CN110765965B - Quick dictionary learning algorithm for sparse representation of mechanical vibration signals - Google Patents
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Abstract
The invention belongs to the technical field of mechanical vibration signal processing. In order to solve the problem of long dictionary training time in a K-SVD algorithm, the invention discloses a quick dictionary learning algorithm for sparse representation of mechanical vibration signals, which specifically comprises the following steps: step S1, selecting a training sample to determine an initial dictionary and determining the number of atoms ml of a plurality of adjacent samples with optimal time sequence; step S2, adopting a Synchronous Orthogonal Matching Pursuit (SOMP) method to carry out atomic synchronous sparse coding on a plurality of adjacent columns of samples in a training sample time sequence, and obtaining a sparse coefficient matrix A; s3, fixing a sparse coefficient matrix subjected to synchronous sparse coding, and carrying out dictionary updating by adopting a least square method (SGK); and S4, repeating the step S2 and the step S3 until the iteration stop condition is met, and completing dictionary training to obtain a learning dictionary. The dictionary learning algorithm can greatly and effectively improve the dictionary training rate under the condition of guaranteeing the compression and reconstruction performances of the vibration signals.
Description
Technical Field
The invention belongs to the technical field of mechanical vibration signal processing, and particularly relates to a rapid dictionary learning algorithm for sparse representation of mechanical vibration signals.
Background
When the sensor based on the traditional Nyquist sampling theorem is used for carrying out real-time state monitoring and fault diagnosis analysis on mechanical equipment by collecting mechanical vibration signals, the sampling frequency is twice higher than the highest frequency of the vibration signals, so that the mechanical vibration signals can be accurately collected. With the rapid development of modern industrial technology, the frequency band of the vibration signal of modern mechanical equipment is wider and wider, and mass data can be brought when the signal is acquired by adopting Ness specific theory for increasingly large-scale, integrated and intelligent mechanical equipment, and particularly in the aspect of real-time monitoring of remote equipment, the real-time transmission and synchronous storage of the data become engineering technical problems to be solved urgently.
The compressed sensing theory proposed in recent years better solves the problems. The compressed sensing theory breaks the limit of the traditional sampling theorem, synchronously performs data sampling and compression, and provides a key technical theory for realizing low-speed signal sampling. Wherein, sparse representation is a precondition for compressed sensing, and directly determines the merits of compression reconstruction performance.
At present, more and more scholars begin to research and obtain a certain result based on the compression measurement reconstruction of the vibration signal based on the orthogonal basis, the fixed dictionary and the sparse representation of the learning dictionary, for example, the compression measurement reconstruction is performed on the vibration signal by using a series of orthogonal basis or fixed dictionary with rapid construction, simple structure, low sparse representation performance, such as wavelet basis, fourier basis and the like, but the compression reconstruction performance is low. By combining with the structural characteristics of the mechanical vibration signals, some researches learn from training sample signals through dictionary learning algorithms to obtain an overcomplete dictionary, so that sparse representation performance is improved, and compression reconstruction performance is further improved, and the details are shown in LEEs S J, LUAN J, CHOUP H.ECG Signal reconstruction from undersamplete measurement using a trained overcomplete dictionary [ J ]. Contemporary Engineering Scgineering Science,2014,7 (29): 162-1632. Wherein Guo Junfeng, shi, wei Xingchun, li Haiyan, wang Zhiming et al propose a compression reconstruction performance of a signal is greatly improved by performing sparse representation on a vibration signal by adopting a K-SVD dictionary learning algorithm and improving the sparsity of the vibration signal by adjusting dictionary parameters, so that the sparse representation performance of the vibration signal is effectively improved by means of the K-SVD dictionary learning algorithm, the compression reconstruction performance of the vibration signal is further improved, and a sparse representation vibration signal compression measurement reconstruction method [ J ] based on the K-SVD dictionary learning algorithm is detailed in mechanical engineering theory, 2018, 54 (07): 97-106.
