A noise reduction method, bearing fault diagnosis method and system based on dual sparse dictionary adaptive approach

Abstract

This invention discloses a noise reduction method, a bearing fault diagnosis method, and a system based on dual sparse dictionary adaptive learning. The method performs wavelet decomposition on the signal to be denoised to obtain high-frequency and low-frequency signals, constructing high-frequency and low-frequency matrices. Then, threshold-adaptive DDTF dictionary learning is applied to both the high-frequency and low-frequency matrices. Specifically, an initial dictionary is set and learned to obtain an initial sparse coefficient matrix. An adaptive threshold update is then applied to the initial sparse coefficient matrix, selecting sparse coefficients from the initial sparse coefficient matrix in descending order as dynamic thresholds during the iteration process to update the initial sparse coefficients. After determining the final threshold, the final sparse coefficient matrix is ​​obtained, and the dictionary is updated again to obtain sub-signals. Finally, inverse transformation and matrix rearrangement inverse operations are performed on the obtained sub-signals to obtain the denoised signal. This invention combines wavelet decomposition and DDTF to construct a dual sparse pattern, effectively improving the sparse representation capability of a fixed basis.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal denoising, and particularly relates to a denoising method based on double-sparse dictionary self-adaption, a bearing fault diagnosis method and a system. BACKGROUND

[0002] In the past few decades, in order to optimize the effect of bearing data denoising processing, researchers have proposed many methods. 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 local damage of a rolling bearing is separated as an intrinsic mode function by EMD decomposition, and then the envelope signal thereof is obtained by Hilbert transform, the envelope spectrum is calculated, and the rolling bearing fault characteristic frequency is extracted. This method is used to analyze the vibration signals of rolling bearings with inner ring damage and outer ring damage collected on an experimental platform. Since the EMD method has the characteristics of self-adaption and is suitable for the decomposition of non-stationary signals, this method is applied to the analysis of the fault vibration signals of rolling bearings. However, EMD has the problem of mode mixing, resulting in poor denoising performance. In view of the mode mixing problem of empirical mode decomposition (EMD), scholars have improved EMD, such as combining singular value decomposition (SVD) with improved empirical mode decomposition and variational mode decomposition (VMD), that is, first performing SVD denoising on the fault signal, then adding a high-frequency harmonic signal according to the signal characteristics and performing EMD decomposition, which effectively reduces the mode mixing phenomenon; for VMD, it does not add noise in IMFs but is based on the angle of Wiener filtering, strictly requires IMFs to be a time series of amplitude modulation frequency modulation with limited bandwidth, and the decomposition layer number of VMD can be manually set, and the envelope of Hilbert transform of the signal can be set to a reasonable decomposition layer number to solve the mode mixing problem. However, VMD is difficult to process strong human interference, and it is difficult to preset a reasonable module, thereby reducing the denoising effect.

[0003] Except for the denoising application of mathematical decomposition method in bearing data processing, sparse representation is also widely used in this field, such as the method of Fourier transform, that is, the signal is analyzed in frequency spectrum, but when processing signal-to-noise separation, it lacks the ability to process local detail information, which can lead to the loss of a large amount of effective signal. In order to solve this problem, researchers have developed a short-time Fourier transform denoising method, which has better local description ability and can more effectively preserve important information in the signal. However, the size of the time window of the short-time Fourier transform is difficult to adapt, and the wavelet transform can solve this problem well. However, when using wavelet transform to process more complex signals, it cannot effectively remove noise, so many super wavelet transforms have been developed, such as contourlet transform, which is a multi-scale decomposition method based on super wavelet, especially suitable for signals with strong directionality and smooth boundaries; shearlet transform is a multi-scale transform similar to super wavelet transform, which adds a shear operation to the signal during decomposition, thereby better capturing the local features of the signal. Band wave transform is a multi-scale transform method for feature extraction, which decomposes the signal in different directions and processes each sub-band using banding technology. Using the above methods to denoise the signal has achieved certain effect.

