ID is a value between 0 and 127. Default is 0.−P,−−pptv=TIpartial pathway timeout value. The units are microseconds and the permitted values are between 0and 15 inclusive.7microseconds is recommended by sas2r07.−r,−−rawsend the response to stdout in binary.All error messages are sent to stderr.−s,−−sa=SAS_ADDRspeciﬁes the SAS address of the SMP target device. Typically this is an expander.This option maynot be needed if the SMP_DEVICE has the target’s SAS address within it. The SAS_ADDR is indecimal but most SAS addresses are shown in hexadecimal. To giv e a number in hexadecimaleither preﬁx it with ’0x’ or put a trailing ’h’ on it.−v,−−verboseincrease the verbosity of the output. Can be used multiple times−V,−−versionprint the version string and then exit.CONFORMING TOThe SMP PHY CONTROL function was introduced in SAS-1 .AUTHORSWritten by Douglas Gilbert.REPORTING BUGSReport bugs to <dgilbert at interlog dot com>.COPYRIGHTCopyright © 2006−2008 Douglas GilbertThis software is distributed under a FreeBSD license. There is NO warranty; not even for MER-CHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.SEE ALSOsmp_utils, smp_discover(smp_utils)。

2014年考研英语一真题答案解析（完整版）

2014年考研英语一真题答案解析（完整版）2014年全国硕士研究生入学统一考试英语(一)试题解析Section I Use of English1、【答案】A where【解析】本句的句义是：我们突然不能回忆起刚才把钥匙放在哪里了，或者一个老熟人的姓名，或者是一个老乐队的名称。

这根据句义，这里是表示忘记了钥匙所放在的地点，where 作为宾语从句的引导词，和后面的部分一起，作为remember的宾语，因此正确答案为A。

B、when 引导表示时间的状语从句，C、that放在这里不合适，DWhy引导表示原因的状语从句。

B、C、D均不符合题意。

2、【答案】B fades【解析】本句的句义是：本句的句义是关于大脑的退化，我们婉转地把它称作“老年时分”(老年人的瞬间记忆丧失)。

从前文可以看出，文章讲的是随着年龄增长，记忆力的衰退。

由语境确定B。

fade away 是一个固定搭配，表示消失、衰弱、消退、消歇。

A. Improve 表示提高;C. recover表示恢复、D.collapse表示崩塌。

A、C、D均不符合题意。

3、【答案】B while【解析】本句的句义是：这看起来问题不大，但精神集中能力的丧失，对于我们的职业生涯，社会交往以及个人生活都能产生有害影响。

这个空在句首，需要填一个连接词，看起来问题不大和后面的内容之间存在转折关系，因此正确答案为B。

A选项unless表示让步关系;C选项Once作为连词表示条件关系，表示一……就;D选项也是条件关系。

A、C、D均不符合题意。

4、【答案】A damaging【解析】本句的句义同第3题。

通过整篇文章语境，我们可以看出注意力的丧失会对我们造成不好的影响，造成损害，因此正确答案是damaging，表示损害。

B选项limited表示有限，局限性;C选项uneven表示不均匀，奇数;D选项obscure表示晦涩的不清楚的。

B、C、D均不符合题意。

5、【答案】C well-being【解析】本句的句义同第3题。

the fundamentais of the logital testing

RS_500K / RS_125K / RS_31.25K / RS_7.81K / RS_1.95K / RS_500 / RS_125 / RS_31.25
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DAC PPMU unit
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LOGIC_SET_DRIVE_MODE_PIN(ALL_PINS,ACTIVE_LOAD); //Select pins for active load
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• 如何判斷 Open ?
一、Check tester( L/B) ( 無 correlation wafer ) 1. 將 open 的 channel (P/C) short to Gnd 2. 執行程式 2-1.PMU measure = 0 V 機台 (配件) 正常 2-2.PMU measure = 5 V 機台 (配件) 不正常二、Check P/C contact 1.P/C contact to wafer 2.check 針痕是否正常 3.用電表從 open channel 的 pogo pin 去量測 diode
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一、Check tester( L/B) ( 無 correlation wafer ) 1. 執行程式 1-1.PMU measure = 5 V 機台 (配件) 正常 1-2.PMU measure = 0 V 機台 (配件) 不正常二、Check P/C contact 1.P/C contact to wafer 2.check 針痕是否正常 3.用電表從 short channel 的 pogo pin 去量測 diode

