High-speed train transmission system fault diagnosis method based on tensor sparse representation

Abstract

A high-speed train transmission system fault diagnosis method based on tensor sparse representation is disclosed, in the method, the time domain vibration signal of the high-speed train transmission system is measured in real time, the tensor data is constructed, the time domain vibration signal is transformed into a frequency domain signal or a wavelet packet signal to construct a tensor; the tensor data of the normal operation of the high-speed train transmission system is measured as a normal sample, the Kronecker product is used to generalize to the tensor based on the K-SVD dictionary learning algorithm, and the dictionaries of each dimension of the tensor are obtained by using the normal sample as a training set; a weight tensor is generated as the distribution prior of the normal sample, after the dictionary training is completed, the training set sample is subjected to tensor sparse decomposition on the learned dictionary to obtain a core sparse tensor, the tensor sparse decomposition loss is calculated, the threshold of the abnormal state is adaptively determined from the decomposition result of the normal sample, and if the threshold is exceeded, it is determined that the high-speed train transmission system has a fault.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed train fault, and particularly relates to a high-speed train transmission system fault diagnosis method based on tensor sparse representation. BACKGROUND

[0002] With the development of high-speed railway, high-speed trains have become one of the main choices of passenger travel tools, and bear more and more important social responsibilities in railway passenger transport. In order to ensure the safe travel of the general public, the driving safety of high-speed trains has become a top priority. The transmission system of the high-speed train set, as an important part of the bogie, is composed of key components such as motors, shaft couplings, gearboxes, transmission shafts, and axle boxes, and is responsible for power transmission and driving. Once a fault occurs, it will seriously threaten the safe operation of the train.

[0003] The existing high-speed train fault diagnosis method uses sensors to collect the vibration signals of the key components of the high-speed train transmission system, uses the vibration signals for signal processing or uses intelligent diagnosis methods to explore the abnormal vibration of the high-speed train transmission system, so as to determine the type of fault.

[0004] Nowadays, most of the high-speed train transmission system monitoring uses multiple sensors. Multiple sensors can better capture global information, but the length of the multi-channel vibration signal vector data collected by multiple sensors increases sharply with the increase of the number of sensors, which leads to the increase of the algorithm operation amount to an unacceptable level. The existence of multi-channel data makes the monitoring and diagnosis method have to consider how to use multi-channel signals for data fusion to improve the accuracy of diagnosis, but the existing diagnosis methods are all in the decision layer or the feature layer for data fusion, and it is difficult to fully fuse the data in the data layer, which leads to the decrease of the diagnosis accuracy.

[0005] The above information disclosed in the background section is only used to enhance the understanding of the background of the application, and therefore can contain information that does not constitute prior art known to those of ordinary skill in the art in the country. SUMMARY

[0006] In view of the problems in the prior art, the application provides a high-speed train transmission system fault diagnosis method based on tensor sparse representation. The use of tensor data structure can reduce the computer storage space occupied by the fault diagnosis algorithm, speed up the running speed of the fault diagnosis algorithm, and improve the accuracy of fault diagnosis.

[0007] The purpose of the application is achieved by the following technical scheme. A high-speed train transmission system fault diagnosis method based on tensor sparse representation comprises:

[0008] Step one, real-time measurement of time domain vibration signals of the high-speed train transmission system to construct a tensor, wherein the time domain vibration signals are transformed into frequency domain signals or wavelet packet signals to construct a tensor;

[0009] Step two, using the data of normal operation of the high-speed train transmission system as normal samples, based on the K-SVD dictionary learning algorithm, using Kronecker product to generalize the dictionary learning algorithm to the tensor, using the normal samples as the training set to obtain the dictionary of each dimension of the training set tensor, wherein the objective function is:

[0010]

[0011] s.t. B j X j ×1D1×2D2…× N D N ,

[0012] || X j ||0=K,1≤j≤S,1≤n≤N,

[0013] wherein s.t. represents being constrained, D n is the dictionary of each dimension of the training set tensor, N is the number of dimensions of the training set tensor, X j is the core sparse tensor of the training set tensor, S is the number of training set samples, Y j represents a training set composed of tensors constructed by normal samples, B j represents the product of the core sparse tensor of the training set tensor and each dimension dictionary, F represents F norm, and K represents sparsity;

[0014] Step three, through the core sparse tensor of the training set X j The frequency of selection of the upper coordinates x, y and z generates a weight tensor as the distribution prior of the normal samples, after the dictionary training is completed, the training set samples are sparsely decomposed on the learned dictionary to obtain the core sparse tensor, wherein the Kronecker-OMP algorithm is used, and the objective function is:

[0015]

[0016] wherein λ is a regularization parameter.