[0004] Due to the inadaptability of fixed basis transform, the matching degree between mother base and signal is poor, noise residues are generated, and the denoising effect is reduced. Therefore, a single fixed basis transform is difficult to adapt to sparse representation signals, and many people have proposed learning basis denoising methods. Learning basis transform, also known as dictionary learning, is a sparse representation method that directly extracts signal features from samples to construct sparse bases by relying on certain optimization algorithms. It solves the shortcoming of fixed basis in sparse representation process that cannot change its own structure, and improves the sparse representation ability. Among them, KSVD, which was first proposed by Aharon in 2006, is a sparse basis that uses singular value decomposition for multiple updates. This method can adaptively sparse represent signals and achieve good denoising effect, but the time spent on denoising is too long. 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 adds an orthogonal constraint to the dictionary, so that DDTF can complete dictionary update only once SVD, greatly improving the running speed, and the sparse representation ability of DDTF is not weaker than KSVD.

[0005] However, in order to improve the sparse representation ability of the sparse basis, solve the problem of weak sparse representation ability of the fixed basis and the problem of introducing new noise due to the lack of structural constraints of human noise in the learning basis, and the problem of low precision due to self-set parameters still need further research and exploration in this field. SUMMARY

[0006] The present application is dedicated to solving the technical problem of improving the noise reduction effect, and further provides a double sparse dictionary adaptive noise reduction method, a bearing fault diagnosis method and system. Among them, the present application fully considers that wavelet decomposition and DDTF dictionary learning are both sparse representation categories, therefore, a double sparse mode is constructed by combining the two, the wavelet transform can transmit the structural information of the human noise to the DDTF through the wavelet sparse coefficient, the DDTF can perform secondary sparse representation on the wavelet sparse coefficient, extract the residual human noise in the wavelet sparse coefficient at each scale, and thus effectively improve the sparse representation ability of the fixed basis; at the same time, the wavelet denoising is fixed basis denoising, and the DDTF is learning basis denoising, the advantage of the fixed basis is that it is not easy to produce 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 produce pseudo noise, the present application combines wavelet decomposition and DDTF, fully utilizes the advantages of the two algorithms, and weakens the respective defects; and further optimizes the DDTF algorithm, realizes the threshold self-adaptation by utilizing the sparsity of the block, and improves the noise reduction effect.

[0007] Therefore, the present application provides the following technical scheme:

[0008] On the one hand, the present application provides a double sparse dictionary adaptive noise reduction method, including the following steps:

[0009] Step 1: obtaining a signal to be denoised, and performing 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, K being a positive integer;

[0010] Step 2: performing window sliding selection on the high-frequency signals and the low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix, the high-frequency matrices and the low-frequency matrix being regarded as over-complete sample libraries

[0011] Step 3: performing DDTF dictionary learning based on threshold self-adaptation on the high-frequency matrices 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, and then an initial sparse coefficient matrix is obtained by using DDTF dictionary learning, and in the iteration process, the sparse coefficients are selected as dynamic thresholds in descending order from the initial sparse coefficient matrix, so as to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficients greater than or equal to the dynamic threshold remain unchanged, otherwise, they are set to 0; the iteration is terminated to obtain the final sparse coefficient matrix under the best threshold; finally, the dictionary is updated based on the final sparse coefficient matrix, and then a sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix;

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

[0014] wherein the matrix rearrangement refers to the sub-signal form restored from the wavelet decomposition signal, and the inverse transform refers to the form before the wavelet decomposition.

