The performance of proper orthogonal decomposition in discontinuous flows
高延性水泥基复合材料(ECC)正交试验
Hans Journal of Civil Engineering 土木工程, 2023, 12(3), 298-306 Published Online March 2023 in Hans. https:///journal/hjce https:///10.12677/hjce.2023.123034高延性水泥基复合材料(ECC)正交试验吴倩倩1，蔡海兵1*，胡 时1，丁祖德21安徽理工大学土木建筑学院，安徽 淮南 2昆明理工大学建筑工程学院，云南 昆明收稿日期：2023年2月27日；录用日期：2023年3月19日；发布日期：2023年3月29日摘 要本文利用正交试验设计原理，开展了9组高延性水泥基复合材料(ECC)的坍落度、立方体抗压强度、劈裂抗拉强度和抗折强度试验，研究了硅灰、改性脱硫石膏、膨胀剂和减水剂四种因素对ECC 物理、力学性能的影响，并采用多元线性回归的方法，建立了ECC 的性能预测模型。
试验结果表明：最优组为硅灰掺量20%，脱硫石膏掺量4%，膨胀剂掺量6%，减水剂掺量1.9%；通过对正交试验的结果进行回归分析，得出了ECC 物理、力学性能预测模型，模型精度较高。
关键词正交试验，高延性水泥基复合材料，力学性能，修复工程Orthogonal Test of High DuctilityEngineering Cementitious Composites (ECC)Qianqian Wu 1, Haibing Cai 1*, Shi Hu 1, Zude Ding 21School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan Anhui 2Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming YunnanReceived: Feb. 27th, 2023; accepted: Mar. 19th, 2023; published: Mar. 29th, 2023AbstractIn this paper, using the orthogonal experiment design principle, carry out 9 groups of high ductili-ty Engineering Cementitious Composites (ECC) of the slump, cube compressive strength, splitting ten-sile strength and flexural strength test, study the effect of silica fume, modified desulfurization gyp-sum, expansive agent and water reducing agent of four factors on the physical and mechanical proper-ties of ECC, and adopt multiple linear regression method. The performance prediction model of ECC was established. The results show that the optimal group is silica fume content of 20%, desulfuri-*通讯作者。
LS-DYNA混凝土本构模型的性能 Performance of LS-DYNA Concrete Constitutive Models
(1)
where I1 is the 1st invariant of stress tensor, which represents volumetric responses; J 2 and J 3 are the 2nd and 3rd invariants of deviatoric stress tensor and they account for deviatoric responses. In general, the primary difference between various concrete constitutive models is how the deviatoric and volumetric responses are characterized. 2.1. Karagozian & Case Concrete (KCC) Model – MAT072 Intended for analyzing RC structural responses to blast and impact loadings, the KCC model was initially developed in early 1990s in DYNA3D and was ported to LS-DYNA in 2004. This model allows automatic generation of all the parameters by inputting only the unconfined compressive strength and density of the concrete. It has been applied in analyzing many RC structures subjected to quasi-static, blast, and impact loads [5, 9, 10]. A comprehensive model review and validation application is provided in Reference [11]. The KCC model has three independent strength surfaces and they can be formulated in a generalized form as:
Orthogonal Frequency Division Multiplexing
AbstractMulti-Carrier Modulation is a technique for data-transmission by dividing a high-bit rate data stream is several parallel low bit-rate data streams and using these low bit-rate data streams to modulate several carriers. Multi-Carrier Transmission has a lot of useful properties such as delay-spread tolerance and spectrum efficiency that encourage their use in untethered broadband communications. OFDM is a multi-carrier modulation technique with densely spaced sub-carriers, that has gained a lot of popularity among the broadband community in the last few years. This report is intended to provide a tutorial level introduction to OFDM Modulation, its advantages nd demerits, and some applications of OFDM.Overview of the ReportThis report is organized as follows:●The first section of the report presents the OFDM System Model. Details of generation and demodulation of OFDM are presented, along with system design issues.●The second section of the report presents some of the important advantages of OFDM that suit its use in Broadband communications.●The third section of the report discusses the Peak Power Problem in OFDM and sometechniques used to overcome the problems of Power Amplifier Non-Linearity.●The fourth section of the report discusses Synchronization Issues associated with OFDM and some synchronization methods commonly used in OFDM●The fifth section of the report discusses a relatively new technique of combining OFDM with CDMA called Multi-Carrier CDMA(MC-CDMA). Transmitter and Receiver structures for MC-CDMA and some of the advantages offered by MC-CDMA are discussed.●The final section of the report presents some of the applications of OFDM for broadband communications. Applications such as DAB, DVB and WLAN are considered in some detail.1. OFDM System ModelOFDM is a multi-channel modulation system employing Frequency Division Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital stream.1.1. IntroductionIn older multi-channel systems using FDM, the total available bandwidth is divided into N non-overlapping frequency sub-channels.Each sub-channel is modulated with a separate symbol stream and the N sub-channels are frequency multiplexed.Even though the prevention of spectral overlapping of sub-carriers reduces (or eliminates) Inter-channel Interference, this leads to an inefficient use of spectrum.The guard bands on Either side of each sub-channel is a waste of precious bandwidth.To overcome the problem of bandwidth wastage,,we can instead use N overlapping (but orthogonal) sub-carriers, each carrying a baud rate of 1/T and spaced 1/T apart. Because of the frequency spacing selected, the sub-carriers are all mathematically orthogonal to each other. This permits the proper demodulation of the symbol streams without the requirement of non-overlapping spectra. Another way of specifying the sub-carrier orthogonality condition isto require that each sub-carrier have exactly integer number of cycles in the interval T.It can be shown that the modulation of these orthogonal sub-carriers can be represented as an Inverse Fourier Transform.Alternatively,one may use a DFT operation followed by low-pass filtering to generate he OFDM signal. The details of this method are explained in the next section.It must be noted that OFDM can be used either as a modulation or a multiplexing techniq.1.2. OFDM using Inverse DFTThe use of Discrete Fourier Transform (DFT) in the parallel transmission of data using Frequency Division Multiplexing was investigated in 1971 by Weinstein and Ebert [1].Consider a data sequence d0, d1, …,d N-1, where each dn is a complex symbol. (The data sequence could be the output of a complex digital modulator, such as QAM, PSK etc).Suppose we perform an IDFT on the sequence 2d n (the factor 2 is used purely for scaling purposes), we get a result of N complex numbers Sm (m = 0,1…,N-1) as:Where,Where, Ts represents the symbol interval of the original symbols. Passing the real part of the symbol sequence represented by equation (2.1) thorough a low-pass filter with each symbol separated by a duration of Ts seconds, yields the signal,Figure 1 : A OFDM ModulatorWhere, T is defined as NTs. The signal y(t) represents the baseband version of the OFDM signal.Figure 2 : Three Subcarriers within an OFDM symbolIt is easy to note from (2.3), that●The length of the OFDM signal is T.●The spacing between the carriers is equal to 1/T.●The OFDM symbol-rate is N times the original baud rate.●There are N orthogonal sub-carriers in the system.The signal defined in equation (2.3) is the basic OFDM symbol.1.3. Guard Time and Cyclic ExtensionOne of the main advantages of OFDM is its effectiveness against the multi-path delay spread frequently encountered in Mobile communication channels.The reduction of the symbol rate by N times, results in a proportional reduction of the relative multi-path delay spread,relative to the symbol time.To completely eliminate even the very small ISI that results,a guard time is introduced for each OFDM symbol.The guard time must be chosen to be larger than the expected delay spread, such that multi-path components from one symbol cannot interfere with the next symbol. It the guard time is left empty, this may lead to inter-carrier interference (ICI), since the carriers are no longer orthogonal to each other.To avoid such a cross talk between sub-carriers, the OFDM symbol is cyclically extended in the guard time. This ensures that the delayed replicas of the OFDM symbols always have an integer number of cycles within the FFT interval as long as the multi-path delay spread is less than the guard time.Figure 4 : Guard Time and Cyclic Extension - Effect of Multipath1.4. Raised Cosine WindowingIf the ODFM symbol were generated using equation (2.3), the power spectral density of this signal would be similar to the one shown in Fig (psd).The sharp-phase transitions caused by phase modulation results in very large side-lobes in the PSD and the spectrum falls off rather slowly (according to a sinc function). If the number of sub-carries were increased, the spectrum roll-off will be sharper in the beginning,but gets worse at frequencies a little further away from the 3-dB cut-off frequency. To overcome this problem of slow spectrum roll-off, a windowing may be used to reduce the side-lobe level.The most commonly used window is the Raised Cosine Window given by [2]:Here Tr is the symbol interval which is chosen to be shorter than the actual OFDM symbol duration, since the symbols are allowed to partially overlap in the roll-off region of the raised cosine window. Incorporating the windowing effect, the OFDM symbol can now be represented as:It must be noted that filtering can also be used as a substitute for windowing, for tailoring the spectrum roll-off. But windowing is preferred to filtering because, it can be carefully controlled. With filtering,one must be careful to avoid rippling effects in the roll-off region of the OFDM symbol.Rippling causes distortions in the OFDM symbol, which directly leads to less-delay spread tolerance.1.5. OFDM GenerationBased on the previous discussions, the method for generating an ODFM symbol is as follows.●First, the N input complex symbols are padded with zeros to get Ns symbols that are used to calculate the IFFT.The output of the IFFT is the basic OFDM symbol.●Based on the delay spread of the multi-path channel,a specific guard-time must be chosen (say Tg).A number of samples corresponding to this guard time must be taken from the beginning of the OFDM symbol and appended at the end of the symbol.Likewise,the same number of samples must be taken from the end of the OFDM symbol and must be inserted at the beginning.●The OFDM symbol must be multiplied with the raised cosine window to remove the powerof the out-of-band sub-carriers.The windowed OFDM symbol is then added to the output of the previous OFDM symbol with a delay of Tr, so that there is an overlap region of βTr between each symbol.Figure (modem) shows the block diagram of an OFDM transmitter and receiver.Figure 5 : OFDM Sytem Block Diagram1.6. OFDM System DesignOFDM system design, as in any other system design, involves a lot of tradeoff’s and conflicting requirements.The following are the most important design parameters of an OFDM system.The following parameters could be a part of a general OFDM system specification:●Bit Rate required for the system.●Bandwidth available.●BER requirements. (Power efficiency)●RMS delay spread of the channel.Guard TimeGuard time in an OFDM system usually results in an SNR loss in an OFDM system, since it carries no information.The choice of the guard time is straightforward once the multi-path delay spread is known. As a rule of thumb, the guard time must be at least 2-4 times the RMS delay spread of the multi-path channel. Further, higher-order modulation schemes (like 32 or 64 QAM) are more sensitive to ISI and ICI than simple schemes like QPSK.This factor must also be taken into account while deciding on the guard-time.Symbol DurationTo minimize the SNR loss due to the guard-time, the symbol duration must be set much larger than the guard time.But an increase in the symbol time implies a corresponding increase in the number of sub-carriers and thus an increase in the system complexity.A practical design choice for the symbol time is to be at least five times the guard time,which leads to an SNR loss that is reasonable.Number of Sub-carriersOnce the symbol duration is determined, the number of sub-carriers required can be calculated by first calculating the sub-carrier spacing which is just the inverse of the symbol time (less the guard period).The number of sub-carriers is the available bandwidth divided by the sub-carrier spacing.Modulation and Coding ChoicesThe first step in deciding on the coding and modulation techniques is determining the number of bits carried by an OFDM symbol.Then, a suitable combination of modulation and coding techniques can be selected to fit the input data rate into the OFDM symbols and, at the same time, satisfying the bit-error rate requirements.The choice of modulation and coding techniques are lot easier now, since each channel is assumed to almost A WGN and one doesn’t need to worry about the effects of multi-path delay spread.2. Advantages of OFDMOFDM possesses some inherent advantages for Wireless Communications.This section glances on few of the most important reasons on why OFDM is becoming more popular in the Wireless Industry today.2. 1. Multi-path Delay Spread ToleranceAs discussed earlier,the increase in the symbol time of the OFDM symbol by N-times (N being the number of sub-carriers), leads to a corresponding increase in the effectiveness of OFDM against the ISI caused due to multi-path delay spread.Further,using the cyclic extension process and proper design, one can completely eliminate ISI from the system.2.2. Effectiveness against Channel DistortionIn addition to delay variations in the channel, the lack of amplitude flatness in the frequency response of the channel also causes ISI in digital communication systems.A typical example would be the twister-pair used in telephone lines.These transmission lines are used to handle voice calls and have a poor frequency response when it comes to high frequency transmission.In systems that use single-carrier transmission, an equalizer might be required to mitigate the effect of channel distortion.The complexity of the equalizer depends upon the severity of the channel distortion and there are usually issues such as equalizer non-linearities and error propagation etc that cause additional trouble.In OFDM systems on the other hand, since the bandwidth of each sub-carrier is very small, the amplitude response over this narrow bandwidth will be basically flat (of course,one can safely assume that the phase response will be linear over this narrow bandwidth).Even in the case of extreme amplitude distortion, an equalizer of very simple structure will be enough to correct the distortion in each sub-carrier.。