However, in the dictionary training process in the K-SVD algorithm, the sparse coding stage uses OMP algorithm to perform column-by-column sparse coding on training sample atoms, and the dictionary updating stage uses SVD decomposition algorithm to update dictionary atoms, so that the whole dictionary training time is long, and a certain limitation still exists when the mechanical equipment is monitored in real time by using the method of compression measurement reconstruction, so that the dictionary training time needs to be optimally shortened.
Disclosure of Invention
In order to solve the problem of long dictionary training time in a K-SVD algorithm, the invention provides a quick dictionary learning algorithm for sparse representation of mechanical vibration signals, which specifically comprises the following steps:
step S1, selecting a training sample to determine an initial dictionary and determining the number of atoms ml of a plurality of adjacent samples with optimal time sequence;
step S2, adopting a Synchronous Orthogonal Matching Pursuit (SOMP) method to carry out atomic synchronous sparse coding on a plurality of adjacent columns of samples in a training sample time sequence, and obtaining a sparse coefficient matrix A;
s3, fixing a sparse coefficient matrix subjected to synchronous sparse coding, and carrying out dictionary updating by adopting a least square method (SGK);
and S4, repeating the step S2 and the step S3 until the iteration stop condition is met, and completing dictionary training to obtain a learning dictionary.
Preferably, in the step S1, an existing mechanical vibration signal is selected as a training sample, and K column atoms of the training sample are selected as an initial dictionary by random selection.
Preferably, in the step S1, the specific step of determining the number of atoms ml of the samples of the adjacent columns with the optimal time sequence is as follows:
step T1, determining the range of the atomic numbers ml of the samples of the adjacent multiple columns of the optimal time sequence and measuring and reconstructing the optimal compression rate by adopting the overcomplete dictionary training time under the atomic numbers of the samples of the adjacent multiple columns of the different time sequence and the compression reconstruction errors of test signals under different compression rates;
and step T2, determining the atom number ml of the adjacent multiple columns of samples with the optimal time sequence according to the linear combination atom number L when the signals to be decomposed are diluted and expressed.
Preferably, in the step S2, the specific process of synchronous sparse coding of training samples by using a Synchronous Orthogonal Matching Pursuit (SOMP) method is as follows:
step S21, constructing training samples as follows by dictionary atom length n and optimal time sequence adjacent multiple columns of sample atom number mlN1＝N/m1,s i ∈R n×m1 Synchronous sparse coding time sequence adjacent multi-column training sample s i ；
Step S22, determining the iteration times k, r t ＝s i ,t＝1；
Step S23, according to each iterationSelecting the best dictionary atom d t ；
Step S24, Λ t All best dictionary atom sets selected for each iteration, i.e., Λ t ＝Λ t-1 ∪d t ；
Step S25, solving S according to the least square method i Optimal sparse coefficient of t th iteration
Step S26, updating residual error
Step S27, t=t+1, repeating the steps S23 to S26 until t is greater than k, stopping iteration, and obtaining S i Is a sparse coefficient matrix a of (2) i ；
Step S28, all training samples are subjected to synchronous sparse coding, and a sparse coefficient matrix A= [ A ] is obtained 1 ,A 2 ,…,A N1 ]。
Preferably, in the step S4, it is first determined whether all the dictionary atom d is updated, and when all the dictionary atom d is updated, it is further determined whether the number of dictionary training times is reached.
Further preferably, if it is judged that the dictionary atom d is not completely updated, step S3 is repeated to fixedly update the dictionary atomPost-deriving residual term->And its related coefficient matrix>And utilizeUpdate dictionary atom->
Further preferably, if it is determined that the number of dictionary training times is not reached, step S2 and step S3 are repeated until the predetermined number of dictionary training times is reached, and training is stopped.
