Bearing fault diagnosis method and system

Abstract

The invention discloses a bearing fault diagnosis method and system, and belongs to the technical field of fault diagnosis, and the method comprises the steps: obtaining a fault period of a bearing according to a collected bearing fault signal, and determining an optimization objective function of bearing fault signal sparse representation; constructing a comprehensive index by taking an adaptive parameter in the optimization objective function as an optimization objective, determining an optimal adaptive parameter by taking the minimization of the comprehensive index as an objective, determining an optimal sparse representation optimization objective function, and performing sparse denoising on the bearing fault signal; according to the bearing fault signal after sparse denoising, constructing a fitness function of a filter length and a displacement number through correlation kurtosis, obtaining a parameter combination of the filter length and the displacement number with the maximum correlation kurtosis, filtering the bearing fault signal after sparse representation, obtaining a signal enhanced periodic fault component, and performing envelope spectrum analysis to obtain a signal enhanced periodic fault component; and obtaining the characteristic frequency and the frequency multiplication of the fault signal. The method can realize accurate diagnosis of bearing faults under strong noise.

Description

Technical Field

[0001] The present invention relates to the technical field of fault diagnosis, and more particularly to a bearing fault diagnosis method and system. Background Art

[0002] Bearings are important components in rotating mechanical equipment. They play key roles such as supporting, guiding, and reducing friction during the rotation of the rotor, ensuring the normal operation of the mechanical system. However, long-term operation, high-load work, and use under harsh environmental conditions can cause faults such as wear, fatigue, and cracks in the bearings. These faults not only lead to equipment shutdown and production interruption but may also trigger safety accidents, causing serious impacts. Therefore, researching efficient and accurate bearing fault diagnosis technology has become an urgent problem to be solved in the industrial field.

[0003] When a bearing fails, due to the periodic impact between the rolling elements and the inner and outer rings of the bearing, the vibration signal of the local bearing fault contains periodic pulse responses or quasi-periodic pulse responses with relatively small fluctuations, which can reflect the working state of the bearing and the possible fault types. Therefore, vibration analysis methods are widely used in the field of bearing fault diagnosis. However, since the bearing vibration signals collected by the equipment are relatively complex and are usually masked by strong background noise and other interference components, the process of extracting weak features is relatively difficult.

[0004] Currently, sparse representation has been widely used in the field of signal processing. The core idea of sparse representation is to represent a signal as a linear combination of a small number of basis elements using a given overcomplete learning dictionary to achieve the representation of the original signal, making the signal show the sparse characteristics of the original signal after sparse transformation while removing redundant information, and having a good effect on extracting the characteristics of the vibration signals generated by local bearing faults. However, for traditional sparse representation in practical applications, the design and learning process of the dictionary are relatively complex, with high computational complexity, vulnerable to noise interference, and still relying on the theoretical values of bearing faults for periodic priors, unable to effectively extract the characteristics of fault signals, affecting the extraction and diagnosis of bearing fault information under strong noise. Summary of the Invention

[0005] Aiming at the problems existing in the above fields, the present invention proposes a bearing fault diagnosis method and system. According to the characteristics of the fault signal, sparse denoising is performed on the fault signal, and the fault information of the denoised fault signal is enhanced. This method has good anti-noise performance and fault feature extraction ability, and can achieve accurate diagnosis of bearing faults under strong noise.

[0006] To solve the above technical problems, the present invention discloses a bearing fault diagnosis method, including the following steps: Based on the collected bearing fault signals, the estimated period value of the signals is determined by obtaining the spectral information of the signals and screening out the fault frequencies, and the fault period of the bearing is obtained. Based on the fault period of the bearing, the optimization objective function for the sparse representation of the bearing fault signals is determined; the adaptive parameter in the optimization objective function is taken as the optimization objective, a comprehensive index is constructed, and with the minimization of the comprehensive index as the goal, the optimal adaptive parameter is determined; based on the optimal adaptive parameter, the optimal sparse representation optimization objective function is determined to perform sparse denoising on the bearing fault signals; wherein, the comprehensive index is the ratio of the error between the sparse denoised signal and the noiseless original signal to the envelope spectrum peak factor, which is used to characterize the relationship between the adaptive parameter and the noise level. Based on the bearing fault signals after sparse denoising, the fitness function of the filter length and displacement number is constructed through the correlation kurtosis, the parameter combination of the filter length and displacement number with the maximum correlation kurtosis is obtained, and the bearing fault signals after sparse representation are filtered to obtain the periodic fault components with enhanced signals. Envelope spectrum analysis is performed on the periodic fault components with enhanced signals to obtain the characteristic frequencies and multiple frequencies of the fault signals.

