Adaptive noise reduction method based on double sparse dictionaries, bearing fault diagnosis method and system

Abstract

The invention discloses a noise reduction method based on double sparse dictionary self-adaption and a bearing fault diagnosis method and system. The method comprises the following steps: performing wavelet decomposition on a signal to be subjected to noise reduction to obtain a high-frequency signal and a low-frequency signal, and constructing a high-frequency matrix and a low-frequency matrix; dDTF dictionary learning based on threshold self-adaption is carried out on the high-frequency matrix and the low-frequency matrix, namely, an initial dictionary is set, learning is carried out to obtain an initial sparse coefficient matrix, and self-adaption threshold updating is carried out on the initial sparse coefficient matrix, namely, the initial sparse coefficient matrix is updated according to the sequence from large to small; selecting a sparse coefficient as a dynamic threshold value in an iteration process to update an initial sparse coefficient; determining a final threshold value to obtain a final sparse coefficient matrix, updating the dictionary again to obtain sub-signals, and finally performing inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals to obtain noise reduction signals. According to the method, wavelet decomposition and DDTF are combined to construct a double sparse mode, and the sparse representation capability of a fixed base is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal noise reduction, and in particular relates to a noise reduction method based on dual sparse dictionary adaptation, a bearing fault diagnosis method and a system. Background Art

[0002] For decades, researchers have proposed many methods to optimize the effect of bearing data denoising. Mathematical decomposition is one of the commonly used denoising methods in bearing denoising, such as empirical mode decomposition (EMD). The high-frequency amplitude modulation signal component generated by the locally damaged rolling bearing is separated as the eigenmode function by EMD decomposition, and then its envelope signal is obtained by Hilbert transform, and the envelope spectrum is calculated to extract the characteristic frequency of the rolling bearing fault. This method is used to analyze the vibration signal of the rolling bearing with inner ring damage and outer ring damage collected on the test bench. Since the EMD method has the characteristics of self-adaptation and is suitable for the decomposition of non-stationary signals, this method is applied to the analysis of the fault vibration signal of the rolling bearing. However, EMD has the problem of modal aliasing, which leads to poor denoising performance. In response to the modal aliasing problem of EMD, scholars have improved EMD, such as proposing a combination of singular value decomposition (SVD) and improved EMD and variational mode decomposition (VMD), that is, first SVD denoises the fault signal, then adds high-frequency harmonic signals according to signal characteristics and performs EMD decomposition, effectively reducing modal aliasing; for VMD, it does not add noise to IMFs but is based on the perspective of Wiener filtering, strictly requiring IMFs to be a time series of amplitude-frequency modulation with limited bandwidth, and the number of decomposition layers of VMD can be manually set. With the help of the envelope of the signal Hilbert transform, a reasonable number of decomposition layers can be set to solve the modal aliasing problem. However, VMD is difficult to handle strong human interference, and a reasonable modulus is difficult to preset, which reduces the denoising effect.

[0003] In addition to the denoising application of mathematical decomposition methods in bearing data processing, sparse representation is also widely used in this field, such as the Fourier transform method, that is, the signal is spectrally analyzed, but it lacks the ability to process local detail information when processing signal-to-noise separation, which will lead to the loss of a large number of effective signals. In order to solve this problem, researchers have developed a short-time Fourier transform denoising method, which has better local description capabilities and can more effectively retain important information in the signal. However, the time window size of the short-time Fourier transform is difficult to adapt, and the wavelet transform can solve this problem well, but when the wavelet transform is used to process more complex signals, it cannot effectively remove noise, so many ultra-wavelet transforms have been developed, such as the contourlet transform, which is a multi-scale decomposition method based on ultra-wavelets, which is particularly suitable for signals with strong directionality and smooth boundaries; the shearlet transform is a multi-scale transform similar to the ultra-wavelet transform, which adds a shearing operation to the signal during decomposition, so as to better capture the local characteristics of the signal. Bandlet transform is a multi-scale transform method for feature extraction, which decomposes the signal in different directions and uses banding technology to process each sub-band. The above methods have achieved certain results in denoising the signal.