The dictionary learning algorithm is used for the compressed sensing process of the mechanical vibration signal, and has the following beneficial technical effects:
the dictionary learning algorithm of the invention firstly determines the optimal synchronous sparse coding atomic number, then adopts a Synchronous Orthogonal Matching Pursuit (SOMP) method to synchronously sparse code training samples, and finally utilizes a least square method (SGK) to update dictionary atoms. Therefore, starting from the number of single sparse coding training sample atoms, the sequential adjacent multi-column sample atoms in the training samples are subjected to synchronous sparse coding by adopting a Synchronous Orthogonal Matching Pursuit (SOMP), and the reasonable sequential adjacent multi-column sample atoms are selected, so that the sparse coding part in the dictionary learning algorithm is improved, and meanwhile, the dictionary atoms are updated by adopting a least square method (SGK), so that the dictionary updating part in the dictionary learning algorithm is improved again, and the dictionary training rate is greatly improved under the condition of guaranteeing the compression reconstruction performance of vibration signals.
Drawings
FIG. 1 is a schematic flow chart of a dictionary learning algorithm for sparse representation of mechanical vibration signals in the invention;
FIG. 2 is a flow chart of determining the number of sample atoms in adjacent columns of the optimal timing sequence according to the present invention;
FIG. 3 is a graph of the number of sample atoms in adjacent columns of different sequences versus dictionary training time;
FIG. 4 is a graph of atomic numbers of adjacent columns of samples at different timings as a function of compression ratio and relative reconstruction error;
FIG. 5 is a graph showing the relationship between the number of linearly combined atoms and the training time of a dictionary when different signals to be decomposed are sparsely represented under the condition of a plurality of adjacent columns of sample atoms in different sequences;
FIG. 6 is a graph showing the relationship between the number of linearly combined atoms and relative reconstruction errors for sparse representation of different signals to be decomposed for a plurality of adjacent columns of sample atoms at different timings;
fig. 7 (a) is a vibration signal diagram of an original signal, fig. 7 (b) is a vibration signal diagram obtained in the example, fig. 7 (c) is a vibration signal diagram obtained in comparative example 1, and fig. 7 (d) is a vibration signal diagram obtained in comparative example 2;
FIG. 8 is a graph of the number of dictionary training iterations versus dictionary training time for different dictionary learning algorithms.
Detailed Description
Referring to fig. 1, when the method of the invention is used for dictionary training of sparse representation of mechanical vibration signals, the method specifically comprises the following steps:
step S1, selecting a training sample, determining an initial dictionary and determining the number of atoms ml of a plurality of adjacent columns of samples with optimal time sequence.
Wherein, by selecting the existing mechanical vibration signal as the training sample x= [ X ] 1 ,x 2 ,…,x N ],x i ∈R n×1 And K columns of atoms of training samples are randomly selected as an initial dictionary D= [ D ] 1 ,d 2 ,…d k ],d i ∈R n×1 。
Referring to fig. 2, the specific steps for determining the number of atoms ml of the sample in the adjacent columns with the optimal time sequence are as follows:
and step T1, determining the range of the atomic numbers of the adjacent multiple columns of samples of the optimal time sequence and measuring and reconstructing the optimal compression rate by vibration compression by adopting the overcomplete dictionary training time under the atomic numbers of the adjacent multiple columns of samples of the different time sequence and the compression reconstruction errors of test signals under different compression rates.
And step T2, determining the number of the sample atoms of the adjacent columns of the optimal time sequence according to the number of the linear combination atoms when the signals to be decomposed are diluted and expressed.
And S2, adopting a Synchronous Orthogonal Matching Pursuit (SOMP) method to carry out synchronous sparse coding on the training samples, and obtaining a sparse coefficient matrix A.
