A fault diagnosis approach for diesel engine valve train based on improved ITD and SDAG-RVM

Home Search Collections Journals About Contact us My IOPscienceA fault diagnosis approach for diesel engine valve train based on improved ITD and SDAG-RVMThis content has been downloaded from IOPscience. Please scroll down to see the full text.2015 Meas. Sci. Technol. 26 025003(/0957-0233/26/2/025003)View the table of contents for this issue, or go to the journal homepage for moreDownload details:IP Address: 115.154.143.184This content was downloaded on 20/05/2016 at 13:22Please note that terms and conditions apply.1. IntroductionThe valve train is an important component of a diesel engine. However, due to adverse working conditions and a complex structure, faults occur frequently during the operation of the diesel engine. According to statistics, the valve train fault can account for a noticeably large proportion (about 15.1%) of all diesel engine faults [1]. It will inevitably lead to economic loss and even threaten personal safety if not detected in time. Therefore, it is critically important to assess the working condition and identify the fault of the valve train. The fault diagnosis process of a diesel engine valve train can be mainly divided into three stages: signal acquisition, feature extraction and pattern recognition.Many kinds of signals have been used in the fault diag-nosis of diesel engines, including cylinder pressure signal [2],vibration signal [1, 3], temperature signal [4], acoustic emis-sion signal [5], etc. The vibration signal is the most acknowl-edged one, because it can provide a variety of information about the reciprocating and rotating motions, mechanical impacts and high-speed flow of gas. Moreover, the acquisition of vibration signal is very convenient and non-intrusive [3]. Therefore, vibration signal is collected for the fault diagnosis of diesel engine valve train in this paper.After the signal acquisition step, effective fault features need to be extracted. For the past few years, the autoregres-sive (AR) model has attracted increasing attention in feature extraction [6, 7]. As a typical time series analysis method, the AR model can effectively reflect the essential character-istics of a dynamic system, and its AR coefficients are very sensitive to condition variation. Moreover, there is no need to construct a complex mathematical model and study the faultA fault diagnosis approach for diesel engine valve train based on improved ITD and SDAG-RVMLiu Yu, Zhang Junhong, Bi Fengrong, Lin Jiewei and Ma WenpengState Key Laboratory of Engines, Tianjin University, Tianjin 300072, People’s Republic of China E-mail: liuyu2012@Received 24 September 2014, revised 6 November 2014Accepted for publication 18 November 2014Published 17 December 2014AbstractTargeting the non-stationary characteristics of the vibration signals of a diesel engine valve train, and the limitation of the autoregressive (AR) model, a novel approach based on the improved intrinsic time-scale decomposition (ITD) and relevance vector machine (RVM) is proposed in this paper for the identification of diesel engine valve train faults. The approach mainly consists of three stages: First, prior to the feature extraction, non-uniform B-spline interpolation is introduced to the ITD method for the fitting of baseline signal, then theimproved ITD is used to decompose the non-stationary signals into a set of stationary proper rotation components (PRCs). Second, the AR model is established for each PRC, and the first several AR coefficients together with the remnant variance of all PRCs are regarded as the fault feature vectors. Finally, a new separability based directed acyclic graph (SDAG) method is proposed to determine the structure of multi-class RVM, and the fault feature vectors are classified using the SDAG-RVM classifier to recognize the fault of the diesel engine valve train. The experimental results demonstrate that the proposed fault diagnosis approach can effectively extract the fault features and accurately identify the fault patterns.Keywords: diesel, fault diagnosis, non-uniform B-spline, intrinsic time-scale decomposition, directed cyclic graph, relevance vector machine, autoregressive model (Some figures may appear in colour only in the online journal)doi:10.1088/0957-0233/26/2/025003Meas. Sci. Technol. 