Temperature dependent magnetization dynamics of magnetic nanoparticles

a rX iv:082.1740v1[c ond-mat.ot her]12Feb28Temperature dependent magnetization dynamics of magnetic nanoparticles A.Sukhov 1,2and J.Berakdar 21Max-Planck-Institut f¨u r Mikrostrukturphysik,Weinberg 2,D-06120Halle/Saale,Germany 2Institut f¨u r Physik,Martin-Luther-Universit¨a t Halle-Wittenberg,Heinrich-Damerow-Str.4,06120Halle,Germany Abstract.Recent experimental and theoretical studies show that the switching behavior of magnetic nanoparticles can be well controlled by external time-dependent magnetic ﬁelds.In this work,we inspect theoretically the inﬂuence of the temperature and the magnetic anisotropy on the spin-dynamics and the switching properties of single domain magnetic nanoparticles (Stoner-particles).Our theoretical tools are the Landau-Lifshitz-Gilbert equation extended as to deal with ﬁnite temperatures within a Langevine framework.Physical quantities of interest are the minimum ﬁeld amplitudes required for switching and the corresponding reversal times of the nanoparticle’s magnetic moment.In particular,we contrast the cases of static and time-dependent external ﬁelds and analyze the inﬂuence of damping for a uniaxial and a cubic anisotropy.PACS numbers:75.40.Mg,75.50.Bb,75.40.Gb,75.60.Jk,75.75.+a1.IntroductionIn recent years,there has been a surge of research activities focused on the spin dynamics and the switching behavior of magnetic nanoparticles[1].These studies are driven by potential applications in mass-storage media and fast magneto-electronic devices. In principle,various techniques are currently available for controlling or reversing the magnetization of a nanoparticle.To name but a few,the magnetization can be reversed by a short laser pulse[2],a spin-polarized electric current[3,4]or an alternating magneticﬁeld[5,6,7,8,9,10,11,12,13].Recently[6],it has been shown for a uniaxial anisotropy that the utilization of a weak time-dependent magneticﬁeld achievesa magnetization reversal faster than in the case of a static magneticﬁeld.For this case[6],however,the inﬂuence of the temperature and the diﬀerent types of anisotropy on the various dependencies of the reversal process have not been addressed.These issues,which are the topic of this present work,are of great importance since,e.g. thermal activation aﬀects decisively the stability of the magnetization,in particular when approaching the superparamagnetic limit,which restricts the density of data storage[14].Here we study the possibility of fast switching atﬁnite temperature with weak externalﬁelds.We consider magnetic nanoparticles with an appropriate size as to display a long-range magnetic order and to be in a single domain remanent state(Stoner-particles).Uniaxial and cubic anisotropies are considered and shown to decisively inﬂuence the switching dynamics.Numerical results are presented and analyzed for iron-platinum nanoparticles.In principle,the inclusion ofﬁnite temperatures in spin-dynamics studies is well-established(cf.[19,20,23,15,16,1]and references therein) and will be followed here by treatingﬁnite temperatures on the level of Langevine dynamics.For the analysis of switching behaviour the Stoner and Wohlfarth model (SW)[17]is often employed.SW investigated the energetically metastable and stable position of the magnetization of a single domain particle with uniaxial anisotropy in the presence of an external magneticﬁeld.They showed that the minimum static magneticﬁeld(generally referred to as the Stoner-Wohlfarth(SW)ﬁeld or limit)needed to coherently reverse the magnetization is dependent on the direction of the applied ﬁeld with respect to the easy axis.This dependence is described by the so-called Stoner-Wohlfarth astroid.The SWﬁndings rely,however,on a static model at zero temperature.Application of a time-dependent magneticﬁeld reduces the required minimum switchingﬁeld amplitude below the SW limit[6].It was,however,not yet clear howﬁnite temperatures will aﬀect theseﬁndings.To clarify this point,we utilize an extension of the Landau-Lifshitz-Gilbert equation[18]includingﬁnite temperatures on the level of Langevine dynamics[19,20,23].Our analysis shows the reversal time to be strongly dependent on the damping,the temperature and the type of anisotropy. These dependencies are also exhibited to a lesser extent by the critical reversalﬁelds. The paper is organized as follows:next section2presents details of the numerical scheme and the notations whereas section3shows numerical results and analysis for Fe50Pt50 and Fe70Pt30nanoparticles.We then conclude with a brief summary.2.Theoretical modelIn what follows we focus on systems with large spins such that their magnetic dynamics can be described by the classical motion of a unit vector S directed along the particle’s magnetizationµ,i.e.S=µ/µS andµS is the particle’s magnetic moment at saturation. The energetics of the system is given byH=H A+H F.(1) where H A(H F)stands for the anisotropy(Zeeman energy)contribution.Furthermore, the anisotropy contribution is expressed as H A=−Df(S)with D being the anisotropy constant.Explicit form of f(S)is provided below.The magnetization dynamics,i.e.the equation of motion for S,is governed by the Landau-Lifshitz-Gilbert(LLG)equation [18]∂S(1+α2)S× B e(t)+α(S×B e(t)) .(2) Here we introduced the eﬀectiveﬁeld B e(t)=−1/(µS)∂H/∂S which contains the external magneticﬁeld and the maximum anisotropyﬁeld for the uniaxial anisotropy B A=2D/µS.γis the gyromagnetic ratio andαis the Gilbert damping parameter.The temperatureﬂuctuations will be described on the level of the Langevine dynamics[19]. This means,a time-dependent thermal noiseζ(t)adds to the eﬀectiveﬁeld B e(t)[19].ζ(t)is a Gaussian distributed white noise with zero mean and vanishing time correlator ζi(t′)ζj(t) =2αk B TB A,τ=ωa t,ωa=γB A.(4) The LLG equation reads then∂S(1+α2)S× b(τ)+α(S×b(τ)) ,(5) where the eﬀectiveﬁeld is now given explicitly byb(τ)=−1∂S+Θ(τ)(6)withΘi(τ′)Θj(τ) =ǫδi,jδ(τ−τ′);ǫ=2αk B TD.(8) q is a measure for the thermal energy in terms of the anisotropy energy.And d=D/(µS B A)expresses the anisotropy constant in units of a maximum anisotropyenergy for the uniaxial anisotropy and is always1/2.The stochastic LLG equation(5) in reduced units(4)is solved numerically using the Heun method which converges in quadratic mean to the solution of the LLG equation when interpreted in the sense of Stratonovich[20].For each type of anisotropy we choose the time step∆τto be one thousandth part of the corresponding period of oscillations.The values of the time interval in not reduced units for uniaxial and cubic anisotropies are∆t ua=4.61·10−15s and∆t ca=64.90·10−15s,respectively,providing us thus with correlation times on the femtosecond time scale.The reason for the choice of such small time intervals is given in [19],where it is argued that the spectrum of thermal-agitation forces may be considered as white up to a frequency of order k B T/h with h being the Planck constant.This value corresponds to10−13s for room temperature.The total scale of time is limited by a thousand of such periods.Hence,we deal with around one million iteration steps for a switching process.Details of realization of this numerical scheme could be found in references[21,22,20].We note by passing,that attempts have been made to obtain, under certain limitations,analytical results forﬁnite-temperature spin dynamics using the Fokker-Planck equation(cf.[15,16]and references therein).For the general case discussed here one has however to resort to fully numerical approaches.3.Results and interpretationsWe consider a magnetic nanoparticle in a single domain remanent state(Stoner-particle) with an eﬀective anisotropy whose origin can be magnetocrystalline,magnetoelastic and surface anisotropy.We assume the nanoparticle to have a spherical form,neglecting thus the shape anisotropy contributions.In the absence of externalﬁelds,thermal ﬂuctuations may still drive the system out of equilibrium.Hence,the stability of the system as the temperature increases becomes an important issue.The time t at which the magnetization of the system overcomes the energy barrier due to the thermal activation,also called the escape time,is given by the Arrhenius lawt=t0e DπµS k B TαγThe relation between K u and D u is D u=K u V u,where V u is the volume of Fe50Pt50nanoparticles.In the calculations for Fe50Pt50nanoparticles the following q valueswere chosen:q1=0.001,q2=0.005or q3=0.01which correspond to the realtemperatures56K,280K or560K,respectively(these temperatures are below theblocking temperature).The corresponding escape times are t q1≈2·10217s,t q2≈1075s and t q3≈7·1031s,respectively.In some cases we also show the results for an additional temperature q01=0.0001with the corresponding real temperature to be equal to5K.The corresponding escape time for this is t q01≈104300s.These times should be compared with the measurement period which is about t m≈5ns,endorsing thus the stability ofthe system during the measurements.For Fe70Pt30the parameters are as follows:The diameter of the nanoparticles2.3nm, the strength of the anisotropy K c=8·105J/m3,the magnetic moment per particle µp=2000·µB,the Curie-temperature is T c=420K[24],and D c=K c V c(V c is the volume.)For Fe70Pt30nanoparticles the values of q we choose in the simulations are q4=0.01,q5=0.03or q6=0.06which means that the temperature is respectively 0.3K,0.9K