The specific process of synchronous sparse coding of training samples by adopting a Synchronous Orthogonal Matching Pursuit (SOMP) method is as follows:
step S21, constructing training samples as follows by dictionary atom length n and optimal time sequence adjacent multiple columns of sample atom number mlN1＝N/m1,s i ∈R n×m1 Synchronous sparse coding time sequence adjacent multi-column training sample s i ；
Step S22, determining the iteration times k, r t ＝s i ,t＝1；
Step S23, according to each iterationSelecting the best dictionary atom d t ；
Step S24, Λ t All best dictionary atom sets selected for each iteration, i.e., Λ t ＝Λ t-1 ∪d t ；
Step S25, solving S according to the least square method i Optimal sparse coefficient of t th iteration
Step S26, updating residual error
Step S27, t=t+1, repeating steps S23 to S26 until t is greater than k, stopping iteration, and obtaining S i Is a sparse coefficient matrix a of (2) i ；
Step S28, all training sample atoms are subjected to synchronous sparse coding, and a sparse coefficient matrix A= [ A ] is obtained 1 ,A 2 ,…A N1 ]。
And S3, fixing the sparse coefficient matrix A after synchronous sparse coding, and updating the dictionary by adopting a least square method (SGK).
Step S4, repeating the step S2 and the step S3 until the iteration stop condition is met, and completing dictionary training to obtain a learning dictionary D (t) ，
Preferably, it is first determined whether all updating of the dictionary atom d is completed, and then it is determined whether the number of dictionary training times is reached. If it is determined that the dictionary atom d is not completely updated, step S3 is repeated to fixedly update the dictionary atomPost-deriving residual term->And its related coefficient matrix>And utilize->Updating dictionary atomsIf the dictionary atom d is judged to be updated completely, judging whether the number of dictionary training times is reached. And when judging that the dictionary training times are not reached, repeating the step S2 and the step S3 until the preset dictionary training times are reached, stopping training, and obtaining the learning dictionary.
Next, the present scheme will be described in detail by way of examples and comparative examples, and the effectiveness of the dictionary learning algorithm proposed by the present scheme will be analyzed and judged. Wherein, at the same compression ratio CR, the vibration signal reconstruction performance can be evaluated by the relative reconstruction error σ, and the smaller the relative reconstruction error σ is, the better the vibration signal reconstruction performance is.
Compression Ratio (CR) is used to measure the Compression of vibration signals, the greater the CR, the higher the signal Compression ratio. The definition is as follows:where n is the original vibration signal f length and m is the compressed measurement signal y length.
The relative error is the ratio of the absolute error of the vibration signal to the original signal, which is defined as:wherein f is the original vibration signal, +.>To reconstruct the vibration signal. The smaller the relative error, the better the signal compression reconstruction performance.
The pearson correlation coefficient measures the waveform similarity of the original signal and the reconstructed signal, and is defined as:wherein r is a pearson correlation coefficient, and a value of r closer to 1 indicates a reconstructed signal +.>The more similar the original signal fwaveform.
First, an initial dictionary is determined, and learning dictionary parameters are set.
Bearing databases of university of western storage in united states are selected to verify the validity of the dictionary learning algorithm proposed by the present invention. By installing acceleration sensors on the bearing driving end and the fan end respectively, single-point faults with depths of 0.007 ', 0.014', 0.021 '(1' =2.54 cm) are arranged on the driving end bearing outer ring, the driving end bearing inner ring and the driving end bearing rolling bodies, and each fault load is 0HP and 1HP (1 HP=746W), 10 types of data shown in table 1 are obtained. Sampling frequency f z (Hz) =12 KHz, bearing rotation speed n s (r/min) =1796 r/min, vibration signal period T 0 ＝(f s ·60)/n s 。
TABLE 1
| Data | Normal | OR007@6 | OR014@6 | OR021@6 | IR007 |
| Category(s) | 1 | 2 | 3 | 4 | 5 |
| Data | IR0014 | IR0021 | B007 | B014 | B021 |
| Category(s) | 6 | 7 | 8 | 9 | 10 |
Wherein, 10 kinds of data in table 1 are Normal data (Normal), bearing outer ring data (OR), inner ring data (IR), and ball fault data (B), respectively, and the numbers after the data indicate fault depths, the numbers after the data indicate the orientations where the faults are located, for example, OR007@6 indicates that the bearing outer ring 3 o' clock direction sets a single point of fault point, and the fault depths are 0.007″.