OMRON FC25A FC25B截面距离传感器商品说明书
1Real-time 3D sensing of distance to humans or objects•Ambient light immunity equivalent to 100,000 lx, allowing measure-ment even in bright places. *1•High output accuracy of ±2% (2 m) for compensated signals. *2•Long life of approx. 5 years under continuous driving thanks to OMRON’s unique circuit design and heat emission design. *3•With interference prevention function *4*1.The accuracy of product specifications is not guaranteed.*2.According to OMRON’s evaluation method*3.The result of reliability acceleration test at the ambient temperature of 20°C and thehumidity of 65%RH, not the product warranty period.*4.Up to 17 ID settings can be made depending on the command.When this function runs, the accuracy of product specifications is not guaranteed for settings other than ID=8 (default).Part Number StructureType■Body [Dimensions ➜P .6]Product-related materials, such as:• Datasheet• User’s Manual (Manual No.: E596-E1)• Evaluation Software • Sample Codecan be downloaded from the following website:https:///product-detail?partNumber=B5L●Definition of terms used in this document“The Product”: Refers to B5L-A2S-U01-010, consisting of “Device” and “SDK”.“The Product” as described herein refers to the entirety or part of its composition.“Device”: Refers to 3D TOF sensor module.“SDK”: Refers to User’s Manual, Evaluation Software and Sample Code.“NIR”: Near infrared radiation.Refer to “Precautions” on page 7.B5L-A @ @-@01-@ @ @(1)(1) Light source2: LED NIR 940 nm(2)(3)(2) Angle of viewS: 90°(3) CommunicationU: USB2.0(4) NIR transmission filter010: Available (Built-in)(4)2B5L3D TOF Sensor ModuleRatings/Specifications■Ratings*1.Standard mode/exposure time setting=850 (default)*2.With no condensation or icing *3.With no condensation■Specifications*4.Distance accuracy and repeating accuracy are obtained under the following conditions:• Based on OMRON’s measurement environment • Ambient temperature: 25°C• Standard mode/LED light projecting frequency ID=8 (default)*5.Target object: Reflectance ratio 70% (white paper)• Distance accuracy: Average of 100 measurements (10,000 pieces of data in total) at the central part (10×10 pixels) 2 m away from this product• Repeating accuracy: Standard deviation of 100 measurements (10,000 pieces of data in total) at the central part (10×10 pixels) 2 m away from this product Standard mode/exposure time setting=850 (default)*6.Time from power ON until communication is possible *7.Time from power ON until performance becomes stable■Communication specifications■Operation mode*8.HDR function: A function that changes the shutter speed and performs the measurement multiple times.ItemSpecificationsLight sourceLED NIR 940 nm Power supply voltage VDC24+/-10%Power consumption (current consumption)Average during measurement: 0.3 A *1Maximum: 3 A (Reference) *1Ambient temperature Operation: 0 to +50°C *2Storage: -20 to +60°C *2Ambient humidityOperation/storage: 35 to 85%RH or less *3Tightening torque of mounting hole0.91 to 1.37 N·mVibration (durability)10 to 150 Hz, 50 m/s 2, complex amplitude of 0.7 mm or less Scanning 3 times each in X, Y , Z directions for 8 min Impact (durability)300 m/s 2 3 times each in X, Y , Z directions Appearance Approx. 103×64.3×43.1 mmApprox. 108.6×64.3×43.1 mm (including the Connector)Protective structure IEC60529 IP10WeightApprox. 305 gMaterialsFrame: die-cast aluminumCover: polycarbonate (PC)Filter: acrylic resin (PMMA)Heat sink: aluminumItemSpecificationsMeasurement distance 0.5 to 4 m Detection resolution Approx. 0.3°Horizontal detection range (angle of view)87° or above Vertical detection range (angle of view)67° or aboveDistance accuracy ±2% (±4 cm) or less *4*5at 2 m central part 10×10 pixels Repeating accuracy 1% (2 cm) or less *4*5at 2 m central part 10×10 pixels Frame rate Approx. 10 fps *4Starting time 30 seconds or less *6Warm-up timeApprox. 30 minutes *7ItemSpecificationsFunction Receive commands from the host and return execution results.InterfaceUSB2.0 CDC classCommunication protocolUnique specifications. Refer to User’s Manual (Manual No.: E596-E1) for details.Operation modeContentsStandard mode Turn on the HDR function *8, and calculate the distance from two measurements.High-speed modeTurn off the HDR function *8, and calculate the distance from one measurement.3B5L3D TOF Sensor Module■Specifications of output dataNote 1.Refer to User’s Manual (Manual No.: E596-E1) for details.Note 2.When the form of orthogonal coordinate or orthogonal coordinate rotation is specified, the distance data will be outputted in the form of PCD (Point Cloud Data).■Data output order■ Data output directionData is output in the order of 76799 to 0 from the lower right to the upper left of the 320×240 image.■Field of viewData nameDescriptionDistance dataIndicate the 3D distance between B5L ’s coordinate origin and the target object Distance data in the form of orthogonal coordinate Xo, Y o, Zo: XYZ coordinates with the coordinate origin as the originDistance data in the form of orthogonal coordinate rotation Xr, Yr, Zr: Orthogonal coordinates after rotating around axes Xo, Y o, Zo at an angle set by the command Distance data in the form of polar coordinate r, θ, φ: Polar coordinates based on orthogonal coordinates Amplitude dataLight-receiving sensitivity of each pixel when LED is illuminated 16 bits (256 gradations)ZoYoXoYrZrXrPolar coordinate formOrthogonal coordinaterotation formOrthogonal coordinateformPixel 0321……032012240319320…7679976798…7648076479240 p i x e l320 pixel300 pixel (87° or above): Image sensor size : Lens image circle: Photography range4B5L3D TOF Sensor ModuleConnector Pin Configuration and Connection Structure■Connection structureNote 1.To be certified by standards on radiated emission intensity limits (CISPR22 Class A, etc.), carry out confirmation and countermeasures for products into whichthe product is assembled.Countermeasures against noise on connection wires are estimated to reduce the emission noise level.Make the decision after fully evaluating the cable used and the routing of GND (connection with FG, etc.).Note 2.Consideration should be given to creepage distance, etc., so that no static electricity will be applied to the frame part other than the light projecting and receiving surfaces.Also separate the mounting hole of the product from FG.■ConnectorPower connector: S2P-VH (manufactured by JST Connector)(Recommended mating connector)Housing: VHR-2M or VHR-2N (manufactured by JST Connector)Contact: SVH-21T -P1.1 (manufactured by JST Connector)USB connector: MicroUSB T ype BUSB2.0 standard compliant (Vbus rating: 0.5 A or less)This sensor is a USB device. The power source of Vbus should be supplied from the host side.Supply power source: The Product alone is not compliant with the requirements on fire-proof enclosure. Therefore, when it is assembled, use a supply power source that meets IEC 62368-1 LPS (conditions of limited power source).Name of each partThe Product The Customer's system+24VGNDVbus D+D-GND CaseSGFGSGPower cableUSB cableM i c r o U S B2S P -V HL i g h t -p r o j e c t i n g & r e c e i v i n g s i d ePin numberSignalDescription1Vcc Power source DC24 V±10% 3 A 2GNDGround (0 V)ItemContentsLED for operation confirmationInitial stateStarting/running: light on, Abnormal: flickering Light off by command is possible when running Starting: light on, Running/abnormal: light offPower connectorSideHeat sinkEmitter5B5L3D TOF Sensor ModuleCharacteristic data (reference value)●Influence of sunlightConditions:Target: white PP film Angle: 0°Measurement distance: 2 mIllumination: 100,000 lx or above with sunlight present●Distance accuracyConditions:Target: reflectance ratio 70% (white paper)Angle: 0°●Distance accuracy in angle directionConditions:Target: reflectance ratio 70% (white paper),reflectance ratio 15% (grey paper)Angle: -43.5°, 0°, +43.5°Measurement distance: 0.5 m, 2 m, 4 m Ambient temperature: 25°CPrecautions on the principle of TOF sensor•The Product projects light and measures the distance according to the phase difference from the reflected light.In addition, the measurement takes time in order to accumulate the received light.As a result, the measurement may not be performed correctly under the following conditions:•Objects with high reflectance ratio (mirrors, objects with luster, etc.), objects with low reflectance ratio (black objects, etc.), transparent objects (glass, plastics, etc. with high transmission rate)•Objects at a distance more than (light speed/light source modulating frequency)/2 (approx. 12.5 m) (short distance measured).•Obstacles other than the target object for measurement are set.•The Product or the target object for measurement moves or vibrates.0.511.522.5Without sunlightWith sunlightM e a s u r e d v a l u e (m)0123456701234567M e a s u r e d v a l u e (m )Distance (m)-60-40-200204060Angle (°)M e a s u r e d v a l u e (m )1234570%15%B5L3D TOF Sensor Module Dimensions Please visit our CAD Data website, which is noted on the last page.(Unit: mm)B5L-A2S-U01-0106B5L3D TOF Sensor Module PrecautionsMake sure to read these precautions for a safe use of the Product.•The contents included are to ensure proper use of the Product and prevent harm and/or property damage to the user or other people.•Warnings and cautions are defined as follows.●Definition of Warning and Caution"Damage" indicates property damage to a building, produc-tion line, household goods, other products, livestock, pets, etc.●Examples of indicationsRegarding the use or handling of the ProductDo not use the Product for safety of life or crime prevention purposes.Do not use the Device on automobiles or othervehicles, including bikes as it may result in acci-dents.Regarding the prevention of fire, electric shock, etc.The following will result in fire, electric shock, injury or dam-age if ignored.Do not touch the Device or any connected cableduring a lightning storm.Do not use the Device if it is cracked or damaged.Do not insert foreign objects in the connector or inthe holes on the various parts of the Device.Do not use the Device in bathrooms or any otherplace where it may get in contact with water.Do not touch the Device or any connected cablewith wet hands.Do not touch the electrode at the side opening ofthe Device during power-on.Do not disassemble, repair, or modify the Device.Turn the power off and stop using the Product ifyou notice any anomaly, including foul odor,heating, distortion or discoloration to the Device during use.Install the cables for connecting the Device in a waythat would not put strong force on them, including making sure they are not crushed in a door.Regarding the prevention of accident or injuryThe following will result in accident or injury if ignored.Do not touch sharp parts or the exposed interiorof the Device that was damaged.Regarding the use or handling of the ProductMake sure to follow the warnings and cautions indicated in this document when using theProduct.Regarding installationThe following will result in accident, injury or damage if ignored.Do not install the Device in an unstable location.Install the cables in a safe way, out of the way ofhands or feet.Regarding heatingThe following will result in burns if ignored.The Device may produce heat.Do not touch it during power-on or shortly after powering it off.Denotes a potentially hazardous situation which, ifnot avoided, may result in minor, moderate orserious injury, or death.It may also result in serious damage.Denotes a potentially hazardous situation which, ifnot avoided, may result in minor or moderate injury,or damage.Indicates forbidden actions.Indicates required actions.7B5L3D TOF Sensor ModuleCheck the Product for physical damage upon opening its package. It is recommended to wear gloves when opening the package. Follow the indications listed below for a safe use of “the Product”.(1) Installation EnvironmentThere is potential internal deterioration and damage of internal parts of the Device.•Do not use “the Product” in conditions exceeding the ratings for temperature and humidity.•Do not use “the Product” in an environment where condensation occurs.•Do not use “the Product” in an environment subjected to water, oil or chemicals spills.•Do not use “the Product” in an environment subjected to corrosive, combustible or explosive gas.•Do not use “the Product” in an environment where dust, salt or iron powder are present.(2) Power Supply and WiringThe following will result in fire if ignored.•Make sure there is no faulty wiring of I/O terminals, etc.•Do not connect the DC power supply terminal to AC power.•Do not connect “the Product” to DC voltage above the rated capacity.•Do not reverse-connect the DC power supply.•Make sure to turn the Device off before removing cables.•Make sure to check the Device and the connector pins for distortion or physical damage before connecting the Device to the Connector.•Check the cables for physical damage.(3) Others•Treat “the Product” as industrial waste when disposing of it.•Use the M4 screws on the fixing holes on the Device when fixing it.•Make sure not to twist, bend or break the Device when fastening the screws. The following will result in accident or deterioration if ignored.•Install “the Product” with attention being paid to dust prevention so that foreign objects will not enter during use. The following will result in short circuit or long-term reliability decline due to foreign objects if ignored.•For safety’s sake, installation and wiring should be performed by professional technicians.•Do not drop “the Product” during installation and use. The following will result in accident or deterioration if ignored.•Install “the Product” after confirming that there are no people around under the place of installation.Observe the following precautions to prevent failure to operate and malfunctions, and to prevent adversely affecting the performance and function of “the Product”.•Store the Device at a temperature of -20°C to +60°C and a relative humidity level of 35% to 85%.•Do not touch the board mounted parts with bare hands. Discharge any static electricity from the user before use.•Take proper measures against static electricity by using an antistatic wrist strap, etc. before handling “the Product”.•Make sure to properly ground the connector's earth terminal in order to prevent malfunction due to noise.•Do not use “the Product” in places where the surrounding temperature goes above the rating range.•Do not use “the Product” in a location where it would be subjected to direct sunlight.•Do not use “the Product” in a location subject to excessive inductive or power supply noise, such as in strong magnetic or electric fields.•Do not use “the Product” in a location where it would be subjected to strong UV light.