[0017] Then the distribution of non-zero elements in the core sparse tensor is counted, and the frequency of each atom of the training set dictionary appearing in the entire training set decomposition is calculated, and the weight tensor calculation formula is as follows: ​

[0018]

[0019] wherein, wherein w x，y，z is a weight tensor W element value at coordinates x, y, z, k x，y，z is a core sparse tensor of the training set X the frequency of being selected at coordinates x, y, z;

[0020] Step four, calculate the tensor sparse decomposition loss to determine the threshold of the abnormal state adaptively from the decomposition loss of the normal sample tensor, the tensor sparse decomposition loss includes two parts of reconstruction error and distribution error, a and b respectively represent the proportion of reconstruction error and distribution error in the tensor decomposition loss index, the expression of reconstruction error is:

[0021]

[0022] Calculate the reconstruction error R i of each sample in the training set , get the decomposition loss set on the training set After that, calculate the mean μ and standard deviation σ of the data,

[0023]

[0024]

[0025] wherein, S is the number of training set samples, R i is the decomposition loss of each signal in the training set,

[0026] The threshold is set to μ+3σ, and it is determined that the high-speed train transmission system has a fault after exceeding the threshold.

[0027] In the high-speed train transmission system fault diagnosis method based on tensor sparse representation, step five, solve the structured multi-modal dictionary, wherein c is the total number of categories, and the tensor data input of the training set is represented as Y = Y 1, Y 2, Y 3, …, Y c ] Y i , which means that the subset belonging to the i-th category sample in the entire training set is represented as X i Y i The core sparse tensor set obtained by doing tensor sparse decomposition on the global dictionary set (D1, D2, D3), ​denotes the part of the sparse tensor obtained from the i-th sample corresponding to the j-th sub-dictionary , where the subscript denotes the sample class, and the superscript denotes the sub-dictionary class.

[0028]

[0029] c denotes the number of classes of the training set samples.

[0030] Step six, block constraint sparse enhancement, in the Kronecker-OMP algorithm, the matching degree between the dictionary atom and the signal to be decomposed is determined by correlation, the correlation between vectors is measured by inner product, and the correlation between tensors and dictionary atoms is measured by corresponding modal product as follows:

[0031]

[0032] R denotes the tensor signal in the training set.

[0033] Step seven, using tensor sparse representation classification to determine the fault class, using the Kronecker-OMP algorithm to project each mode of the test tensor onto the dictionary to obtain the core sparse tensor, then using the sub-dictionary of each class in the structured multi-modal dictionary (D1, D2, D3) and the subset of the sparse tensor X i to restore the test tensor, and finally using the minimum reconstruction error to predict the fault class of the test tensor.

[0034] In the high-speed train transmission system fault diagnosis method based on tensor sparse representation, in the first step, the time domain vibration signal is converted into a frequency domain signal through Fourier transform, and the Fourier transform is represented as:

[0035]

[0036] where f(t) is the time domain signal, F(f(t)) is the frequency domain transform result, the time domain vibration signal is converted into a frequency spectrum through Fourier transform, the channel number is N, the frequency spectrum length is L, and the multi-channel frequency spectrum forms a spectrum matrix with a size of L×N; the spectrum matrix of each channel is divided according to the frequency band, the frequency band size is l, then the single spectrum matrix divided according to the frequency band has a size of l×N, and then the spectrum matrix is stacked in the third dimension to form a tensor with a size of .

[0037] In the high-speed train transmission system fault diagnosis method based on tensor sparse representation, in the first step, the time domain vibration signal is converted to the wavelet domain through wavelet packet transform, the Reverse-biorthogonal wavelet basis is used to perform four-layer wavelet packet decomposition on the time domain vibration signal with the Reverse-biorthogonal wavelet as a base, 16 sub-bands are obtained, all the sub-bands are arranged into a matrix from low frequency to high frequency, the wavelet packet coefficient matrix can be obtained for each channel through wavelet packet decomposition, and then a plurality of matrices are stacked according to the channel number to obtain a third-order tensor.

[0038] In the high-speed train transmission system fault diagnosis method based on tensor sparse representation, in the tensor sparse decomposition loss calculation process, the termination condition of the Kronecker-OMP algorithm for tensor sparse decomposition is set to end when the decomposition residual reaches a preset value, at this time, the decomposition residual is the reconstruction error under the current coefficient.