[0004] Due to the inadaptability of fixed basis transformation, the matching degree between the parent basis and the signal is poor, which produces residual noise and reduces the denoising effect. A single fixed basis transformation is difficult to adaptively sparsely represent the signal. Therefore, many people have proposed learning basis denoising methods. Learning basis transformation is also called dictionary learning. It is a sparse representation method that relies on a certain optimization algorithm to directly extract signal features from samples to construct a sparse basis. It solves the shortcoming that the fixed basis cannot change its own structure during the sparse representation process and improves the sparse representation capability. Among them, the most typical one is KSVD, which was first proposed by Aharon in 2006. It is a sparse basis that uses singular value decomposition for multiple updates. This method can adaptively sparsely represent the signal and obtain a good denoising effect. However, this method takes too long to denoise. In order to solve this problem, many adaptive denoising methods have been proposed, such as DDTF (data-driven tight frame (DDTF). Compared with KSVD, DDTF only has one more orthogonal constraint of the dictionary, so that DDTF can complete the dictionary update by only doing one SVD, which greatly improves the running speed. In addition, the sparse representation ability of DDTF is not inferior to KSVD.

[0005] However, in order to improve the sparse representation ability of sparse bases, solving the problems of weak sparse representation ability of fixed bases and the introduction of new noise by learning genes due to structural constraints lacking human noise and low accuracy due to self-set parameters are still issues that need further research and exploration in this field. Summary of the invention

[0006] The present invention is committed to solving the technical problem of improving the noise reduction effect, and further provides a noise reduction method based on dual sparse dictionary adaptation, a bearing fault diagnosis method and a system. Among them, the technical solution of the present invention fully considers that wavelet decomposition and DDTF dictionary learning are both sparse representation categories. Therefore, the two are combined to construct a dual sparse mode. The wavelet transform can pass the structural information of human noise to DDTF in the form of wavelet sparse coefficients. DDTF can perform secondary sparse representation on the wavelet sparse coefficients and extract the residual human noise in the wavelet sparse coefficients of each scale, thereby effectively improving the sparse representation ability of the fixed basis; at the same time, wavelet denoising is fixed basis denoising, and DDTF is learning basis denoising. The advantage of the fixed basis is that it is not easy to generate new noise, but the denoising effect of the signal is not very good, and the characteristic of the learning basis is that the processing effect is good, but it is easy to generate pseudo noise. The technical solution of the present invention combines wavelet decomposition and DDTF, fully utilizing the advantages of the two algorithms, while weakening their respective defects; and further optimizes the DDTF algorithm, adopts the sparsity of the block to achieve threshold adaptation, and improves the noise reduction effect.

[0007] To this end, the present invention provides the following technical solutions:

[0008] On the one hand, the present invention provides a denoising method based on dual sparse dictionary adaptation, comprising the following steps:

[0009] Step 1: Obtain the signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer;

[0010] Step 2: Perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library F;

[0011] Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix;

[0012] Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix;

[0013] Step 4: Perform inverse transformation and matrix rearrangement inverse operation on the sub-signals of the high-frequency matrix and the low-frequency matrix obtained in step 3 to obtain a noise reduction signal.

[0014] Among them, matrix rearrangement refers to restoring the sub-signal form obtained by wavelet decomposition signal, and inverse transformation refers to restoring the form before wavelet decomposition.

[0015] Preferably, the process of DDTF dictionary learning based on threshold adaptation is as follows:

[0016] First, fix an initial dictionary to obtain the initial sparse coefficient matrix;

[0017] Selecting the maximum value in the initial sparse coefficient matrix as a dynamic threshold, then keeping the coefficients in the initial sparse coefficient matrix that are greater than or equal to the dynamic threshold unchanged, setting the coefficients that are less than the dynamic threshold to 0, and updating the sparse coefficient matrix row by row;

[0018] The correlation parameter between the data block and the dictionary based on the updated sparse coefficient matrix is ​​calculated according to the following formula;

[0019]

[0020] In the formula, is an overcomplete sample library, D and a are overcomplete sample libraries respectively. The corresponding dictionary and the sparse coefficient matrix corresponding to the current threshold; r is the residual; μ(r,D) is the correlation parameter, max(·) is the maximum value calculation function, d β is the βth row of the dictionary, and N is the total number of rows in the dictionary;

[0021] Based on the correlation parameter, it is determined whether the iteration termination condition is met. If the following formula is satisfied, the iteration termination condition is deemed to be met, and the sparse coefficient matrix corresponding to the current data block is obtained; otherwise, the next sparse coefficient in the initial sparse coefficient matrix is ​​selected in descending order as the dynamic threshold to update the initial sparse coefficient matrix, and the above iterative process is repeated until the iteration termination condition is met:

[0022]

[0023] Finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after the dictionary learning process is obtained based on the updated dictionary and the final sparse coefficient matrix.