or1.9K.The escape times are t q4≈1034s,t q5≈2·105s and t q6≈2·10−2s, respectively.Here we also choose an intermediate value q04=0.001and the realtemperature0.03K with the corresponding escape time to be equal to t q04≈10430s. The measurement period is the same,namely about5ns.All values of the escape timeswere given forα=0.1.Central to this study are two issues:The critical magneticﬁeld and the corresponding reversal time.The critical magneticﬁeld we deﬁne as the minimumﬁeld amplitude needed to completely reverse the magnetization.The reversal time is the corresponding time for this process.In contrast,in other studies[6]the reversal time is deﬁned as the time needed for the magnetization to switch from the initial position to the position S z=0,our reversal time is the time at which the magnetization reaches the very proximity of the antiparallel state(Fig.1).The diﬀerence in the deﬁnition is in so far important as the magnetization position S z=0atﬁnite temperatures is not stabile so it may switch back to the initial state due to thermalﬂuctuations and hence the target state is never reached.3.1.Nanoparticles having uniaxial anisotropy:Fe50Pt50A Fe50Pt50magnetic nanoparticle has a uniaxial anisotropy whose direction deﬁnes the z direction.The magnetization direction S is speciﬁed by the azimuthal angleφand the polar angleθwith respect to z.In the presence of an externalﬁeld b applied at an arbitrarily chosen direction,the energy of the system in dimensionless units derives from˜H=−d cos2θ−S·b.(11) The initial state of the magnetization is chosen to be close to S z=+1and we aim at the target state S z=−1.Figure1.(Color online)Magnetization reversal of a nanoparticle when a staticﬁeldis applied at zero Kelvin(q0=0,black)and at reduced temperature q3=0.01≡560K(blue).The strengths of theﬁelds in the dimensionless units(4)and(8)are b=1.01and b=0.74,respectively.The damping parameter isα=0.1.The start position ofthe magnetization is given by the initial angleθ0=π/360between the easy axis andthe magnetization vector.3.1.1.Staticﬁeld For an external static magneticﬁeld applied antiparallel to the z direction(b=−b e z)eq.(11)becomes˜H=−d cos2θ+b cosθ.(12) To determine the criticalﬁeld magnitude needed for the magnetization reversal we proceed as follows(cf.Fig.1):Atﬁrst,the externalﬁeld is increased in small steps. When the magnetization reversal is achieved the corresponding values of the critical ﬁeld versus the damping parameterαare plotted as shown in the inset of Fig.3.The reversal times corresponding to the critical staticﬁeld amplitudes of Fig.3are plotted versus damping in Fig.4.In the Stoner-Wohlfarth(static)model the mechanism of magnetization reversal is not due to damping.It is rather caused by a change of the energy proﬁle in the presence of theﬁeld.The curves displayed on the energy surface in Fig.2mark the magnetization motion in the E(θ,φ)landscape.The magnetization initiates fromφ0=0andθ0and ends up atθ=π.As clearly can be seen from theﬁgure,reversal is only possible if the initial state is energetically higher than the target state.This”low damping”reversal is,however,quite slow,which will be quantiﬁed more below.For the reversal at T=0, the SW-model predicts a minimum staticﬁeld strength,namely b cr=B/B A=1(the dashed line in Fig.3).This minimumﬁeld measured with respect to the anisotropyﬁeld strength does not depend on the damping parameterα,provided the measuring time is inﬁnite.For T>0 the simulations were averaged over500cycles with the result shown in Fig.3.The one-cycle data are shown in the inset.Fig.3evidences that with increasing temperature thermalﬂuctuations assist a weak magneticﬁeld as to reverse the magnetization. Furthermore,the required criticalﬁeld is increased slightly at very large and strongly at very small damping with the minimum criticalﬁeld being atα≈1.0.The reason forthe magnetization starts atθ0=0(the vector product in equation(2)vanishes).The reversal time in the SW-limit is then given byt rev=g(θ0,b)1+α22γD 1b−cosθ πθ0.(14)From this relation we infer that switching is possible only if the appliedﬁeld is larger than the anisotropyﬁeld and the reversal time decreases with increasing b.This conclusion is independent of the Stoner-Wohlfarth model and follows directly from the solution of the LLG equation.An illustration is shown by the dashed curve in Fig.4,which was a test to compare the appropriate numerical results with the analytical one.As our aim is the study of the reversal-time dependence on the magnetic moment and on the anisotropy constant,we deem the logarithmic dependence in Eq.(14)to be weak and writeg(b,µS,D)≈µSB2µ2S−4D2.(15)This relation indicates that an increase in the magnetic moment results in a decreaseof the reversal time.The magnetic moment enters in the Zeeman energy and thereforethe increase in magnetic moment is very similar to an increase in the magneticﬁeld.An increase of the reversal time with the increasing anisotropy originates from the factthat the anisotropy constant determines the height of the potential barrier.Hence,thehigher the barrier,the longer it takes for the magnetization to overcome it.For the other temperatures the corresponding reversal times(also averaged over500cycles)are shown in Fig. 4.In contrast to the case T=0,where an appreciabledependence on damping is observed,the reversal times forﬁnite temperatures showa weaker dependence on damping.Ifα→0only the precessional motion of themagnetization is possible and therefore t rev→∞.At high damping the system relaxes on a time scale that is much shorter than the precession time,giving thus rise to anincrease in switching times.Additionally,one can clearly observe the increase of thereversal times with increasing temperatures,even though these time remain on thenanoseconds time scale.3.1.2.Alternatingﬁeld As was shown in Ref.[6,7,15]theoretically and in Ref.[5] experimentally,a rotating alternatingﬁeld with no staticﬁeld being applied can also be used for the magnetization reversal.A circular polarized microwaveﬁeld is applied perpendicularly to the anisotropy axis.Thus,the Hamiltonian might be written in form of equation(11)and the appliedﬁeld isb(t)=b0cosωt e x+b0sinωt e y,(16) where b0is the alternatingﬁeld amplitude andωis its frequency.For a switching of the magnetization the appropriate frequency of the applied alternatingﬁeld should beFigure4.(Color online)Reversal times corresponding to the critical staticﬁelds inFig.3vs.damping averaged over500cycles.Inset shows the as-calculated numericalresults for q3=0.01≡560K(one cycle).Figure 5.(Color online)Magnetization reversal in a nanoparticle using a timedependentﬁeld forα=0.1and at a zero temperature.Theﬁeld strength and frequencyin the units(4)are respectively b0=0.18andω=ωa/1.93.Inset shows for this casethe magnetization reversal for the temperature q3=0.01≡560K with b0=0.17andthe same frequency.chosen.In Ref.[15]analytically and in[6]numerically a detailed analysis of the optimal frequency is given which is close to the precessional frequency of the system.The role of temperature and diﬀerent types of anisotropy have not yet been addressed,to our knowledge.Fig.5shows our calculations for the reversal process at two diﬀerent temperatures. In contrast to the static case,the reversal proceeds through many oscillations on a time scale of approximately ten picoseconds.Increasing the temperature results in an increase of the reversal time.Fig.6shows the trajectory of the magnetization in the E(θ,φ)space related to the case of the alternatingﬁeld pared with the situation depicted in Fig. 2,the trajectory reveals a quite delicate motion of the magnetization.It is furthermore, noteworthy that the alternatingﬁeld amplitudes needed for the reversal(cf.Fig.7)are substantially lower than their static counterpart,meaning that the energy proﬁle of the.(17)αThe proportionality coeﬃcient contains the frequency of the alternatingﬁeld and the critical angleθ.The solution(17)follows from the LLG equation solved for the case when the phase of the externalﬁeld follows temporally that of the magnetization,which we checked numerically to be valid.The reversal times associated with the critical switchingﬁelds are shown in(Fig.8).Qualitatively,we observe the same behavior as for the case of a staticﬁeld.The values of the reversal times for T=0are,however,signiﬁcantly smaller than for the static case.For the same reason as in the staticﬁeld case,an increased temperature results in an increase of the switching times.Figure7.(Color online)Critical alternatingﬁeld amplitudes vs.damping fordiﬀerent temperatures averaged over500times.Inset shows not averaged data for.q3=0.01≡560Kto the criticalﬁeld amplitudes of Fig.7for diﬀerent temperatures.Inset shows thecase of zero Kelvin.3.2.Nanoparticles with cubic anisotropy:Fe70Pt30Now we focus on another type of the anisotropy,namely a cubic anisotropy which is supposed to be present for Fe70Pt30nanoparticles[24].The energetics of the system is then described by the functional form˜H=−d(S2x S2y+S2y S2z+S2x S2z)−S·b,(18) or in spherical coordinates˜H=−d(cos2φsin2φsin4θ+cos2θsin2θ)−S·b.(19) In contrast to the previous section,there are more local minima or in other words more stable states of the magnetization in the energy proﬁle for the Fe70Pt30nanoparticles. It can be shown that the minimum barrier that has to be overcome is d/12which is twelve times smaller than that in the case of a uniaxial anisotropy.The maximal one is only d/3.The magnetization of these nanoparticles isﬁrst relaxed to the initial state close toFigure9.