26 (2015) 025003 (14pp)mechanism before the AR model is established. However, one noticeable problem is that the AR model can only be used to process stationary signals [8], while the vibration signals of a diesel engine valve train are highly transient and non-sta-tionary. Therefore, a non-stationary signal processing method is needed to preprocess the vibration signals before the estab-lishment of the AR model. Empirical mode decomposition (EMD) is a typical non-stationary signal processing method [9, 10], by which a complicated signal can be decomposed into finite stationary intrinsic mode functions (IMFs). Then the fault feature vectors can be obtained by applying AR model to each IMF. It is acknowledged that the application limitation of the AR model can be solved to a certain extent by using EMD, but some inherent deficiencies of EMD, such as the end effects, mode mixing, interpolation method and the unexplainable negative frequency cannot be neglected [11]. Aimed at these problems of EMD, a self-adaptive signal processing method named local mean decomposition (LMD) was proposed by Smith in 2005 [12]. Some researchers have applied LMD to the fault diagnosis of rotating machine and illustrated the LMD method is better than the EMD method in mode mixing, end effects, etc [11, 13, 14]. Nevertheless, LMD is inherently dedicated for the decomposition of the AM-F M signals; when used in the processing of transient impact signals, such as valve collision signal, the algorithm usually does not converge. Intrinsic time-scale decomposi-tion (ITD) is a newly developed signal processing method [15, 16], which decomposes a non-stationary signal into a sum of proper rotation components (PRCs) based on the local characteristic time-scale of signal. Compared with EMD and LMD, more information of the signal can be utilized by ITD and the computational efficiency can also be improved. However, when used to process the complex fault signals of diesel engine valve train, there still remain problems of interpolation method and decomposition termination condi-tion. Therefore, to overcome these drawbacks, an improved ITD method based on non-uniform B-spline interpolation and cumulative variance contribution rate is proposed in this paper. Afterwards, AR model and improved ITD is combined for the feature extraction.Pattern recognition is the last step of fault diagnosis. Artificial neural network (ANN) has once been used in fault diagnosis and provided satisfying results [17, 18]. However with insufficient samples, the inherent deficiencies such as under-fitting and local optimal solution will become obvious issues [19]. Therefore, the application of ANN is limited. Support vector machine (SVM) is an outstanding method of pattern recognition, which is based on statistical learning theory and especially suitable for small sample cases. Additionally, SVM has better generalization ability compared to ANN, and it can guarantee the local and global optimal solution are exactly the same [20, 21]. However, SVM still cannot provide a perfect solution due to the low sparsity of the model and because the margin trade-off parameter must be estimated. Targeting these problems, a sparse probability model called relevance vector machine (RVM) is proposed by Tipping [22]. Compared to SVM, the training of RVM is carried out under Bayesian framework, thus a probabilistic interpretation of its outputs can be obtained. Moreover, the rel-evant vectors required for training are less than that of SVM. Therefore, fault diagnosis with RVM method is more efficient [23]. RVM theory was originally developed for binary-class problem. However, the fault diagnosis of diesel engine is usu-ally a multi-class problem, so a multi-class strategy for RVM is required. Generally, there are three typical methods to extend the binary RVM to multi-class