•Do not use “the Product” in a location where it would be subjected to radiation.•Sufficiently evaluate the electrical characteristics of any connection to the Device.•If the Customer designs such structures as NIR transmission filter and installs them in front of the light-projecting part or the light-receiving part, the detection performance will deteriorate due to NIR light transmittance. Therefore, design with margins giving consideration to deviation and other factors.•The Customer should choose the power cable and USB cable after fully validating their applicability.•Do not strongly pull the cable connected to the Device.•Do not reversely insert the Connector.•Do not forcibly insert any non-standard connector.•Do not touch the light-projecting part or the light-receiving part. Clean the light-projecting part or the light-receiving part if fouled. Clean with a soft and dry cloth, avoiding damage to the light-projecting part or the light-receiving part. Never use volatile solvents such as benzine and thinner or chemical wipers, etc.•In order to improve long-term reliability of the Device, pay sufficient attention to heat emission during installation.•Install “the Product” at a sufficient distance from surrounding heat generating parts.•When installing “the Product”, do not block the top surface, side surface and heat sink surface of the Device. Otherwise, heat cannot be emitted.•“The Product” generates heat during operation. Since the surrounding temperature rises due to heating, sufficient consideration should be given to heat emission so that the surrounding temperature will not go above the rating temperature range. In addition, do not fix “the Product” upside down.•In case of instantaneous stop or power outage, when power is restored, make sure to use “the Product” after resetting.•If abnormality occurs in received data, restart the power or reset.•Do not peel off the QR code label. Otherwise, lot tracing of “the Product” will become impossible.•Do not use “the Product” under conditions where it would be subjected to strong interfering light.•If multiple units of “the Product” are used simultaneously, measurement may not be performed correctly due to the influence of NIR light transmitted from sources other than the Device.•Before using “the Product”, fully confirm if “the Product” can be used at the actual installation location.1) Since “the Product” is intended for assembly into otherdevices, single units of “the Product” are not certified byvarious standards in each country.2) “The Product” is not used for crime prevention and does notguarantee safety.3) “The Product” has face detection function. As such, theCustomer shall take proper care of privacy, portrait right,copyright or any other rights of people.4) “The Product” cannot be used for purposes that cause hazardor damage to people's life, body and asset.Do not do or allow any third party to do the following to the “Firmware” contained in “the Product” (built-in software for operating the Device) and “SDK”.(a)Withdrawal of the “Firmware” from the “Device”(b)Reverse engineering of “Firmware” and “SDK”, includingdisassembling and decompiling, etc.T echnical information provided by OMRON is treated as OMRON’s confidential information. Do not disclose to any third party.Precautions for Safe UsePrecautions for Correct UsePrecautions for Correct UseProtection of intellectual assets8Please check each region's Terms & Conditions by region website.OMRON CorporationElectronic and Mechanical Components CompanyRegional ContactCat. 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基于变可信度代理模型的气动优化
基于变可信度代理模型的气动优化黄礼铿;高正红;张德虎【摘要】对于复杂的多设计变量优化设计问题,构造高精度的代理模型需要大量的高可信度样本,并带来巨大的计算量.利用较小的计算代价构建高精度的代理模型具有很强的工程意义.采用Co-Kriging方法,基于两组相互独立的高、低可信度模型样本,构建了一种高效的变可信度代理模型.Co Kriging变可信度代理模型通过构建高、低可信度模型之间的关系模型,充分利用低可信度模型信息来提高代理模型整体的预测精度,在保证预测精度的前提下,大大减少了构造代理模型所需的计算时间.使用两个函数算例分析了不同选样方案对近似精度的影响,并用一个基于不同代理模型的RAE2822气动优化设计的对比证明了该方法在工程设计优化中的可行性.【期刊名称】《空气动力学学报》【年(卷),期】2013(031)006【总页数】6页(P783-788)【关键词】Co-Kriging;代理模型;变可信度;气动优化【作者】黄礼铿;高正红;张德虎【作者单位】西北工业大学翼型叶栅空气动力学国家重点试验室,陕西西安710072;西北工业大学翼型叶栅空气动力学国家重点试验室,陕西西安710072;西北工业大学翼型叶栅空气动力学国家重点试验室,陕西西安710072【正文语种】中文【中图分类】V211.30 引言随着飞行器性能要求的不断提高，气动外形设计面临更大的挑战，出现了越来越多的高可信度气动分析方法。
高可信度方法通常需要很大的计算量，虽然在过去的几十年间计算能力发生了巨大的变化，但高可信度模型仍然无法直接应用于优化设计。
为了提高优化过程的效率，一种有效的方法是构造基于代理模型的优化方法［1－2］。
代理模型方法最基本的思路是通过构建目标函数的近似模型即代理模型，替代优化设计中复杂的气动特性分析方法，从而减少优化问题求解的计算量。
目前可行的代理模型技术包括数据拟合模型、降阶模型、以及启发式模型，数据拟合模型，通常通过对高可信度模型的样本数据进行拟合或者退化得到高可信度模型输入与输出之间的关系，构造简化的近似模型，常用的方法有BP神经网络（Backpropogation Neural Net，BPNN）［3］、径向基函数（Radial Basis Function，RBF）［4］、Kriging 模型［5］、高斯过程（Gaussian Process，GP）［6］、多项式响应面（Polynomial Response Surface Method，PRSM）［7］等等；降阶模型，降阶模型的构建依赖于控制方程信息，通常由偏微分方程或者常微分方程描述的系统可以构建降阶模型，降阶模型不适合于控制方程未知或基于经验关系的情形，如使用正规正交分解（Proper Orthogonal Decomposition，POD）［8］和模型分析一类的方法得到的降阶模型；启发式模型，也被称为多可信度、变可信度、变复杂度模型，变可信度模型利用两个不同可信度的计算工具对相同的物理过程进行数值模拟，一般高可信度的方法精度较高，但需要更大的计算代价，低可信度的方法精度较低，但是需要的计算代价很低，利用大量低可信度数据来提高少量高可信度数据构造的代理模型精度，减少得到合理精度代理模型所需要的计算代价［9］。
20101212（练习答案汇总）
20101212（练习答案汇总）Unit 1 Mathematics1. Match the Chinese in the left column with the English in the right column.迭代函数iterative function优先权之争priority battle分形特征fractal properties有意义make sense以越来越小的规模重复同一模式patterns repeat themselves at smaller and smaller scales混沌理论chaos theory季刊a quarterly journal数学界the mathematics community波纹线crisp lines会议公报proceedings of a conference3. Translate the sentences into Chinese.1) He is best known for coining the term fractal to describe phenomena (such as coastlines, snowflakes,mountains and trees) whose patterns repeat themselves at smaller and smaller scales.他主要是因为用分形这个概念来描述（海岸线，雪花，山脉和树木）等不规则形状等现象而闻名于世，这些不规则形状在越来越小的规模上不断重复同一模式。
2) A closer look reveals that the borders of the set do not form crisp lines but seem to shimmer like flames.如果再仔细观察，就可以发现集的边界并没有呈波纹线，而是像火焰一样闪光。
3) Krantz introduced a new element into the debate, however, by stating that the Mandelbrot set "was notinvented by Mandelbrot but occurs explicitly in the literature a couple of years before the term 'Mandelbrot set' was coined."但是，克朗兹在这场辩论中引入了一个新东西，他说曼德布洛特集不是曼德布洛特发明的，而是早在“曼德布洛特集”这个术语出现几年以前就已经明确地在数学文献中出现了。
OFDM系统中的差分调制及其性能
OFDM系统中的差分调制及其性能第28卷第1期2006年2月铁道JOURNALOFTHECHINARAILW AYS0CIETYV01.28No.1February2006文章编号:10018360(2006)01—0059一O4OFDM系统中的差分调制及其性能秦雅娟,刘元安(1.北京交通大学电子信息工程学院,北京100044;2.北京邮电大学电信工程学院,北京100876)摘要:基于子载波采用高阶差分幅度相移键控(MDAPSK)的正交频分复用(OFDM)系统,针对其独特的数据帧结构,提出并定义了OFDM系统的几种差分调制方案,仿真了不同信道环境下各种方案的误码性能.仿真结果表明,针对时间选择性和频率选择性衰落信道衰落程度的不同,在满足一定的时间相关性和(或)频率相关性的条件下,采用相应的时域和(或)频域差分调制方案,可以保证MDAPSK—OFDM系统的误比特率(BER)维持在较低的水平.关键词:正交频分复用;差分幅度相移键控;时域差分;频域差分;时间相关性;频率相关性中图分类号:TN939文献标识码:A DifferentialModulationandItsPerformanceinOFDMSystemsQINY a—juan,LIUYuan～an.(1.SchoolofElectronicsandInformationEngineering,BeijingJiaotongUniversity,Beijing100044,China;2.SchoolofTelecommunicationsEngineering,BeijingUniversityofPostsandTelecommun ications,Beijing100876,China)Abstract:Consideringthespecialstructureoftransmitteddatainorthogona1frequencydivisi onmultiplexing(()FDM)systems,somedifferentialmodulationschemesarepresentedanddefinedfordiffer entialamplitudeandphaseshiftkeying(DAPSK)modulationinoFDMsystems.Thebiterrorrate(BER)perfo rmanceissire- ulatedwiththesemodulationschemesrespectivelyindifferentchannels.Thesimulationresu ltsshowthattheBERsofMultileventDAPSK(MDAPSK)OFDMsystemscanbemaintainedatalowerlevelr elativelyifthetimecorrelationor(and)frequencycorrelationissatisfiedandapropertime—-domainor(and)frequency——domain differentialmodulationschemeisappliedundertime—selectiveandfrequency—selectivefadingchannels.Keywords:orthogonalfrequencydivisionmultiplexing(OFDM)ldifferentialamplitudean dphaseshiftkeying(DAPSK);timedomaindifferential;frequency—domaindifferential;timecorrelation;frequencycorrelation差分幅度相移键控(DAPSK)已成为OFDM系统子载波调制方式之一E1~43.由于采用了差分编码,DAPSK可以用非相干的方法进行解调.与QAM调制相比,DAPSK系统的复杂度和计算量可以降低.而且由于不需在数据流中插入训练序列,系统的有效信息传输速率更高.目前DAPSK—OFDM在一些实验系统中得到应用Ⅲ5j.由于OFDM系统的数据成帧传输,其差分方式可以在时间和频率两个方向进行,本文基于子载波采用高阶DAPSK(MDAPSK)的编码OFDM(COFDM)系统,比较了各种差分方案的效率以及在不同信道下的收稿日期:2004—12—14;修回日期:20050615基金项目:国家863计划课题任务合同(2001AA123016) 作者简介;秦雅娟(1963一),女,山西晋城人,副教授.E-mail:****************误码性能.1OFDM系统中的差分调制方法设OFDM系统的保护时间足够长,各子信道相互独立,则第k个子载波上接收的第i个复信号R= H"S+N.这里,H¨是信道第i个OFDM符号第k个子载波的频率响应,N¨是相应的高斯白噪声,S和R㈧分别是第k个子载波上发送和接收的第i个复信号.根据信道状况的不同,OFDM系统可以采用以下几种差分调制:(1)时域差分当信道的相关时间大于符号持续时间时,以第一个0FDM符号作为参考符号,在时域上进行差分设第i(i≠1)个OFDM符号第k个子载波上的时域差分60铁道第28卷系数为DXmPme,,则S.一DX.?S1.(1)由于存在一个OFDM符号的系统开销,传输的数据量越大,信息传输效率越高.(2)频域差分当信道的相关带宽大于子载波间隔时,可将第一个OFDM子载波信道作为参考符号传输信道,在频域上进行差分.设第i个OFDM符号第k(愚≠1)个子载波上的频域差分系数为Dyf.一ymeJA则S.一DY,S,1(2)采用频域差分,子载波的数目越多,信息传输效率越高.(3)时频域混合差分为提高信息传输效率,可将时域和频域差分结合起来应用.①频域一时域差分以第一个OFDM符号内第一个子载波上的信号S作为参考信号,第一个OFDM符号内做频域差分;随后第i(>1)个OFDM 符号的第k个子载波相对第i一1个OFDM符号的同一子载波做时域差分,即fS1,一DY1,?SI,1,,1S一DXm?S1.(i-/-1)②时域一频域差分以S¨作为参考信号,第一个OFDM符号内做频域差分;随后的OFDM符号的第一个子载波相对前一个OFDM符号的第一个子载波做时域差分,OFDM符号内做频域差分,即fS,1=DX,1?S1,1,.,1S,—DY.?S,l由于这两种方法都只需要一个参考符号,系统的信息传输效率达到最大.目前采用的差分调制主要是高阶差分幅度和相移键控(MDAPSK,M≥l6),如l6DAPSK,64DAPSK等.MDAPSK信号星座图上的信号矢量集Js为S={D?ej△Jm∈{0,N.一l},∈{0,…,N一1}}其中,N.是幅度状态数;N是相位状态数;信号总状态数M—N?N;矢量的最小相位差△一27c/N.为实常数,由M和解调方法的不同优化选择.差分相位和差分幅度与比特流的映射关系用Gray码编码. 对非相干解调16DAPSK系统,Js---{口-eJm∈{0,1),∈{0,…,7}},N一2,N=8,△一7c/4,优化的口==:2.2差分调制信号的解调差分调制信号通常采用非相干解调.频域差分用同一OFDM符号内相邻子载波上的两个复值之比进行解调,即DY一生一拿哉㈩S,l?H.¨+N,1时域差分由OFDM符号间同一子载波上的两个复值之比进行解调,即bxm一一一警拿薏一声i,kejM~6S1,?H1.+N一1.…由于各比特位独立地映射到MDAPSK信号的幅度和相位,因此可分别对差分系数复值的振幅和相角进行处理,再进行硬判决或软判决译码;也可由差分系数复值得到相应的各比特位值,再逐比特进行硬判决或软判决译码.硬判决译码根据给定的判决门限确定logN比特幅度信息,logN比特相位信息,即由dec{m}或d~cIbⅢ}确定幅度比特,由dec{,}或dec,}确定相位比特,再进行硬判决译码.为提高系统的误码性能,解调器可提供比特软输出,泽码器进行Viterbi软判决译码,本文的仿真就采用这种方法.3OFDM系统信道的相关性能3.1信道的时间相关性时间选择性衰落导致信道对不同OFDM符号的衰减不同.OFDM系统两个相邻OFDM符号上信道的相关性取决于符号持续时间T和最大多普勒频移,"的相对大小,可以用归一化时间问隔j'br来衡量相邻OFDM符号信道的相关程度.若移动无线信道多普勒功率谱用Jakes模型描述,则相距m个OFDM符号间隔的两点的时问自相关函数()为[7]()一Jo(2丌厂d丁)(7)式中,J.()是第一类零阶贝塞尔函数,对连续的OFDM符号进行差分,m一1.相邻OFDM符号信道衰落的差异导致系统信噪比的损失,这种影响与系统采用的调制方法及编码速率有关.若相邻OFDM符号信道之间存在一定的相关性,采用时域差分调制可降低信道时间选择性衰落对系统误码性能的影响. 3.2信道的频率相关性多径造成的频率选择性衰落使OFDM系统不同子载波的衰落不同.当信道的相干带宽大于子载波问距时,相邻子载波的衰落存在一定的相关性,其相关性的大小取决于信道的相干带宽和子载波间隔t/r的第6期OFDM系统中的差分调制及其性能相对大小,可以用归一化子载波间隔r/丁来衡量.其中r为信道的均方根时延扩展.若多径衰落的功率分布为指数衰减,则频域上相距,2个子载波间隔的两点的频域自相关函数r()为1一再'8)对连续的子载波进行差分,取一1.与时变信道类似,相邻子载波信道衰落的差异也会导致系统信噪比的损失.采用频域差分可以有效对抗频率选择性衰落对系统BER的影响.4各种差分方案BEN性能匕较本文的仿真基于一个室内毫米波宽带无线接入16DAPSK—OFDM系统.系统载频fo一36GHz,由四路射频信号频分复用构成.基带采用DSP四路并行处理,每路子载波数K一64,子载波间隔Af一250 kHz,保护时间间隔r一1s.系统信道编码采用删余卷积码,编码速率2/3,由码率1/2母码删余产生,收端采用Viterbi软判决译码.4.1四种差分调制方法的BER比较为比较四种差分调制方法的误码性能,本文选择了两种信道模型:AwGN和最大多普勒频移为8kHz 的2径Rayleigh衰落信道.这里最大多普勒频移取8kHz并不是室内毫米波OFDM系统的真实值,而仅仅是为lr对比在这种信道环境下,四种差分方法的BER性能.图1和图2分别仿真了两种信道下长数据帧和短数据帧的BER.图中所列的差分方法1,2, 3,4分别对应式(1),式(2),式(3)和式(4)定义的时域差分,频域差分,频域时域差分及时域一频域差分.从方法1和方法3的定义上看,两者的基本方法都是时域差分,区别仅在于第一个OFDM符号的不同.由仿真结果可以看出,方法1和方法3的误码性能接近,但两者的接近程度与信道模型及数据帧的长度有关.同样的结论也适合于基于频域差分的方法2 和方法4.值得注意的是,将图1(b)和图2(b)比较可以看出,在最大多普勒频移为8kHz的2径Rayleigh 衰落信道下,传输长数据帧和短数据帧的误码性能有很大差别.传输短数据帧时,其误码性能与AWGN信道下的误码性能相当,且时域差分性能的优势降低. 由此说明在这种信道环境下,短数据帧降低了对信道的敏感程度.这对通信系统信令的传输极为有利.本文旨在研究时域差分和频域差分的BER,因此这里只是为了说明方法1和方法3及方法2和方法4 误码性能相当为清楚起见,后面的仿真曲线只画出了方法1和方法2的对比结果.(EdNo)/dB(a)AWGN信道(EbINo)/dB㈣2径信道,最大多普勒频移fd=8kHz图1长数据帧4种差分方法的对比4.2时间选择性衰落信道下的BER比较为了比较多普勒频移对差分方式的影响,图3仿真了平坦Rayleigh衰落倍道下,多普勒频移取一200Hz,22kHz和25kHz(归一化时间间隔T如图中所注)时的误码性能.仿真结果说明,随着的增大,相邻OFDM符号的相关性变差,导致时域差分(方法1)误码率增大.图3中看不出对频域差分(方法2)误码性能有明显的影响,这是由于这里仿真的是平坦衰落信道.对多径衰落信道,这种影响还是存在的. 另外,只要多普勒频移不是足够的大,时域差分的性能总是优于频域差分.从仿真结果看,室内无线信道都能满足这一要求.4.3多径衰落信道下的BER比较图4仿真了最大多普勒频移fd一100Hz时,信道均方根时延扩展r对两种差分调制方式误码性能的影响,给出r一60ns,96ns,160ns和200ns](归一化子载波间隔r/了,值列于图中)时的误码性能.可见随着多径路径数目的增加,多径不仅对频域差分的误码性能产生影响,也严重影响时域差分的误码性能但在室内无线信道下,信道时间上的相关性总能得到保证,因此与频域差分相比,多径信道下时域差分仍有62铁道第28卷它的优势.营(E/dB《'a)AWGN信道b|N/dB(b)2径信道,最大多普勒频移f~=Skm图2短数据帧4种差分方法的对比45结论(EN/dB图3信道多普勒频移对BER的影响利用OFDM数据帧结构的特点,针对不同的信道环境,采用不同的差分调制方法,可以保证MDAPSK- OFDM系统的BER维持在较低的水平.因此在满足一定的信道时域和(或)频域相关的条件下,采用时域和(或)频域差分,可以提高MDAPSKOFDM系统的(EN/dB图4信道多径对BER的影响抗信道衰落能力.仿真结果表明,在室内无线频率选择性和时间选择性衰落信道下,由于信道时间上的相关性基本上能得到保证,时域差分对抗信道选择性衰落的能力总体上优于频域差分.对短数据帧的进一步研究将由后续工作完成.参考文献:[1]RohlingH,EngelsV.Differentialamplitudephaseshift keying(DAPSK)一AnewmodulationmethodforDTVB EA].InternationalBroadcastingConvention,14—18Sep tember1995,ConferencePubhcationNo.413rC].102—108.[2]RohlingH,MayT,BruninghausK,GrunheidR.Broaf- Band0FDMRadioTransmissionforMultimediaApphca--tion[J].Proc.oftheIEEE,1999,87(10):1778—1789.[3]RohhngH,BruninghausK.HighRateOFDMMODEM withQuasicoherentDAPSK[A].In:V ehicularTechnolo—gYConference,1997IEEE47[C].V o1.3.Melbourne,1997.2055—2O59.[4]SchubertH,RichterA,IversenK.DifferentialModulation forOFDMinFrequencyVS.TimeDomianEa].ACTSMo-- bileCommunicationSummit'97rC],1997.[5]滨口清,进宏之,小川博世.三IJ波J2:带域移助7,夕电叉天于厶用100Mbps-一OFDM乇厶明冕[J].信学技鞭,TechnicalReportofIEICE,CS2001—44,RCS2001—51, 2001,(06):1—7.[6]MoriyamaS,TsuchidaK,SasakiM.DigitalTransmission ofHighBitRateSignalsUsing16DAPSK-?OFDMModula.--tionScheme[J].IEEETrans,.OnBroadcasting,1998,44 (1):¨5—122.[7]AhmadR,BahaiS,BurtonRSaltzberg,.Multi—carrierdig—italcommunications--TheoryandapplicationofOFDM [M].NewY ork:Mc—Graw-Hill,1999.95—115.r8]TheodoreS.W'irelessCommunicationsPrinciplesandPrac—tice[M].Prentice-Hal1.Inc.aSimon&SchusterCompa—ny,1996.188—189.(责任编辑江峰)l曲1;;∞。
Design and Performance of a General-Purpose Software Cache
Arun Iyengar IBM Research T. J. Watson Research Center P. O. Box 704 Yorktown Heights, NY 10598
Abstract
Software caches are a critical component in improving the performance of many applications including Web servers, databases, and le systems. In order for an application to bene t from caching, it must repeatedly use data which is expensive to calculate or fetch. By caching such data, the application only needs to calculate or fetch the data once. Whenever the data is needed after it has been cached, the application can fetch the data from the cache instead of recalculating it or fetching it from a remote location. Software caches are generally several order of magnitudes slower than processor caches. Processor caches can return data in several nanoseconds. By contrast, caches for dynamic Web pages on Web servers can provide near-optimal speedup by handling several hundred hits per second 6]. Since software caches can a ord to be much slower than processor caches, software caches can provide more features such as complex invalidation and replacement strategies as well as logging cache transactions. This paper describes a General-Purpose Software Cache (GPS Cache) designed to improve performance of a wide variety of applications such as Web servers and databases. Applications add, delete, and query the cache via a set of API function calls. The GPS cache can be con gured to store data in memory, on
The proper orthogonal decomposition in the analysis of turbulent flows
Annu. Rev. Fluid Mech. 1993.25: 539-75 Copyrinht 0 1993 by Annual Reviews Inc. All rights reserved
Annu. Rev. Fluid Mech. 1993.25:539-575. Downloaded from by University of Science & Technology of China on 02/15/12. For personal use only.