[0015] Preferably, the process of threshold-adaptive DDTF dictionary learning is as follows:

[0016] First, an initial dictionary is fixed to obtain an initial sparse coefficient matrix;

[0017] The maximum value in the initial sparse coefficient matrix is selected as a dynamic threshold, and then the coefficients greater than or equal to the dynamic threshold in the initial sparse coefficient matrix are kept unchanged, and the coefficients less than the dynamic threshold are set to 0, and the sparse coefficient matrix is updated row by row;

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

[0019]

[0020] In the formula, is an over-complete sample library, D and a are over-complete sample libraries 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 of the dictionary;

[0021] Based on the correlation parameter, it is judged whether the iteration termination condition is reached. If the following formula is satisfied, it is considered that the iteration termination condition is satisfied, 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 as a dynamic threshold in the order from large to small to update the initial sparse coefficient matrix, and the above iteration process is repeated until the iteration termination condition is satisfied:

[0022]

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

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

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

[0026] Next, at least calculate the energy contribution rate of the outermost layer and set it as a reference value. The outermost layer is the layer where the value of the current decomposition layer is located.

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

[0028] Determine whether the energy contribution rate of the outermost layer is less than the current reference value. If it is less than the current reference value, 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 for the energy contribution rate is as follows:

[0030]

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

[0032] Preferably, the initial decomposition layer number is set to 1, and each time the current decomposition layer number is updated, the current decomposition layer number is incremented by 1.

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

[0034]

[0035] In the formula, a i These are the i-th rows of the sparse coefficient matrices before and after the update, respectively. For signal overcomplete sample library The i-th column; D is the dictionary before the update. Let I be the updated dictionary, and T0 be the identity matrix, where T0 is the maximum number of non-zero elements. Let ||x| be the square of the L2 norm, ||x|| = 0, and p be the sample size. It is the square of the F-norm.

[0036] Secondly, 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-level 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 levels.

[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 considered as an overcomplete sample library.

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

[0040] The process involves setting an initial dictionary for each matrix, then using DDTF dictionary learning to obtain an initial sparse coefficient matrix. From this initial sparse coefficient matrix, sparse coefficients are selected in descending order as dynamic thresholds during the iteration process. These thresholds are used to update the initial sparse coefficient matrix in each iteration; initial sparse coefficients greater than or equal to the dynamic threshold remain unchanged, otherwise they are set to 0. The iteration terminates, yielding the final sparse coefficient matrix under the optimal threshold. Finally, the dictionary is updated based on the final sparse coefficient matrix, and the sub-signal after dictionary learning is obtained based on the updated dictionary and the final sparse coefficient matrix.

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

[0042] Step 5: Use the noise-reduced bearing vibration signal to diagnose bearing faults.

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

[0044] The wavelet decomposition module is used to acquire the signal to be denoised and to perform K-level 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] The 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, where both the high-frequency matrix and the low-frequency matrix are considered as an overcomplete sample library.

[0046] 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.

[0047] The process involves setting an initial dictionary for each matrix, then using DDTF dictionary learning to obtain an initial sparse coefficient matrix. From this initial sparse coefficient matrix, sparse coefficients are selected in descending order as dynamic thresholds during the iteration process. These thresholds are used to update the initial sparse coefficient matrix in each iteration; initial sparse coefficients greater than or equal to the dynamic threshold remain unchanged, otherwise they are set to 0. The iteration terminates, yielding the final sparse coefficient matrix under the optimal threshold. Finally, the dictionary is updated based on the final sparse coefficient matrix, and the sub-signal after dictionary learning is obtained based on the updated dictionary and the final sparse coefficient matrix.

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

[0049] In four aspects, the present invention also provides a computer device, comprising:

[0050] One or more processors;

[0051] A memory that stores one or more computer programs;

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

[0053] 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.

[0054] Fifthly, the present invention also provides a computer-readable storage medium storing a computer program that is invoked by a processor to implement:

[0055] 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.