[0007] Preferably, the obtaining of the fault period of the bearing specifically includes: Performing a first-order difference operation on the signal to obtain , and calculating the analytic signal of the signal through Hilbert transform: ; Performing FFT on to obtain spectral information. The obtained frequency-domain information is symmetric left and right, and only its right half is selected to obtain the frequency index after descending order sorting of the spectral energy information. According to the sorted index, the first 20 largest frequencies are selected as the active frequency set : ; wherein, f s is the sampling frequency, f c is the fault frequency, n is the index of the fault frequency set; For the obtained active frequency set , the frequency individuals with a frequency interval less than are removed, and the current active frequency set is updated; For the updated current active frequency set Perform a cyclic search on each element in it, calculate the multiple relationship between them, and from the active frequency set Filter out the active frequencies with a multiple relationship; Perform a weighted average on the filtered active frequencies with a multiple relationship to calculate the fault frequency with the highest occurrence probability ; According to the fault frequency , determine the estimated period value of the signal P .

[0008] Preferably, the optimization objective function for determining the sparse representation of the bearing fault signal includes the following steps: The mathematical expression for obtaining the dictionary-free sparse representation of the signal is: ; Where is the original signal without noise, is the sparse denoised signal, is the adaptive parameter, P ( x ) is the penalty function; Obtain a binary weight vector : ; Where is the estimated length of a fault impulse, is the interval length between adjacent fault impulses, is the group size, is the number of complete fault shocks contained in each group, is the length occupied by each complete fault shock, that is, the estimated period value of the signal; According to the sampling frequency and the fault frequency , the parameter P satisfies the equation: ; According to the binary weight vector , the penalty function and the mathematical expression of the dictionary-free sparse representation, the optimization objective function for the sparse representation of the bearing fault signal is obtained as: ; Where i is the group leading coefficient, is the set leading, is the sparsity penalty function, , is the constant value for controlling the non-convex degree of the penalty, is the balance parameter, For reweighting l The penalty of 1; , ; Wherein, is a diagonal matrix, and the diagonal elements contain , is defined as: ; Wherein, is a small positive constant used to avoid division by zero; When and at this time, is convex.

[0009] Preferably, the determination of the optimal adaptive parameter includes the following steps: The adaptive parameter in the optimization objective function for the sparse representation of the bearing fault signal is used as the optimization objective; Based on the adaptive parameter being , a comprehensive index is constructed to characterize the relationship between the adaptive parameter and the noise level; The more the number of periodic impulses in the vibration signal, the greater the peak value at the impulse occurrence frequency in the signal envelope spectrum ; The ratio of the maximum value to the effective value of the filtered signal envelope spectrum within the range of is used as the envelope spectrum peak factor , expressed as: ; Wherein, is the rotational frequency; The larger the value, the higher the signal-to-noise ratio and the greater the energy of the signal, and the stronger the periodic impulse component; The envelope spectrum peak factor is used as a measure of the impulse component in the signal; The error between the sparse denoised signal and the noiseless original signal is: ; RMSE The smaller the value of , the better the fitting degree between the denoised signal and the original noiseless signal, indicating that the model is more accurate in estimation; and RMSE are respectively placed in the denominator and numerator of the fraction to construct a comprehensive index : ; Comprehensive index It is used to simultaneously reflect the denoising ability and estimation accuracy of the model; Comprehensive index The smaller the value, the closer the denoised signal is to the original fault pulse; when the value reaches the minimum, it means that the adaptive parameter is optimal; By minimizing the comprehensive index the optimal adaptive parameter is determined, and the best under different noise levels is determined through a linear fitting curve, and the relationship between and the noise level is obtained.