problem, namely, one-against-all, one-against-one and directed acyclic graph (DAG) [24]. The DAG method is more efficient and has no unclas-sifiable regions that usually exist in other typical strategies. However, error accumulation often happens in the classifica-tion process of DAG-RVM. In other words, when classifica-tion error happens in the upper nodes, the misclassification will continue into the following nodes. To solve this problem, a separability based DAG (SDAG) method is proposed, and the SDAG-RVM is applied to the fault diagnosis of diesel engine valve train.The rest of the paper is organized as follows. Section 2 describes the theory of improved ITD and the novel SDAG method is presented for multi-class RVM in section 3. In sec-tion 4, a fault diagnosis approach based on improved ITD and SDAG-RVM is given. In section 5, the proposed approach is applied to the fault diagnosis of diesel engine valve train and compared against other conventional methods. F inally, sec-tion 6 presents the conclusion of the paper.2. Improved ITDIn the original ITD method, the baseline is obtained by using linear interpolation, but linear interpolation is not accurate enough for processing the vibration signal of diesel engine valve train. Additionally, in order to satisfy the ter-mination condition, ITD often produces a large number of pseudo components. Generally, the pseudo components have no obvious physical meaning and lead to an increase of decomposition time. Therefore, to solve these problems, an improved ITD method based on non-uniform B-spline interpolation and cumulative variance contribution rate is proposed.2.1.Non-uniform B-splineB-spline curve not only possesses the advantages of the Bezier curve, but also has good continuity and local properties [25], which can effectively guarantee the accuracy of the interpola-tion results. For any given knot set u, the B-spline curve can be expressed as a linear combination of B-spline basis functions, as given in (1):∑==p u d B u()()ini i k,(1)where d i are the control points, B i,k(u) are the B-spline basis functions, k is the order of the curve. The expression for the basis function B i,k(u) can be derived by means of a recursion formula, as given in equation (2).=≤≤=−−+−−++−++++++−{B u u u u B u u u u u B u u uu u B u ()1if 0otherwise()()()i i i i k i i k ii k i k i k i i k ,01,,11111,1(2)where u i is a no-decreasing knot vector of real num-bers. It can be seen from equation (2) that the knot vector =⋯++U u u u [,,,]n k 011 is also needed for the definition ofthe B-spline curve. For uniform B-spline, the knots are uni-formly distributed, where the influence of the actual length ofthe curve segment is not considered. Aimed at this problem,a more suitable method, called non-uniform knots parameter-ization is used in this paper.In order to make the B-spline curve pass through thedata points =⋯=−+q i m m n k (0,1,,;1)i , generally,two end points of curve and their data are set identical, andthe data points q i are made to correspond to the knot vector u k in the domain of the curve p (u ), as q i have knot point =⋯=−++u i m m n k (0,1,,;1)k 1. According to the request of interpolation at the end points, ⋯u u u ,,k 01 are set as 0, and⋯++++u u u ,,,n n n k 121 are set as 1. Finally, the knot vector can be determined by the accumulated chord length parametric method: =⋯+++⋯+++⋯⋯⎡⎣⎢⎤⎦⎥U l l L l l l L l l l l L0,,0,,,,1,,1m12123123(3)where ∑==L l i ni 1, and l i can be expressed as=−=−+−=⋯−−−l q q x x y y i m ()()1,2,i i i i i i i 11212(4)where x i and y i are the position coordinates of data point ofq i . Then the control point d i can be calculated with the knot vector, in other words, the B-spline curve can be completely specified by the knot vector.Suppose the B-spline curve p (u ) for a parameter value ∈⊂++u u u u u [,][,]t i i k n 11 requires evaluation, the corre-sponding point in the curve can be calculated by DeBoor algo-rithm [26], which is an efficient process for the calculation of equation (1).