[0056] Beneficial effects

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

[0058] 1. This invention combines wavelet denoising with DDTF dictionary learning. From a sparse representation perspective, this invention constructs a dual-sparse model. Wavelet transform can transfer the structural information of human noise to DDTF through wavelet sparse coefficients, compensating for the lack of structural constraints in dictionary learning. DDTF can perform secondary sparse representation on the wavelet sparse coefficients, extracting residual human noise from the wavelet sparse coefficients at various scales, thereby effectively improving the sparse representation capability of the fixed basis. Furthermore, wavelet denoising is used for fixed basis denoising, while DDTF is used for learned basis denoising. This invention combines wavelet denoising and DDTF, leveraging their respective advantages while mitigating their respective shortcomings, thus improving the denoising effect.

[0059] 2. This invention further employs DDTF adaptive thresholding based on the wavelet layer data signals obtained from wavelet decomposition. In DDTF, due to the sparsity of noise, when the correlation between the data block and the dictionary is relatively small, it indicates that the data block is difficult to represent sparsely, and the contained mechanical vibration signal is extracted, leaving only noise. Therefore, this invention proposes to calculate the correlation and set the threshold to the value in the dictionary's sparsity coefficients, thereby achieving threshold adaptation. Using an adaptive method to determine the threshold through correlation calculation can, to some extent, reduce errors caused by manually setting parameters and improve denoising accuracy.

[0060] 3. The technical solution of this invention is widely used in bearing fault diagnosis. It fully considers that in wavelet transform, since the energy of noise in the wavelet sparse coefficients is less than the energy of the mechanical vibration signal, this invention uses the energy contribution rate to achieve adaptive wavelet decomposition level, that is, uses the energy contribution rate to determine the optimal decomposition level, thereby improving the noise reduction effect and accuracy. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating a noise reduction method based on dual sparse dictionaries adaptively provided in an embodiment of the present invention.

[0062] Figure 2 It is an adaptive determination process for the number of wavelet decomposition levels;

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

[0064] Figure 4 This is a comparison of the time-frequency plots after denoising. (a) Analog signal. (b) Analog noisy signal. (c) Wavelet denoising. (d) VMD denoising. (e) DDTF denoising. (f) VMD-DDTF denoising. (g) Denoising using the method presented in this paper. Detailed Implementation

[0065] This invention provides a noise reduction method, bearing fault diagnosis method, and system based on dual sparse dictionary adaptive approach for signal denoising. It introduces sparse representations of wavelet denoising and DDTF (data-driven tight frame, DDTF) to form a dual sparse model, effectively improving sparse representation capabilities. Simultaneously, both DDTF and wavelet denoising are optimized to achieve adaptive denoising. Specifically, a dynamic threshold is introduced into the DDTF algorithm to achieve threshold adaptation; secondly, a dynamic decomposition level is introduced into the wavelet decomposition to obtain the optimal wavelet decomposition level, effectively improving the signal denoising effect. This noise reduction method demonstrates outstanding performance in bearing vibration signal denoising applications. It should be understood that this technical approach is also applicable to the denoising of other time-series signals, such as electromagnetic signals and geological signals, where low-frequency signals are considered useful signals and high-frequency signals are considered noise signals. The invention will be further described below with reference to embodiments.

[0066] Example 1:

[0067] This embodiment will take bearing vibration signal as an example. The present invention provides a noise reduction method based on dual sparse dictionary adaptive method, including the following steps:

[0068] Step 1: Obtain the signal to be denoised, and perform K-level 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 bearing vibration signal processing, useful signals are typically low-frequency signals or relatively stable signals, while noise signals are typically high-frequency signals. This embodiment performs wavelet decomposition on the bearing vibration signal. Each decomposition layer yields both high-frequency and low-frequency signals. The next decomposition layer decomposes the low-frequency signal obtained from the previous layer, until the Kth layer yields the low-frequency signal required in step 1. The high-frequency signal obtained from each decomposition layer is the high-frequency signal described in step 1.