[0010] Preferably, the sparse denoising of the bearing fault signal specifically includes: Substitute the optimal adaptive parameter into the optimization objective function of the sparse representation of the bearing fault signal to obtain the optimal sparse representation optimization objective function; Use the iterative optimization process of the MM algorithm to solve the optimal sparse representation optimization objective function to obtain the bearing fault signal after sparse denoising.

[0011] Preferably, the obtaining of the periodic fault component with enhanced signal includes the following steps: Taking the maximum value of the correlation kurtosis of the bearing fault signal after sparse denoising as the condition, the fault signal is filtered to extract the fault characteristics; The essence of the MCKD algorithm is to find a filter FIR to recover the continuous impact signal submerged by noise; through the correlation kurtosis, the signal is filtered, and when the correlation kurtosis is the largest, the signal recovered by the solved filter satisfies the periodic impact characteristic; The correlation kurtosis is expressed as: ; The condition for maximizing the correlation kurtosis is: ; Calculate the filter coefficients: ; where is the deconvolution period, is the shift number, m ∈[0, M , is the filter length; The coefficients in the formula are: ; ; ; ; For the filter length L and the displacement number M , construct the fitness function of the filter length and the displacement number through the relevant kurtosis; Through the grid search method, search for the parameter combination of the filter length and the displacement number that maximizes the relevant kurtosis, and obtain the optimized filter length, displacement number, and deconvolution period. The optimized filter length, displacement number, and deconvolution period are the periodic fault components for signal enhancement.

[0012] Preferably, the steps of obtaining the optimized filter length, displacement number, and deconvolution period specifically include: Determine the search range and search step size of the filter length L and the displacement number M ; Initialize the parameter filter length L and the displacement number M according to the search range, and assign a value to the deconvolution period T according to the period estimation result; According to the initialized parameter filter length L , displacement number M and the deconvolution period T assigned according to the period estimation result, calculate the corresponding relevant kurtosis as the relevant kurtosis A ; Update the parameters according to the search step size, and calculate the relevant kurtosis corresponding to the updated parameters as the relevant kurtosis B ; Compare the relevant kurtosis B with the relevant kurtosis A ; when the relevant kurtosis B is less than the relevant kurtosis A , retain the relevant kurtosis B ; when the relevant kurtosis B is greater than the relevant kurtosis A , retain the relevant kurtosis A ; After completing the search, output the parameters corresponding to the finally retained relevant kurtosis as the optimal filter length L , displacement number M and deconvolution period T .

[0013] Preferably, the obtaining of the characteristic frequency and multiple frequency of the fault signal specifically includes: According to the optimized filter length, displacement number, and deconvolution period, the fault feature of the bearing fault signal after sparse denoising is enhanced by the MCKD algorithm. The envelope spectrum analysis is performed on the enhanced result to obtain the extraction and diagnosis results of the characteristic frequency and multiple frequency of the bearing fault under strong noise.