THE PROPER ORTHOGONAL DECOMPOSITION IN THE ANALYSIS OF TURBULENT FLOWS
Gal Berkooz, Philip Holmes, and John L. Lumley
Cornell University, Ithaca, New York 14853
space of a strange attractor in phase space. Since 1971 we have witnessed great advances in dynamical-systems theory and manyapplications of it to fluid mechanics, with, alas, mixed results in turbulence--despite the attractive notion of using deterministic chaos in resolving the apparent paradox of a deterministic model(Navier-Stokes) that exhibits apparently random solutions. This is due not solely to the technical difficulties involved: Proof of global existence and a finite-dimensional strange attractor for the 3-D equations in a general setting wouldbe a great mathematical achievement, but wouldprobably be of little help to specific problemsin, say, turbomachinery. For a start, rigorous estimates of attractor dimension (T6man1988) indicate that any dynamical system which captures all the relevant spatial scales will be of enormousdimension. Advancesin such areas will most probably nccessitate a dramatic reduction in complexity by the removal of inessential degrees of freedom. The first real evidence that this reduction in complexitymight be possible for fully developed turbulent flows came with the experimental discovery of coherent structures around the outbreak of the second world war, documented by J. T. C. Liu (1988). The existence of these structures was probably first articulated by Liepmann(1952), and was thoroughly exploited by Townsend(1956). Extensive experimental investigation did not take place until after 1970, however (see Lumley 1989). Coherent structures are organized spatial features which repeatedly appear (often in flows dominatedby local shear) and undergo a characteristic temporal life cycle. The proper orthogonal decomposition, which forms the subject of this review, offers a rational methodfor the extraction of such features. Before we begin our discussion of it, a few more general observations on turbulence studies are appropriate. Simulations, Analysis, and Understanding 1.2 Experiments, In analytical studies of turbulence, two grand currents are clear: statistical and deterministic. The former originates in the work of Reynolds (1894). Thelatter is harder to pin down;linear stability theory is felt to havelittle to do with turbulence. Nonlinear stability, however, and such things as amplitude equations, definitely are relevant, so perhaps L. D. Landau and J. T. Stuart should be credited with the beginnings of an analytical nonstatistical approach. Lorenz’ work was certainly seminal. Over the past twenty years a third stream has emerged and grown to a torrent which threatens to carry everything in its path: computational fluid dynamics. Both analytical approaches have drawbacks. Statistical methods, involving averaged quantities, immediately encounter closure problems (Monin & Yaglom 1987), the resolution of which, even in sophisticated renormalization group theories (cf McComb 1990) usually requires use
降维方法与奇异性理论
现代非线性动力学的两个研究主题:降维方法与奇异性理论*曹登庆†陈予恕于海秦朝红哈尔滨工业大学航天学院137信箱，哈尔滨 150001摘要：随着复杂性科学和高技术的发展，高维、多场耦合、强非线性和复杂外部激励正逐渐成为我们面临的动力系统的主要特征。
本文综述近年来在复杂非线性动力系统的降维处理技术和奇异性理论在非线性动力学中的应用方面的研究成果。
在降维方面，主要介绍非线性动力学系统现有降维方法的基本思想、特点与局限性，这些方法包括：基于中心流形理论的降维方法，Lyapunov-Schmidt(L-S)方法，非线性Galerkin方法和Proper Orthogonal Decomposition (POD)方法，并简单介绍了基于正规形理论和快慢流形动力系统的降维方法。
在奇异性理论方面，主要涉及奇异性理论的基本思想、研究现状及其在共振系统、约束系统、对称系统、滞回系统、多参数系统和高余维分岔系统中的应用。
最后提出关于高维非线性动力系统降维以及奇异性理论在非线性动力学中德应用方面的一些新设想，并指出今后研究工作的方向。
关键词：非线性动力学，降维，Galerkin方法，POD，分岔，奇异性理论Two Research Topics in Modern Nonlinear Dynamics: DimensionReduction Methods and Singularity TheoryCAO Dengqing, CHEN Yushu, YU Hai and Qin Zhaohong The School of Astronautics, Harbin Institute of Technology, PO Box 137, Harbin 150001, ChinaAbstract:With the development of complexity science and high technology, high-dimensional, multiple fields coupling, strong nonlinear, and complexity external excitation are becoming primary characteristics of the dynamical systems to be dealt with. This paper is an attempt to categorize recent research achievements in dimension reduction techniques of complexity nonlinear dynamic systems and the applications of singularity theory in nonlinear dynamics. In aspect of dimension reduction, the basic concepts and the features and the limitations of the existing dimension reduction methods of nonlinear dynamic systems are presented. In addition to the typical dimension reduction methods (such as the model reduction method based on center manifold theorem, the Lyapunov-Schmidt method, the Galerkin method and the method of Proper Orthogonal Decomposition), the methods in terms of the normal form and the slow-fast dynamics are briefly presented. In aspect of singularity theory, the basic concepts, current research achievements and its applications in resonant systems, constrained systems, symmetric systems, hysteretic systems; multi-parametric systems, and high co-dimensional bifurcation systems are presented. Finally, considerations on both the dimension reduction of high-dimensional dynamical systems and the applications of singularity theory in nonlinear dynamics are proposed, and the future research directions are indicated.Keywords: Nonlinear dynamics; Dimension reduction; Galerkin method, POD; Bifurcations; Singularity theory1 引 言非线性科学是研究各个不同学科领域中非线性现象共性的一门国际前沿学科，它是在以非线性为特征的各门分支学科的基础上逐步发展起来的综合性学科。
Performance Comparison of Persistence Frameworks
Performance Comparison of Persistence FrameworksSabu M. Thampi* Asst. Prof., Department of CSE L.B.S College of Engineering Kasaragod-671542 Kerala, India smtlbs@yahoo.co.in Ashwin A.K S8, Department of CSE L.B.S College of Engineering Kasaragod-671542 Kerala, India ashwin_a_k@yahoo.co.inAbstractOne of the essential and most complex components in the software development process is the database. The complexity increases when the "orientation" of the interacting components differs. A persistence framework moves the program data in its most natural form to and from a permanent data store, the database. Thus a persistence framework manages the database and the mapping between the database and the objects. This paper compares the performance of two persistence frameworks – Hibernate and iBatis’s SQLMaps using a banking database. The performance of both of these tools in single and multi-user environments are evaluated.1. IntroductionWhen a component based on one kind of approach (e.g. object oriented) tries to interact directly with another object having its roots in another kind of approach (e.g. relational), the complexity increases due to the knots and knaves of cross approach communication. This is evident in all the database APIs provided by different languages. The best example of this is the Java Database Connectivity (JDBC) API. Though JDBC provides an easy method for accessing different databases without much ado, it is basically a low level API providing only a thin layer of abstraction. This is adequate for small and medium projects, but is not well suited for enterprise level applications. With JDBC opening and closing the connection involves a lot of code. What is required is a framework that can act as a mediator between both parties. In OOP, it is typically the behavior of objects (usecases, algorithmic logic) being emphasized. On the other hand, it is the data that counts in database technology. This fact serves as a common motive for the combination of these two paradigms [1]. The core component of this coupling is what is called “object*relational mapping” which takes care of the transitions of data and associations from one paradigm into the other (and vice versa). In order to make a program's object persistent, which means to save its current state and to be able to load that data later on, it is necessary to literally map its attributes and relations to a set of relational tuples. The rules defining such mappings can be quite complex. Here, the term “mapping“ can be defined as the application of rules to transfer object data to a unique equivalent in an RDBMS (relational database management system) and vice-versa. Viewed from the object's perspective, this ensures that all relevant object data can be saved to a database and retrieved again. A persistence framework moves the program data in its most natural form (in memory objects) to and from a permanent data store, the database. The persistence framework manages the database and the mapping between the database and the objects. Persistence framework simplifies the development process. There are many persistence frameworks (both Open Source and Commercial) in the market. Hibernate and iBatis are examples for ORM frameworks for Java. Hibernate [2] is an open source project being covered by BossTM. It is intended to be a full-scale ORM environment and features interesting functionality, such as “real transparency”: a data class does not have to extend special classes of Hibernate; it only has to make properties available through standard get-/set-methods. Hibernate uses bytecode processing to extend from these classes and implement persistence. It also supports – according to the project homepage – a sophisticated caching mechanism (duallayer, which can be distributed as well) using pluggable cache providers. Hibernate is an object/relational persistence and query service for Java. Hibernate lets you develop persistent classes following common Java features - including association, inheritance, polymorphism, composition and the Java collections framework. The HibernateCorresponding AuthorQuery Language, designed as a "minimal" objectoriented extension to SQL, provides a bridge between the object and relational worlds. Hibernate also allows you to express queries using native SQL or Java-based Criteria and Example queries.Apache Software Organization is an open source framework for building web applications that integrate with standard technologies, such as Java Servlets, JavaBeans, and JavaServer Pages. Struts offer many benefits to the web application developer, including Model 2 implementation of Model-View-Controller (MVC) design patterns in JSP web applications. The MVC Model 2 paradigm applied to web applications separate display code (for example, HTML and tag libraries) from flow control logic (action classes).Figure 1: Full Cream Architecture of Hibernate The SQLMaps product of iBatis [3,4] does not represent an ORM environment at the scale of Hibernate. Just as the name suggests, it is heavily SQL-centric and provides means to access centrally stored SQL-statements in a convenient way. The mapping functionality is able to create objects based on query data, but there is no transaction support. The SQLMaps product is light-weight and is expected to run faster than the heavy loaded full-scale ORM toolsIt uses a special mapping files in which the developer should expose object’s properties to be made persistent as well as respective database tables and columns these properties should be mapped to. In addition to that there are something called dynamic queries, caching of queries, transactions and calling stored procedures. The framework maps JavaBeans to SQL statements using a XML descriptor. The performance comparison of Hibernate and iBATIS are explored in this paper. Both of the above tools have their advantages and disadvantages. The remaining sections of the paper are organized as follows. Section 2 gives an overview of protype banking application. Simulation results are presented in section 3. Section 4 concludes the paper.Figure 2: iBATIS Data Mapper framework2. Online Banking systemA very simple prototype version of an online banking application using struts framework and iBatis/ Hibernate framework is developed to analyze the performance of persistence frameworks. The Jakarta Project's Struts framework, version 1.1b2, fromFigure 3: E-R Diagram for banking application The Banking application has a number of functionality such as summary, account details, transfer, transactions, update and contact details. The entity relationship diagram in figure 3 illustrates the relationship among different entities in the prototype system.The figure 4 shows the architecture of the Demo Banking application. The request is given through the browser. The DAO layer contains only method names. When the username and password are entered through GUI and the login button is clicked, the application through the struts framework calls for a login action class which first generates a hash code with the entered data .This is supposed to be the account id. Then the application checks the validity of the entered data by querying from the database based on account id. If they are correct, entry is given otherwise an error page is displayed. The jsp page stores the value of the account id to be referenced in future pages.transfer money to others account as well as to the different account types he has.3. Simulation ResultsPerformance between Hibernate and iBatis is measured using a java program which uses both hibernate and iBatis to perform basic sql operations on the banking database and the RTT (Round Trip Time) is calculated and used to measure the way these mapping tools perform under various situations. The aim is to get the time from generation of sql to querying bank database and then getting back the data. The program was run from one system and the SQL Server was located in another system. The conditions were the same for both the Hibernate and iBatis. The test also included simulation for a single user and multi user. The simulation of multi user was made through the creation of threads. Java supports multithreading environment. The number of threads is passed as input to the program. The response of Hibernate and iBatis under multi user environment is monitored. The RTT is monitored for both the cases.Figure 4: Architecture of Banking applicationFigure 5: Account Summary Page Each account type is a link. When a particular link is clicked the account id and the account number corresponding to the particular link is passed to transactionaction class. From here the transaction list corresponding to the respective account number is retrieved and is passed to the jsp. There is a unique id for each transaction, which is denoted by Transid. When the user clicks the transfer button in the jsp page the pretransferaction class is called which checks the account types belonging to the account holder from the data table named Ac_details and displays it in a drop down menu. The holder canFigure 6: An example of Transaction details of Banking Application The tests were conducted in the following environment: Operating system: Microsoft Windows 2000 Processor: Intel Xeon 4 Processor Memory: 1024 MB DDR RAM The following inputs are needed for the test program: Whether hibernate or iBatis: The user can specify which DAO to be executed whether Hibernate or iBatis. Number of records: The number of records to be inserted, deleted, updated is also given at a time. Insert, update, select, delete or all the operations specified: The user can also specify what operation to be monitored whether insert, update, delete or all operations together can be done.Number of iterations: Number of times the particular set is to be repeated can also be given as input. Number of threads: This simulates number of user accessing the application. The data shown below is how the raw data is recorded and stored into a text file. It is this data that is summarized into graph in figures 8. Average time (with 5000 records, 10 iterations & 50 threads for hibernate) Avg_Insert=3917 Avg_Update=1462 Avg_Select(First Time)=37182 Avg_Select(Second Time)=2361 Avg_Delete=1414 --------------------------------------------Average Time (With 5000 Records, 10 Iterations & 50 Threads For Ibatis) Avg_Insert=6272 Avg_Update=5556 Avg_Select(First Time)=5197 Avg_Select(Second Time)=5157 Avg_Delete=5414 --------------------------------------------Avg_Insert,Avg_Update,,Avg_Select (First Time), Avg_Select (Second Time),Avg_Delete corresponds to average time taken for insert, update, select1, select2 & delete. The above values are computed as follows: i. Find the time taken for an operation in each set of record is noted. ii. The sum of the time taken for all the iterations is found. iii. The average for that set of iterations is computed. iv. If multiple threads (say x no of threads) are present we will have many number of averages (here x) v. The final values are obtained by computing the averages of all the averages previously obtained in step iv. In the figure 7, y-axis represents time in milli seconds and the x-axis represents the various operations performed (such as insert, update, select1, select2) for both hibernate and iBatis. The graph shows that there are minute differences the time taken between hibernate and iBatis except for select1. The large variation in time taken for select1 is caused due to the complex caching algorithms employed by hibernates. Such techniques have proved to be useful in case of subsequent searches as seen in the graph. The graph in figure 8 shows the results of time taken when there are 5 threads 5000 records and 10 iterations. As shown in the graph the time taken forhibernate for the first select is very large compare to iBatis, but in all other cases hibernate has an upper hand over iBatis in terms of time taken. Even in the second select operation time taken by hibernate is less compared to that of iBatis. This implies that barring the initial overhead caused by hibernate during the first select it fares well compared to iBatis.Figure 7: 1 Thread 5000 records 10 iterationsFigure 8: 5 Threads 5000 records 10 iterationsFigure 9: 50 Threads 5000 records 10 iterations Figure 9 represents the time taken when there are 50 threads involved for 5000 records and 10 iterations. In this case it is seen that the large variation that was noticed in case of select1 operation in figures 7 and 8 has now been minimized. When the number of threads was increased to simulate multiple user environments, it is seen that in this case it is iBatis, which lagsbehind, hibernate compared to the previous cases. The only operation in which hibernate consumes more time is for the insert operation.