(Color online)Trajectories of the magnetization in theθ(φ)space(q0=0).In the units(4)we choose b=0.82andα=0.1.√φ0=π/4andθ0=arccos(1/3).In order to be close to the starting state for the uniaxial anisotropy case we chooseφ0=0.2499·π,θ0=0.3042·π.3.2.1.Static drivingﬁeld A staticﬁeld is applied antiparallel to the initial state of the magnetization,i.e.√b=−b/B A.3In principle,the criticalﬁeld turns out to be constant for allαbut for an inﬁnitely large measuring time.Since we set this time to be about5nanoseconds,the criticalﬁelds increase for small and high damping.On the other hand,at lower temperatures smaller criticalﬁelds are suﬃcient for the(thermal activation-assisted)reversal process.The behaviour of the corresponding switching times presented in Fig.12only supplements the fact of too low measuring time,which is chosen as5ns for a better comparison of these results with ones for uniaxial anisotropy.Indeed,constant jumps in the reversal times for T=0K as a function of damping can be observed.The reasonFigure10.(Color online)Magnetization reversal of a nanoparticle when a staticﬁeldb=0.82is applied and forα=0.1at zero temperature(black).The magnetizationreversal forα=0.1,b=0.22and q6=0.06≡1.9K is shown with blue color.Figure11.(Color online)Critical staticﬁeld amplitudes vs.the damping parametersfor diﬀerent temperatures averaged over500times.Inset shows not averaged data forq6=0.06≡1.9K.Fig.11vs.damping averaged over500times.why the reversal times forﬁnite temperatures are lower is as follows:The initial state for T=0K is chosen to be very close to equilibrium.This does not happen forﬁnite3).The magnetization trajectories depicted in Fig.13reveal two interesting features: Firstly,particularly for small damping,the energy proﬁle changes very slightly(due to the smallness of b0)while energy is pumped into the system during many cycles. Secondly,the system switches mostly in the vicinity of local minima to acquire eventually the target state.Fig.14hints on the complex character of the magnetization dynamics in this case.As in the staticﬁeld case with a cubic anisotropy the criticalﬁeld amplitudes shown in Fig.15are smaller than those for a uniaxial anisotropy.Obviously, the reason is that the potential barrier associated with this anisotropy is smaller in this case,giving rise to smaller amplitudes.As before an increase in temperature leads to a decrease in the criticalﬁelds.The reversal times shown in Fig.16exhibit the same feature as in the cases for uniaxial anisotropy:With increasing temperatures the corresponding reversal times increase.A physically convincing explanation of the(numerically stable)oscillations for the reversal times is still outstanding.Figure14.(Color online)Magnetization reversal in a nanoparticle using a time dependentﬁeld forα=0.1and q0(black)and for q6=0.06≡1.9K(blue).Other parameters are as in Fig.13.Figure15.(Color online)Critical alternatingﬁeld amplitudes vs.damping for diﬀerent temperatures averaged over500cycles.Inset shows the single cycle data at q6=0.06≡1.9K.Figure16.(Color online)The damping dependence of the reversal times corresponding to the critical ﬁelds of the Fig.15for diﬀerent temperatures averaged over500runs.Inset shows the T=0case. 4.SummaryIn this work we studied the criticalﬁeld amplitudes required for the magnetization switching of Stoner nanoparticles and derived the corresponding reversal times forstatic and alternatingﬁelds for two diﬀerent types of anisotropies.The general trends for all examples discussed here can be summarized as follows:Firstly,increasing the temperature results in a decrease of all criticalﬁelds regardless of the anisotropy type. Anisotropy eﬀects decline with increasing temperatures making it easier to switch the magnetization.Secondly,elevating the temperature increases the corresponding reversal times.Thirdly,the same trends are observed for diﬀerent temperatures:The criticalﬁeld amplitudes for a staticﬁeld depend only slightly onα,whereas the critical alternating ﬁeld amplitudes exhibit a pronounced dependence on damping.In the case of a uniaxial anisotropy weﬁnd the critical alternatingﬁeld amplitudes to be smaller than those for a staticﬁeld,especially in the low damping regime and forﬁnite pared with a staticﬁeld,alternatingﬁelds lead to smaller switching times(T=0K).However, this is not the case for the cubic anisotropy.The markedly diﬀerent trajectories for the two kinds of anisotropies endorse the qualitatively diﬀerent magnetization dynamics. In particular,one may see that for a cubic anisotropy and for an alternatingﬁeld the magnetization reversal takes place through the local minima leading to smaller amplitudes of the appliedﬁeld.Generally,a cubic anisotropy is smaller than the uniaxial one giving rise to smaller slope of criticalﬁelds,i.e.smaller alternatingﬁeld amplitudes. It is useful to contrast our results with those of Ref.[15].Our reversal times for AC-ﬁelds increase with increasing temperatures.This is not in contradiction with the ﬁndings of[15]insofar as we calculate the switchingﬁelds atﬁrst,and then deduce the corresponding reversal times.If the switchingﬁelds are kept constant while increasing the temperature[15]the corresponding reversal times decrease.We note here that experimentally known values of the damping parameter are,to our knowledge,not larger than0.2.The reason why we go beyond this value is twofold.Firstly,the values of damping are only well known for thin ferromagneticﬁlms and it is not clear how to extend them to magnetic nanoparticles.For instance,in FMR experiments damping values are obtained from the widths of the corresponding curves of absorption.The curves for nanoparticles can be broader due to randomly oriented easy anisotropy axes and,hence,the values of damping could be larger than they actually are.Secondly,due to a very strong dependence of the critical AC-ﬁelds(Fig.7,e.g.)they can even be larger than staticﬁeld amplitudes.This makes the time-dependentﬁeld disadvantageous for switching in an extreme high damping regime.Finally,as can be seen from all simulations,the corresponding reversal times are much more sensitive a quantity than their criticalﬁelds.This follows from the expression(13), where a slight change in the magneticﬁeld b leads to a sizable diﬀerence in the reversal time.This circumstance is the basis for our choice to average all the reversal times and ﬁelds over many times.This is also desirable in view of an experimental realization,for example,in FMR experiments or using a SQUID technique quantities like criticalﬁelds and their reversal times are averaged over thousands of times.The results presented in this paper are of relevance to the heat-assisted magnetic recording,ing a laser source.Our calculations do not specify the source of thermal excitations but they capture the spin dynamics and switching behaviour of the system upon thermalexcitations.AcknowledgmentsThis work is supported by the International Max-Planck Research School for Science and Technology of Nanostructures.References[1]Spindynamics in conﬁned magnetic structures III B.Hillebrands,A.Thiaville(Eds.)(Springer,Berlin,2006);Spin Dynamics in Conﬁned Magnetic Structures II B.Hillebrands,K.Ounadjela (Eds.)(Springer,Berlin,2003);Spin dynamics in conﬁned magnetic structures B.Hillebrands, K.Ounadjela(Eds.)(Springer,Berlin,2001);Magnetic Nanostructures B.Aktas,L.Tagirov,F.Mikailov(Eds.),(Springer Series in Materials Science,Vol.94)(Springer,2007)and references therein.[2]M.Vomir,L.H.F.Andrade,L.Guidoni,E.Beaurepaire,and J.-Y.Bigot,Phys.Rev.Lett.94,237601(2005).[3]J.Slonczewski,J.Magn.Magn.Mater.,159,L1,(1996).[4]L.Berger,Phys.Rev.B54,9353(1996).[5]C.Thirion,W.Wernsdorfer,and D.Mailly,Nat.Mater.2,524(2003).[6]Z.Z.Sun and X.R.Wang,Phys.Rev.B74,132401(2006).[7]Z.Z.Sun and X.R.Wang,Phys.Rev.Lett.97,077205(2006).[8]L.F.Zhang,C.Xu,Physics Letters A349,82-86(2006).[9]C.Xu,P.M.Hui,Y.Q.Ma,et al.,Solid State Communications134,625-629(2005).[10]T.Moriyama,R.Cao,J.Q.Xiao,et al.,Applied Physics Letters90,152503(2007).[11]H.K.Lee,Z.M.Yuan,Journal of Applied Physics101,033903(2007).[12]H.T.Nembach,P.M.Pimentel,S.J.Hermsdoerfer,et al.,Physics Letters90,062503(2007).[13]K.Rivkin,J.B.Ketterson,Applied Physics Letters89,252507(2006).[14]R.W.Chantrell and K.O’Grady The Magnetic Properties ofﬁne Particles in R.Gerber,C.D.Wright and G.Asti(Eds.),Applied Magnetism(Kluwer,Academic Pub.,Dordrecht,1994).[15]S.I.Denisov,T.V.Lyutyy,P.H¨a nggi,and K.N.Trohidou,Phys.Rev.B74,104406(2006).[16]S.I.Denisov,T.V.Lyutyy,and P.H¨a nggi,Phys.Rev.Lett.97,227202(2006).[17]E.C.Stoner and E.P.Wohlfarth,Philos.Trans.R.Soc.London,Ser A240,599(1948).[18]ndau and E.Lifshitz,Phys.Z.Sowjetunion8,153(1935).[19]W.F.Brown,Phys.Rev.130,1677(1963).[20]J.L.Garcia-Palacios and zaro,Phys.Rev.B58,14937(1998).[21]Algorithmen in der Quantentheorie und Statistischen Physik J.Schnakenberg(Zimmermann-Neufang,1995).[22]U.Nowak,p.Phys.9,105(2001).[23]adel,Phys.Rev.B73,212405(2006).[24]C.Antoniak,J.Lindner,and M.Farle,Europhys.Lett.70,250(2005).[25]I.Klik and L.Gunther,J.Stat.Phys.60,473(1990).[26]C.Antoniak,J.Lindner,M.Spasova,D.Sudfeld,M.Acet,and M.Farle,Phys.Rev.Lett.97,117201(2006).[27]S.Ostanin,S.S.A.Razee,J.B.Staunton,B.Ginatempo and E.Bruno,J.Appl.Phys.93,453(2003).。