[0014] Preferably, it further includes a bearing fault diagnosis system, including: A fault signal period acquisition module, configured to determine the estimated period value of the signal and obtain the fault period of the bearing by acquiring the spectrum information of the collected bearing fault signal and screening out the fault frequency. A fault signal sparse denoising module, configured to determine the optimized objective function for the sparse representation of the bearing fault signal according to the fault period of the bearing; use the adaptive parameter in the optimized objective function as the optimization target, construct a comprehensive index, and determine the optimal adaptive parameter with the minimization of the comprehensive index as the goal; according to the optimal adaptive parameter, determine the optimal sparse representation optimized objective function, and perform sparse denoising on the bearing fault signal; wherein, the comprehensive index is the ratio of the error between the sparse denoised signal and the noise-free original signal to the envelope spectrum peak factor, and is used to characterize the relationship between the adaptive parameter and the noise level. A fault signal enhancement module, configured to construct a fitness function for the filter length and displacement number through relevant kurtosis according to the bearing fault signal after sparse denoising, obtain the parameter combination of the filter length and displacement number with the maximum relevant kurtosis, filter the bearing fault signal after sparse representation, and obtain the periodic fault component with enhanced signal. A fault signal diagnosis module, configured to perform envelope spectrum analysis on the periodic fault component with enhanced signal to obtain the characteristic frequency and multiple frequency of the fault signal.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The bearing fault diagnosis method proposed by the present invention constructs an optimization objective function for the sparse representation of bearing fault signals, takes the adaptive parameters in the optimization objective function as the optimization objectives, constructs a comprehensive index, aims at minimizing the comprehensive index, determines the optimal adaptive parameters, performs sparse denoising on the bearing fault signals, and dynamically estimates the possible fault periods in the fault signals without any information about the faulty bearings according to the characteristics of the fault signals, and constructs them into binary vectors and embeds them into the penalty function to promote the intra-group and inter-group sparsity of the fault signals, realizes the denoising of the fault signals, and obtains the fault signals after sparse representation denoising. According to the bearing fault signals after sparse denoising, a fitness function for the filter length and displacement number is constructed through the relevant kurtosis, and the parameter combination of the filter length and displacement number with the maximum relevant kurtosis is obtained, and the bearing fault signals after sparse representation are filtered to obtain the periodic fault components with enhanced signals. The fault information of the bearing fault signals after sparse denoising is enhanced, effectively combining the advantages of pulse extraction and pulse feature enhancement of the adaptive sparse cycle group lasso, so that it has good anti-noise performance and fault feature extraction ability for vibration signals. This method has good anti-noise performance and fault feature extraction ability, and can realize the accurate diagnosis of bearing faults under strong noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flowchart of the method AdaSRMD for the bearing fault diagnosis method proposed by the present invention; Figure 2 It is for several traditional penalty functions provided by the embodiments of the present invention and L 0 the relationship between the norms; Figure 3 It is provided by the embodiments of the present invention and the noise level the relationship diagram; Figure 4 It is the fault pulse component provided by the embodiments of the present invention; Figure 5 It is the period estimation result under different noise levels provided by the embodiments of the present invention; Figure 6 It is the comparison of the fault pulse extraction performance of the simulated signals provided by the embodiments of the present invention; Figure 7 It is the comparison of the simulation results under different noise levels provided by the embodiments of the present invention; Figure 8 It is the processing result of the bearing inner ring fault provided by the embodiments of the present invention; Figure 9 It is the result of processing the bearing inner ring fault by using AdaSRMD and AdaSR respectively provided by the embodiments of the present invention; Figure 10Processing result of bearing outer ring fault provided by the embodiment of the present invention; Figure 11 Extraction result of bearing inner ring fault provided by the embodiment of the present invention; Figure 12 Update curve of fault period with the number of iterations provided by the embodiment of the present invention; Figure 13 Extraction result of bearing outer ring fault provided by the embodiment of the present invention. Detailed implementation manners

[0017] Next, in combination with the attached drawings in the embodiments of the present invention Figures 1 - 13 the technical solutions in the embodiments of the present invention will be clearly and completely described. It should be understood that the terms described in the present invention are only for describing specific embodiments and are not used to limit the present invention.

[0018] As Figure 1 shown, the present invention proposes a bearing fault diagnosis method, including the following steps: Determine the sparse denoising model Define a binary weight vector : ; Wherein, is an estimated length of a fault impulse pulse, is the interval length between adjacent fault impulses, is the group size, is the number of a complete fault impact included in each group, is the length occupied by each complete fault impact, that is, the estimated period value of the signal.

[0019] According to the sampling frequency and the fault characteristic frequency , the parameter P satisfies the equation: ; According to the binary weight vector , the penalty function and the mathematical expression of the sparse representation without a dictionary, the optimization problem, that is, the mathematical expression form of the optimization objective function of the sparse representation of the bearing fault signal, can be obtained as: ; Wherein, i is the group index coefficient, is the set index, is the sparsity penalty function, , is a constant value for controlling the non-convex degree of the penalty, is a balance parameter, for reweighting l a penalty of 1.

[0020] , ; wherein, is a diagonal matrix, and the diagonal elements contain , is defined as: ; wherein, is a small positive constant used to avoid division by zero.

[0021] When and , is convex, so the optimization problem can be solved using the MM algorithm.