∑∑===⋯===−−−−p u d B u d B u d ()()()t j nj j k t j i ki lj l j k l t i k k 0,,(5)where==−+=⋯=−−+⋯−−+−⎪⎪⎧⎨⎩d d l a d a d l k j i k i k i l(1)1,2,;,1,,j l j j l j l j l j l 111(6)with=−−++++a u u u u j l t j l j k j l1(7)According to the different precision requirement, a reasonabledensity of knot values can be set, and then the whole B-spline curve p (u ) is obtained by equation (5).2.2. Improved ITDThe detailed improved ITD method is described as follows:Step 1:S uppose x (t ) is a composite signal, identify all its local extreme points (T k , X k ) (k = 1,2,…, M ), where M is the number of extreme points.Step 2:F or any three successive extreme points (T k , X k ), (T k+1, X k+1) and (T k+2, X k+2), the value of baseline control point L k+1 corresponding to T k+1 can be calculated by twice linear transformation as follows:=++−−−=⋯+++++⎧⎨⎩⎡⎣⎢⎤⎦⎥⎫⎬⎭L X X T T T T X X k M 12()1,2,,k k k k k k k k k 11122(8)where the second term in braces is the linear interpolation of extreme points (T k , X k ) and (T k+2, X k+2) at time T k+1. It can be noted that the subscript of L k is from 2 to M − 1. Hence, theboundaries of the data must be extended.Step 3: A pply mirror extension method [10] to the sequence of extreme points, and two additional extreme points (a local maximum and a local minimum) on both ends of the signal are obtained. Then L 0, L 1, L M and L M+1 can be calculated according to equation (8).Step 4: T he baseline L 11(t ) is obtained by using non-uniform B-spline interpolation to fit all control points L k .Step 5: S ubtract the baseline L 11(t ) from the input signal x (t )and the residue is recorded as H 11(t ).=−H t x t L t ()()()1111(9)Theoretically, H 11(t ) can be regarded as the first PRC, how-ever, for a complex signal, especially for the mechanicalvibration signal, single decomposition cannot ensure a mean-ingful PRC [27]. Therefore, the standard deviation (SD) crite-rion [9], which has been successfully used in EMD, is selected as the criterion for PRC. H 11(t ) is treated as the original signal and steps 1–5 are repeated k times until H 1k (t ) satisfies theSD criterion. H 1k (t ) is the first PRC of x (t ), and is denoted as PRC 1(t ).Step 6: T he PRC 1(t ) is then subtracted from the original signalx (t ), and a new signal u 1(t ) can be obtained. Compared to the original signal, u 1(t ) is a smoothed version, because the highest frequency oscillations have been removed.=−u t x t PRC t ()()()11(10)Step 7: T hen u 1(t ) is treated as the original signal and steps1–6 are repeated p times until cumulative variance contribution rate c is more than 0.99, where c can reflect the contribution of the already obtained PRCs to the original signal [28].∑∑=+==c t t u t Var (PRC ())Var (PRC ())Var (())i pi i p i n 11(11)Step 8: F inally, the original signal x (t ) is decomposed into the sum of p PRCs and a residual signal u p (t )∑=+=x t PRC t u t ()()()i pi p 1(12)2.3. Simulated analysisTo validate the effectiveness and efficiency of the proposed improved ITD method, the following simulated signal x (t ) is considered:ππππ=+=++++x t x t x t t t t t ()()()(1cos (20))sin(200300)2sin (600.25)122(13)where ∈t [0,1]. x 1(t ) is an AM-FM signal, x 2(t ) is a sinusoidal signal. The time domain waveform of the simulated signalis shown in figure 1. For figure 1 and the following figures,the abscissa label t /s stands for time and its unit is seconds. Figures 2 and 3 are the decomposition results of signal x (t ) by using ITD and improved ITD. In order to reduce the endeffects, mirror extension [10] is applied to the boundary forITD and improved ITD.F rom figures 2 and 3, it can be observed that PRC 1 andPRC 2 are in accordance with x 1(t ) and x 2(t ), respectively.Moreover, there are two pseudo components e 1 and e 2 and aresidual signal e 3 in figure 2, while there is no pseudo compo-nent and only a residual signal e in the decomposition result of improved ITD method in figure 3. This illustrates the effec-tiveness of using the cumulative variance contribution rate asthe decomposition termination condition in the improved ITD method. In order to further compare the two methods, correla-tion coefficients cc i and mean square errors mse i between the