硅酸盐通报格式

硅酸盐通报格式【篇一：硅酸盐通报格式要求】一下红色文字为对文章格式、字体等的解释说明，不属于作者文章内容。

文章中的字体汉字：宋体，英文：new times roman正文字号：五号行距：单倍行距溶胶-凝胶法制备ca3co4o9粉的工艺研究张丽鹏，于先进，董云会，刘欣（山东理工大学化学工程学院单位名称淄博单位所在城市 255049邮编）摘要：采用溶胶-凝胶法制备了ca3co4o9粉，确定了适用于ca3co4o9粉制备的方法及工艺条件，并利用xrd、sem等方法分析表征样品。

实验结果表明，以乙二醇为溶剂，柠檬酸为螯合剂，加入添加剂制得凝胶，干凝胶在750～900℃下烧结2h，制得了20～30nm的片状单晶ca3co4o9粉。

关键词： ca3co4o9粉；溶胶-凝胶法；工艺关键词与关键词之间用分号分割图书分类号文献标示码process research of ca3co4o9 powders by the sol-gel method zhang li-peng, yu xian-jin, dong yun-hui, liu xin请注意，如：张小兵 = zhang xiao-bing，请注意使用斜体并注意大小写规则，以及连接线（school of chemical engineering, shandong university of technology, zibo 255049, china）abstract: ca3co4o9 powders were prepared by sol-gel process. the efficient processes were made sure. ca3co4o9 powders were characterized by xrd and sem. the results show that the gel can be obtained by using glycol, citrate and additive. theca3co4o9 powders can be obtained after the dry gel calcined at 750-900℃ for 2h,and ca3co4o9 single-crystal with the average size of 20-30nm.key word: ca3co4o9 powders; technique; sol-gel这里的“序言”等标题类文字去掉热电材料是一种将热能和电能直接转换的功能陶瓷材料，随着当今新的材料合成技术的发展，以及用x射线衍射技术和计算机来研究化合物能带结构参数等新技术的出现，使得目前热电材料的研究日新月异，除了对传统热电材料的进一步研究外，各种新材料的报道层出不穷。

A vision inspection system for the surface defects of strongly reflected metal based multi-classSVM