[3] F. Gianneschi: “JDBC vs. iBATIS a case study”, /vqwiki/jsp/Wiki? Action=action_view_attachment&attachment=EN _iBATISCaseStudy.pdf, (Oct. 2005) [4] iBATIS Developer Guide, available at /DevGuide.html#d 0e112, (Sept. 2005) [5] /enterprise/ persistenceframework.shtml [6] Ambler, Scott W, “Mapping Objects to Relational Databases”, An AmbySoft Inc. White Paper, /mappingObjects.html, October 2004 [7] Fussell, Mark L., Foundations of Object Relational Mapping, v0.2 [mlf-970703], published online at , copyright by Mark Fussell, 1997 [8] Various authors, Object Relational Tool Comparison,Online-Wiki, /cgi/wiki?ObjectRelationalToolCom parison, October 2004 [9] Sun Microsystems, “Enterprise JavaBeansTM Specification,Version 2.1”,November 12, 2003, available at /products/ejb/docs.html, (Oct.2005) [10] E. Roman, R. P. Sriganesh, G. Brose: “Mastering Enterprise JavaBeans“, Third Edition, Jan. 2005, available at /books/wiley/maste ringEJB/downloads/MasteringEJB3rd Ed.pdf, (Oct. 2005) [11] iBATIS Mail Archive, available /userjava@ /, (Oct. 2005) at4. ConclusionObject relational mapping became important due to increasing coupling between relational database management systems and object oriented application concepts and development. There are tools to automate these mapping tasks, which can be distinguished by the degree to which they abstract the storage logic for the application. Choosing a suitable product can significantly cut down development efforts, costs and time. After conducting the DAO tests on banking database and comparing a similar application using hibernate and iBatis we come to the following conclusions: 1. In terms of round trip delays iBatis takes lesser time. The slighter increase in time in case of hibernate can be accounted to the time taken for automatically generating the queries and the complex caching algorithms used by hibernate. 2. In terms of flexibility iBatis has an upper hand over hibernate. 3. Considering the learning curve iBatis has a smaller curve since it is more similar to JDBC. 4. Programming using iBatis requires an SQL guru in the team but while using hibernate in-depth knowledge in SQL is not required. 5. Considering the features provided by both the tools, hibernate is much stronger since it supports lazy fetching and mapping associations.5. References[1] Schirrer, “Object-Relational Mapping, Theoretical Background and Tool Comparison”, Bachelor Thesis, Nov. 2004. [2] The Hibernate Project, “Hibernate Reference Documentation, version 2.1.6”, , October 2004, page 61ff。
TPO-30 Reading 2 解析
Q1正确答案：A解析：innumerable，无数的，数不清的；这个单词是numerable(可数的，可计算的)加否定前缀in-，可以推断出近义词是countless，无数的，多得数不清的；occasional，偶尔的，不经常的；repeated，反复的，再三的，重复的。
Q2正确答案：C解析：在第一段中，A选项对应第2句的意思，B选项对应第3句的意思，D选项对应最后一句的意思。
C选项与原文不符，原文一直在说D达尔文的进化论被人们广泛接受。
Q3正确答案：D解析：高亮句的主干部分意思：间断平衡论（punctuated equilibrium hypothesis）挑战了进化论；高亮句的定语从句部分意思：间断平衡轮的内容是新种族的崛起是相对突发的，不需要长时间的转型期。
人物和年份不属于核心信息，可以忽略。
D选项意思和高亮句主干和从句部分意思相符。
A选项which修饰指代不明，容易产生误解；B选项与原文主干部分意思矛盾；C与原文不符，cannot occur without a lengthy transition period与间断平衡论正相反。
Q4正确答案：C解析：根据原文，进化论是说物种演变是通过长时间的缓慢改变发生的；间断平衡论是说物种演变是短期爆发的，所以两个理论的不同在于演变速度，C选项对应原文内容，进化是否是匀速发生的。
Q5正确答案：C解析：题干中的lack of intermediate fossils第三段第3句内容一致，定位到上一句，第2句的大意是，很多生物的化石上百年都不变，这一情况与达尔文学的进化论是不相符的，be at odds with, a与…不和”。
对应C选项。
这一段的最后也用clam or coral举例证明有物种突然被新物种替换，而不是渐渐进化改变的，据此排除B。
第三段第1句说的是间断平衡理论has usually been ignored，排除A；段落最后一句话说的clam or coral species的情况是In most localities而不是most common，排除D。
PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITI
Journal of Sound and<ibration(2002)000(0),000}000doi:10.1006/jsvi.2001.3930,available online at onPHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUEDECOMPOSITIONG.K ERSCHEN AND J.C.G OLINVAL¸¹AS-<ibrations et Identi,cation des Structures,;niversite de¸ie ge,Chemin des Chevreuils, 1(Batiment B52)4000¸ie ge,Belgium.E-mail:g.kerschen@ulg.ac.be(Received12November2000,and in,nal form6April2001)Proper orthogonal decomposition is a statistical pattern analysis technique for"nding the dominant structures,called the proper orthogonal modes,in an ensemble of spatially distributed data.While the proper orthogonal modes are obtained through a statistical formulation,they can be physically interpreted in the"eld of structural dynamics.The purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition2002Academic Press1.INTRODUCTIONProper orthogonal decomposition(POD)is a procedure for extracting a basis for a modal decomposition from an ensemble of signals.A very appealing property of the POD is its optimality.Among all possible decompositions of a random"eld,the POD is the most e$cient in the sense that for a given number of modes,the projection on the subspace used for modelling the random"eld will on average contain the most energy possible.Although POD has been regularly applied to non-linear problems,it is essential to underline that it is a linear technique and that it is optimal only with respect to other linear representations. The applications of this procedure are extensive in modelling of turbulence[1,2]and image processing[3],and POD is now emerging as a useful tool in the"eld of structural dynamics.For instance,it has been applied to estimate the dimensionality of a system[4], to build reduced order models[5,6],and to the identi"cation and updating of non-linear systems[7}9].The purpose of this paper is to determine whether a physical interpretation can be attributed to the modes obtained from the decomposition,i.e.,the proper orthogonal modes (POMs).Particularly,it is inquired when the POMs are related to the vibration eigenmodes.This work is closely related to the paper of Feeny and Kappagantu[10]. However,in the present paper,the emphasis is shifted towards the singular value decomposition of the displacement matrix rather than the eigenvalue problem of the covariance matrix.Furthermore,the case of linear systems under harmonic and white noise excitations is discussed in greater detail.The paper is organized as follows.In Section2,the POD is brie#y introduced.Section 3gives a brief review of the singular value decomposition and its properties that are relevant in the context of this paper.Sections4,5and6study the physical interpretation of the POMs of discrete linear systems,respectively,for the free response in the undamped and damped cases,and for the harmonic response.Section7o!ers a geometric approach to thecomparison between vibration eigenmodes and POMs.It also investigates the relationship between non-linear normal modes (NNMs)and POMs.Finally,the discussion of the stationary random response of a linear system to a white noise excitation is included in Appendix A.2.PROPER ORTHOGONAL DECOMPOSITIONProper orthogonal decomposition,also known as Karhunen }Loeve transform,was introduced by Kosambi [11].It is also worth pointing out that POD is closely related to principal component analysis (PCA)introduced by Hotelling [12].For a detailed historical review of POD or PCA,the reader is referred to references [10,13].Let v (x ,t )be a zero mean random "eld on a domain .In practice,the "eld is sampled at a "nite number of points in time.Then,at time t G ,the system displays a snapshot v G (x )which is a continuous function of x in .The aim of the POD is to "nd the most persistent structure (x )among the ensemble of n snapshots.This is equivalent to minimizing the objective function :Minimize "L G( (x )!v G (x )) ∀x 3 .(1)Equation (1)can also be written in terms of a maximization problem [6]:Maximize "(1/N ) ,L ( (x )v L (x )d ) (x ) (x )d ∀x 3 .(2)Finally,the optimization problem can be reduced to the following integral eigenvalue problem [6]:K (x ,x ) (x )d x " (x ),(3)where K is the two-point correlation functionK (x ,x )"1n L G v G (x )v G (x ).(4)Equation (3)has a "nite number of orthogonal solutions G (x ),called the proper orthogonal modes (POMs)with corresponding real and positive eigenvalues G .In practice,the snapshots are available at discrete measurement points x I where k "1,2,m and the integral eigenvalue problem (3)reduces to "nd the eigensolution of an (m ;m )space correlation tensorG "K (x ,x )2K (x ,x K )222K (x K ,x )2K (x K ,x K ).(5)2G.KERSCHEN AND J.C.GOLINVALTo summarize,if the responses(e.g.,the displacements)q I(t)of a discrete dynamical system with m degrees of freedom(d.o.f.)are sampled n times and if the(m;n)matrixQ"q (t )2q (t L)222q K(t )2q K(t L)"[q(t)2q(t K)](6)is formed,then the POMs are merely the eigenvectors of G"(1/n)QQ2and the corresponding eigenvalues are the proper orthogonal values(POVs).A POV measures the relative energy of the system dynamics contained in the associated POM.3.SINGULAR VALUE DECOMPOSITIONThe objective of this section is to review the singular value decomposition(SVD)and its features that are relevant in the context of POD.Particularly,it is pointed out that the POMs are optimal with respect to energy content.For a detailed description of SVD and its several possible applications in structural dynamics,the reader is referred to references [14,15].Since the matrices considered throughout the paper are built from system responses,e.g.,displacements,the discussion is restricted to real matrices only.For any real(m;n)matrix A,there exists a real factorizationA"U V2,(7) where U is an(m;m)orthonormal matrix.Its columns form the left singular vectors. is an (m;n)pseudo-diagonal and semi-positive-de"nite matrix with diagonal entries containing the singular values G.V is an(n;n)orthonormal matrix.Its columns form the right singular vectors.3.1.GEOMETRIC INTERPRETATIONThe SVD of a matrix,seen as a collection of column vectors,provides important insight into the oriented energy distribution of this set of vectors.It is worth recalling that1.the energy of a vector sequence a I building an(m;n)matrix A is de"ned via theFrobenius normE(A)"#A# $"KGLHa GH"NII where p"min(m,n),(8)so that the energy of a vector sequence is equal to the energy in its singular spectrum;2.the oriented energy of a vector sequence in some direction p with unit vector e N of them-dimensional column space is the sum of squared projections of the vectors on to direction pE N(A)"LI (e2N a I) .(9)PROPER ORTHOGONAL MODE DECOMPOSITION3One essential property of SVD is that extrema in this oriented energy distribution occur at each left singular direction[15].The oriented energy measured in the direction of the i th left singular vector is equal to the i th singular value squared.Since the POMs are directly related to the left singular vectors,it can be stated that they are optimal with respect to energy content in a least-square sense,i.e.,they capture more energy per mode than any other set of basis functions.3.2.RELATION WITH THE EIGENVALUE PROBLEMThe SVD of a matrix can be calculated by means of solving two eigenvalue problems,or even one if only the left or the right singular vectors are required.Indeed,AA2"U U2A2A"V V2.(10) Consequently,the singular values of A are found to be the square roots of the eigenvalues of AA2or A2A.The left and right singular vectors of A are the eigenvectors of AA2and A2A respectively.Applying this reasoning to POD,it is now clear that the POMs,de"ned as the eigenvectors of the covariance matrix G"(1/n)AA2,are the left singular vectors of A.The POVs,de"ned as the eigenvalues of the covariance matrix,are the square of the singular values divided by the number of samples n.In conclusion,POD can be carried out directly by means of an SVD of matrix A.An interesting interpretation of the eigenvalue problem is that if a matrix is real, symmetric and positive de"nite,then the eigenvectors of the matrix are the principal axes of the associated quadratic form which is an n-dimensional ellipsoid centered at the origin of the Euclidean space[16].Since AA2is real,symmetric and positive de"nite,the POMs as eigenvectors of the covariance matrix are the principal axes of the family of ellipsoids de"ned by y2Gy"c where y is a real non-zero vector and c is a positive constant.It is worth pointing out that Feeny and Kappagantu showed that if each data has unit mass,then the POMs are the principal axes of inertia[10].4.UNDAMPED AND UNFORCED LINEAR SYSTEMSThe aim of this section is to"nd the existing relationships between the POMs and the eigenmodes of an undamped and unforced linear system with m.d.o.f.The equation of motion may be written as follows:Mq#Kq"0,(11) where M and K are the mass and sti!ness matrices,respectively,and q is the vector of displacement co-ordinates.The system response due to initial conditions may be expressed asq(t)"KG (A G cos G t#B G sin G t)x G "KGe G(t)x G ,(12)4G.KERSCHEN AND J.C.GOLINVALwhere G,x G are the natural frequencies(in rad/s)and eigenmodes of the system;A G and B G are constants depending on the initial conditions;and e G(t)"A G cos G t#B G sin G t represents the time modulation of mode x G .The time discretization of the system response leads to n sampled values of the time functions which form an(m;n)matrix whose columns are the members of the data ensembleQ"[q(t )2q(t L)]" K G e G(t )x G 2K G e G(t L)x G ,(13) which can also be written asQ"[x 2x K ]e (t )2e (t L) 22e K(t )2e K(t L)"[x2x K ]e2 2e2K"[x2x K ][e 2e K]2"XE2"X[I Z][E R]2,(14)where X is the(m;m)modal matrix whose columns are the eigenmodes of the system;E is an(n;m)matrix whose columns are the functions e G(t)at times t ,2,t L;I is an(m;m) identity matrix;Z is an(m;(n!m))matrix full of zeros;R is an(n;(n!m))matrix;and e G"[e G(t )2e G(t L)]2.Attention should be paid to the fact that R does not in#uence Q since it is multiplied by a matrix full of zeros.Equation(14)can be expressed in a more familiar form asQ"[X][I Z][E R]2"U V2.(15)GHI GHI GHIU V2Accordingly,the above decomposition of Q may be thought of as the SVD of this matrix. However,this decomposition requires matrices U and V to be orthonormal as mentioned in Section3.The aim now is to"nd the conditions when the columns of U(,X)and V(,[E R])are orthogonal.1.The columns of U are formed by the eigenmodes of the structure.The eigenmodes areorthogonal to each other in the metrics of the mass and sti!ness matrices.If the mass matrix is proportional to the identity matrix,it turns out that x2 G x H " GH.Consequently,X is orthogonal if the mass matrix is proportional to the identity matrix.PROPER ORTHOGONAL MODE DECOMPOSITION52.It remains to determine when the columns of V are orthogonal.For this purpose,equation(14)may be rewritten as follows:Q"X[I Z][E R]2(16)"X[diag(#eG#)Z][E diag(#e G#\ )R]2"[x2x K ]#e #0200200#e #200202222222002#e K#020e e 2e K K R 2.If the natural frequencies G are distinct,it can be easily argued that the columns of E diag(#e G#\ )are orthogonal if we consider an in"nite set of sampled values,i.e.,e G G e HHP0if n P R,i O j.(17)Since R does not have an in#uence on Q,its columns can be computed in order that they are orthogonal to those of E diag(#e G#\ ).As can also be seen from equation(16),POD is a bi-orthogonal decomposition that uncouples the spatial and temporal information contained in the data.To summarize,if the mass matrix is proportional to the identity matrix and if the number of samples is in"nite,the singular value decomposition of Q is such that(1)the columns of U are the eigenmodes;(2)the"rst n columns of V are the normalized time modulations of the modes.As stated in section3.2,the POD basis vectors are just the columns of the matrix U in the singular value decomposition of the displacement matrix.Therefore,it can be concluded that the POMs converge to the eigenmodes of an undamped and unforced linear system whose mass matrix is proportional to identity if a su.cient number of samples is considered. Feeny and Kappagantu[10]previously obtained the same conclusion by a di!erent way. They based their demonstration on the fact that the POMs are the eigenvectors of the covariance matrix.In the case of a mass matrix not proportional to identity,the POMs no longer converge to the eigenmodes since the former are orthogonal to each other while the latter are orthogonal with respect to the mass matrix.However,knowing the mass matrix,it is still possible to retrieve the eigenmodes from the POMs.Equation(11)has to be rewritten through the co-ordinate transformation q"M\ p asp#M\ KM\ p"0.