[0024] Preferably, in step 1, the K-layer wavelet decomposition process of the signal to be denoised is performed by using an adaptive decomposition strategy based on energy contribution rate to determine the optimal number of decomposition layers;

[0025] Among them, the initial decomposition layer number of wavelet decomposition is set first, and wavelet decomposition is performed;

[0026] Then at least the energy contribution rate of the outermost layer is calculated and set as a reference value, where the outermost layer is the layer where the value of the current decomposition layer number is located;

[0027] Update the current decomposition layer number and perform wavelet decomposition, and then calculate the energy contribution rate of the outermost layer;

[0028] Determine whether the energy contribution rate of the current outermost layer is less than the current reference value. If so, output the previous decomposition layer number as the optimal decomposition layer number. Otherwise, set the current outermost layer contribution rate as the reference value, update the current decomposition layer number again, and repeat the above steps to enter the next iteration until the optimal decomposition layer number is obtained.

[0029] Preferably, the formula of the energy contribution rate is as follows:

[0030]

[0031] In the formula, They represent the energy contribution rate, high-frequency energy mean, and low-frequency energy mean of the kth layer, respectively. K is the number of decomposition layers, and E k and k They represent the mean energy and wavelet sparse coefficient of the kth layer respectively, nuk is the number of wavelet sparse coefficients, and ||·||2 represents the L2 norm.

[0032] Preferably, the initial decomposition level is set to 1, and each time the current decomposition level is updated, 1 is added to the current decomposition level.

[0033] Preferably, in the DDTF dictionary learning, sparse coefficient encoding and dictionary updating are expressed as follows:

[0034]

[0035] In the formula, a i are the i-th row in the sparse coefficient matrix before and after the update, respectively. Overcomplete sample library for signal The i-th column of; D is the dictionary before update, is the updated dictionary, I is the identity matrix, T0 is the upper limit of the number of non-zero elements, is the two-norm, || ||0 is the 0-norm, p is the number of samples, is the F-norm.

[0036] In another aspect, the present invention also provides a bearing fault diagnosis method based on dual sparse dictionary adaptation, comprising the following steps:

[0037] Step 1: Obtain the bearing vibration signal to be denoised, and perform K-layer wavelet decomposition on the bearing vibration signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer; wherein an adaptive decomposition strategy based on energy contribution rate is used to determine the optimal number of decomposition layers;

[0038] Step 2: Perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library.

[0039] Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix;

[0040] Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix;

[0041] Step 4: performing inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals of the high-frequency matrix and the low-frequency matrix to obtain a noise-reduced bearing vibration signal;

[0042] Step 5: Use the de-noised bearing vibration signal to perform bearing fault diagnosis.

[0043] In a third aspect, the present invention also provides a processing system based on the above-mentioned noise reduction method, comprising:

[0044] A wavelet decomposition module is used to obtain a signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer;

[0045] A matrix construction module is used to perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library.

[0046] A dictionary learning module, used for performing threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix;

[0047] Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix;

[0048] The inverse transformation module is used to perform inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals to obtain the noise reduction signal.

[0049] In a fourth aspect, the present invention further provides a computer device, comprising:

[0050] one or more processors;

[0051] a memory storing one or more computer programs;

[0052] The processor calls the computer program to implement:

[0053] The invention discloses a method for noise reduction based on dual sparse dictionary adaptation or a method for bearing fault diagnosis based on dual sparse dictionary adaptation.

[0054] In a fifth aspect, the present invention further provides a computer-readable storage medium storing a computer program, wherein the computer program is called by a processor to implement:

[0055] The invention discloses a method for noise reduction based on dual sparse dictionary adaptation or a method for bearing fault diagnosis based on dual sparse dictionary adaptation.