In the present validity analysis, test data in an empty state are used, and test analysis is performed under MATLAB R2014 a. Wherein, the test operation environment is: ADFX 8300 and 8G memory of the processor 3.3GHz, a Window7-64 bit operating system, compression measurement reconstruction of all test signals by adopting a Gaussian random matrix and an orthogonal matching pursuit method, reconstruction errors, pearson correlation coefficients, dictionary training time, and 10 times of running average are obtained.
The OR007@6 signal data collected by a motor driving end 12 o' clock direction acceleration sensor are selected for experimental test,the signal is a periodic signal. The sampling points of the signals 0-121991 are expanded to 0-731964, wherein 0-62000 sampling points are dictionary training sample signals, and 620001 ～ 731964 sampling points are test signals. According to the dictionary atom length being greater than the mechanical vibration signal vibration period T 0 Dictionary atom length n=512 is determined. According to the dictionary atom length N, setting other dictionary learning parameters, wherein the dictionary atom number K=800, the sample set X atom number N=1200, the linear combination atom number L=10 and the dictionary training iteration number J=10 when the signals to be decomposed are sparsely represented. The compressed sensing test signal at least comprises a complete vibration signal period, and a signal segment with 1024 sampling points started by 640001 is used as a test signal.
Next, the optimal time sequence adjacent columns of sample atoms ml are determined.
And training an overcomplete learning dictionary by adopting a plurality of adjacent columns of sample atomic numbers ml with different time sequences, and carrying out compression measurement reconstruction on test signals under different compression ratios based on the trained overcomplete learning dictionary to obtain test results shown in fig. 3 and 4. Wherein, fig. 3 shows a graph of the number of sample atoms m1 of adjacent columns of different time sequences and dictionary training time, and fig. 4 shows a graph of the number of sample atoms of adjacent columns of different time sequences and compression ratio and relative reconstruction error.
Referring to fig. 3 and 4, when the number of atoms m1>5 of the samples in the time-sequence adjacent columns, the training time of the dictionary increases suddenly, and the compression and reconstruction errors of the test signals are larger; when the number m1 of the atoms of the samples in the time-sequence adjacent columns is 2-5, the dictionary training time is steadily reduced, and the compression reconstruction error of the test signals is smaller and similar. And determining the value range of the number of the sample atoms of the adjacent columns of time sequence to be 2-5 according to the dictionary training time and the compression reconstruction error of the test signal. Meanwhile, as shown in fig. 4, when the compression ratio is smaller than 60%, the compression reconstruction of the test vibration signal is relatively stable, so that the original test vibration signal can be better reconstructed on the premise of guaranteeing the compression performance, and the optimal effective compression ratio of the vibration compression measurement reconstruction is determined to be 60%.
Further, under the condition that the number L of the linear combination atoms and the parameters of the learning dictionary are unchanged when different signals to be decomposed are sparsely represented, an overcomplete dictionary is trained by adopting a plurality of adjacent sample atomic numbers m1 with different time sequences, and compression measurement reconstruction is carried out on test signals under the compression ratio of 60% based on the trained overcomplete dictionary, so that test results shown in fig. 5 and 6 are obtained.
Referring to fig. 5 and fig. 6, the number of atoms L of the linear combination directly affects the selection of the number m1 of the samples of adjacent columns of time sequence when the signal to be decomposed is sparsely represented. Along with the increase of the value of the linear combination atomic number L when the signal to be decomposed is sparsely represented, the dictionary training time of the adjacent multiple columns of sample atomic numbers m1 in different time sequences and the compression reconstruction performance of the test signal tend to be stable when the value of the L is larger than a certain numerical value. When m1 is 2 and the L value range is 2-10, the dictionary training time is kept stable and increased, the compression reconstruction error is kept relatively stable, and therefore the optimal time sequence adjacent multiple columns of sample atomic numbers m1 are determined to be 2.