A vision inspection system for the surface defects of strongly reﬂected metal based on multi-class SVMZhang Xue-wu a ,Ding Yan-qiong a ,⇑,Lv Yan-yun a ,Shi Ai-ye a ,Liang Rui-yu a ,ba Computer and Information Engineering College,Hohai University,Nanjing 210098,China bInformation Science and Engineering College,Southeast University,Nanjing 210096,Chinaa r t i c l e i n f o Keywords:Defect classiﬁcation Strongly reﬂected metal Wavelet transform Feature extractionSupport vector machinea b s t r a c tThis paper describes the designing and testing process of a vision system for strongly reﬂected metal’s surface defects detection.In the authors’view,an automatic inspection system has the following stages:image acquisition,image pre-processing,feature extraction and classiﬁcation.Thus,the system includ-ing four subsystems is designed,and image processing method and pattern recognition algorithm that perform speciﬁc functions are outlined.First,the study uses wavelet smoothing method to eliminate noise from the images.Then,the images are segmented by Otsu threshold.At last,ﬁve characteristics based on spectral measure of the binary images are collected and input into a support vector machine (SVM).Furthermore,kernel function selection and parameters settings which are used for SVM method are evaluated and discussed.Also,a very difﬁcult detection case for the surface defects of strongly reﬂected metal is depicted in details.The classiﬁcation results demonstrate that the proposed method can identify seven classes of metal surface defects effectively,and the results are summarized and interpreted.Ó2010Elsevier Ltd.All rights reserved.1.IntroductionGenerally,strongly reﬂected metals include aluminum,gold,copper and silver,etc.Currently,those metals have been widely used in different areas,and become the dispensable raw materials in several industries such as power electronics,automobile industries,shipping,domestic electronics,communications and construction industries,etc.Obviously,the surface quality of those metals will directly inﬂuence the capability and quality of the ﬁnal products.However,defect inspection of strongly reﬂected metal is a simply repetitive and highly concentrated work.For traditional methods such as artiﬁcial visual detection and frequency ﬂashlight detection,due to the disadvantages of their low random inspection rate,bad real-time capability,low inspection conﬁdence and bad inspection environment,they could not meet the industrial requirements properly.As a result,the developments of on-line vision-based systems which are capable of performing inspection tasks have been promoted.Enhanced quality measurement helps to improve the performance of the system as follows:1.Improve controlling of the process, e.g.faster reaction of processing faults,avoidance of disaster events,etc.2.Improve overall process efﬁciency, e.g.avoidance of down-stream processing of faulty material,optimizing downstream processing (repair,downgrading,and upgrading).3.Improve customer relationships,e.g.reducing the claims deliv-ering documented quality.Most of the presently applied inspection systems perform de-fect detection.However,defect classiﬁcation still remains a re-search subject.The strongly reﬂected metal is the one who can be described as the most difﬁcult classifying metal in defects clas-siﬁcation.Most metal surface defects are tiny involving obvious faulty items such as holes,stains,scratches,pilling,indentation,burrs and other ill-deﬁned defects.These defects are small in size,refractive in light and can not be described using explicit measures,which make automatic defect detection difﬁcult.The research issues in defect inspection are widely open.In early days,with the absence of appropriate algorithms,the re-searches mostly focus on hardware design,especially in sensory system.And most frequently,sensory systems use CCD chips (Per-nkopf &O’Leary,2003;Zhang et al.,2008).However,alternative strategies,including laser scanning (Abuazza,Brabazon,&El-Bara-die,2003,2004),ultrasound (Kercel,Kisner,Klein,Bacher,&Pouet,1999),and X-ray image sensor systems (Boerner &Strecker,1988;Mery &Filbert,2002;Naso &Pantaleo,2005)are gaining ground.In recent years,developments in image processing,computer vision,artiﬁcial intelligence and other related ﬁelds have0957-4174/$-see front matter Ó2010Elsevier Ltd.All rights reserved.Corresponding author.Tel./fax:+8651985106049.E-mail address:ding.yanqiong@ (D.Yan-qiong).signiﬁcantly improved the capability of visual inspection tech-niques.Up to now,several kinds of inspection systems have been proposed and have completely used image processing technologies and pattern recognition technologies.Piironen,Silven,Pietikainen, and Laitinen(1989,1990)described a prototype for an automated visual on-line metal strip inspection system which is based on morphological preprocessing and combined statistical and struc-tural defect recognition.The computational requirements for this system are large.Frayman,Zheng,and Nahavandi(2006)devel-oped a machine vision system for automatic inspection of surface defects in aluminum die casting.The system used a hybrid image processing algorithm based on mathematic morphology to detect defects with different sizes and shapes.The feed-forward neural network technique has been used to detect defects of cold rolled strips(Kang&Liu,2005),but FFN has some problems,e.g.easily getting into local minimum and long learning time,etc.Also the feature vectors used in this paper are simple and are non sensitive to distinguish diverse defects.Liang,Ding,Zhang,and Chen(2008) proposed a surface defect detection algorithm of copper strips based on RBF network and support vector machine that can detect all kinds of defects efﬁciently in real-time environment,and used Pseudo Zernike moments as the feature vectors.Similarity-based algorithms as well as texture algorithms have been developed for aluminum casting(Fernandez,Platero,Campoy,&Aracil,1993). Jia,Murphey,Shi,and Chang(2004)described a real-time visual inspection system that used support vector machine to automati-cally learn complicated defect patterns of hot rolled steel.In order to achieve efﬁcient computed results,the authors used roughﬁl-tering,and defect candidateﬁnding to extract features.Experimen-tal results demonstrate the potential of a support vector machine as a promising classiﬁer for defect(seam)data with application in real-time manufacturing environment.However,this system has some limitations,e.g.it aims at detecting some special defect ‘‘seams’’,and the accuracy is not satisﬁed.Wang,Zhang,Mu,and Wang(2008)proposed an inspection system which adopted a self-adaptive weight averagingﬁltering method to preprocess im-age,and used the moment invariants to pick up the characters of typical defects.Furthermore,the eigenvectors were identiﬁed by the RBF neural networks.However,as the input space is in high dimension,the RBF network requires a prohibitively large number of Gaussian basis functions to cover a large number of inputs. Zheng,Kong,and Nahavandi(2002)used GAs for generating mor-phology processing parameters.This approach has the feasibility for the detection of structural defects and high detection accuracy for defects such as holes and cracks.However,due to the complex-ity of structural defects,the training sets selected manually some-times do not reﬂect the common features of structural defects.Feature extraction is a key step for the classiﬁcation,and all the aforementioned references focus on gray value based feature extraction.Actually,metal surface defects are mostly similar to texture patterns.Numerous methods have been proposed to ex-tract textural features either directly from spatial domain or from the spectral tif-Amet,Ertuzun,and Ercil(1999)used co-occurrence matrices based on wavelet sub-image characteris-tics to detect defects of textile fabrics.Co-occurrence matrices method is one of statistic methods in the spatial domain.Tech-niques in the spectral domain extract textural features by conduct-ing frequency transforms such as Fourier transform(Tsai&Huang, 2003),Gabor transform(Tsa&Wu,2000),or wavelet transform (Lee,Choi,Choi,Kim,&Choi,1996;Lee,Choi,Choi,&Choi, 1997).Fourier transform is a global method,which just depicts the spatial-frequency distribution without regarding to the spatial domain information.Gabor is non-orthogonal and redundancy ex-ists in different feature components,which results in computation-ally intensive in analyzing texture image.Wavelet based method isFrom Bayes classiﬁers to neural networks(Li,2009;Liu,2003; Pernkopf,2004),there are many possible choices for an appropri-ate classiﬁer.Among these,SVM would appear to be a good candi-date for a high generalization performance without the need to add a priori knowledge,even when the dimension of the input space is very high(Chapelle,Haffner,&Vapnik,1999).This paper concentrates on research issues related to defect classiﬁcation in strongly reﬂected metal and discussed the general methodology as well as speciﬁc examples of the algorithms.Fur-thermore,a case of copper strip surface defects classiﬁcation using SVM is described.The paper is organized as follows:the requirements for strongly reﬂected metal inspection systems and the proposed inspection system are described in Section2,while the speciﬁc defect charac-terization and classiﬁcation algorithms are detailed in Section3. Section4showed the experimental results and discussed the per-formance of these algorithms.In Section5,the authors summa-rized the results.2.Inspection system analysis and design2.1.Issues in metal defects inspectionAt present,there are commercially