[0039] Compared with the prior art, the application has the following advantages: the existing vector sparse representation fault diagnosis can only perform data fusion at the decision layer or the feature layer, but the multi-channel data of the multi-sensor itself has some coupling relationship, the sparse representation fault diagnosis using the tensor data structure can realize comprehensive fusion at the data layer, so that the accuracy of diagnosis is improved. The existing vector sparse representation fault diagnosis has only one dictionary. However, in the tensor sparse representation fault diagnosis, the dictionary has one in each dimension. Due to the characteristics of the tensor structure, the dictionary in each dimension is much smaller than the entire vector. For example, assuming that the size of the vector data is N 3 , and the tensor formed is N x N x N. Assuming that the number of over-complete dictionary atoms used is twice the length of the atom, the total number of dictionary atoms in the vector sparse representation is N 3 x 2N 3 , and the total number of dictionaries in the tensor sparse representation is 3 (N x 2N). In actual application, the value of N is generally large, so the tensor sparse representation can significantly reduce the total number of dictionary atoms, thereby saving computer storage space and speeding up the algorithm running time. BRIEF DESCRIPTION OF DRAWINGS

[0040] Various other advantages and benefits of the present application will become apparent to those of ordinary skill in the art, upon reading the following detailed description of the preferred embodiments. The accompanying drawings are included to provide a better understanding of the preferred embodiments, and are not to be considered as limitations of the present application. Obviously, the drawings described below are only some embodiments of the present application, and other drawings can be obtained from these drawings without creative labor for those of ordinary skill in the art. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0041] In the drawings:

[0042] Figure 1 is a tensor sparse representation schematic diagram;

[0043] Figure 2 is a tensor abnormal state monitoring flowchart;

[0044] Figure 3 is a structured multi-modal dictionary;

[0045] Figure 4 is a core sparse tensor structured representation schematic diagram;

[0046] Figure 5 is a block constraint enhancement schematic diagram;

[0047] Figure 6 is a tensor sparse representation classification flow schematic diagram;

[0048] Figure 7 is a set of 8-channel vibration signals for constructing a frequency domain tensor;

[0049] Figure 8 is a spectrum diagram of channel 1 of the original signal for constructing a frequency domain tensor;

[0050] Figure 9 is an 8-channel signal spectrum matrix;

[0051] Figure 10 is a constructed frequency domain tensor;

[0052] Figure 11 is a wavelet packet coefficient matrix of a channel 1 signal;

[0053] Figure 12 is a constructed wavelet packet tensor;

[0054] Figure 13 is a learning dictionary sparse representation process comparison;

[0055] Figure 14 is a training set coefficient distribution and fitting result;

[0056] Figure 15 is a tensor decomposition loss schematic diagram;

[0057] Figure 16 is a sub-dictionary reconstruction error of each fault type test sample;

[0058] Figure 17 is a core sparse tensor before block constraint sparse enhancement;

[0059] Figure 18 is a core sparse tensor after block constraint sparse enhancement;

[0060] Figure 19is the tensor decomposition loss before block constraint sparse enhancement;

[0061] Figure 20 is the tensor decomposition loss before block constraint sparse enhancement.

[0062] The application will be further explained below with reference to the drawings and embodiments. DETAILED DESCRIPTION

[0063] The application will be further explained below with reference to the drawings and embodiments. Figures 1 to 20 The specific embodiments of the application will be described in more detail with reference to the drawings. Although the specific embodiments of the application are shown in the drawings, it should be understood that the application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided so that the application can be more thoroughly understood and the scope of the application can be fully conveyed to those skilled in the art.

[0064] It should be noted that certain terms are used in the specification and claims to refer to certain components. Those skilled in the art will understand that the same component can be referred to by different names. The specification and claims do not distinguish components based on the difference in names, but rather on the difference in function. As used throughout the specification and claims, "comprise" or "include" is an open term, which should be interpreted as "including but not limited to". The subsequent description describes preferred embodiments of the application for the purpose of illustrating the general principles of the application, and is not intended to limit the scope of the application. The scope of the application is defined by the appended claims.

[0065] For the sake of understanding the embodiments of the application, the following will be further explained with reference to the drawings and specific embodiments, and each drawing does not constitute a limitation on the embodiments of the application.

[0066] For a better understanding, Figures 1 to 20 as shown, the high-speed train transmission system fault diagnosis method based on tensor sparse representation includes,

[0067] The application proposes a fault diagnosis method based on tensor sparse representation, and the tensor sparse representation refers to Figure 1 The method comprises the following steps:

[0068] Step 1, constructing a tensor data, transforming the measured time domain vibration signal into a frequency domain signal or a wavelet packet signal. The time domain signal can be transformed into a frequency domain signal by Fourier transform, which can be expressed as:

[0069]

[0070] where f(t) is the time domain signal, F(f(t)) is the frequency domain transform result. The time domain vibration signal is converted into frequency spectrum by Fourier transform, assuming that the number of channels is N and the length of the frequency spectrum is L, the multi-channel frequency spectrum constitutes a spectrum matrix with size LxN; the spectrum matrix of each channel is divided according to the frequency band, assuming that the size of the frequency band is l, then the size of the single spectrum matrix divided according to the frequency band is l x N, and then the spectrum matrix is stacked in the third dimension to form a tensor signal with size .