[0070] In this embodiment, we assume 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 follows:

[0071]

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

[0073] In this embodiment, the preferred wavelet decomposition level is determined using an adaptive decomposition strategy based on the energy contribution rate. The formula for the energy contribution rate is as follows:

[0074]

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

[0076] Based on the above formula, such as Figure 2 As shown, the adaptive process for obtaining the optimal decomposition level is as follows:

[0077] 1. Set the initial number of wavelet decomposition levels and perform wavelet decomposition. For example... Figure 2 In this embodiment, the initial number of decomposition layers is preferably set to 1.

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

[0079] 3. Update the current decomposition level and perform wavelet decomposition, then calculate the energy contribution rate of the outermost layer. For example... Figure 2 In this embodiment, it is preferable to update the current decomposition level by adding 1 to the current decomposition level.

[0080] 4. Determine whether the energy contribution rate of the outermost layer is less than the current reference value. If it is less than the current reference value, 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 the high-frequency and low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency and low-frequency matrices are considered as overcomplete sample libraries.

[0082] like Figure 3As shown, this embodiment utilizes a "window" to perform sliding processing on the group signals after K-level decomposition. For example, if there are 4096 one-dimensional data points, assuming the sliding window size is set to 1x256, a sliding step size of 1 needs to be set simultaneously. After each sliding process, a row of 1x256 data points is obtained. This data is then transposed to obtain a 256x1 column of data. When this group of data is slid until the sliding window can no longer slide, the 4096 data points become 3841 single rows of data. Each slide involves transposition, ultimately resulting in a 256x3841 matrix. The size of this matrix changes with the length of the decomposed data signal. The size of the sliding window has no special requirements; it can be determined through repeated trials to find the optimal value.

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

[0084] The DDTF dictionary learning is existing technology and will not be described in detail in this invention. It should be understood that DDTF dictionary learning on high-frequency and low-frequency matrix data yields a dictionary and a sparse coefficient matrix for each column.

[0085] The sparse encoding and dictionary update representation are as follows:

[0086]

[0087] In the formula, a i These are the i-th rows of the sparse coefficient matrices before and after the update, respectively. For signal overcomplete sample library The i-th column; D is a dictionary. Let I be the updated dictionary, and T0 be the identity matrix, where T0 is the maximum number of non-zero elements. Let ||x| be the square of the L2 norm, ||x|| = 0, and p be the sample size. It is the square of the F-norm.

[0088] To improve noise reduction, this invention employs an adaptive dynamic region, unlike traditional methods that use a fixed hard threshold to update sparse coefficients. For example... Figure 3 As shown, the process of DDTF dictionary learning based on threshold adaptation is as follows:

[0089] 1. First, a fixed initial dictionary is used, and then DDTF dictionary learning is performed to obtain the initial sparse coefficient matrix. This step is existing technology, and the learning is performed according to the aforementioned sparse coding and dictionary update model, that is, the sparse coefficient matrix is ​​updated row by row according to Formula 6; initializing the dictionary is also existing technology and no specific restrictions are imposed.

[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, and set the coefficients that are less than the dynamic threshold to 0, and update the sparse coefficient matrix.

[0091] 3. The correlation parameters between the data blocks and the dictionary are updated based on the following formula;

[0092]

[0093] In the formula, To ensure an incomplete sample database, D and a represent the dictionary and updated sparse coefficient matrix corresponding to this column, respectively; r is the residual; μ(r,D) is the correlation parameter; max is the maximum value calculation function; d β Let β be the β-th row of the dictionary, and N be the total number of rows in the dictionary;

[0094] Based on the correlation parameters, determine whether the iteration termination condition has been met. If the following formula is satisfied, it is considered that the iteration termination condition has been met, and the sparse coefficient matrix corresponding to the current data block is obtained; otherwise, select the next sparse coefficient in the initial sparse coefficient matrix in descending order as the dynamic threshold to update the initial sparse coefficient matrix, and repeat the above iteration process 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-signals after dictionary learning are obtained based on the updated dictionary and the final sparse coefficient matrix. That is, the dictionary is updated column by column, referring to Formula 7.