available systems that can perform surface defect detection in strongly reﬂected metal at a high cost.However,the problem of defect classiﬁcation,i.e.loca-tion of the defect region,prediction of the defect feature,and the optimal classiﬁer are still open research issues.Inspection within metallic surfaces is conditioned by:ually,metal surface has a high reﬂection coefﬁcient thatmakes it difﬁcult to design a proper lighting system for defect enhancing.2.The metal surface moves fast under the inspection devices andresults in extremely high data volume:a typical metal is1–2m wide and moves with speeds ranging from2–3m/s.Conse-quently,data volume for100%inspection is tremendous.3.Diversity:there are a great variety of defect types and a singleclass of defects can be different in appearance such as size or orientation.Small changes in the production process can result in entirely new classes of defects.Furthermore,there are some ‘‘false defects’’such as oil spots.2.2.System designA typical machine vision system will consist of several among the following components:1.One or more digital or analog cameras with suitable opticsfor acquiring images.2.Camera interface for digitizing images.3.A processor(often a PC or embedded processor,such as aDSP).4.A smart camera which combined all of the above.5.Input/Output hardware(e.g.digital I/O)or communicationlinks(work connection or RS-232)to report results.6.Lenses to focus the desiredﬁeld of view onto the imagesensor.7.Light sources.8.A software to process images and detect relevant features.9.A synchronizing sensor for part detection(often an opticalor magnetic sensor)to trigger image acquisition and processing.Z.Xue-wu et al./Expert Systems with Applications38(2011)5930–59395931In this paper,the authors consider a development environment consisting of four subsystems:image acquisition,image process-ing,feature extraction and defect classiﬁcation.Fig.1shows the major stages of the surface defect detection system designed in this study.First,the image is captured by the frame grabber which con-verts the output of the camera to digital format and places the im-age in computer memory.So it may be processed by the machine vision software.Next,the image processing software will typically take several steps to process an image.Often the image is ﬁrst manipulated to reduce noise and to convert to a binary image.Fea-ture extraction is used to obtain a feature discriminatory.Then,features obtained are input pattern to support vector machine (SVM),and SVM is employed for the metal defect classiﬁcation task.As a ﬁnal step,the software passes or fails the part according to programmed criteria.If a part fails,the software may inform a mechanical device to reject the part.Alternately,the system may stop the production line and warn a human worker to ﬁx the prob-lem that caused the failure.2.2.1.Image acquisition subsystemImage acquisition subsystem can serve as tools to improve manufacturing processes,as well as quality control in industries.Image acquisition hardware includes four parts:illumination,lenses,cameras,and camera-computer interfaces.Illumination is a particularly important component of the image acquisition sys-tem,which makes the essential features of an object visible.Lenses produce a sharp image on the sensor.The sensor convertsage into an analog or digital video signal.Finally,interfaces accept the video signal and convert it into an the computer’s memory.The goal of illumination in machine vision is to make the tant features of the object visible and reduce undesired the object.In order to do so,we have to consider how interacts with the object.One important aspect is the ponent of the light and the object.To enhance the visibility tain features,we can use the following issues,such composition of light,the directional properties of the Often,screens are used to prevent ambient light from the object and thereby lowering the image quality.A light-emitting diode (LED)is a semiconductor device duces narrow-spectrum light through has many advantages:longevity,little power,produces furthermore,they can be used as ﬂashes with fast reaction and almost no aging.Since LEDs have so many practical ges,they are currently the primary illumination in machine vision application.Reﬂection at metal causes light to become partially To suppress this light,the authors mount a polarizing ﬁler of the camera and turn it in such a way that the polarized When taking all the above into consideration,the object of this paper:strongly reﬂected metal,are usually illuminated with a dif-fuse bright-ﬁled back light illumination,as shown in Fig.2.The camera’s purpose is to create an image from the light fo-cused in the image plane by the lens.The most important compo-nent of the camera is a digital sensor.The two main sensor technologies are CCD (charge-coupled device)and CMOS (comple-mentary metal-oxide–semiconductor).They differ primarily in their readout architecture,i.e.,in the manner in which the image is read out from the chip.The CCD sensor consists of a line of light-sensitive photo detectors;typically,they are photo gates or photodiodes.CMOS sensor typically uses photodiodes for photo detection.In contrast to CCD cameras,the charge of the photodi-odes is not transported sequentially to a readout register.Instead,each row of the CMOS sensor can be selected directly for readout through the row and column select circuits.Neither technology has a clear advantage in image quality.CMOS can potentially be implemented with fewer components,use less power and/or pro-vide faster readout than D is a more mature technology and is in most respects the equal of CMOS.2.2.2.Preprocessing subsystemSmoothing is often used to reduce noise within an image or to produce a less pixelated image.In production environment,the performance of the inspection system is seriously inﬂuenced by some noise e.g.camera thermal noise,digitizing noise,etc.To get the better performance in posterior stage,a good denoising pro-cessing of the image is necessary.In recent years,as the wavelet Fig.1.Framework of inspection system.coefﬁcients are set to zero if their indexes are greater than a number.By changing the level for decomposition and thetype,we can obtain the optimal combination for best Segmentation is an important part of any automated image ognition system.The goal of segmentation is to simplify orthe representation of an image into something that is moreingful and easier to analyze.More precisely,image segmentation the process of assigning a label to every pixel in an image such pixels with the same label share certain visual characteristics.Image thresholding is crucial to the application of image seg-mentation.So it’s necessary toﬁnd an optimal overall threshold that can be used to convert the gray scale image into a binary im-age,which separates an object’s pixels from the background pixels. Thus,the authors used Otsu’s method(Otsu,1979),a threshold selection method from gray-level histograms,which chooses the threshold to minimize the intraclass variance of the threshold black and white pixels.2.2.3.Characterization subsystemIn this subsystem,a set of known features that characterize de-fects are computed.The objective is to achieve a better classiﬁca-tion by using as few as possible features to represent the defects. The most difﬁcult problem is the defects of the same class are vary-ing in different position,size,and orientation.So an available for-mation of feature vectors should make the defects with the same class invariant to expected transformation,i.e.translation,size, and rotation.Examples of such features include size,shape charac-teristics,as well as texture measurements on regions.Such fea-tures can be computed and analyzed by statistical or other computing techniques.On the other hand,sometimes the more complete feature vectors we apply,the better the classiﬁcation re-sults we could get.However,due to the curse of dimensionality, the feature set should be large enough to accurately predict the output as well as not be too huge.The set of computed features forms the input vectors to support vector machine.2.2.4.Classiﬁcation subsystemA classiﬁer can predict a class label of the input object.Actually, classiﬁer performance depends greatly on the characteristics of the data to be classiﬁed.Typically,any trainable classiﬁer uses a refer-ence set of manually classiﬁed samples.These samples are referred as the training sets.The quality of the results for such a classiﬁer depends mainly on two factors:the quality of the aforementioned feature set and the quality of the training set.The more complete the training set we use,the better the classiﬁcation results we ob-tain for new samples.As a classiﬁer model has been selected,the engineer then runs the learning algorithm on the gathered training set.Parameters of the learning algorithm may be adjusted by opti-mizing performance on a subset of the training set.As the optimal parameters have been obtained,the performance of the algorithm may be measured on a testing set which is separated from the training set.3.Methodology3.1.Wavelet transform for defect detectionThe main advantages of wavelet are that they have a varying window size,which can be wide for slow frequencies and narrow for the fast ones,thus leading to an optimal time–frequency reso-lution in all frequency ranges.Furthermore,owing to the fact that windows are adapted to the transients of each scale,wavelets lack of the requirement of stationary.As using the wavelet in image area,image is decomposed i.e.,as shown in Fig.3(a).These sub-bands are named as L-H1,H-L1, and H-H1that represent theﬁnest scale