Then, three different dictionary learning algorithms of the embodiment, the comparative example 1 and the comparative example 2 are adopted to perform sparse representation on the vibration signals to complete dictionary training, a learning dictionary is obtained, and under the compression ratio of 60%, compression measurement reconstruction is performed on the test vibration signals, so that the effectiveness of compression measurement reconstruction on the test vibration signals by adopting different dictionary learning algorithms is analyzed.
The embodiment adopts the dictionary learning algorithm provided by the invention, namely adopts a Synchronous Orthogonal Matching Pursuit (SOMP) method to carry out synchronous sparse coding on training samples, and adopts a least square method (SGK) to carry out dictionary updating; in the comparative example 1, a K-SVD dictionary learning algorithm is adopted, namely, a training sample is subjected to synchronous sparse coding by adopting an Orthogonal Matching Pursuit (OMP), and a SVD decomposition algorithm is adopted to update a dictionary; comparative example 2 training samples were subjected to synchronous sparse coding using an Orthogonal Matching Pursuit (OMP) method, and dictionary updating was performed using a least squares method (SGK). Thus, the vibration signal diagram under different working conditions shown in fig. 7 and the compression reconstruction performance of the dictionary training time and the vibration signal based on different learning dictionaries under three dictionary learning algorithms shown in table 2, namely dictionary training time, relative reconstruction error and pearson correlation coefficient are obtained. Fig. 7 (a) is an original vibration signal diagram of the test vibration signal, fig. 7 (b) is a vibration signal diagram obtained after the compression measurement reconstruction of the test vibration signal in the embodiment, fig. 7 (c) is a vibration signal diagram obtained after the compression measurement reconstruction of the test vibration signal in the comparative example 1, and fig. 7 (d) is a vibration signal diagram obtained after the compression measurement reconstruction of the test vibration signal in the comparative example 2.
TABLE 2
As can be seen from fig. 7 and table 2, compared with the original signal, the test vibration signal is finally measured and reconstructed by compression, and the compression and reconstruction performances obtained by the three are almost the same, regardless of whether the dictionary learning algorithm in the embodiment or the dictionary learning algorithm in the comparative example 1 or the comparative example 2 is adopted. Further, as can be seen from table 2, the use of the dictionary learning algorithm in the example was reduced by 57.2% compared to the use of the dictionary learning algorithm in comparative example 1, and 44.6% compared to the use of the dictionary learning algorithm in comparative example 2.
Therefore, the dictionary learning algorithm in the embodiment is adopted as the dictionary learning algorithm for sparse representation of the mechanical vibration signals, so that the dictionary training time rate can be greatly improved on the premise of guaranteeing the compression and reconstruction performances of the mechanical vibration signals, and the whole mechanical vibration signal processing efficiency is further improved.
Further, under the condition that other learning dictionary parameters are unchanged, the number of dictionary training iterations is adjusted, the dictionary learning algorithm in the embodiment is verified, compression reconstruction performance is achieved under different dictionary training iterations, and finally the data of fig. 8 and table 3 are obtained. FIG. 8 is a graph of the relationship between the number of dictionary training iterations and the dictionary training time under different dictionary learning algorithms; table 3 shows the compression reconstruction performance, i.e., relative reconstruction error and pearson correlation coefficient, corresponding to different dictionary learning algorithms for different iterations.
TABLE 3 Table 3
As can be seen from fig. 8 and table 3, the time for training the dictionary by using the algorithm of the embodiment is significantly shorter than that of the algorithm of comparative example 1 and comparative example 2, and the compression reconstruction performance of the vibration signal between the three is always almost the same. The time increment of the algorithm training dictionary of the comparison example 1 and the comparison example 2 is larger than that of the algorithm training dictionary of the embodiment along with the continuous increase of the dictionary training iteration times, namely the time of the algorithm training dictionary of the comparison example 1 and the comparison example 2 is longer and longer than that of the algorithm training dictionary of the embodiment along with the continuous increase of the dictionary training iteration times, and the efficiency of the algorithm training dictionary of the embodiment is more remarkable.