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

[0098] The inverse transform refers to multiplying the dictionary and sparse coefficients to obtain the processed overcomplete sample library, then restoring the overcomplete sample library (i.e., the inverse operation of steps 1 and 2) to obtain the processed signal. The K+1 groups thus yield the K+1 groups of processed signals. Performing an inverse wavelet transform yields the original signal processed by this method. In other words, the technical solution of this invention removes some noise through wavelet decomposition, obtaining sub-signals at different levels; then, secondary denoising is performed using DDTF. Therefore, matrix rearrangement and inverse transform restore the sub-signals from the secondary denoising to their original form, resulting in the denoised signal.

[0099] Example 2:

[0100] This invention also 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-level 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 the high-frequency and low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency and low-frequency matrices are considered as overcomplete sample libraries.

[0103] Step 3: Perform threshold-adaptive DDTF dictionary learning on both the high-frequency matrix and the low-frequency matrix to obtain the dictionary and sparse coefficient matrix; wherein, the implementation process of step 3 refers to the detailed description of embodiment 1. In this embodiment, it is also preferred to use an adaptive decomposition layer for wavelet denoising and 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 noise-reduced bearing vibration signal;

[0105] Step 5: Perform bearing fault diagnosis using the noise-reduced bearing vibration signal. How to use the noise-reduced bearing vibration signal for fault identification is existing technology in this field; therefore, this invention will not describe it in detail.

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

[0107] Example simulation:

[0108] Simulated bearing clean data such as Figure 4 As shown, Figures (a) and (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 method in this paper. Figure 4 The series of figures demonstrates the advantages of the method studied in this paper for denoising analog signals in the time domain.

[0109] Example 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 transform module.

[0111] The wavelet decomposition module is used to acquire the signal to be denoised and to perform K-level wavelet decomposition on the signal to be denoised to obtain K sets of high-frequency signals and 1 set 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 and low-frequency signals to construct K high-frequency matrices and 1 low-frequency matrix. Both the high-frequency and low-frequency matrices are considered to be from an incomplete sample library. The dictionary learning module is used to perform threshold-adaptive DDTF dictionary learning on both high-frequency and low-frequency matrices to obtain the dictionary and sparse coefficient matrix; the inverse transform module is used to perform inverse transform and matrix rearrangement inverse operation on the obtained sub-signals to obtain the denoised signal.

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

[0113] It should be understood that the specific implementation process of each module is described in the above method. This invention will not repeat the details here. The above division of functional modules is only for illustrative purposes. In some embodiments, some functional modules can be combined and some functional modules can be separated. Each functional module can be implemented in software, hardware, or a combination of software and hardware. The software and hardware devices include, but are not limited to, general-purpose computer equipment, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0114] Example 4:

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

[0116] The steps of a noise reduction method based on dual sparse dictionary adaptation or a bearing fault diagnosis method based on dual sparse dictionary adaptation are described below. The specific implementation process can be found in the descriptions of Embodiments 1 and 2.

[0117] Please refer to the explanation of the method above for the specific implementation process of each step.

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

[0119] Example 5:

[0120] The present invention also provides a computer-readable storage medium storing a computer program, which is invoked by a processor to implement: 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 be referred to the descriptions of Embodiments 1 and 2.

[0121] Please refer to the explanation of the method above for the specific implementation process of each step.

[0122] The readable storage medium is a computer-readable storage medium, which can be an internal storage unit of the hardware and software device described in any of the foregoing embodiments, such as the hard drive or memory of the controller. The readable storage medium can also be an external storage device of the controller, such as a plug-in hard drive, Smart MediaCard (SMC), Secure Digital (SD) card, or Flash Card equipped on the controller. Further, the readable storage medium can include both internal storage units and external storage devices of the controller. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium can also be used to temporarily store data that has been output or will be output.