wavelet coefﬁcients of de-tail images as well as sub-band L-L1corresponds to low frequency level coefﬁcients of approximation image.The sub-band L-L1alone is further decomposed to obtain the next coarse level of discrete wavelet coefﬁcients.For a two-level DWT decomposition as shown in Fig.3(b).L-L2 will be used to obtain further decomposition.This decomposition process continues untilﬁnal scale is reached.Coefﬁcients obtained from DWT of approximation and detail images(sub-band images) are the basic features that are shown here as the useful characters for the texture classiﬁcation.Micro-textures and macro-textures are statistically characterized by using the features in approxima-tion and detail of ly,the values of the L-L,H-L,L-H, and H-H sub-band images or combinations of these sub-bands or the obtained features from these sub-bands characterize a texture images very well.3.2.Feature extractionAn important method for region description is to quantify its texture content.Two kinds of methods used for computing texture are statistical approach and spectral measure(Gonzalez&Woods, 2002).In this paper,we used spectral measure approach which based on Fourier spectral to compute texture.Detection and inter-pretation of the spectral features are simpliﬁed by expressing the spectrum in polar coordinates to yield a function S(r,h),where S is the spectrum function while frequency r and direction h are the variables in this coordinate system.For each frequency r, S(r,h)is considered as1-D function S h(r),Analyzing S h(r)for aﬁxed value of h yields the behavior of the spectrum along a radial direc-tion from origin.Analyzing S r(h)for aﬁxed value of r yields the behavior along a circle centered at the origin.By summing these functions,a global description is obtained:SðrÞ¼X ph¼0S hðrÞð1ÞSðhÞ¼X R0r¼0S rðhÞð2ÞS(r)and S(h)constitute a spectral-energy description for an en-tire image or region under consideration.We use some descriptors of the function S(h)to characterize their behavior,including,the maximum value,the minimum value,mean,standard deviation, and distance between maximum value and mean.That is,totally 5characteristics of S(h)are obtained.3.3.Support vector machine classiﬁerSVM have recently been proposed as popular tools for classiﬁca-tion problem(Cristianini&Shawe-Taylor,2000).For linearly sepa-rable problem,the main goal is to deﬁne a hyperplane which divides sample set so that all points with the same label are on the same side of the hyperplane while maximizing the distance Fig.3.Image decomposition(a)one level and(b)two levels.Z.Xue-wu et al./Expert SystemsFor linearly non-separable problem,the input data would be mapped into a high-dimensional feature space,and then the opti-mal separating hyperplane is constructed in the feature space. 3.3.1.Optimal separating hyperplaneLet j(x i,y i)j i=1,...,N be a training example set,each example x2R d belongs to a class labeled by y2j+1,À1j.If linear decision function exists in d-dimensional space:gðxÞ¼x T xþbð3Þwhere,x is the input vector,x is the adjustable weight vector,and b is the bias,which makes x T x i+b P0corresponding to y i=+1,x T x i+b60corresponding to y i=À1.Accordingly,we can know that the sample set is linearly sepa-rable.The pair(x,b)deﬁnes a separating hyperplanegðxÞ¼x T xþb¼0ð4ÞThe hyperplane makes the distance maximal.Hence,the optimal separating problem is equivalent to the following constraint optimi-zation problem:min/ðxÞ¼12k x k2¼12x T xð5Þyi½x T x iþb À1P0;i¼1;2;...;Nð6ÞBy means of the classical method of Lagrange multipliers,if3.3.2.Linearly non-separable caseIf the set S is not linearly separable,we must introduce N non-negative variables such thatyi½x T x iþb À1þn i P0;i¼1;2;...;Nð9Þn i P0,i=1,2,...,N are called slack variables.The generalized optimal separating hyperplane is then regarded as the solution of the following minimizing problem:min/ðxÞ¼1k x k2þCX Ni¼1n i"#ð10ÞThere into,C is a regularization parameter.3.3.3.Nonlinear support vector machinesFor the training example set that the authors want to classify is usually linearly non-separable,so the input data would be mapped into a high-dimensional feature space,and then the optimal sepa-rating hyperplane is constructed.If we replace x by its mapping in the feature space U(x),Eq.(7) becomesQðaÞ¼X Ni¼1a iÀ12X Ni¼1X Nj¼1a i a j yiyjUðx iÞUðx jÞð11Þ5934Z.Xue-wu et al./Expert Systems with Applications38(2011)5930–5939Fig.5.Wavelet decomposition results.Fig.7.Sobelﬁlter results.In LIBSVM,the authors used a‘‘grid-search’’on C and c using cross-validation.Basically pairs of(C,c)are tried and the one with the best cross-validation accuracy is picked.Accordingly,the parameters were set in the range of c=[2À4,2À3,...,22], C=[26,27,...,212]to test the classiﬁcation accuracy.All of the experiments were conducted using the one-against-one method (Krebel,1999)via m-fold-cross-validation toﬁnd the best parame-ters,where m equal to7.The sample set includes420defect images and of each class with60images.All of the data were di-vided into2/3training data sets(280data)and1/3testing data sets(140data).As shown in Table1,the cross-validation ranged from76.8%to 91.3%by adjusting the parameter(C,c)from(26,2À4)to(212,22). Comparing with the experimental results,the best accuracy can be obtained when the parameter(C,c)to be(210,20).So the authors used parameters C=1024,c=1to train the whole training set and then test it.Table2shows the number of training data and test data sets for each pair using the one-against-one method.Table3lists the clas-siﬁcation results using the one-against-one approach on copper strips surface defects.From Table3,we can see that the one-against-one approach leads to high classiﬁcation accuracy.There-fore,the proposed defect detection and classiﬁcation method is well suited with the texture recognition of defects on strongly re-ﬂected metal surface.In order to compare the performance of the proposed approach, we also use back-propagation neural network(BPNN)classiﬁer to solve the same classiﬁcation problem.As described in the previous section,the parameter pair of SVM are(C,c)=(210,20).The network structure of BP is5Â7Â11.The same,the data set have been di-vided into2/3(280images)for training,and1/3(140images)for testing.The classiﬁcation accuracies of SVM classiﬁer and BPNN are shown in the Table4,it is obvious that the SVM classiﬁer out-performs BPNN classiﬁer.Table1Cross-validation results for one-against-one.Class Accuracy(%)(26,2À4)(27,2À3)(28,2À2)(29,2À1)(210,20)(211,21)(212,22)1vs.279.583.085.487.189.788.485.8 1vs.382.483.686.187.690.588.687.0 1vs.481.583.785.487.890.189.287.6 1vs.581.284.085.988.491.389.487.9 1vs.680.983.785.387.589.688.686.4 1vs.782.684.586.188.787.987.486.5 2vs.378.680.583.485.387.185.984.6 2vs.481.382.984.686.488.786.485.1 2vs.582.683.885.787.689.487.286.5 2vs.682.183.985.787.288.988.187.0 2vs.780.582.583.985.487.586.685.9 3vs.481.283.485.086.788.587.286.0 3vs.580.782.384.086.488.787.285.9 3vs.676.879.282.584.986.785.284.6 3vs.782.984.586.787.989.488.286.7 4vs.582.684.385.988.089.489.588.0 4vs.683.485.987.688.788.287.686.1 4vs.780.683.084.686.387.687.586.9 5vs.681.382.884.786.487.988.287.4 5vs.780.582.483.985.086.785.885.3 6vs.781.983.485.687.188.988.387.6Table2Training/testing set for one-against-one method(seven classes).Class Training set Testing setNumber of labeled+1Number oflabeledÀ1Number oflabeled+1Number oflabeledÀ11vs.25624355 1vs.350303010 1vs.44238337 1vs.54832364 1vs.640403010 1vs.72357733 2vs.32654634 2vs.430501129 2vs.53149832 2vs.62654634 2vs.75228535 3vs.458223010 3vs.55723319 3vs.650303010 3vs.71862337 4vs.55624355 4vs.658223010 4vs.72357733 5vs.64832346 5vs.73149832Table3Classiﬁcation results for one-against-one((C,c)=(210,20)).Class Trainingaccuracy(%)Testingaccuracy(%)Class Trainingaccuracy(%)Testingaccuracy(%) 1vs.210087.53vs.4100751vs.3100753vs.510077.51vs.410082.53vs.6100751vs.5100903vs.710082.51vs.6100754vs.510087.51vs.710082.54vs.6100752vs.3100854vs.710082.52vs.410072.55vs.6100852vs.5100805vs.7100802vs.6100856vs.710077.52vs.710087.5Average10085Table4Comparison between the SVM and BP classiﬁer.Method Training accuracy(%)Testing accuracy(%) SVM10085.05938Z.Xue-wu et al./Expert Systems with Applications38(2011)5930–5939。

PHYS1002_Physics I (Foundamentals)_2013 Semester 1_module2_mechanics_mechanics10

5What is Work?Work is the process of transferring energy from the environment to a system, or from the system to the environment, by the application of forces.KJF §10.27θ1112Gravitational Potential Energy Two bodies are attracted because of gravity caused by theirmass, so we have to do work to push them apart.When we do this, energy is transferred to the system — called gravitational potential energy. Near earth's surfaceis a property of the system is earth + ball, but usually we simplify and say "the ball has potential energy"Because gravitational potential energy depends onlyon the height of the object above the reference level, PE is independent of path the potential energy does notdepend on the path taken.In both cases the G.P.E increasedby the same amount: mghKJF §10.621Conservative ForcesIf work done by a force in moving anobject from A to B does NOT dependon the path taken, we call it aconservative forcesprings).EVERY conservative force has “potential energy” associated with it(e.g. gravity ! gravitational P.E., spring force elastic P.E. ).KJF §10.6An object moving under the influence of a conservativeforce always conserves mechanical energy:ME = K i + U iIf an object moves in a closed loop underB under theof a conservative force is the exact negative of worke.g. Work done by gravity going upstairs and back downstairs again.23。