[0071] The time domain signal is converted into the wavelet domain by wavelet packet transform. For a signal with non-stationary characteristics, wavelet packet decomposition can effectively reduce the cross leakage between different frequency bands by using a wavelet basis with a compact support set, so that the distribution of information in a specific frequency range is as stable as possible, and the degree of redundancy and leakage of information is sequentially weakened. Reverse-biorthogonal is a biorthogonal wavelet that retains the partial orthogonality of orthogonal wavelets, so that the wavelet has the characteristics of short support set and linear phase. Therefore, the Reverse-biorthogonal wavelet basis is used in the patent. Four-layer wavelet packet decomposition is performed on the time domain signal based on the Reverse-biorthogonal wavelet, and a total of 16 sub-bands are obtained. Arranging all the sub-bands in the order of sub-band frequency from low frequency to high frequency to form a matrix, then each channel can obtain a wavelet packet coefficient matrix through wavelet packet decomposition, and then a three-order tensor is obtained by stacking multiple matrices according to the number of channels.

[0072] The state monitoring stage of the key components: the state monitoring stage process refers to Figure 2 .

[0073] Step 2, the K-SVD dictionary learning algorithm is extended to tensors using Kronecker product, and the normal samples are used as the training set to obtain the dictionaries of each dimension of the tensor. The objective function is:

[0074]

[0075] s.t. B j = X j ×1D1×2D2…× N D N ,

[0076] || X j ||0=K,1≤j≤S,1≤n≤N

[0077] where s.t. means subject to, D n is the dictionary of each dimension of the training set tensor, N is the number of dimensions of the training set tensor, X jS is the number of training set samples, Y j representing the training set composed of tensors constructed by normal samples, B j representing the product of the core sparse tensor of the training set tensor and each dimension dictionary, F represents the F norm, and K represents the sparsity;

[0078] Step 3, generating a weight tensor as a distribution prior of normal samples. After the dictionary training is completed, the training set samples are decomposed on the learned dictionary, and the Kronecker-OMP algorithm is used, and the objective function is:

[0079]

[0080] where λ is a regularization parameter.

[0081] Then, the distribution of non-zero elements in the core sparse tensor is counted, and the frequency of each atom of the training set dictionary appearing in the entire training set decomposition is calculated. In the calculation of the classification index, the more commonly used atom weight value on the training set should be smaller, so that the atom is selected without causing a large distribution error, and therefore the weight tensor calculation formula is as follows:

[0082]

[0083] wherein, wherein w x，y，z is the weight tensor W the element value at coordinates x, y, z, k x，y，z is the core sparse tensor of the training set X selected at coordinates x, y, z on the training set.

[0084] Step 4, calculating the tensor sparse decomposition loss to determine the threshold of the abnormal state adaptively according to the decomposition loss of the normal sample tensor. The tensor sparse decomposition loss includes two parts of reconstruction error and distribution error, and a and b represent the proportion of reconstruction error and distribution error in the tensor decomposition loss index, respectively. The expression of the reconstruction error is:

[0085]

[0086] In order to eliminate the influence of the values of a and b on the final result, in the process of calculating the tensor decomposition loss, the termination condition of the Kronecker-OMP algorithm used for tensor sparse decomposition is set to end when the decomposition residual reaches the preset value, at which time the decomposition residual is the reconstruction error under the current coefficient, which can ensure that the reconstruction error part of the test sample is the same on different dictionaries, and only the distribution error part needs to be calculated. The decomposition loss set on the training set is obtained After that, The mean μ and the standard deviation σ of the calculated data are calculated.

[0087]

[0088]

[0089] where S is the number of samples in the training set, R i is the decomposition loss of each signal in the training set.

[0090] The threshold size is set to μ + 3σ. If the threshold is exceeded, it is determined that the high-speed train transmission system has failed.

[0091] Fault classification stage:

[0092] Step 5, solve the structured multi-modal dictionary, the structured multi-modal dictionary refers to Figure 3 . Taking a third-order tensor data input as an example, a dictionary set (D1, D2, D3) needs to be learned in each dimension, and each dictionary has a structured feature, which can be represented as where is a sub-dictionary related to a class, the subscript indicates the tensor dimension to which it belongs, and the superscript indicates that the sub-dictionary corresponds to the i-th class in this dimension, and c is the total number of classes.

[0093] Let Y = [ Y 1, Y 2, Y 3, …, Y c ] represent the tensor data input of the training set, where Y i means the subset of the entire training set belonging to the i-th class of sample. It should be noted that Y i here does not represent only one sample, but the collection of all samples of the same class, and means that all elements in the set participate in the calculation. Corresponding to the training data, we represent X i Y i The core sparse tensor set obtained by doing tensor sparse decomposition on the global dictionary set (D1, D2, D3), and on this basis X i can be further represented in a structured form , which represents the part of the coefficient corresponding to the j-th class sub-dictionary in the sparse tensor obtained by the i-th class sample, the subscript indicates the sample class, and the superscript indicates the sub-dictionary class. The structured representation of the core sparse tensor refers to Figure 4 . The objective function for solving the structured dictionary is: ​

[0094]

[0095] where s.t. means subject to constraint, D n is the dictionary for each dimension, c is the number of training samples, F is the F-norm, and K is the sparsity.