[0022] The core idea of the MM algorithm is to gradually approximate the original non-convex optimization objective function by constructing a simple convex function (called the master function), and find the minimum point of the master function at each step. The optimization iteration formula is derived as follows: ; ; ; wherein, , is the number of algorithm iterations.

[0023] The penalty function is based on the within-group and between-group sparsity (SWAG) of the fault signal containing periodic pulses.

[0024] A penalty function ESGL with both non-convex and reweighting proposed in the prior art divides the periodic fault signal into groups, assuming that the size of each group has the same value , and selects the maximum overlap to retain the most information. For , if the length of the signal is , and the size of each group is .

[0025] Each group is defined as: ; wherein, is the group index coefficient.

[0026] The non-convex and reweighting penalty term that enhances the SWAG property has the following expression: ; Among them, is the balance parameter, which controls the sparsity within each group.

[0027] Table 1 gives the penalty functions for some attributes , such as Figure 2 shown, is the visualization corresponding to each penalty function. Among them, the variable is the input of the penalty, is the constant value that controls the non-convex degree of the penalty, is the function used in the MM algorithm derivation. Compared with penalty, , penalties are more inclined to promote sparsity while effectively maintaining the amplitude.

[0028] Table 1 Sparsity Penalty Function

[0029] In addition, is called the penalty of reweighting , and its definition is as follows: ; Among them, is a diagonal matrix, and the diagonal elements contain , is defined as: ; The mathematical expression of the dictionary-free sparse representation is as follows: ; Among them, is the original signal, is the sparse signal, is the regularization parameter, P ( x ) is the penalty function.

[0030] The expression consists of two parts: a fidelity term and a regularization term. The fidelity term retains the original information of the signal, and the regularization term promotes the fault features through penalty to make the signal sparser. The classical dictionary-free SR model uses norm as the penalty function to promote the sparsity of the signal, but norm has the defect of amplitude underestimation. The amplitude underestimation defect of the

[0031] The basic idea of the Maximum Correlation Kurtosis Deconvolution (MCKD) method is to find a Finite Impulse Response (FIR) filter to recover the continuous impulse signal submerged by noise; through the correlation kurtosis, filter the signal. When the correlation kurtosis is maximized, the signal recovered by the solved filter satisfies the periodic impulse characteristic, and the signal is filtered to extract the fault characteristics.

[0032] Among them, the expression of the correlation kurtosis is as follows: ; The condition for maximizing the correlation kurtosis is: ; Calculate the filter coefficients: ; Among them, is the deconvolution period, is the shift number, m ∈[0, M , is the filter length.

[0033] The coefficients in the above formula are: ; ; ; .

[0034] The bearing fault diagnosis method based on adaptive sparse periodic group lasso and maximum correlation kurtosis deconvolution proposed by the present invention, namely the bearing fault diagnosis method based on (Adaptive Sparse periodic group lasso and Maximum correlation kurtosis Deconvolution, AdaSRMD) MCKD highlights the continuous pulses submerged by noise through deconvolution operation and improves the correlation kurtosis value of the original signal. However, when the noise is large, the noise component of the signal has a larger kurtosis value than the fault-related pulse component, and the MCKD algorithm will show a poor signal filtering effect. The previous adaptive sparse periodic group lasso model still depends on the theoretical value of bearing faults for the period prior, and there are still certain defects in maintaining the amplitude of the processed signal.

[0035] To solve these problems, the bearing fault diagnosis method based on AdaSRMD proposed by the present invention has a flow chart as Figure 1 shown. According to the characteristics of bearing fault signals, this method studies a new method for estimating the bearing fault cycle without any information of faulty bearings, and estimates the possible cycles in the signals; embeds the cycle sequence dynamically into a non-convex penalty function for iterative processing to reveal the intra-group and inter-group sparsity of the fault signals, studies a method for adaptively optimizing the regularization parameters of sparse representation, and proposes an effective method for denoising bearing fault signals; studies the optimal optimization method for the key parameters of maximum correlation kurtosis deconvolution based on grid search, and proposes a method for enhancing the periodic fault components of bearings to achieve accurate diagnosis of bearing faults under strong noise. Among them, the adaptive cycle estimation method (AdaFP)