[0056] Beneficial Effects

[0057] Compared with the existing method, the advantages of the present invention are:

[0058] 1. The technical solution of the present invention combines wavelet denoising and DDTF dictionary learning. From the perspective of sparse expression, the present invention constructs a dual sparse model. The wavelet transform can transfer the structural information of human noise to DDTF in the form of wavelet sparse coefficients, making up for the lack of structural constraints in dictionary learning. DDTF can perform secondary sparse representation on the wavelet sparse coefficients and extract the residual human noise in the wavelet sparse coefficients of each scale, thereby effectively improving the sparse representation ability of the fixed basis. In addition, wavelet noise is fixed basis denoising, and DDTF is learning basis denoising. The technical solution of the present invention combines wavelet denoising and DDTF, which can take advantage of their respective advantages while weakening their respective defects and improve the denoising effect.

[0059] 2. The present invention also uses DDTF adaptive threshold processing based on different wavelet layer data signals obtained by wavelet decomposition. In DDTF, due to the sparsity of noise, when the correlation between the data block and the dictionary is relatively small, it means that the data block is difficult to be sparsely represented, and the mechanical vibration signal contained is extracted, and the rest is noise. Therefore, it is proposed to calculate the correlation and set the threshold to the value in the dictionary sparse coefficient, so as to achieve threshold adaptation. The adaptive method is to determine the threshold by calculating the correlation, which can reduce the error caused by artificially setting parameters to a certain extent and improve the denoising accuracy.

[0060] 3. The technical solution of the present invention is widely used in bearing fault diagnosis. It fully takes into account that in wavelet transform, since the energy of noise in the wavelet sparse coefficient is smaller than the energy of the mechanical vibration signal, the present invention adopts the energy contribution rate to realize the adaptation of the number of wavelet decomposition layers, that is, the energy contribution rate is used to determine the optimal number of decomposition layers, thereby improving the noise reduction effect and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flowchart of a denoising method based on dual sparse dictionary adaptation provided by an embodiment of the present invention;

[0062] Figure 2 It is the process of adaptively determining the number of wavelet decomposition layers;

[0063] Figure 3 It is a dynamic threshold adaptive determination process;

[0064] Figure 4 The comparison of denoising time-frequency diagram. (a) Simulated signal. (b) Simulated noisy signal. (c) Wavelet denoising. (d) VMD denoising. (e) DDTF denoising. (f) VMD-DDTF denoising. (g) Denoising by the proposed method. DETAILED DESCRIPTION

[0065] The present invention provides a noise reduction method based on dual sparse dictionary adaptation, a bearing fault diagnosis method and a system for realizing signal noise reduction. Among them, the sparse expression of wavelet denoising and the sparse expression of DDTF (data-driven tight frame (DDTF)) are introduced to form a dual sparse model, which effectively improves the sparse expression ability; at the same time, both DDTF and wavelet denoising are optimized to realize adaptive noise reduction. Among them, on the one hand, a dynamic threshold is introduced into the DDTF algorithm to realize threshold adaptation; on the other hand, a dynamic decomposition layer is introduced into the wavelet decomposition to obtain the optimal wavelet decomposition layer, which effectively improves the signal noise reduction effect. The noise reduction method of the present invention has outstanding performance in the application of bearing vibration signal noise reduction. It should be understood that the technical idea of ​​the present invention is also applicable to the noise reduction of other time series signals, such as electromagnetic signals and geological signals, in which low-frequency signals are expressed as useful signals and high-frequency signals are expressed as noise signals. The present invention will be further described below in conjunction with the embodiments.

[0066] Embodiment 1:

[0067] This embodiment takes the bearing vibration signal as an example. The embodiment of the present invention provides the following denoising method based on dual sparse dictionary adaptation, including the following steps:

[0068] Step 1: Obtain the signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer.

[0069] In the bearing vibration signal processing, useful signals are usually low-frequency signals or relatively stable signals, while noise signals are usually high-frequency signals. In this embodiment, the bearing vibration signal is decomposed by wavelet, and high-frequency signals and low-frequency signals are obtained after each layer of decomposition. The next layer of decomposition is to decompose the low-frequency signal obtained by the previous layer of decomposition, until the low-frequency signal obtained by the Kth layer is the low-frequency signal required in step 1; the high-frequency signal obtained by each layer of decomposition is the high-frequency signal described in step 1.