[0096] Step 6, block constraint sparse enhancement, refer to Figure 5 . The structured dictionary under the tensor model is not limited to the coefficients in the tensor block composed of the c-class sub-dictionary, i.e., it will appear in the first dimension belonging to the i-th dictionary and in the second dimension belonging to the j-th dictionary. Such sparse coefficients are not calculated in the reconstruction error of any class in the classification criterion of TSRC (Tensor Sparse Representation Classification), which will increase the reconstruction error of the sample on the corresponding type dictionary, thus having a certain influence on the classification accuracy.

[0097] To solve the above problems, improvements are made on the algorithm of sparse decomposition, and additional constraints are added in the process of selecting atoms. The coefficients that do not contribute to the reconstruction error of all classes in the classification criterion are re-constrained to the tensor block composed of the sub-dictionary, which is called block constraint sparse enhancement.

[0098] In the Kronecker-OMP algorithm, the matching degree between the dictionary atom and the signal to be decomposed is determined by correlation, and the correlation between vectors is measured by inner product, and the correlation between tensors and vector dictionary atoms is measured by corresponding modal product, i.e.:

[0099]

[0100] where R represents the tensor signal in the training set.

[0101] In order to achieve the purpose of collecting the coefficients outside the sub-dictionary tensor block into the tensor block, the corresponding dictionary atom can be set to zero before calculating the correlation, so that the result is also zero when calculating the correlation, so as to ensure that the atom combination will not be selected in the process of selecting the most relevant dictionary atom.

[0102] Step 7, use tensor sparse representation classification to determine the fault category, refer to the process of tensor sparse representation classification Figure 6 . Use the Kronecker-OMP algorithm in step 6. Project each mode of the test tensor onto the dictionary to obtain the core sparse tensor, and then use the sub-dictionary of each category in the structured multi-modal dictionary (D1, D2, D3) and the sparse tensor X i to restore the test tensor; finally, use the minimum reconstruction error to predict the fault category of the test tensor.

[0103] Specific example:

[0104] Example 1, corresponding to step 1, constructs the tensor data. First, the frequency domain tensor is constructed, and the specific steps include: the time domain signal is converted into the frequency spectrum by Fourier transform, and the multi-channel frequency spectrum constitutes the frequency spectrum matrix; according to the length of the frequency spectrum sequence, a suitable number of frequency bands is selected, and the frequency spectrum matrix is divided into several frequency band matrix blocks; finally, the segmented several frequency band matrices are arranged in a new dimension according to the frequency band order to form the frequency domain tensor. In the process of tensor construction, although there are segmentation and rearrangement operations, due to the orthogonal characteristics of the Fourier transform basis, each spectrum line is independent of each other, and there is no continuity in the sequence, so this construction process will not cause loss of information, and still can contain all the information of the original frequency spectrum. Take a group of 8-channel vibration signals as an example to demonstrate the above tensor construction process, the sampling frequency of the signal is 20480 Hz, and the time domain waveform of each channel is as shown in Figure 7 .

[0105] For each channel, 1s of signal is intercepted each time, and 20480 points of signal are used to construct a frequency domain tensor sample. The 8-channel signal constitutes a 20480x8 matrix. The signal of channel 1 is subjected to fast Fourier transform, and the spectrum data points of the positive frequency part are taken, as shown in Figure 8 , which is a 10240x1 vector; after the above transformation process is performed on all channel signals, the matrix is arranged according to the number of channels to form a 10240x8 matrix, as shown in Figure 9 ; finally, in order to ensure the relative balance of the length of the tensor in each dimension, the spectrum is further divided into frequency bands, 80 points of spectrum are intercepted each time, the multi-channel frequency spectrum matrix is divided into 80x8 blocks, and then arranged in the third dimension in turn to finally form the 80x128x8 tensor as shown in Figure 10 .

[0106] The wavelet packet tensor is constructed, and the 8-channel vibration signal in the frequency domain tensor is used as the original data. 0.2 seconds of signal is taken, i.e. a 4096x8 matrix is used to construct the wavelet packet tensor. The signal of channel 1 is subjected to four-layer wavelet packet decomposition using Reverse-biorthogonal wavelet as the basis, and a total of 16 subbands are obtained. Arranging the matrix according to the subband frequency from low frequency to high frequency, each channel obtains a 262x16 wavelet packet coefficient matrix through wavelet packet decomposition, and the wavelet packet coefficient matrix of channel 1 is as shown in Figure 11 , the horizontal and vertical coordinates represent the number of subbands and the subband coefficient sequence respectively. The remaining seven channels of the original data are also processed in the same manner, and a matrix is generated from the data of each channel. Finally, as shown in Figure 12 , a plurality of matrices are stacked according to the number of channels to obtain a three-order tensor with a size of 262x16x8.