[0036] In actual work, when the parameters of the bearing are unknown, the theoretical fault frequencies of its various parts cannot be obtained, which poses certain difficulties for fault extraction and diagnosis. Therefore, the present invention proposes a method for estimating the fault cycle, which is of certain significance for finding the fault frequency. Since the first-order difference can highlight the changes or trends in the signal, the signal

[0037] is subjected to a first-order difference operation to obtain , and the analytic signal of the signal is calculated through Hilbert transform : ; Performing FFT on to obtain the spectrum information, and the obtained frequency domain information is symmetric left and right. Only the right half of the subsequent calculation data is selected. The frequency index after descending order sorting of the spectrum energy information is obtained, and the first 20 largest frequencies are selected as the active frequency set : ; To avoid interference, for the frequency individuals in the obtained set with a frequency interval less than , they are removed and the current active frequency set is updated.

[0038] Performing a cyclic search on each element in the updated current active frequency set , calculating the multiple relationship between them, and screening out the active frequencies with a multiple relationship from the active frequency set .

[0039] Perform weighted averaging on the active frequencies with a multiple relationship that are screened out, and calculate the fault frequency with the highest occurrence probability. ; According to the fault frequency , determine the estimated period value of the signal P .

[0040] Fault signal denoising method based on optimized sparse representation There are several parameters mainly involved in sparse representation . For the parameter , it is mainly used to construct a binary weight vector to enhance fault information. Therefore, the present invention mainly focuses on the period of each pulse rather than the specific duration. Based on experience, it is set as to roughly estimate the length of each pulse. The parameter represents the number of periods in the sequence. For fast implementation, it is set as . According to Figure 2 , it can be seen that is when promoting sparsity while maintaining the amplitude, the effect is closest to norm. At the same time, in order to most promote this property, it is set as . The prior art verifies that affects the sparsity within each group and has nothing to do with the noise level. Therefore, it is set as . The number of algorithm iterations has little impact on the solution of the optimization problem. An early stopping strategy is adopted and set as . For the adaptive regularization parameter , also known as the adaptive parameter, it needs to be further discussed according to the signal being at different noise levels.

[0041] By constructing a comprehensive index used to characterize the relationship between the adaptive parameter and the noise level to evaluate the performance of the algorithm.

[0042] The more the number of periodic impulses in the vibration signal, the greater the peak value at the impact occurrence frequency in the signal envelope spectrum . The ratio of the maximum value to the effective value of the filtered signal envelope spectrum within the range of is called the envelope spectrum peak factor and is expressed as: ; Among them, is the rotational frequency, n can take 2 to eliminate the influence of the rotational frequency on the value.

[0043] The larger the value, the higher the signal-to-noise ratio and the greater the energy of the signal, and the stronger the periodic impact component. Therefore, the envelope spectrum peak factor can be used as a measure of the impact component in the signal.

[0044] The error between the sparse denoised signal and the noise-free original signal is: ; where represents the denoised signal, represents the noise-free analog signal.

[0045] RMSE The smaller the value of

[0046] , the better the fit between the sparse denoised signal and the noise-free original signal, indicating that the model is more accurate in estimation. Since the larger the value of RMSE is better, while the smaller the value of and RMSE is better, and are respectively placed in the denominator and numerator of the fraction to form a comprehensive index : ;

[0047] The comprehensive index can simultaneously reflect the denoising ability and estimation accuracy of the model. The smaller the value of the comprehensive index , the closer the denoised signal is to the original fault pulse. When reaches the minimum, it indicates that the parameter

[0048] is optimal. Therefore, the principle of minimizing the comprehensive index and noise level can be used to select ; where median (·) represents taking the median, and is the orthogonal wavelet (sym8) coefficient of the optimal scale.

[0049] By using minimization to determine the optimal parameter, 100 independent experiments are carried out at different noise levels, the average value of the results of these 100 experiments is calculated, and these results are plotted as shown in Figure 3 .

[0050] From Figure 3It can be clearly observed that the error between the average value of the experiment and each independent experiment is very small. In addition, the difference between the average value and the value obtained by fitting is also negligible. Therefore, a linear fitting curve can be used to determine the optimal , and the specific formula is as follows: .