PRCs and their corresponding signals are calculated:=x t PRC t x t PRC t cc cov ((),())var (())var (())i i i i i (14)Figure 1. The waveform of simulated signal x (t).Figure 2. The ITD decomposition result of x (t)∑=−=Nx n PRC n mse 1[()()]i n Ni i 12(15)where n is the label of sampling point, N is the number ofsampling points. The results are presented in table 1.F rom table 1, it is clear that the PRCs obtained by the improved ITD method have more correlation and smaller error with their corresponding signals, which means that the decom-position results are more accurate. The reason for this is that the improved ITD method adopts the non-uniform B-spline interpolation instead of linear interpolation, which wouldalleviate the problem of low precision and poor smoothness caused by linear interpolation in the original ITD method.3. SDAG-RVM3.1. RVM As a supervised learning method, RVM [22, 29] begins witha series of training samples =x {}n n N 1and their corresponding target vectors =t {}n n N 1, where t stand for the class label, ∈t (0,1)n . From these training samples =x t {,}n n n N 1, we wish to learn a mapping f (x n ) for predicting the target t n . A popularand flexible form for the function f (x ) is as follows:∑=+=f x w K x x w ()(,)n N n n 10(16)where =⋯w w w w (,,)N T 11 is the weight vector, K (x,x n ) is the kernel function and w 0 is the bias. A prior distribution over thevector of model parameters is imposed to construct a Bayesiantraining criterion. RVM adopts a separable Gaussian prior,and for each weight there is a distinct hyper-parameter αi∏αα==−w P N w ()(0,)n N n n 11(17)where αααα=⋯(,,,)N 12. By applying the logistic sigmoid function σ(y ) = 1/(1+e −y ) to y (x ) and adopting the Bernoulli distribution for t x P (), the likelihood function is as follows:∏ασσ=−=−t x w x w P y y (){(;)}[1{(;)}]n Nn t n t 11n n (18)with α the posterior weight distribution conditioned on thedata cannot be obtained using Bayesian rule given byααα=w t t w w t P P P P (,)()()/()(19)where αw t P (,) denotes the weight posterior and αt P ()denotes the marginal likelihood. Thus, a Laplace’s approxi-mation procedure is used.Because αα∝w t t w w P P P (,)()(), for a fixed value of α, find the maximum a posteriori (MAP) weights w MAP is equiv-alent to finding the maximum of∑α=+−−−=⎡⎣⎤⎦()t w w w w P P t y t y A log {()()}log (1)log 112i ni i i i T 1(20)For w MAP , with y i = σ{y (x i ;w )} and ααα=⋯A diag (,,,)N 12for the current values of α. It is a penalized logistic log-likelihood function and requires iterative maximization.Therefore, the iteratively reweighed least-squares (IRLS) isused to estimate the hyper-parameter α and w i . The detailedalgorithm is given in [23]. In the process of optimization,many αi may have large values; find out the correspondingmodel weights and delete them. Then the sparse solution can be obtained, the rest of the samples with ≠w 0i are relevancevectors.Table 1. Comparison of ITD and improved ITD.MethodCorrelation coefficients Mean square errors PRC1PRC2PRC1PRC2ITD 0.97130.97910.04610.0368Improved ITD 0.99310.99090.01060.0100Figure 3. The improved ITD decomposition result of x (t ).3.2. SDAG-RVMIn DAG-RVM [24], a k -class problem can be solved by orga-nizing a tree structure with k (k − 1)/2 internal nodes and k leaf nodes; each internal node corresponds to one binary RVM. The total number of layers in the structure is k and there are i nodes in the i th layer. Suppose the expression ‘m versus n ’ represents the RVM classifier that can discriminate between class m and class n , the j th node in the i th layer node(i ,j ) could be expressed as ‘j versus (k + j − i )’. To classify an unknown sample, starting at the root node, the binary RVM corre-sponding to node(1,1) is evaluated. The node is then exited via the left edge, if the output of the RVM is zero, namely, the sample doesn’t belong to class k ; or the right edge, if the output is one, namely, the sample doesn’t belong to class 1. The next node’s binary RVM is then evaluated, and the sample could finally be classified after k − 1 decisions. The structure of DAG-RVM