(18)In equation(18),the system matrices are still symmetric while the e!ective mass matrix is equal to the identity.Thus,the left singular vectors of P"[p(t )2p(t L)],i.e.,the POMs, converge to the eigenmodes y G of this system.It is a simple matter to demonstrate that the eigenmodes x G of system(11)are related to those of system(18)by the following relationship:x G "M\ y G .(19) 6G.KERSCHEN AND J.C.GOLINVALThis section has investigated the discrete case.A detailed study of distributed systems can be found in reference [17].This paper underlines that the conclusions are still valid if the distributed system is uniformly discretized.5.DAMPED AND UNFORCED LINEAR SYSTEMSConsider now a damped but still unforced linear system with m .d.o.f.for which the equation of motion is given as follows:Mq #Cq #Kq "0.(20)If the structure is lightly damped or with the assumption of modal damping,the system response can be readily written asq (t )"K GA G exp \C G S G R cos((1! G G t # G )x G "K G e G (t )x G .(21)Using the same procedure as in the previous section yieldsQ "[q (t )2q (t L)]" K G e G (t )x G 2K Ge G (t L )x G "[x 2x K ]e 2 2e 2K (22)"XE 2"X [I Z ][E R ]2"X [diag(#e G #)Z ][E diag(#e G#\ )R ]2"[x 2x K ]#e #0200200#e #200202222222002#e K #020 e #e #e #e #2e K #e K #R2."U V 2,where e G "[A G exp \C G S G R cos((1! G G t # G )2A G exp \C G S G R cos((1! G G t L # G )]2.Again,the columns of U (,X )are orthogonal if the mass matrix is proportional to the identity matrix.The main di !erence with the undamped case is that the time modulations e G (t )P 0if t P R since the system returns to the equilibrium position in a "nite time.Consequently,it can no longer be a $rmed that #e G #P R if n P R and that the columns of E diag(#e G #\ )are orthogonal to each other.This causes a set of POMs di !erent from the PROPER ORTHOGONAL MODE DECOMPOSITION 78G.KERSCHEN AND J.C.GOLINVALeigenmodes to be obtained.However,if the damping is low and if a su$cient number of points are considered,E diag(#e G#\ )is almost orthogonal.In conclusion,the POMs of a lightly damped and unforced linear system are a very good approximation of the eigenmodes of this system.This is in accordance with the result obtained in reference[10] using the eigensolution perspective.6.HARMONIC AND FORCED HARMONIC RESPONSES OF A LINEAR SYSTEM This section is divided into two parts.Firstly,the harmonic response of a linear system is considered.By harmonic response,we mean the combination of the free and forced responses.Secondly,attention is focused only on the forced response of the linear system.6.1.HARMONIC RESPONSEThe equation of motion of a linear system with m.d.o.f.excited by an harmonic force with a constant amplitude isMq#Kq"f sin C t.(23)Equation(23)may be transformed by considering a new variable s"sin C t that accounts for the harmonic forceMq#Kq"f swith s(0)"0,s(0)" C,(24)s# C s"0which yieldsM*K*CFDFE CFFDFFEq s " 00 .(25)M001 q s # K!f0CFor the sake of clarity,note( G,x G )the eigensolutions of the initial system(23)and ( * G,x* G )the eigensolutions of the transformed system(24).This latter system may be viewed as an unforced system with m#1d.o.f.(25).If the mass matrix is proportional to identity and if the number of samples is large enough,section4allows us to conclude that the POMs of the transformed system response converge to the eigenmodes of that system. Let us now compute the eigenmodes of the transformed system.These are the solution of(K*! * G M*)x* G "0(26) if * G is a root of the algebraic equationdet(K*! M*"det K!f0 C ! M001 "0.(27)This equation becomesdet K ! M!f 0 C ! "( C ! )det (K ! M )"0.(28)As can be seen from equation (28),the transformed system has m #1eigenvalues.m eigenvalues are equal to those of the initial system (23)* G " G with i "1,2,m (29)and the additional eigenvalue is equal to the square of the excitation frequency (in rad/s)* K> " C .(30)The eigenmodes corresponding to these eigenvalues may now be calculated.As illustrated in equation (26),the eigenmodes are the solution of(K *! * G M *)x * G " K ! * G M !f 0 C ! * G x * G "0.(31)For * G " G,an obvious solution of system (31)is x * G " x G 0 .(32)Accordingly,the eigenmodes of the transformed system corresponding to G have the "rst m components equal to the eigenmodes of the initial system.The last component is equal to 0.It remains to evaluate the eigenmode corresponding to C ,i.e.,x * K> .With this aim,"nding the eigensolutions of the transformed system is also equivalent to "nding theeigensolutions of matrixM *\ K *"M \ 001 K !f 0 C " M \ K !M \ f 0 C (33)andM \ K !M \ f 0 C [x * 2x * K x * K> ]"[x * 2x * K x * K> ] diag( * G ,2, * K )00 * K> (34) M \ K0 !M \ f C X 0 x * K> :K x * K> K> " X0 x * K> :K x * K> K> 0 0 C ,(35)PROPER ORTHOGONAL MODE DECOMPOSITION 9where X"[x 2x K ]and "diag( ,2, K)are the eigensolutions of the initial system.It follows from equation(35)thatM\ KX"X ,(36) M\ Kx* K> :K!M\ f x* K> K> "x* K> :K C,(37)0"0,(38)C x* K> K> "x* K> K> C.(39) Equation(37)allows us to calculate the"rst m components of the last eigenmode x* K> : x* K> :K"[M\ K! C I]\ M\ f x* K> K> "[K! C M]\ f x* K> K> .(40) [K! C M]\ is the dynamic in#uence coe$cient matrix and its spectral expansion is[18][K! C M]\ "KGx G x2 G( G! C) G.(41)Let us now introduce the spectral expansion(41)in equation(40)x* K> :K" K G x G x2 G( G! C) G f x* K> K> .(42) Since an eigenmode is de"ned as a scale factor and since x* K> K> is a scalar,the"nal expression for the eigenmode corresponding to C isx* K> :K" K G x G x2 G( G! C) G f.(43) To summarize,consider a matrix which contains the response of the transformed system (24),i.e.,its"rst m rows contain the response of the initial system(23)and its(m#1)th row is the applied forceQ*" q(t )2q(t L)s(t )2s(t L) .(44) This matrix has m#1POMs that have m#1components.The dominant POM is related to the forced harmonic response of the system and its"rst m components are given by equation(43).Furthermore,if the mass matrix is proportional to density,the"rst m components of the remaining POMs are merely the eigenmodes of the linear system.This perspective should be useful in the context of modal analysis.6.2.FORCED HARMONIC RESPONSEThe forced response is de"ned as the part of the response synchronous to the excitationq(t)"q D sin C t.(45) 10G.KERSCHEN AND J.C.GOLINVALThe forced response amplitude is described by the following expression[18]:q D"" K G x G x2 G( G! C) G f(46) andq(t)" K G x G x2 G( G! C) G f sin C t.(47) The displacement matrix Q becomesQ"[q(t )2q(t L)]" K G x G x2 G( G! C) G f sin C t 2 K G x G x2 G( G! C) G f sin C t L .(48) Equation(48)may be expressed in the formQ" K G x G x2 G( G! C) G f sin C t2sin C t2"qD e2"[qD S]102002000$$$\$$ 0220020[e R]2" q D#q D#S #q D##e#02002000$$$\$$0220020e#e#R 2" q D#q D#S [I ] e#e#R 2(49) GFHFI GHI GFHFI,U V2where S is an(m;(m!1))matrix,I is an(m;n)matrix containing only one non-zero element#q D##e#,and R is an(n;(n!1))matrix.Matrices S and R do not in#uence equation(49)since they are both multiplied by zero elements.If S and R are chosen in order that U and V are unitary matrices,then equation (49)is the singular value decomposition of the matrix Q.PROPER ORTHOGONAL MODE DECOMPOSITION11In conclusion,the following points may be noted.1.Since there is only one non-zero singular value,the forced harmonic response ofa linear system is captured by a single POM whatever the number of d.o.f.is.Nevertheless,all the eigenmodes are necessary to reconstruct the response.This property is independent of the mass distribution and underlines the optimality of the POMs described in section3.1.2.An analytical expression of the POM is obtained:POM"+ KGx G x2 G /( G! C) G,f#+ KG x G x2 G /( G! C) G,f#.(50)Knowing the structural matrices and the spatial discretization of the excitation,the POM may be calculated without"rst simulating the system response as required in the de"nition of the POMs.3.The expression of the POM(50)is equal,to the norm,to the last eigenmode of thetransformed system for the harmonic response(43).This last eigenmode is thus related to the forced harmonic response.4.The convergence of the dominant POM to an eigenmode is no longer guaranteed.ThePOM appears now as a combination of all the eigenmodes.However,if the excitation frequency C tends to a resonant frequency of the system, H for instance,then the denominator H! C of the j th term of combination(50)tends to zero.It is thus observed that this term has a much larger amplitude than the others:POM"+ KGx G x2 G /( G! C) G,f#+ KG x G x2 G /( G! C) G,f#Kx H x2 H /( H! C) H f#x H x2 H /( H! C) H f#" xH if C P H.(51)Since x2 H f represents a scalar product,the POM has the same direction as the eigenmode x H which means that the POM is equal to the resonating mode shape.This is consistent with that obtained in reference[10]using the eigensolution perspective.It is worth pointing out that the non-resonating mode shapes should not be revealed by POD.7.LINEAR NORMAL MODES,NON-LINEAR NORMAL MODES AND PROPERORTHOGONAL MODES:A GEOMETRIC APPROACHFor the sake of clarity,the eigenmodes of a linear system are called here linear normal modes(LNMs).The determination of LNMs is reduced to the equivalent problem of computing the eigensolutions of linear transformations.Obviously,such an approach as well as the superposition principle is inadmissible for non-linear systems.The concept of synchronous non-linear normal mode(NNM)for discrete conservative oscillators was introduced for non-linear systems by Rosenberg[19]:&&A nonlinear system vibrates in normal modes when all masses execute periodic motions of the same period,when all of them pass through the equilibrium position at the same instant,and when,at any time t,the position of all the masses is uniquely de"ned by the position of any one of them.''The objective of this section is to examine the geometric interpretation of LNMs,NNMs and POMs.12G.KERSCHEN AND J.C.GOLINVALG \ m G \ ! G m G !k G> m G G> m G> ! G m G where m "m L> ,R .(53)The transformed equations of motion (53)may be regarded as those of a unit mass which moves in an n -dimensional space.The right-hand side of equation (53)derives from a potential functionG "*;* G ,with ;"!L> G k G 2 G \ m G \ ! G m G .(54)If no external force is present and if the motion is due to an initial displacement,the system occupies at time t "0a position of maximum potential ;"!; .This latter equation de "nes an ellipsoid which is symmetric with respect to the origin.This ellipsoid is called the bounding ellipsoid because all solutions must lie in this domain.In its de "nition of a normal mode for a linear system,Rosenberg [19]stated that it is a straight line in the ( ,2, L )space which passes through the origin of that space and which intersects the bounding ellipsoid orthogonally.It follows from the de "nition that the LNMs are the principal axes of the bounding ellipsoid in the ( ,2, L )space.This result can also be obtained with the interpretation of the eigenvalue problem (section 3.2).Further discussion is given in Appendix B.If the mass matrix is proportional to identity,the LNMs are also the principal axes of the bounding ellipsoid in the (q ,2,q L)space whose expression is ; "L> G k G 2(q G \ !q G ) "12q 2Kq .(55)PROPER ORTHOGONAL MODE DECOMPOSITION 13Figure 2.LNMs and POMs.Principal axes of similar and similarly placed ellipsoids:}},K;)))));G ;**,POM;᭛,LNM.As far as the POMs are concerned,they are the principal axes of the ellipsoid c "q 2Gq where G is the covariance matrix (cf.Section 3.2).Since for an unforced system with a mass matrix proportional to identity,the POMs and the LNMs coincide,it can be concluded that ; " q 2Kq and c "q 2Gq are similar and similarly placed ellipsoids.This is illustrated in Figure 2(two d.o.f.system with an initial displacement).7.2.NON-LINEAR SYSTEMSIf an LNM is a straight line in the co-ordinate space,an NNM is represented by a line,straight (similar NNM)or curved (non-similar NNM).But generally,NNMs are non-similar and the POMs,characterized by straight lines in the co-ordinate space,cannot be merged with NNMs.However,due to their optimality property if the motion is a single,synchronous NNM,the resonant POM minimizes the square of the distance with the NNM under the constraint that it passes through the origin of the co-ordinate system and as stated in reference [10],the POM can be considered as the best linear representation of the NNM.It is also worth pointing out that the LNMs are the tangent space to the NNMs [20].8.CONCLUSIONThis paper has presented a new way,based on the singular value decomposition,of interpreting the POMs in the "eld of structural dynamics.This work has underlined some features of POD which might be useful in the future.Since the POMs are related to the vibration eigenmodes in some cases,POD should be an alternative way of modal analysis for extracting the mode shapes of a structure.POMs could also be used to reconstruct a signal using a minimum number of modes.14G.KERSCHEN AND J.C.GOLINVALPROPER ORTHOGONAL MODE DECOMPOSITION15ACKNOWLEDGMENTSMr Kerschen is supported by a grant from the Belgian National Fund for Scienti"c Research which is gratefully acknowledged.This work presents research results of the Belgian programme on Inter-University Poles of Attraction initiated by the Belgian state, Prime Minister's o$ce,Science Policy Programming.The scienti"c responsibility for this paper is assumed by its authors.REFERENCES1.P.H OLMES,J.L.L UMLEY and G.B ERKOOZ1996¹urbulence,Coherent Structures,DynamicalSystems and Symmetry.Cambridge:New York.2,W.C AZEMIER1997Ph.D.¹hesis,Rijksuniversiteit,Groningen.Proper orthogonal decomposition and low dimensional models for turbulent#ows.3.G.U YTTERHOEVEN1999Ph.D.¹hesis,Katholieke;niversiteit,¸euven.Wavelets:software andapplications.4.J.P.C USUMANO,M.T.S HARKADY and B.W.K IMBLE1993Aerospace Structures:NonlinearDynamics and System Response,American Society of Mechanical Engineers AD-33,13}22.Spatial coherence measurements of a chaotic#exible-beam impact oscillator.5.R.K APPAGANTU and B.F.F EENY1999Journal of Sound and<ibration224,863}877.An optimalmodal reduction of a system with frictional excitation.6.M.F.A.A ZEEZ and A.F.V AKAKIS1998¹echnical Report,;niversity of Illinois at;rbanaChampaign.Proper orthogonal decomposition of a class of vibroimpact oscillations.7.T.K.H ASSELMAN,M.C.A NDERSON and W.G.G AN1998Proceedings of the16th InternationalModal Analysis Conference,Santa Barbara;.S.A.,644}651.Principal component analysis for nonlinear model correlation,updating and uncertainty evaluation.8.V.L ENAERTS,G.K ERSCHEN and J.C.G OLINVAL2000Proceedings of the18th InternationalModal Analysis Conference,San Antonio,;.S.A.Parameter identi"cation of nonlinear mechanical systems using proper orthogonal decomposition.9.V.L ENAERTS,G.K ERSCHEN and J.C.G OLINVAL2001Mechanical Systems and Signal Processing15,31}43.Proper orthogonal decomposition for model updating of non-linear mechanical systems.10.B.F.F EENY and R.K APPAGANTU1998Journal of Sound and<ibration211,607}616.On thephysical interpretation of proper orthogonal modes in vibrations.11.D.K OSAMBI1943Journal of Indian Mathematical Society7,76}88.Statistics in function space.12.H.H OTELLING1933Journal of Educational Psychology24,417}441and498}520.Analysis ofa complex of statistical variables into principal components.13.B.R AVINDRA1999Journal of Sound and<ibration219,189}ments on&&On the physicalinterpretation of proper orthogonal modes in vibrations''.14.D.O TTE1994Ph.D.¹hesis,Katholieke;niversiteit,¸euven.Development and evaluation ofsingular value analysis methodologies for studying multivariate noise and vibration problems.15.J.S TAAR1982Ph.D.¹hesis,Katholieke;niversiteit,¸euven.Concepts for reliable modelling oflinear systems with application to on-line identi"cation of multivariate state space descriptions.16.L.M EIROVITCH1980Computational Methods in Structural Dynamics.Alphen a/d Rijn:Sijtho!and Noordho!.17.B.F.F EENY1997Proceedings of ASME Design Engineering¹echnical Conferences,Sacramento,;.S.A.Interpreting proper orthogonal modes in vibrations.18.M.G ERADIN and D.R IXEN1994Mechanical<ibrations,¹heory and Application to StructuralDynamics.Paris:Masson.19.R.M.R OSENBERG1962Journal of Applied Mechanics29.The normal modes of nonlinearn-degree-of-freedom systems.20.S.W.S HAW and C.P IERRE1993Journal of Sound and<ibration164,85}124.Normal modes fornon-linear vibratory systems.21.A.E.B RYSON and Y.C.H O1975Applied Optimal Control(Optimization,Estimation and Control).New York:Wiley.22.D.F.M ORRISON1967Multivariate Statistical Methods,McGraw-Hill Series in Probability andStatistics.New York:McGraw-Hill.。
流体微团作用与流动结构变化试验分析
术，拍摄流向 - 展向平面流场，采用本征正交分解方法提取湍流流动中不同尺度的含能结构。采用矢量象限组合分析方法，将流场
中流体微团所受作用分为肿胀作用、弯曲作用和旋转作用。结果表明：流动结构变化机理与这 3 种作用相关；肿胀型条带间流体微
团受到的主要作用是弯曲作用，在弯曲作用下直条带会弯曲，弯曲条带在肿胀作用下汇聚成肿胀型条带；随着流动结构尺度减小，
XU Kai-chi1袁 ZHANG Jia-qi2 渊1. AECC Shenyang Engine Research Institute袁Shengyang 110015袁China曰2. School of Mechanical Engineering袁Dalian Unversity of
Technology袁Dalian Liaoning 116024袁China冤
收稿日期：2019-10-02 基金项目：航空动力基础研究项目资助 作者简介：徐凯池（1990），男，硕士，工程师，主要从事航空发动机六性与适航研究工作，E-mail：chifei09124@。
引用格ቤተ መጻሕፍቲ ባይዱ：
Copyright©博看网 . All Rights Reserved.