[0107] Example 2, corresponding to Step 2, verifies the performance of the multi-modal dictionary learning algorithm with the Cincinnati IMS multi-channel vibration signal dataset, and the representation ability of the dictionary to the original tensor signal is reflected by the convergence of the residual error, i.e. the reconstruction error of the current coefficient in the sparse decomposition process. Figure 13 The convergence of the residual error when performing tensor sparse representation with the learned dictionary and the fixed dictionary is compared, including the discrete cosine transform dictionary, the wavelet dictionary, among which the Daubechies, Coiflets, Symlets three wavelets are selected to construct. The multi-modal dictionary learning algorithm randomly selects 100 samples from the first 5% of the full life data as the training set. In terms of the reconstruction effect of the dictionary, the learned dictionary converges faster than the random dictionary, in other words, the learned dictionary can obtain a better representation of the original signal with fewer atoms. From the convergence trend of the learned dictionary, it can be seen that the energy of the original signal is more concentrated on the first few coefficients of the core sparse tensor, which effectively shows that the dictionary learning algorithm has learned the essential features of the training data and has better representation ability for similar data in the training set.

[0108] Example 3, corresponding to Step 3 and Step 4, verifies the proposed tensor sparse representation abnormal state monitoring method with the Cincinnati IMS experimental dataset. Only the health data at the beginning of the experiment is used to train the dictionary and the model, and the change of the proposed degradation index tensor decomposition loss is observed during the process of failure occurrence to bearing failure. The larger the loss, the greater the deviation of the current signal features compared with the normal signal, so as to verify the effect of the loss for monitoring the entire process from normal to failure of the bearing.

[0109] The experiment runs continuously from the healthy state to the bearing failure without disassembly, and the data is collected every certain time interval for one second. Four bearings are installed on one shaft. Each sample has a length of 1024 points, a total of eight channels, and the original state of the sample is a 1024x8 matrix. The vibration signal of each channel is subjected to 5-layer wavelet packet transform, and 32 wavelet packet subbands are obtained at the last layer. Through the tensor construction method, it is converted into a 38x32x8 tensor as the input of the model. The first 10% of the full life data is randomly selected for training, and the number of training samples is 100. The test samples are equally spaced from the entire dataset according to the standard of one per second, and are arranged in order. Finally, a total of 4312 test samples are obtained.

[0110] The ability of the proposed tensor decomposition loss to indicate the severity of fault development is verified by experiment. First, the multi-modal dictionary learning and weight tensor calculation are completed on the training set, and then the tensor decomposition loss distribution of the model on the training set is calculated. The results are shown in Figure 14 The fitted Gaussian distribution and the corresponding threshold value are obtained based on the adaptive threshold calculation process.

[0111] Finally, the test sample is input into the model, and the core sparse tensor of the test sample is calculated after the tensor sparse representation, and the tensor decomposition loss is calculated as shown in Figure 15 The red dashed line represents the adaptive threshold calculated according to the decomposition result of the training set. The tensor decomposition loss is basically stable before 25 days, obviously increases from 25 days to about 28 days, exceeds the adaptive threshold at the 26th day and continuously remains above the threshold, and then increases again after a period of stable state to about 34 days. According to the analysis of some scholars on the Cincinnati data set, bearings 3 and 4 have early weak faults before 30 days. Therefore, it can be shown that the proposed tensor decomposition loss can reflect the development process of bearing faults, and can effectively detect the occurrence of early faults. The adaptive threshold can effectively indicate the occurrence of faults and timely alarm.

[0112] Example 4, corresponding to steps 5, 6 and 7. The proposed tensor sparse representation classification method is verified by using high-speed rail traction motor experimental data. A total of eight fault combinations are used for the drive end and non-drive end bearings of the motor. Different positions and different fault degrees are combined for the experiment. Each group is tested at 1804, 2606, 4100 and 4712 r / min. The collected signal has 10 channels. The frequency domain tensor is constructed. Each tensor sample is truncated to 1s in time domain signal time length, 25600 points, and the frequency resolution is 1Hz after Fourier transform. At a speed of 2606 r / min, the power frequency is 43.4Hz, the frequency spectrum below 1600Hz is truncated, and 40 frequency bands are divided. Finally, the input tensor sample size is 40x40x10. The structured multi-modal dictionary learning parameters include sub-dictionary size 40x25, 40x25, 10x6. Eight sub-dictionaries corresponding to eight fault types are arranged to form a dictionary with a size of 40x200, 40x200, 10x48. The sparsity K=100.