and its classification principle is illustrated in figure 4.From figure 4, it can be noticed that the DAG is equiva-lent to operating on a list, which is initialized with all of the class labels, and each node eliminates one class label from the list. For any node(i , j ) (i < k ; j < k ; k ∈R), the nodes which connect to node(i , j ) in the next layer are node(i + 1, j ) and node(i + 1, j + 1). Suppose that the list for node(i , j ) is {a 1, a 2,…, a k − i+1}, the lists corresponds to node(i + 1, j ) and node(i + 1, j + 1) should be {a 1, a 2,…, a k − i+2} and {a 2, a 3,…, a k − i+1}, which are obtained by eliminating the first or last elements from the list for node(i , j ). It can be found that any node could be determined by its upper nodes. Therefore, once the order of class labels in the root list for node(1,1) is fixed, the structure of DAG is determined. However, the order of the root list is selected randomly in the original DAG method. Generally, root list is from class 1 to class k , namely, {1, 2,…, k }.For k -class classification problem, there are k ! kinds of order for the root list. If improper order is selected, more classification errors will happen in upper nodes and the error accumulation phenomenon will seriously affect the DAG-RVM. To overcome this issue, the SDAG methodFigure 4.The structure of DAG-RVM and its classification principle.Figure 5.The flow chart of the proposed fault diagnosis method.which can guarantee a proper order of the root list is pre-sented in the following:Step 1: C alculate the class centers c i and variance σi for eachcondition∑==⋯=⋯∈c n x i k m n 1(1,,;1,,)i ix X m i m i(21)∑σ=−−=⋯=⋯∈n x c i k m n 11()(1,,;1,,)i i x X m i i 2m i(22)where i is condition label, k is the number of conditions, X i isthe set of samples belong to the i th condition, n i is the number of samples in the i th condition, m is the sample label.Step 2: C alculate the Mahalanobis distance d ij between any two conditionsFigure 6. Experimental set-up. (a ) Diesel engine; (b ) LMS SCADA III multi-analyzer system and a computer; (c ) 3D accelerometer attached to the first cylinder head; (d) 3D accelerometers attached to the top, center and bottom of the first cylinder block.Figure 7.Schematic diagram of fault diagnosis system.Table 2. Specifications of the WP7 diesel engine.ItemValueNumber of cylinder 6Firing sequence 1-5-3-6-2-4Rating power 220 kW Rating speed 2300 rpm Bore 108 mm Stroke130 mm Compression ratio 18:1Intake typeCharge inter-cooling Intake valve train clearance 0.3 mm Exhaust valve train clearance0.5 mmΣ==−−=⋅⋅⋅=⋅⋅⋅−d d cc cci k j k ()()(1,,;1,,)ij ji i j T ij i j 1(23)where i and j are condition labels, Σij is the covariance matrix of condition i and j .Step 3: I nitialize the candidate condition set S with all condi-tion labels.Step 4: F ind the maximum d mn from all d ij , then compare σm with σn , the condition label corresponding to the smaller variance is placed in the beginning of theroot list, and label it as a 1, the other condition labelis placed at the end of the root list, and label it as a k . Then remove a 1 and a k from S .Step 5: F ind the maximum Mahalanobis distance between condition a 1 and the rest of the conditions in S , and label it as a k − 1. Place a k − 1 left to a k and remove it from S .Step 6: F ind the maximum Mahalanobis distance between condition a k and the rest of the conditions in S , and label it as a 2. Place a 2 right to a 1 and remove a 2 from S .Step 7: R egard a 2 and a k-1 as a 1 and a k , and repeat steps 5–6, a 3 and a k − 2 can be obtained. Recursively, a complete root list {a 1, a 2, …, a k } can be obtained until S = ϕ,where ∈⋯a k {1,2,,}i , i = 1, 2,…, k .After establishing the root list, the structure of SDAG-RVMis determined. More separable classes will be separated at theupper nodes with this structure. Therefore, the error accumu-lation phenomenon can be alleviated.4. The proposed fault diagnosis approach based onimproved ITD and SDAG-RVM The fault diagnosis approach for diesel engine valve trainbased on improved ITD and SDAG-RVM is given as follows:Step 1: C ollect