[0070] In this embodiment, it is assumed that the one-dimensional time series f(t) of the signal to be denoised is square integrable, and the wavelet transform and its inverse transform are defined as:

[0071]

[0072] In formula (3) a, b are real numbers, a is the scale parameter, which determines the frequency of the decomposed signal, b is the positioning parameter, which determines the time position function of the signal ψ is called the basis wavelet, ψ a,b (t) is called wavelet, which is composed of the scaling and translation of the base wavelet.

[0073] The preferred wavelet decomposition number in this embodiment is the optimal decomposition number determined by using an adaptive decomposition strategy based on energy contribution rate. The formula of energy contribution rate is as follows:

[0074]

[0075] In the formula, They represent the energy contribution rate of the kth layer, the high-frequency energy mean (calculated from the high-frequency signal decomposed from the kth layer, refer to Formula 5), ​​and the low-frequency energy mean (calculated from the low-frequency signal decomposed from the kth layer, refer to Formula 5), ​​K is the current decomposition layer number, E k represents the energy mean of the kth layer (calculated from the low-frequency and high-frequency signals decomposed from the kth layer), s k represents the wavelet sparse coefficient of the kth layer, nuk is the number of wavelet sparse coefficients, and ||·||2 represents the L2 norm.

[0076] Based on the above formula, Figure 2 As shown in Figure 2, the adaptive acquisition process of the optimal number of decomposition layers is:

[0077] 1. Set the initial decomposition layer number of wavelet decomposition and perform wavelet decomposition. Figure 2 , the initial decomposition level number of this embodiment is preferably set to 1.

[0078] 2. Calculate at least the energy contribution rate of the outermost layer and set it as the reference value. The outermost layer is the layer where the value of the current decomposition layer is located. For example, when the current decomposition layer is 3, the outermost layer is the 3rd layer.

[0079] 3. Update the current decomposition layer number and perform wavelet decomposition, and then calculate the energy contribution rate of the outermost layer. Figure 2 , this embodiment preferably updates the current decomposition level by adding 1 to the current decomposition level.

[0080] 4. Determine whether the energy contribution rate of the current outermost layer is less than the current reference value. If so, input the previous decomposition layer number as the optimal decomposition layer number; otherwise, set the current outermost layer contribution rate as the reference value, update the current decomposition layer number again, and repeat the above steps to enter the next iteration until the optimal decomposition layer number is obtained;

[0081] Step 2: Perform window sliding selection on high-frequency signals and low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are considered as over-complete sample libraries.

[0082] like Figure 3As shown, this embodiment uses a "window" to perform sliding processing on the group signal after K-layer decomposition. For example, there are 4096 one-dimensional data in total. Assuming that the sliding window size is set to 1X256, a sliding step size needs to be set synchronously, which is set to 1. After each sliding process, a group of 1X256 row data will be obtained. At this time, the data is transposed to obtain a 256X1 column data. When the group of data is slid until the sliding window can no longer slide, 4096 data will obtain 3841 single-row data. Each sliding is transposed, and finally a 256X3841 matrix is ​​obtained. The size of this matrix will change with the length of the decomposed data signal. Among them, there is no special requirement for the size setting of the sliding window, and it can be repeated to find the best.

[0083] Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix.

[0084] Among them, DDTF dictionary learning is a prior art content, and the present invention will not elaborate on it in detail. It should be understood that DDTF dictionary learning is performed on high-frequency matrix and low-frequency matrix data to obtain a dictionary and a sparse coefficient matrix corresponding to each column.

[0085] Sparse coding and dictionary update are expressed as follows:

[0086]

[0087] In the formula, a i are the i-th row in the sparse coefficient matrix before and after the update, respectively. Overcomplete sample library for signal The i-th column of; D is a dictionary, is the updated dictionary, I is the identity matrix, T0 is the upper limit of the number of non-zero elements, is the two-norm, || ||0 is the 0-norm, p is the number of samples, is the F-norm.

[0088] In order to improve the noise reduction effect, the present invention adopts an adaptive dynamic region, which is different from the traditional method of using a fixed hard threshold to update the sparse coefficient. Figure 3 As shown in the figure, the process of DDTF dictionary learning based on threshold adaptation is as follows:

[0089] 1. First, fix an initial dictionary, and then use DDTF dictionary learning to obtain an initial sparse coefficient matrix. This step is a prior art, and is learned according to the aforementioned sparse coding and dictionary update model, that is, referring to Formula 6, updating the sparse coefficient matrix row by row; initializing the dictionary is also a prior art, and no specific limitation is made.