[0123] Based on this understanding, the technical solution of the present invention, in essence, or 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned readable storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0124] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application refers to flowchart illustrations and / or instructions executed by a processor of a method, apparatus (system), and computer program product according to embodiments of this application to create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more blocks of a block diagram.

[0125] It should be emphasized that the examples described in this invention are illustrative rather than limiting. Therefore, this 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 solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A method for noise reduction based on dual-sparse dictionary adaptation, characterized in that: The method comprises the following steps: Step 1: obtaining a signal to be de-noised, and performing K-layer wavelet decomposition on the signal to be de-noised to obtain K groups of high-frequency signals and one group of low-frequency signals, K being a positive integer; Step 2: window sliding selection is performed on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix, and the high-frequency matrices and the low-frequency matrix are regarded as an over-complete sample library Step 3: performing DDTF dictionary learning based on a threshold value to obtain a dictionary and a sparse coefficient matrix for each of the high-frequency matrix and the low-frequency matrix; Wherein, an initial dictionary is set for each matrix, and then an initial sparse coefficient matrix is obtained by using DDTF dictionary learning, and in the iteration process, a sparse coefficient is selected as a dynamic threshold value in descending order from the initial sparse coefficient matrix, so as to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficient greater than or equal to the dynamic threshold value remains unchanged, otherwise, it is set to 0; the iteration is terminated to obtain the final sparse coefficient matrix under the optimal threshold value; 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 sub-signals of the high-frequency matrix and the low-frequency matrix obtained in step 3 to obtain a de-noised signal.

2. The method of claim 1, wherein: The process of DDTF dictionary learning based on a threshold value is as follows: First, an initial sparse coefficient matrix is obtained by fixing an initial dictionary; The maximum value in the initial sparse coefficient matrix is selected as a dynamic threshold value, and then the coefficients greater than or equal to the dynamic threshold value in the initial sparse coefficient matrix are kept unchanged, and the coefficients less than the dynamic threshold value are set to 0, and the sparse coefficient matrix is updated row by row; The correlation parameter of the data block based on the updated sparse coefficient matrix and the dictionary is calculated according to the following formula: wherein, 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 of the dictionary; Whether the iteration termination condition is reached is judged based on the correlation parameter, if the following formula is satisfied, it is considered that the iteration termination condition is satisfied, 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 as a dynamic threshold value in descending order to update the initial sparse coefficient matrix, and the above iteration process is repeated until the iteration termination condition is satisfied: 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.

3. The method of claim 1, wherein: The K-layer wavelet decomposition process of the signal to be de-noised in step 1 is to determine the optimal decomposition layer number by using an adaptive decomposition strategy based on energy contribution rate; Wherein, the initial decomposition layer number of wavelet decomposition is first set, and wavelet decomposition is performed; Then, the energy contribution rate of the outermost layer is calculated and set as a reference value, and the outermost layer is the layer where the current decomposition layer number is located; The current decomposition layer number is updated and wavelet decomposition is performed, and the energy contribution rate of the outermost layer is calculated again; Whether the energy contribution rate of the current outermost layer is less than the current reference value is judged, if it is less than the current reference value, the previous decomposition layer number is output as the optimal decomposition layer number; otherwise, the contribution rate of the current outermost layer is set as the reference value, the current decomposition layer number is updated again, and the above steps are repeated for the next iteration until the optimal decomposition layer number is obtained.

4. The method of claim 3, wherein: The formula of the energy contribution rate is as follows: In the formula, respectively represent the energy contribution rate, the high-frequency energy mean value, and the low-frequency energy mean value of the kth layer, K is the decomposition layer number, E k and s k respectively represent the energy mean value and the wavelet sparse coefficient of the kth layer, nuk is the number of wavelet sparse coefficients, and ||·||2 represents an L2 norm.