旋转作用逐渐增大。
关键词：湍流流动结构；粒子图像测速；本征正交分解；航空发动机
中图分类号：V211.76
文献标识码：A
doi：10.13477/ki.aeroengine.2020.02.013
Test Analysis of Fluid Micelle Action and Flow Structure Change
Abstract: In order to study the relationship between the action of fluid micelle and the change of flow structure in turbulent flow袁the flow-to-spread plane flow field was captured by Particle Image Velocimetry (PIV) technique in the turbulent boundary layer of the channel. Energy-bearing structures at different scales in turbulent flow were extracted by means of proper orthogonal decomposition. By means of vector quadrant combined analysis袁the actions of fluid micelle in the flow field were divided into swelling袁bending and rotation. The results show that the mechanism of flow structure change is related to these three actions. The main action of the fluid micelle between the swelling bands is bending. The straight band bends under the action of bending袁and the bending band converges into a swelling band under the action of swelling. As the scale of the flow structure decreases袁the rotation gradually increases.
Plastic-damage model for concrete in principal directions
robust “mixture” of kinematic and isotropic hardening with a-priori correct behavior under tension and compression, which is important for practical applications. The representation of damage through damage variables and the assumption of orthotropy are formally similar to the general framework developed by Carol et al. (2001). The important difference and, at the same time a simplification, is that the evolution laws for damage variables are not formulated directly using normality rules in the space of thermodynamically conjugate forces, which suffer from the lack of physical meaning. The actual values of damage variables are obtained implicitly from the projected of the stress tensor onto loading surface and from the stress equivalence hypothesis. This allows the use of any loading surface and not only that of Rankine (“cutoff”) – type. At the same time, the introduction of damage variables within the framework of orthotropy “fills” the tensor product of two normals, used by Meschke et al. (1998) for definition of evolution law of compliance tensor, with physical meaning. 2 FORMULATION OF THE MODEL 2.1 Loading surface One of the main difficulties in applying theory of plasticity to the concrete-like materials is the proper definition of the shape and kinematic of the loading surface. Under kinematic we understand the evolution of loading surface during increase of inelastic deformations. The most general way to do it offers the use of Haigh-Westergaard coordinates. Several authors have successfully employed this approach for modeling of geomaterials (Willam & Warnke 1975). The disadvantage of this approach is that the models are quite complex what their calibration with the available experimental data make difficult. For two-dimensional stress-strain conditions, which is the main objective of this paper, the definition of the shape and the kinematic of the loading surface can be considerably simplified. The central idea here was proposed by Feenstra & de Borst (1996). They assumed that the actual shape of the loading surface is for inelastic loading completely described by the actual value of tensile and compressive ‘strength’, respectively. Their dependencies from accumulated inelastic strains were taken from uniaxial experiments. The obvious and attractive feature of this model is the a-priori correct behavior under uniaxiall tensile and compressive loading. This idea was also exploited in the formu-
专业英语四级(阅读)模拟试卷170(题后含答案及解析)
专业英语四级（阅读）模拟试卷170(题后含答案及解析)题型有：1. The purpose of this year’s World Intellectual Property Day is to encourage young people to recognize their own ability to create; to increase understanding of how protecting IP rights helps to foster creativity and innovation; and to raise awareness of the importance in daily life of patents, copyright, trademarks and designs. WIPO has also organized an exhibition on intellectual property and sports. The exhibition entitled “Striving for Excellence: an exhibition on intellectual property and sport”will open at WIPO’s Information Center in Geneva on World Intellectual Property Day. The exhibition offers a glimpse of the technological advances that have enhanced sport both on and off the track: by enhancing the performance and natural ability of athletes and in creating opportunities for us all to share in the spectacle, capture the images and savor the glory and wonder that comes when ordinary people achieve extraordinary feats. The exhibition is open to the public and will run through August 2005.1．What is the style of the passage?A．Illuminative, local and humorous.B．Idyllic, beautiful and fluent.C．Strong, pervasive and convincing.D．Simple, plain and illustrative.正确答案：C解析：推理题。
Shertech 铜板挂载旋钮近接外旋齿泵说明书
Please read and save this Repair Parts Manual. Read this manual and the General Operating Instructions carefully before attempting to assemble, install,operate or maintain the product described. Protect yourself and others by observing all safety information. The Safety Instructions are contained in the General Operating Instructions. Failure to comply with the safety instructions accompanying this product could result in personal injury and/or property damage! Retain instructions for future reference.Bronze Plate-Mount RotaryClose-Coupled External Gear PumpsDescriptionShertech self-priming, positive displacement, external rotary gear pumps are ideal for a wide range of light-duty industrial,marine, agricultural, and commercial applications, providing a nearly pulseless flow. Close-coupled models are available directly mounted to NEMA framed AC ODP single-phase, thermally overload-protected motors or as pump heads only for custom installations. All models include a pressure relief valve. Motor-driven models are HP configured to handle up to 500SSU at 100 PSI (specific gravity of 1.0).Uses: For use with non-particulate and non-abrasive fluids compatible with pump wet-end construction component materials.Excellent for water-based fluids. Feature 303 stainless steel shafts, carbon graphite bushings, and Buna-N lip seal with a temperature range of -20°to 210°F . Pressure relief valve is standard. Wet-end parts are constructed from bronze, brass, stainless steel (17-7, 300 series and/or 18-8), graphite, carbon, vellumoid gasket and Buna-N.For more intermittent duty applications, refer to the “Carbonator Series of Rotary Gear Pumps” available in Bronze and Cast Iron.•Flows to 4.4 GPM.•Max. RPM: 1725.•Max. PSI:100.•Suction lift to 3.6 feet.•Maximum viscosity of 500 SSU at 1725 RPM (max. input torque of 45 in-lbs.).•Temperature ranges from -20 to 210°F.•Maximum working pressure: 130 PSI.•Pumps can operate bi-directionally (reversible). It should be noted that it is recommended that the pumps be runin the pump rotation indicated in Figure 5 (clockwise as viewed from the pump end of the pump/motor combination). In the opposite rotation, the pump is limited to 15 PSI discharge pressure, and the pressure relief valve will not function.NOTE:Intermittent and heavy duty series gear pump models are also available for continued use.NOTE:See Rotary Gear Pump Selection Guide in the Motor Manual for suggestions concerning installation, selection, options,and accessories.WARNING:Do not use to pump flammable or explosive fluids such as gasoline, fuel oil, kerosene, etc. Do not use in flammable and/or explosive atmospheres. When pumping hazardous or dangerous materials, use only in room or area designated forthat purpose. For your protection, always wear proper clothing, eye protection, etc. in case of any malfunction. For proper handlingtechniques and cautions, contact your chemical supplier, insurance company and local agencies (fire dept., etc.). Failure to comply with this warning could result in personal injury and/or property damage.Bronze Plate-Mount RotaryClose-Coupled External Gear PumpsBronze Models GFBV2, GFBV3, GFBV22 and GFBV33Specifications and Parts ManualModel Ordering Codes and OptionsExample Model: GFBV33(1)(2)(3)(4)(5GFBV33NOTE: Not all order code combinations (configurations) are standard models available from the manufacturer .Custom model configurations may require ordering standard components and/or optional parts that will need to be assembled by the customer.Manufacturer reserves the right to change model order codes, standard models, specifications, and performance without notification.Maximum motor speed is 1725 RPM.PerformanceGPM Pumping 10 Wt. Oil at 70°F (500 SSU)Bronze Port Motor RPM Max. Input Suction Free Flow 20 PSI 40 PSI 60 PSI 80 PSI 100 PSIModelsSize*HP Torque in.-lbs.Lift**GPM GPM GPM GPM GPM GPM Models with Motors EquippedGFBV221/41/3172545 3.2 2.2 2.1 2.1 1.7 1.5 1.3GFBV333/81/2172545 3.6 4.4 4.1 3.8 3.5 3.3 3.0Models without Motors Suggested GFBV21/41/3***172545 3.2 2.2 2.1 2.1 1.7 1.5 1.3GFBV33/81/2***1725453.64.44.13.83.53.33.0Test data taken on SAE 10 wt. oil at 70°F (500 SSU).Pump performance when pump is new. As pump wears, the performance will decrease.(*) NPT inlet and outlet (in inches).(**) Suction lift requires wetted gears and primed seal chamber.(***) Motor not providedNOTES:Pumps with motors are HP rated to handle up to 500 SSU at 100 PSI and specific gravity of 1.0.Max. PSI = 100Max. Viscosity = 500 SSU Max. RPM = 1725Max. Specific Gravity = 1.1 at 100 PSI, up to 1.6 at lower PSI & viscosity.Max. Input Torque = See chart above.Reverse Rotation = Pumps are equipped with pressure relief valves and can be run in reverse rotation; however, pressure relief valve will not func-tion when pump is reversed unless pump relief valve cover is rotated 180 degrees. Maximum reverse pressure is 15 PSI or seal damage will occur.The pump relationship between volume (GPM), pressure (PSI), speed (RPM) and horsepower is shown on performance chart in Shertech MotorManual form L-4082. When pumping a more viscous liquid, a slower speed, a larger pipe size pump, and possibly a larger motor should be selected.Driver data is subject to change without notice; see label on driver for specifications and wiring information.Manufacturer reserves the right to change performance without notification.DimensionsF Approx.E BDHJIG0.34CK SlotNPT Intake &Discharge PortFigure 1 - DimensionsShaft size 1/2”A***Specifications and Parts ManualBronze Models GFBV2, GFBV3, GFBV22 and GFBV33BZ = Bronze BR = Brass SS = Stainless Steel CG = Carbon Graphite ODP = Open Drip-Proof(*) Motor not provided, but suggested. Pump head only provides the ability to adjust HP for viscosity and to use existing and/or special motors.(**NPT inlet and outlet (in inches).(***) Lip seal components include 303 stainless steel case and garter spring.(****) Models are made of stainless steel (17-7, 300 series and/or 18-8), brass and/or bronze.(†) Thermal overload protection reset may be automatic or manual.NOTES:Motor may be split-phase or capacitor start.Motor base may be removable, movable or fixed.Driver data is subject to change without notice; see label on driver for specifications and wiring information.Manufacturer reserves the right to change specifications without notification.InletOutletMotors not included on allM†Relief Valve Position ShownFor Clockwise MotorM†L Pumps with NEMA 48 Frame MotorModelsA***B**C**D**EF**G**H**I**J**K**L M(†)GFBV2* & GFBV221/4 .47 2.44 3.00 2.88 14.06 2.75 5.69 4.25 5.75 1.06 2.50 4.875GFBV3* & GFBV333/8 1.53 2.44 3.00 3.31 15.00 2.75 5.69 4.25 5.75 1.06 2.50 4.875(*) Motor not supplied, head only.Dimensions are typical when mounted to 48 frame motors.(**) This dimension may vary due to motor manufacturer’s specifications.(***) NPT inlet and outlet (in inches).(†) Accommodates motor bolt circles of 5.13 to 5.83 and hole diameter of .34".NOTE:Dimensions have a tolerance of (+ or -) 1/8".Manufacturer reserves the right to change dimensions without notification.Check motor.It may be equippedwith an automatic resetting thermal protector and may restart unexpectedly (see specifications chart). Protector tripping is an indication of motor overloading as a result of operating the pump at too high a pressure (over 100 PSI), too high of viscosity,too high of specific gravity, excessively high or low voltage, inadequate wiring, incorrect motor connections, too small a motor (sized incorrectly, not enough HP), or a defective motor or pump.Do not handle pump with wet hands or when standing in water.Failure to follow the General Safety Information and all warnings could result in fatal electrical shock!Assembly(If pump and motor arepre-assembled, skip assembly.)The pump is supplied already mounted to an adapter bracket and ready for attaching to your motor.The necessary mounting equipment is packaged separately with pump, and contains (See Figure 8):a.Drive coupling half for motor shaft (Ref. No. 19).b.Flexible coupling insert (Ref. No. 19).c.Four (4) mounting bolts (Ref. No. 18).d.Twelve (12) nuts (Ref. No. 17).To assemble the pump to a motor:1.Remove the four (4) thru-bolt nuts from your motor (See Figure 3). 2.Select threaded end of mounting bolts which matches your motor threaded thru-bolt. Note the bolt is internally threaded size 8 thread at one end and size 10 thread at the other (See Figure 2). Attach four (4)nuts (Ref. No. 17) to mounting bolts at end that mounts to motor thru-bolts. Install mounting bolts in motor thru-bolts. Tighten four (4)nuts against motor frame (See Figure 3).3.After mounting bolts are secured,rotate motor shaft by hand to make sure there is no bind. If bind occurs,adjust thru-bolts accordingly to assure free rotation (See Figure 3).4.Slip coupling half (Ref. No. 19) onto motor shaft end and tighten set screw. Insert flexible insert. (Ref. No. 19 and Figure 3).5.Thread a jam nut on each of four (4) mounting bolts an equal dis-tance from stud end (See Figure 3).6.Place pump and bracket assembly onto the four (4) mounting bolts and position it so that 1/16" free play exists off end face of the flexible member of drive coupling (See Figure 4).7.Bring jam nuts that are on mounting bolts into position against pump bracket to secure this position. At this point, all nuts should be equal distance from end of mounting bolts.8.Finally, check pump alignment. The pump bracket should be square with motor shaft. The coupling halves should be matched and parallel with shaft. The flexible coupling member should be free to slide back and forth in its clearance. The pump should turn freely by hand.9.Rotation: When facing the motor shaft end, proper motor pump rota-tion is clockwise (CW). Flow is left to right (See Figure 5). Standardpumps have pressure relief valves.Failure to followcorrect shaft rotation,or mounting pressure relief valve incorrectly on pump, can result in seal failure.10.Motor should be securely fastenedto a rigid surface, preferably metal-lic. For rigidity, use largest bolts thatwill fit through base holes.Bronze Models GFBV2, GFBV3, GFBV22 and GFBV33Specifications and Parts ManualBronze Plate-Mount RotaryClose-Coupled External Gear PumpsOutFigure 5 - Pump RotationFigure 2 - Mounting StudsFigure 3 - Mounting Stud InstallationSize 10threadRemove thru-bolt nutsPump Mounting Plate &Lock NutsMounting bolts &lock nutsDrive CouplerSize 8threadFigure 4 - Drive Coupling Install1/16” free playSpecifications and Parts ManualBronze Models GFBV2, GFBV3, GFBV22 and GFBV33Bronze Models GFBV2, GFBV3, GFBV22 and GFBV33 Specifications and Parts ManualBronze Plate-Mount Rotary Close-Coupled External Gear PumpsOperation (Continued)rotation. The pressure relief valvemust always be on the inlet portside. If the pump pressure reliefvalve cover is removed, it must bereassembled in the same orientation as it came from the factory. Whenviewing the cover side of the pump, the pressure relief valve will be onthe left side when the pump ismounted with the idler shaft pocket down. (This is the portion of thepump without the shaft.)6.Standard pump models are equippedwith pressure relief valve. The inletport is always on relief valve side. 7.Pressure Relief Valve: Standardmodels are supplied with a built-inpressure relief valve. The valve maybe adjusted and used to set systemoperating pressure or used as a sys-tem pressure relief valve to preventpump and motor damage that occur when discharge line is closed off.However,this is not a full-line pres-sure relief valve, and in cases wherefrequent extended pressure reliefvalve operation is anticipated, anexternal discharge line connectedeither, back to the tank, or welldownstream from the pump suction inlet is recommended. This pressurerelief valve is not factory set.Extended operation (over oneminute) under shut-off conditionscould cause pump to overheat, leakand damage itself.8.To increase the pressure relief valvepressure setting, remove pressurerelief valve stem cap cover and turnthe adjusting valve stem (Ref. No. 4)in (clockwise). Turning the adjustingvalve stem out (counterclockwise)will reduce the pressure setting (SeeFigure 6).MaintenanceMake certain thatthe power supply isdisconnected before attempting to service ordisassemble any components!If the power disconnect point is out of sight,lock in the open position and tag to preventunexpected application of power. If thepower disconnect point is out of sight, lockin the open position and tag to preventunexpected application of power.GENERALPump