[0090] 2. Select the maximum value in the initial sparse coefficient matrix as the dynamic threshold, and then keep the coefficients in the initial sparse coefficient matrix that are greater than or equal to the dynamic threshold unchanged, set the coefficients that are less than the dynamic threshold to 0, and update the sparse coefficient matrix.

[0091] 3. Update the correlation parameter between the data block and the dictionary based on the sparse coefficient matrix according to the following formula;

[0092]

[0093] In the formula, is an overcomplete sample library, D and a are the dictionary and updated sparse coefficient matrix corresponding to the column, r is the residual, μ(r,D) is the correlation parameter, max(·) is the maximum value calculation function, d β is the βth row of the dictionary, and N is the total number of rows in the dictionary;

[0094] Based on the correlation parameter, it is determined whether the iteration termination condition is met. If the following formula is satisfied, the iteration termination condition is deemed to be met, and the sparse coefficient matrix corresponding to the current data block is obtained; otherwise, the next sparse coefficient in the initial sparse coefficient matrix is ​​selected in descending order as the dynamic threshold to update the initial sparse coefficient matrix, and the above iterative process is repeated until the iteration termination condition is met:

[0095]

[0096] Finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix. That is, referring to Formula 7, the dictionary is updated column by column.

[0097] Step 4: Perform inverse transformation and matrix rearrangement inverse operation on the dictionary and sparse coefficient matrix obtained in step 3 to obtain a noise reduction signal. This step is a conventional implementation process and will not be described in detail.

[0098] Among them, inverse transformation refers to the multiplication of the dictionary and the sparse coefficient to obtain the processed overcomplete sample library, and the overcomplete sample library is restored, that is, the inverse operation of step 1 and step 2, that is, the processed signal is obtained, and the K+1 group obtains the K+1 group of processed signals, and the original signal is processed by this method by inverse wavelet transformation. That is, the technical solution of the present invention removes part of the noise through wavelet decomposition to obtain sub-signals of different levels; and then performs secondary denoising through DDTF. Therefore, matrix rearrangement and inverse transformation are to restore the sub-signals of secondary denoising to their original form to obtain noise-reduced signals.

[0099] Embodiment 2:

[0100] The embodiment of the present invention further provides a bearing fault diagnosis method based on dual sparse dictionary adaptation, comprising the following steps:

[0101] Step 1: Obtain the bearing vibration signal to be denoised, and perform K-layer wavelet decomposition on the bearing vibration signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer;

[0102] Step 2: Perform window sliding selection on high-frequency signals and low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are considered as over-complete sample libraries.

[0103] Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; wherein, the implementation process of step 3 refers to the detailed description of embodiment 1, and this embodiment also preferably adopts an adaptive decomposition layer number for wavelet denoising and preferably adopts an adaptive dynamic threshold for the DDTF algorithm.

[0104] Step 4: Perform inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals to obtain the de-noised bearing vibration signal;

[0105] Step 5: Use the noise-reduced bearing vibration signal to perform bearing fault diagnosis. How to use the noise-reduced bearing vibration signal to perform fault identification is a prior art in the art, and therefore, the present invention will not provide a detailed description of this.

[0106] In the preferred step 1 of this embodiment, an adaptive decomposition strategy based on energy contribution rate is used to determine the optimal number of decomposition layers; in step 3, an initial dictionary is set for each matrix, and then the initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order during the iteration process as dynamic thresholds to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and the final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix. The specific implementation process refers to the description of the aforementioned embodiment 1.

[0107] Example simulation:

[0108] The clean data of the simulated bearing is as follows Figure 4 As shown, Figure (a) and Figure (b) are noisy signals, (c), (d), (e), and (f) are analog signals processed by the comparative method, and (g) is the signal processed by the proposed method. Figure 4 The group of figures shows the advantages of the proposed method in denoising analog signals in the time domain.

[0109] Embodiment 3:

[0110] The present invention also provides a processing system based on the above-mentioned noise reduction method, comprising: a wavelet decomposition module, a matrix construction module, a dictionary learning module and an inverse transformation module.