[0113] After the structured multi-modal dictionary training is completed, the test sample is input into the tensor sparse representation classification process, and the reconstruction error of the test sample in each sub-dictionary is calculated, Figure 16 The reconstruction error of the randomly selected fault sample in the test sample set of fault numbers 1-8 is sequentially shown. In each fault condition, the reconstruction error of one type of sub-dictionary is obviously lower than that of the other types, and the lowest reconstruction error of the type can correctly indicate the fault type to which the sample belongs. It is shown that the structured multi-modal dictionary learning algorithm can effectively learn fault-related atoms in each sub-dictionary, and the dictionary has a significant structured feature.

[0114] On the basis of the above results, the influence of adding block constraint sparse enhancement and not adding on the core sparse tensor and the reconstruction error of the sub-dictionary is further compared. When the block constraint sparse enhancement strategy is not added, the core sparse tensor of the test sample is as shown inFigure 17 As shown in FIG. 6, the coefficients are widely distributed in each interval on the structured multi-modal dictionary, and the coefficients scattered in the part other than the diagonal block do not contribute to the reconstruction error of all sub-dictionaries. In this case, although the reconstruction error of each sub-dictionary can also achieve correct classification, the reconstruction error of the correct class is not much different from that of the wrong class. After adding the block constraint sparse enhancement strategy, as shown in FIG. 7, the coefficients of the core sparse tensor of the test sample are all converged into the diagonal sub-dictionary block, and it can be found that the absolute value of the coefficients on the sub-dictionary block corresponding to the fault type is significantly greater than that on other sub-dictionary blocks. At this time, the reconstruction error is as shown in FIG. 8. Figure 18 As shown in FIG. 6, the coefficients are widely distributed in each interval on the structured multi-modal dictionary, and the coefficients scattered in the part other than the diagonal block do not contribute to the reconstruction error of all sub-dictionaries. In this case, although the reconstruction error of each sub-dictionary can also achieve correct classification, the reconstruction error of the correct class is not much different from that of the wrong class. After adding the block constraint sparse enhancement strategy, as shown in FIG. 7, the coefficients of the core sparse tensor of the test sample are all converged into the diagonal sub-dictionary block, and it can be found that the absolute value of the coefficients on the sub-dictionary block corresponding to the fault type is significantly greater than that on other sub-dictionary blocks. At this time, the reconstruction error is as shown in FIG. 8. Figure 19 As shown in FIG. 6, the coefficients are widely distributed in each interval on the structured multi-modal dictionary, and the coefficients scattered in the part other than the diagonal block do not contribute to the reconstruction error of all sub-dictionaries. In this case, although the reconstruction error of each sub-dictionary can also achieve correct classification, the reconstruction error of the correct class is not much different from that of the wrong class. After adding the block constraint sparse enhancement strategy, as shown in FIG. 7, the coefficients of the core sparse tensor of the test sample are all converged into the diagonal sub-dictionary block, and it can be found that the absolute value of the coefficients on the sub-dictionary block corresponding to the fault type is significantly greater than that on other sub-dictionary blocks. At this time, the reconstruction error is as shown in FIG. 8. Figure 20 As shown in FIG. 6, the coefficients are widely distributed in each interval on the structured multi-modal dictionary, and the coefficients scattered in the part other than the diagonal block do not contribute to the reconstruction error of all sub-dictionaries. In this case, although the reconstruction error of each sub-dictionary can also achieve correct classification, the reconstruction error of the correct class is not much different from that of the wrong class. After adding the block constraint sparse enhancement strategy, as shown in FIG. 7, the coefficients of the core sparse tensor of the test sample are all converged into the diagonal sub-dictionary block, and it can be found that the absolute value of the coefficients on the sub-dictionary block corresponding to the fault type is significantly greater than that on other sub-dictionary blocks. At this time, the reconstruction error is as shown in FIG. 8.

[0115] Although the embodiments of the present application are described above with reference to the drawings, the present application is not limited to the above-described specific embodiments and application fields, and the above-described specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of the present application and without departing from the scope protected by the claims of the present application, which all belong to the protection of the present application.