Therefore, under the condition that the compression measurement reconstruction signals of the over-complete dictionary trained by the algorithm in the embodiment are almost the same as those of the over-complete dictionary trained by the algorithm in the comparison example 1 and the comparison example 2 and keep almost similar to the waveforms of the original signals, the time for training the over-complete dictionary by the algorithm in the embodiment can be greatly reduced, so that the compression reconstruction performance can be ensured, and simultaneously, the dictionary training speed under different dictionary training iteration times can be greatly and effectively improved.
Claims (4)
1. The quick dictionary learning algorithm for sparse representation of the mechanical vibration signals is characterized by comprising the following steps of:
step S1, selecting a training sample to determine an initial dictionary and determining the number of atoms ml of a plurality of adjacent samples with optimal time sequence;
step S2, adopting a Synchronous Orthogonal Matching Pursuit (SOMP) method to carry out atomic synchronous sparse coding on a plurality of adjacent columns of samples in a training sample time sequence, and obtaining a sparse coefficient matrix A;
s3, fixing a sparse coefficient matrix subjected to synchronous sparse coding, and carrying out dictionary updating by adopting a least square method (SGK);
step S4, repeating the step S2 and the step S3 until the iteration stop condition is met, and completing dictionary training to obtain a learning dictionary;
in the step S1, the specific steps for determining the number of atoms ml of the adjacent multiple columns of samples with the optimal time sequence are as follows:
step T1, determining the range of the atomic numbers ml of the samples of the adjacent multiple columns of the optimal time sequence and measuring and reconstructing the optimal compression rate by adopting the overcomplete dictionary training time under the atomic numbers of the samples of the adjacent multiple columns of the different time sequence and the compression reconstruction errors of test signals under different compression rates;
step T2, determining the atom number ml of the adjacent multiple columns of samples with the optimal time sequence according to the linear combination atom number L when signals to be decomposed are diluted and expressed;
in the step S2, the specific process of synchronous sparse coding of training samples by using a Synchronous Orthogonal Matching Pursuit (SOMP) method is as follows:
step S21, constructing training samples as follows by dictionary atom length n and optimal time sequence adjacent multiple columns of sample atom number mls i ∈R n×m1 And synchronizing the sparse coding timing adjacent multiple columns of training samples s i ；
Step S22, determining the iteration times k, r t ＝s i ,t＝1；
Step S23, according to each iterationSelecting the best dictionary atom d t ；
Step S24, Λ t All best dictionary atom sets selected for each iteration, i.e., Λ t ＝Λ t-1 ∪d t ；
Step S25, solving S according to the least square method i Optimal sparse coefficient of t th iteration
Step S26, updating residual error
Step S27, t=t+1, repeating steps S23 to S26 until t is greater than k, stopping iteration, and obtaining S i Is a sparse coefficient matrix a of (2) i ；
Step S28, all training samples are subjected to synchronous sparse coding, and a sparse coefficient matrix A= [ A ] is obtained 1 ,A 2 ,…,A N1 ]。
2. The rapid dictionary learning algorithm according to claim 1, wherein in the step S1, an existing mechanical vibration signal is selected as a training sample, and K column atoms of the training sample are selected as an initial dictionary by random selection.
3. The rapid dictionary learning algorithm according to claim 1, wherein in the step S4, it is first judged whether all updating of the dictionary atom d is completed, and when all updating of the dictionary atom d is completed, it is further judged whether the number of dictionary training times is reached.
4. A rapid dictionary learning algorithm as claimed in claim 3, wherein if it is determined that the number of dictionary training times has not been reached, steps S2 and S3 are repeated until the predetermined number of dictionary training times has been reached, and training is stopped.
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