the vibration signals of diesel engine valvetrain in normal and fault conditions and divide theminto two subsets: the training samples and testing samples.Step 2: E ach sample is decomposed into a series of PRCs byimproved ITD method.Step 3: E stablish AR model for each PRC as follows: ∑=−−+=t a t k e t PRC ()PRC ()()i k nik i i 1(24)Table 3. Six work conditions of diesel engine valve train.Work case Intake valve train clearance (mm)Exhaust valve train clearance (mm)Condition10.200.40Tight clearance20.250.45Slightly tight clearance 30.300.50Normal40.350.55Slightly excessive clearance 50.400.60Excessive clearance60.400.60Excessive clearance with bent valve tappetFigure 8. The vibration signals of the diesel engine valve train in normal condition.Figure 9. The vibration signals of the diesel engine valve train in tight clearance condition.where model order n is decided by the most commonly used approach Akaike Information Criterion (AIC) [30], a ik is the AR coefficient and e i (t ) is a Gaussian white noise series with zero mean and variance σi 2. Since the first several a ik contain the major characteristics of dynamic system and the remnant variance σi 2 is closely related to its output characteristics [8],the first several AR coefficients a ik and remnant variance σi 2 of all PRCs are chosen as fault feature vectors.Step 4: C onstruct a multi-class RVM by using SDAG method.Step 5: T he fault features of training samples are used to trainSDAG-RVM.Figure 13.The vibration signals of the diesel engine valve train in excessive clearance with bent valve tappet condition.Figure 10. The vibration signals of the diesel engine valve train in slightly tight clearance condition.Figure 11.The vibration signals of the diesel engine valve train in slightly excessive clearance condition.Figure 12. The vibration signals of the diesel engine valve train in excessive clearance condition.Step 6: T he fault features of testing samples are fed into the trained SDAG-RVM and the working condition can be identified.The flow chart of the fault diagnosis approach is illustrated in figure 5.5. Experiment and application5.1. Experimental rig setupAll the data used in this work have been collected from an exper-imental test rig. The test rig mainly consists of a WP7 diesel engine, a dynamometer, a LMS SCADA III multi-analyzer system and a computer, the test rig and its schematic diagram are shown in figures 6 and 7, respectively. Table 2 summarizes the specifications of the WP7 diesel engine. The dynamometer was coupled to the engine, which allows maintainance of a con-stant speed and load during the tests. The 3D accelerometers were attached to the first cylinder head and the top, center and bottom of the first cylinder block. The angular encoder was used as an external clock in order to synchronize the signals with the crankshaft position. The four accelerometers and the encoderwere sampled at 25 600 samples per second. According toNyquist theorem, this sampling speed allows a maximum band-width of 12.8 kHz. Therefore, it can meet the sampling require-ment for the fault diagnosis of diesel engine. Data acquisitionwas controlled by LMS SCADA III multi-analyzer system and the collected signals were stored in the computer for furtheranalysis.5.2. Fault simulation and data acquisitionSeveral tests were performed to generate a database for the valve train in normal and five fault conditions. The spe-cific parameters of six working conditions are shown in table 3. Abnormal clearances of a valve train (larger or smaller than the clearance specified by the manufacturer) were simulated by adjusting the valve clearance adjust-ment screw of the first cylinder, and the valve tappet was artificially bent.To keep the valve train fault detection as simple as possible, reduce the crankshaft speed fluctuation, and minimize the fuel consumption; the measurement was car-ried out at a speed of 700 rpm, which corresponds to the idle speed of diesel engine. In order to find the optimalFigure 14.The improved ITD decomposition result of diesel engine valve train in excessive clearance condition.。