should be checked for properoperation daily,weekly,monthly,etc. Ifanything has changed (pump noise,motor noise, leaks, etc.) since the pumpwas new,the pump should be removed,examined and repaired if necessary.This is a difficult motor/pump to repair,therefore, only a qualified electrician orservice technician should attempt torepair this unit. Improper repair and/orassembly can cause problems with theelectric motor used with this unit. SeeGeneral Safety Information.Rotary gear pumps must be drainedcompletely if they are used in an areasubject to freezing temperature.If the pump is to be stored, place asmall quantity of light oil or some otherstorage preservative compatible withyour application in the pump androtate the shaft very slowly to work theoil throughout the gears and the body.DISASSEMBLY AND ASSEMBLYRefer to Figure8for disassembly andassembly procedures.1.Remove screws (Ref. No. 8), lockwash-ers (Ref. No. 9), and cover (Ref. No. 13).2.Shafts (Ref. Nos. 10 and 11) can beremoved.3.For replacement only, pry out lip seal(Ref. No. 13) and replace seal withgarter spring towards inside or bodyof pump (See Figure 7).NOTE:Pump drive shaft may haveburrs or scratches. These need to besmoothed off prior to new seal install.4. The relief valve is disassembled byremoving the valve stem cap (6),valve stem lock nut (5), valve stemgasket (7), valve stem (4), valvespring (3), and the ball (2). Partsshould be inspected for wear ordamage. In particular, check insidethe cover on the valve seat forpitting or damage.5.Inspect parts for damage or exces-sive wear.It is recommended, ifpump components are worn, toreplace the complete pump.6.Reassemble pump in reverse orderof disassembly. Tighten cover screwsevenly in opposing sequence toassure proper cover to bodyalignment.7.If the pump performs well but leaks,the lip seal should be replaced (SeeFigure7). If there is excessive wearon gears, shafts or other pumpcomponents, the entire pumpshould be replaced.Figure6-Pressure Relief Valve AdjustmentFigure 7 - Seal ReplacementOriginalsealRelief valveadjustmentscrewLock nutProtective cap&washerPossible burrsor scratcheson shaft.Smooth off.New seal installwith garter springtowards inside of pumpSpecifications and Parts ManualPlease provide following information:-Model number-Serial number (if any)-Part description and number as shown in parts listContact a Shertech DistributorDistributors can be found at or (The factory only sells pumps and parts to distributors.)Figure 8–Repair Parts IllustrationRepair Parts List19161517181717812201167574321102014139DescriptionGFBV2GFBV3GFBV22GFBV33Qty.1Housing assembly (Bronze)NA NA NA NA 1(includes carbon graphite bushings) Optional Housing Without Relief Valve ** 11588S 11587S 11588S 11587S 12Ball (300 Series SS)NA NA NA NA 1 3Valve spring (17-7 SS)NA NA NA NA 1 4Valve stem (Bronze)NA NA NA NA 1 5Valve stem locknut NA NA NA NA 1 6Valve stem capNA NA NA NA 1 7Valve gasket (Fiber)NA NA NA NA 2 8Brass round head machine screw * * * * 6 9Gasket (Vellumoid)11582115821158211582 1 10Driven gear & shaft assembly*** NA NA NA NA 111Drive gear & shaft assembly*** NA NA NA NA 1 12Body assembly (includes bushings)NA NA NA NA 1 13Lip seal Buna-N (assemble with garter spring towards inside or body of pump)11628 11628 11628 11628 1 Optional Lip seal Viton11674 11674 11674 11674 1 14Mounting bracket (zinc-plated steel)NA NA NA NA 1 151/4" Light lockwasher NA NA NA NA 2 16Long steel cap screw NA NA NA NA 2 17Thin mounting nut NA NA NA NA 12 18Mounting boltNA NA NA NA 4 19Flexible coupling (w/Spider) NA NA NA NA 1 20Carbon Graphite Bushings (4) NA NA NA NA4 21Motor †NA NA 24647S 24648S 1OptionalReplacement Pump Head Only*GFBV2GFBV3GFBV2GFBV31(*) Pump heads come without plate, tie rods or shaft coupler.(**) Replaces Ref.No. 1, but without relief valve porting. Comes with carbon bushings. (***) Bronze gears on 303 SS shafts(†) See Specifications chart for motor specifications.It is recommended that the pump be replaced once performance degrades such that the unit no longer satisfies the application. This is the most cost effective course of action as usually all parts have worn.21Bronze Models GFBV2, GFBV3, GFBV22 and GFBV33Specifications and Parts ManualHypro warrants to the original purchaser of its products (the “Purchaser”) that such products will be free from defects in material and workmanship under normal use for the period of six (6) months, and accessories will be free from defects in material and workmanship under normal use for the period of ninety (90) days. Parts carry no warranty.“Normal use” does not include use in excess of recommended maximum speeds, pressures, vacuums and temperatures, or use requiring handling of fluids not compatible with component materials. This warranty does not cover freight damage,freezing damage, pump or motor damage from incorrect wiring (if equipped with motor), normal wear and tear, or damage caused by misapplication, fault, negligence, alterations, dry running pump, or repair that affects the performance or reliability of the product.THIS WARRANTY IS EXCLUSIVE. HYPRO MAKES NO OTHER WARRANTY , EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.Hypro’s obligation under this warranty is, at Hypro’s option, to either repair or replace the product upon return of the entire product to the Hypro factory in accordance with the return procedures set forth below. THIS IS THE EXCLUSIVE REMEDY FOR ANY BREACH OF WARRANTY .IN NO EVENT SHALL HYPRO BE LIABLE FOR ANY INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND, WHETHER FOR BREACH OF ANY WARRANTY , FOR NEGLIGENCE, ON THE BASIS OF STRICT LIABILITY , OR OTHERWISE.Only authorized distributors can return products for Warranty. Contact your distributor or visit to find a distributor for product support.Distributors can obtain an RMA # and contact person’s name by contacting Hypro’s customer service at 800-471-0460.Return Procedures for DistributorsAll pumps or products must be flushed of any chemical (ref. OSHA Section 0910.1200 (d)(e)(f)(g)(h) and hazardous chemicals must be labeled before being shipped* to Hypro for service or warranty consideration. Hypro reserves the right to request a Material Safety Data sheet from the Purchaser for any pump or product Hypro deems necessary. Hypro reserves the right to “disposition as scrap” pumps or products returned without authorization and/or which contain unknown substances, or to charge for any and all costs incurred for chemical testing and proper disposal of components containing unknown substances.Hypro requests this in order to protect the environment and personnel from the hazards of handling unknown substances.Be prepared to give Hypro full details of the problem, including the following information:1. Model number, sale record/invoice, purchase date and from whom you purchased your pump.2. A brief description of the pump problem, including the following:•Liquid pumped. State the pH and any non-soluble •Drive type (gas engine/electric motor; direct/belt drive;materials, and give the generic or trade name. tractor PTO) and rpm of pump.•Temperature of the liquid and ambient environment. • Viscosity of fluid if other than water.•Suction lift or vacuum (measured at the pump). • Specific gravity of fluid if other than water.•Discharge pressure.• Elevation from the pump to the discharge point.•Size, type, and mesh of the suction strainer.•Size and material of suction and discharge line.•Abrasiveness or particulate size in fluids.Hypro may request additional information and may require a sketch to illustrate the problem. Distributors should contact the factory to receive a return material authorization before sending the product. All pumps returned for warranty work should be sent shipping charges prepaid to:[RMA# and Contact Person]HYPRO375 Fifth Avenue NWNew Brighton, Minnesota 55112NOTE:Hypro reserves the right to “disposition as scrap” pumps or products returned without authorization.*Carriers, including U.S.P .S., airlines, UPS, ground freight, etc., require specific identification of any hazardous materials being shipped.Failure to do so may result in a substantial fine and/or prison term. Check with your shipping company for specific instructions.Limited Warranty on Bronze Plate-Mount Rotary Close-Coupled External Gear Pumps。
Sensata Technologies GIGAFUSE高压电池快速断开设备说明书
| GIGAFUSE: HIGH VOLTAGE BATTERY FAST DISCONNECTA FAST AND PRECISE CIRCUIT PROTECTION SOLUTION FOR ADVANCED BATTERY SYSTEMS DURING SHORT CIRCUIT AND OVERCURRENT SITUATIONSSPECIFICATIONSUnitsV A MW ms Device Resistance, beginning of life mΩThe high current levels and power densities in advanced battery systems demand equally high-performance safety components. Available in both passive and passive/active (active version production phase available at 3Q2023) combinations, the GigaFuse from GIGAVAC, a brand of Sensata Technologies, is a fast-acting electromechanical device with low heat generation that allows for circuit trips at exact currents and features a design that easily pairs with contactors and eliminates thermal aging fatigue associated with typical DC fuses.FeaturesSensata’s Value• F unctional Safety: Passive technology with electro-mechanical release mechanism • F ast disconnect: <3ms clear time independent from current level • S ystem protection coordination: tunable trip current to easily pair with HV contactors • O ptional active control: to provide designers flexibility of active/passive protection methods (production phase available at 2Q2023)• U p to 10MW interrupt capability • 400A continuous current carry (4/0 busbars); Consult engineering for higher current• W orld-class automotive component supplier • A pplication expertise, significant automotive knowledge base including quality and supply chain • G lobal/Local approach, engineering, and commercial support • S urety of supply: global manufacturing capabilityDIMENSIONSDimensions are in [inches] millimetersTolerance is +/- 0.5mm for all dimensions, unless stated otherwise.MountingM5 or No. 10 ScrewsTorque 1.7 - 4 Nm [15-35in-lb]Case MaterialThermoplastic Polyamide ResinPower ConnectionM8 x 1.25 FemaleTorque 12-18 Nm [106-159 in-lb]Pyro ConnectionTE 411-78033Qualified Acc. to LV 16 and USCARInitiator Resistance: ≥1.7Ω and ≤2.5ΩTriggering Pulse Current: ≥1.75A / 0.5ms≥1.2A / 2.0msDiagnostic Current: ≤100mANo Trigger Current: ≤0.4A or ≤5.0A / 4μsColor of connector retainer may vary due to supplyavailabilitySIDEMOUNTUPRIGHTORDERING OPTIONSMOMENTARY CURRENT CURVE80°C terminal temperature rise at specified curveExample: GFPA415BPassive/Active, 1500A Trip Current, Horizontal Mount OrientationPage 4Sensata Technologies, Inc. (“Sensata”) data sheets are solely intended to assist designers (“Buyers”) who are developing systems that incorporate Sensata products (also referred to herein as “components”). Buyer understands and agrees that Buyer remains responsible for using its independent analysis, valuation, and judgment in designing Buyer’s systems and products. Sensata data sheets have been created using standard laboratory conditions and engineering practices. Sensata has not conducted any testing other than that specifically described in the published documentation for a particular data sheet. Sensata may make corrections, enhancements, improvements, and other changes to its data sheets or components without notice.Buyers are authorized to use Sensata data sheets with the Sensata component(s) identified in each particular data sheet. HOWEVER, NO OTHER LICENSE, EXPRESS OR IMPLIED, BY ESTOPPEL OTHERWISE TO ANY OTHER SENSATA INTELLECTUAL PROPERTY RIGHT, AND NO LICENSE TO ANY THIRD PARTY TECHNOLOGY OR INTELLECTUAL PROPERTY RIGHT, IS GRANTED HEREIN. SENSATA DATA SHEETS ARE PROVIDED “AS IS”. SENSATA MAKES NO WARRANTIES OR REPRESENTATIONS WITH REGARD TO THE DATA SHEETS OR USE OF THE DATA SHEETS, EXPRESS, IMPLIED, OR STATUTORY, INCLUDING ACCURACY OR COMPLETENESS. SENSATA DISCLAIMS ANY WARRANTY OF TITLE AND ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT, QUIET POSSESSION, AND NON-INFRINGEMENT OF ANY THIRD PARTY INTELLECTUAL PROPERTY RIGHTS WITH REGARD TO SENSATA DATA SHEETS OR USE THEREOF.All products are sold subject to Sensata’s terms and conditions of sale supplied at SENSATA ASSUMES NO LIABILITY FOR APPLICATIONS ASSISTANCE OR THE DESIGN OF BUYERS’ PRODUCTS. BUYER ACKNOWLEDGES AND AGREES THAT IT IS SOLELY RESPONSIBLE FOR COMPLIANCE WITH ALL LEGAL, REGULATORY, AND SAFETY-ELATED REQUIREMENTS CONCERNING ITS PRODUCTS, CONTACT USAmericas+1 (805) 684-8401 *******************GENERAL NOTES1.For customers who can accommodate a vented device, contact Sensata Technologies for more information.2. Current rating (both continuous and momentary) is dependent on bus bar size and customer specific application conditions. Consult with Sensata Technologies for specific details.3. Performance in application will vary based on customer environment and system isolation requirements. Validated at following conditions: 650 V, 15.5kA, 12 µH system inductance. Up to 850 V, 12kA, with 4 µH system inductance. For 1000V application above 3kA, contact Sensata engineering4. Clear time below 5kA can reach up to 4 ms max. IR after 8MW interrupt >1MΩ5. Insulation resistance is dependent on power level of max interrupt load and IR increases with reduced power levels or lower system inductance. IR after standalone short circuit may be below 0.5M at system inductance over 4uH. Performance when tested at system level will show improved IR post interrupt.6. Device can operate in higher ambient temperatures with derated current carry while below maximum terminal temperature.7. Measured on top of the bus bar at the bolted joint. Customer is responsible for ensuring this condition is met otherwise damage to device can occur.8. Sensata Technologies recommends orienting Z axis orthogonal to any mechanical shock pulses to ensure robust performance under load. Sensitivity is dependent on trip setting, consult with Sensata Technologies for more details. See photo for axis orientation.9. Performance depends on specific vibration profile and trip level, consult with Sensata Technologies for your specific requirements. 10. For Automotive Applications please request technical workshop with Sensata Technologies Application Engineering.WARNINGSRISK OF MATERIAL DAMAGE AND HOT ENCLOSURE• The product’s side panels may be hot, allow the product to cool before touching • Follow proper mounting instructions including torque values • Do not allow liquids or foreign objects to enter this productFailure to follow these instructions can result in serious injury, or equipment damage.HAZARD OF ELECTRIC SHOCK, EXPLOSION OR ARC FLASH• Disconnect all power before installing or working with this equipment • Verify all connections and replace all covers before turning on powerFailure to follow these instructions can result in death or serious injury.STRONG MAGNETS PRESENT• This device may present a risk to people with pacemakers if brought within 5 inches (125mm) of device• This device may present a risk to computer drives or other magnetic sensitive electronics or attract small metal tools within 4 inches (100mm) of the device.Failure to follow these instructions can result in death or serious injury.。
科技人员科技英语写作班练习题和测验题-推荐下载
课后练习1I、在下列每个句子的空白处填上适当的冠词（如果必要的话），然后将句子译成汉语：1. There has been _____ ever greater interest in this subject.2. The power rating is the maximum power the resistor can safely dissipate without too great _____ rise in temperature.3. Its primary disadvantage is _____ increase in noise.4. _____ successful design of the equipment requires _____ detailed knowledge of the performance specifications.5. In _____ Bohr model of the hydrogen atom, _____ single electron revolves around _____ single proton in a circle of radius R.6. The unit of frequency is _____ hertz.7. _____ Fig. 5-1 shows _____ Oersted’s experiment.8. _____ machine is _____ device for transmitting force to accomplish _____ definite purpose.9. _____ hydraulic press will be considered in _____ Chapter 14.10. It is easy to determine _____ value of _____ parameter μ.11. By _____ Eq. (2-1) we have _____ following relation.12. It is necessay to use _____ S-shaped tube here.13. The authors work at _____ University of Texas at _____ Arlinton.II、根据所给的汉语文本，改正各英语文本中的错误：1、【汉语原文】UASMA协议采用了独特的幀结构。
科技人员科技英语写作班练习题和测验题-推荐下载
课后练习1I、在下列每个句子的空白处填上适当的冠词（如果必要的话），然后将句子译成汉语：1. There has been _____ ever greater interest in this subject.2. The power rating is the maximum power the resistor can safely dissipate without too great _____ rise in temperature.3. Its primary disadvantage is _____ increase in noise.4. _____ successful design of the equipment requires _____ detailed knowledge of the performance specifications.5. In _____ Bohr model of the hydrogen atom, _____ single electron revolves around _____ single proton in a circle of radius R.6. The unit of frequency is _____ hertz.7. _____ Fig. 5-1 shows _____ Oersted’s experiment.8. _____ machine is _____ device for transmitting force to accomplish _____ definite purpose.9. _____ hydraulic press will be considered in _____ Chapter 14.10. It is easy to determine _____ value of _____ parameter μ.11. By _____ Eq. (2-1) we have _____ following relation.12. It is necessay to use _____ S-shaped tube here.13. The authors work at _____ University of Texas at _____ Arlinton.II、根据所给的汉语文本，改正各英语文本中的错误：1、【汉语原文】UASMA协议采用了独特的幀结构。