5. The method of claim 3, wherein: The initial decomposition layer number is set to 1, and the current decomposition layer number is increased by 1 each time the current decomposition layer number is updated.

6. The method of claim 1, wherein: In the DDTF dictionary learning, sparse coefficient coding and dictionary updating are represented as follows: wherein , a i are the i-th row of the updated and the pre-updated sparse coefficient matrix, respectively, is the i-th column of the signal overcomplete dictionary D is the pre-updated dictionary, is the updated dictionary, I is the identity matrix, T0 is the upper limit of the number of non-zero elements, is the square of the two-norm, ||0 is the zero-norm, p is the number of samples, is the square of the F-norm.

7. A bearing fault diagnosis method based on dual-sparse dictionary adaptation, characterized in that: The method comprises the following steps: Step 1: obtaining a bearing vibration signal to be denoised, and performing K-layer wavelet decomposition on the bearing vibration signal to be denoised to obtain K groups of high-frequency signals and one group of low-frequency signals, K being a positive integer; wherein an adaptive decomposition strategy based on energy contribution rate is used to determine the optimal decomposition layer number; Step 2: window sliding selection is performed on the high-frequency signal and the low-frequency signal to construct K high-frequency matrices and 1 low-frequency matrix, and the high-frequency matrices and the low-frequency matrix are regarded as an over-complete sample library Step 3: performing DDTF dictionary learning based on threshold adaptation on the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; wherein an initial dictionary is set for each matrix, and then an initial sparse coefficient matrix is obtained by using DDTF dictionary learning, and in an iterative process, a sparse coefficient is selected as a dynamic threshold in descending order from the initial sparse coefficient matrix, so as to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficient greater than or equal to the dynamic threshold remains unchanged, otherwise, it is set to 0; the iteration is terminated to obtain a final sparse coefficient matrix under the optimal threshold; finally, the dictionary is updated based on the final sparse coefficient matrix, and then a 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 high-frequency matrix and low-frequency matrix sub-signals to obtain a denoised bearing vibration signal; Step 5: using the denoised 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 by: It comprises: a wavelet decomposition module, configured to obtain a to-be-denoised signal, and perform K-layer wavelet decomposition on the to-be-denoised signal to obtain K groups of high-frequency signals and one group of low-frequency signals, K being a positive integer; A matrix construction module is configured to select the high-frequency signals and the low-frequency signals by window sliding, and construct K high-frequency matrices and 1 low-frequency matrix, wherein the high-frequency matrices and the low-frequency matrix are regarded as an over-complete sample library a dictionary learning module, configured to perform DDTF dictionary learning based on threshold adaptation on the high-frequency matrix and the low-frequency matrix to obtain a dictionary and a sparse coefficient matrix; wherein an initial dictionary is set for each matrix, and then an initial sparse coefficient matrix is obtained by using DDTF dictionary learning, and in an iterative process, a sparse coefficient is selected as a dynamic threshold in descending order from the initial sparse coefficient matrix, so as to update the initial sparse coefficient matrix in each iteration, that is, the initial sparse coefficient greater than or equal to the dynamic threshold remains unchanged, otherwise, it is set to 0; the iteration is terminated to obtain a final sparse coefficient matrix under the optimal threshold; finally, the dictionary is updated based on the final sparse coefficient matrix, and then a sub-signal after dictionary learning processing is obtained based on the updated dictionary and the final sparse coefficient matrix; an inverse transformation module, configured to perform inverse transformation and matrix rearrangement inverse operation on the obtained sub-signals to obtain a denoised signal.

9. A computer device, characterized by: It comprises: one or more processors; a memory storing one or more computer programs; wherein the processor invokes the computer program to implement: the steps of the denoising method based on double sparse dictionaries and adaptation according to any one of claims 1-6 or the steps of the bearing fault diagnosis method based on double sparse dictionaries and adaptation according to claim 7.

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

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