[0111] The wavelet decomposition module is used to obtain the signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer; the matrix construction module is used to perform window sliding selection on the high-frequency signal and the low-frequency signal, and construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as over-complete sample libraries. The dictionary learning module is used to perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; the inverse transformation module is used to perform inverse transformation and matrix rearrangement inverse operations on the obtained sub-signals to obtain a denoised signal.

[0112] In some embodiments, the processing system is also used for bearing fault diagnosis, and further includes a diagnosis module for performing bearing fault diagnosis using the above-obtained noise-reduced bearing vibration signal.

[0113] It should be understood that the specific implementation process of each module please refer to the above method content, the present invention will not be repeated here, and the division of the above functional modules is only for example illustration. In some embodiments, some functional modules can be merged, and some functional modules can be split. Each functional module can be implemented in software or hardware or a combination of software and hardware. Among them, the hardware and software equipment includes but is not limited to general-purpose computer equipment, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0114] Embodiment 4:

[0115] The present invention further provides a computer device, comprising: one or more processors and a memory storing one or more computer programs; wherein the processor calls the computer program to implement:

[0116] The steps of a noise reduction method based on dual sparse dictionary adaptation or the steps of a bearing fault diagnosis method based on dual sparse dictionary adaptation. The specific implementation process can refer to the description of embodiment 1 and embodiment 2.

[0117] For the specific implementation process of each step, please refer to the description of the above method.

[0118] It should be understood that in the embodiments of the present invention, the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the type of device.

[0119] Embodiment 5:

[0120] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program is called by a processor to implement: steps of a noise reduction method based on dual sparse dictionary adaptation or steps of a bearing fault diagnosis method based on dual sparse dictionary adaptation. The specific implementation process may refer to the description of Embodiment 1 and Embodiment 2.

[0121] For the specific implementation process of each step, please refer to the description of the above method.

[0122] The readable storage medium is a computer-readable storage medium, which may be an internal storage unit of the software and hardware device described in any of the aforementioned embodiments, such as a hard disk or memory of a controller. The readable storage medium may also be an external storage device of the controller, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the controller. Furthermore, the readable storage medium may also include both an internal storage unit of the controller and an external storage device. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium may also be used to temporarily store data that has been output or is to be output.

[0123] Based on this understanding, the technical solution of the present invention, in essence or in other words, the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned readable storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., various media that can store program codes.

[0124] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The present application is a device for realizing the function specified in one flow or multiple flows of the flow chart and / or one or multiple blocks of the block diagram with reference to the instructions executed by the processor according to the method, device (system) and computer program product of the embodiment of the present application. These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which realizes the function specified in one flow or multiple flows of the flow chart and / or one or multiple blocks of the block diagram. These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0125] It should be emphasized that the examples described in the present invention are illustrative rather than restrictive, and therefore the present invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solution of the present invention that do not depart from the purpose and scope of the present invention, whether modified or replaced, also fall within the scope of protection of the present invention.

Claims

1. A noise reduction method based on dual sparse dictionary adaptation, characterized in that: The following steps are involved: Step 1: Obtain the signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer; Step 2: Perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library. Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix; Step 4: Perform inverse transformation and matrix rearrangement inverse operation on the sub-signals of the high-frequency matrix and the low-frequency matrix obtained in step 3 to obtain a noise reduction signal.

2. The method according to claim 1, characterized in that: The process of DDTF dictionary learning based on threshold adaptation is as follows: First, fix an initial dictionary to obtain the initial sparse coefficient matrix; Selecting the maximum value in the initial sparse coefficient matrix as a dynamic threshold, then keeping the coefficients in the initial sparse coefficient matrix that are greater than or equal to the dynamic threshold unchanged, setting the coefficients that are less than the dynamic threshold to 0, and updating the sparse coefficient matrix row by row; The correlation parameter between the data block and the dictionary based on the updated sparse coefficient matrix is ​​calculated according to the following formula; In the formula, is an overcomplete sample library, D and a are overcomplete sample libraries respectively. The corresponding dictionary and the sparse coefficient matrix corresponding to the current threshold; r is the residual; μ(r,D) is the correlation parameter, max(·) is the maximum value calculation function, d β is the βth row of the dictionary, and N is the total number of rows in the dictionary; Based on the correlation parameter, it is determined whether the iteration termination condition is met. If the following formula is satisfied, the iteration termination condition is deemed to be met, and a sparse coefficient matrix corresponding to the current data block is obtained; Otherwise, the next sparse coefficient in the initial sparse coefficient matrix is ​​selected in descending order as the dynamic threshold to update the initial sparse coefficient matrix, and the above iterative process is repeated until the iteration termination condition is met: Finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after the dictionary learning process is obtained based on the updated dictionary and the final sparse coefficient matrix.