Claims

1. A method for fault diagnosis of a high-speed train drive system based on tensor sparse representation, characterized in that, It comprises the following steps, Step one, real-time measurement of high-speed train transmission system time domain vibration signal to construct tensor, wherein the time domain vibration signal is transformed into frequency domain signal or wavelet packet signal to construct tensor; Step two, using the data of high-speed train transmission system normal operation as normal sample, based on K-SVD dictionary learning algorithm, using Kronecker product to generalize the dictionary learning algorithm to tensor, using normal sample as training set to obtain the dictionary of each dimension of training set tensor, wherein the objective function is: ， where s.t. means subject to, is the number of dimensions of the training set tensor, is the number of dimensions of the training set tensor, is the core sparse tensor of the training set tensor, is the number of training set samples, represents the training set consisting of tensors constructed from normal samples, represents the product of the core sparse tensor of the training set tensor and each dimension dictionary, F represents the F norm, and K represents the sparsity. Step three, core sparse tensor of training set Upper coordinates The frequency of being selected generates a weight tensor as the distribution prior of normal samples. After the dictionary training is completed, the training set samples are decomposed into core sparse tensors on the learned dictionary. The Kronecker-OMP algorithm is used, and the objective function is: ， Wherein, λ is the regularization parameter; Then the distribution of non-zero elements in the core sparse tensor is counted, the frequency of each atom of the training set dictionary appearing in the whole training set decomposition is calculated, and the weight tensor calculation formula is as follows: ， wherein, wherein is a weight tensor at coordinates has an element value, is a core sparse tensor of the training set is the frequency that the coordinates are selected. Step four, calculate the tensor sparse decomposition loss to determine the threshold of abnormal state adaptively according to the decomposition loss of normal sample tensor, the tensor sparse decomposition loss includes two parts of reconstruction error and distribution error, and respectively represent the proportion of reconstruction error and distribution error in the tensor decomposition loss index, the expression of reconstruction error is: , is a core sparse tensor of the training set tensor, represents a training set consisting of tensors constructed from normal samples, Calculate the reconstruction error for each sample in the training set. This yields the set of decomposition losses on the training set. After that, The mean of the calculated data and standard deviation , ， ， wherein, is the number of training set samples, is the reconstruction error of each sample in the training set, The threshold is set to , and if the threshold is exceeded, it is determined that the high-speed train transmission system has a fault. 2.The tensor sparse representation based fault diagnosis method of high-speed train transmission system according to claim 1, wherein, Step five, solving structured multi-modal dictionary, where c is the total number of classes, to denote the tensor data input of the training set, where denotes the subset of the entire training set belonging to the i-th class sample, to denote the global dictionary set , the core sparse tensor set obtained by tensor sparse decomposition on the global dictionary set , the part of the coefficient corresponding to the j-th class sub-dictionary , , of the sparse tensor obtained by the i-th class sample, the subscript indicates the sample class, and the superscript indicates the sub-dictionary class, and the objective function for solving the structured dictionary is: ， c denotes the number of classes of the training set samples, denotes the part of the coefficients in the sparse tensor obtained from the i-th class of samples corresponding to the i-th sub-dictionary ​ Step six, block constraint sparse enhancement, in the Kronecker-OMP algorithm, the matching degree between dictionary atom and signal to be decomposed is determined by correlation, the correlation between vectors is measured by inner product, and the correlation between tensor and dictionary atom is measured by modal product as follows: ， representing a tensor signal in the training set, is the Nth dictionary atom; Step seven, the determination of the fault category using tensor sparse representation classification, using the Kronecker-OMP algorithm to project each mode of the test tensor onto the dictionary to obtain a core sparse tensor, and then using the structured multi-modal dictionary of each category in the sub-dictionary and sparse tensor restore the test tensor; finally, the fault category of the test tensor is predicted by using the minimum reconstruction error.

3. The tensor sparse representation based fault diagnosis method of high-speed train transmission system according to claim 1, wherein, In the first step, the time domain vibration signal is transformed into frequency domain signal by Fourier transform, and the Fourier transform is represented as: ， wherein is a time domain signal, is a frequency domain transform result, the time domain vibration signal is converted into a frequency spectrum through Fourier transform, the number of channels is N, the length of the frequency spectrum is L, and the multi-channel frequency spectrum is composed of a size of is a spectrum matrix; the spectrum matrix of each channel is divided according to a frequency band, the size of the frequency band is l, and then the size of the single spectrum matrix divided according to the frequency band is , and then the spectrum matrix is stacked in the third dimension to form a tensor with a size of .

4. The tensor sparse representation based fault diagnosis method of high-speed train transmission system according to claim 1, wherein, In the first step, the time domain vibration signal is converted to wavelet domain by wavelet packet transform, and the Reverse-biorthogonal wavelet basis is used to do four-layer wavelet packet decomposition of the time domain vibration signal with Reverse-biorthogonal wavelet as the base, 16 subbands are obtained, all subbands are arranged into a matrix according to the subband frequency from low frequency to high frequency, each channel can obtain a wavelet packet coefficient matrix through wavelet packet decomposition, and then a plurality of matrices are stacked according to the number of channels to obtain a three-order tensor.

5. The tensor sparse representation based fault diagnosis method of high-speed train transmission system according to claim 1, wherein, In the loss calculation process of tensor sparse decomposition, the termination condition of Kronecker-OMP algorithm for tensor sparse decomposition is set to end when the decomposition residual reaches the preset value, at this time the decomposition residual is the reconstruction error under the current coefficient.

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