3. The method according to claim 1, characterized in that: In step 1, the K-layer wavelet decomposition process is performed on the signal to be denoised, and an adaptive decomposition strategy based on energy contribution rate is used to determine the optimal number of decomposition layers; Among them, the initial decomposition layer number of wavelet decomposition is set first, and wavelet decomposition is performed; Then at least the energy contribution rate of the outermost layer is calculated and set as a reference value, where the outermost layer is the layer where the value of the current decomposition layer number is located; Update the current decomposition layer number and perform wavelet decomposition, and then calculate the energy contribution rate of the outermost layer; Determine whether the energy contribution rate of the current outermost layer is less than the current reference value. If so, output the previous decomposition layer number as the optimal decomposition layer number. Otherwise, set the current outermost layer contribution rate as the reference value, update the current decomposition layer number again, and repeat the above steps to enter the next iteration until the optimal decomposition layer number is obtained.

4. The method according to claim 3, characterized in that: The formula for the energy contribution rate is as follows: In the formula, They represent the energy contribution rate, high-frequency energy mean, and low-frequency energy mean of the kth layer, respectively. K is the number of decomposition layers, and E k and k They represent the mean energy and wavelet sparse coefficient of the kth layer respectively, nuk is the number of wavelet sparse coefficients, and ||·||2 represents the L2 norm.

5. The method according to claim 3, characterized in that: The initial decomposition level is set to 1, and each time the current decomposition level is updated, 1 is added to the current decomposition level.

6. The method according to claim 1, characterized in that: In the DDTF dictionary learning, sparse coefficient encoding and dictionary updating are expressed as follows: In the formula, a i are the i-th row in the sparse coefficient matrix before and after the update, respectively. Overcomplete sample library for signal The i-th column of; D is the dictionary before update, is the updated dictionary, I is the identity matrix, T0 is the upper limit of the number of non-zero elements, is the two-norm, || ||0 is the 0-norm, p is the number of samples, is the F-norm.

7. A bearing fault diagnosis method based on dual sparse dictionary adaptation, characterized in that: The following steps are involved: Step 1: Obtain the bearing vibration signal to be denoised, and perform K-layer wavelet decomposition on the bearing vibration signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer; wherein an adaptive decomposition strategy based on energy contribution rate is used to determine the optimal number of decomposition layers; Step 2: Perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library. Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix; Step 4: performing inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals of the high-frequency matrix and the low-frequency matrix to obtain a noise-reduced bearing vibration signal; Step 5: Use the de-noised bearing vibration signal to perform bearing fault diagnosis.

8. A processing system based on the method according to any one of claims 1 to 6, characterized in that: include: A wavelet decomposition module is used to obtain a signal to be denoised, and perform K-layer wavelet decomposition on the signal to be denoised to obtain K groups of high-frequency signals and 1 group of low-frequency signals, where K is a positive integer; A matrix construction module is used to perform window sliding selection on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency matrix and the low-frequency matrix are regarded as an over-complete sample library. A dictionary learning module, used for performing threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; Among them, an initial dictionary is set for each matrix respectively, and then an initial sparse coefficient matrix is ​​obtained by using DDTF dictionary learning, and sparse coefficients are selected from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated, and a final sparse coefficient matrix under the optimal threshold is obtained; finally, the dictionary is updated based on the final sparse coefficient matrix, and then the sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix; The inverse transformation module is used to perform inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals to obtain the noise reduction signal.

9. A computer device, characterized in that: include: one or more processors; a memory storing one or more computer programs; The processor calls the computer program to implement: The steps of a denoising method based on dual sparse dictionary adaptation as described in any one of claims 1 to 6 or the steps of a bearing fault diagnosis method based on dual sparse dictionary adaptation as described in claim 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored, which is called by a processor to implement: The steps of a denoising method based on dual sparse dictionary adaptation as described in any one of claims 1 to 6 or the steps of a bearing fault diagnosis method based on dual sparse dictionary adaptation as described in claim 7.

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