[0051] Periodic Fault Enhancement Method Based on Optimized MCKD Algorithm For the problem that there are still certain defects in the amplitude retention of the fault signal after adaptive sparse cyclic group lasso processing, a method for optimizing the key parameter combination of maximum correlation kurtosis deconvolution based on grid search is proposed to effectively enhance and accurately diagnose bearing fault information.

[0052] The MCKD algorithm has strict requirements for important parameters including the deconvolution period , filter length , and displacement number , which limits the performance improvement of the MCKD algorithm in extracting transient characteristics from noisy signals and identifying mechanical faults. Only by ensuring the accuracy and proper use of these parameters can the superiority of the MCKD algorithm be highlighted. Therefore, for , the AdaFP method can obtain relatively accurate values.

[0053] For parameters, the present invention first constructs a fitness function for the filter length and displacement number using the correlation kurtosis; then, uses the grid search method to search for the parameter combination with the maximum correlation kurtosis, and the specific implementation steps of parameter optimization are as follows: Step 1: Determine the search range and search step size of the filter length and displacement number ; Step 2: Initialize the parameters , according to the search range. For the deconvolution period , it can be assigned according to the period estimation result; Step 3: Calculate the corresponding correlation kurtosis as the correlation kurtosis L M T A B B ; Step 4: Update the parameters according to the search step size and calculate the correlation kurtosis corresponding to the updated parameters as the correlation kurtosis B ; Compare the correlation kurtosis B with the correlation kurtosis AMake a comparison; when the relevant kurtosis B is less than the relevant kurtosis A retain the relevant kurtosis B ; when the relevant kurtosis B is greater than the relevant kurtosis A , retain the relevant kurtosis A ; Step 5: After completing the search, output the parameters corresponding to the finally retained relevant kurtosis as the optimal filter length L , displacement number M and deconvolution period T .

[0054] Use the optimal filter length L , displacement number M and deconvolution period T obtained through the above parameter optimization as the periodic fault component for signal enhancement.

[0055] After obtaining the optimized parameters and for the fault signal after sparse denoising through the above steps, process the fault signal using the MCKD algorithm to enhance the fault features. Then perform envelope spectrum analysis on the final result to achieve the extraction and diagnosis of bearing fault information under strong noise.

[0056] Use the simulated fault signal to evaluate the performance of the proposed fault diagnosis model. The simulated fault signal consists of pulse components and noise caused by rolling bearing faults: .

[0057] Simulate the vibration signal caused by rolling bearing defects x ( i ) as a series of pulse transients, each transient consisting of 10 samples, and the pulse signal z ( t ) is: ; where , is the noise, is a random integer in t , is the time variable, is the sampling interval, is the random slip, is the amplitude of the pulse signal is the natural frequency of the pulse signal, , and Subject to the normal distributions of N(1, 1), N(2000, 10) and N(0, 1) respectively, the pulse signals are combined to form Figure 4 The sampling rate in (a) is the quasi-periodic fault sequence of , the sampling time is , the fault frequency . In order to simulate the periodic uncertainty of real faults, the fault period is set to have a random variation of 0.8%, and the first is set to zero to simulate the healthy state of the bearing. Figure 4 (b) is the fault signal with added Gaussian noise ( ).

[0058] AdaFP period estimation effect To verify the effect of period estimation, the periodic random sliding phenomenon is cancelled, and it is compared with the method proposed in the existing technology. 100 independent experiments are carried out at different noise levels. Calculate the average value of the results of these 100 experiments as a reference, as Figure 5 shown.

[0059] It can be seen from Figure 5 that when , both methods can estimate accurate results p = 80, which is the same as the theoretical value. However, as the noise level increases, the (Adaptive Sparse Periodic Group Lasso, AdaESPGL) estimation method produces the maximum estimated value p = 82 and the minimum estimated value p = 74, and the percentage error is 8.8%. The maximum estimated value of AdaFP proposed by the present invention is p = 81, and the minimum estimated value p = 79.8, and the percentage error generated is 1.3%, indicating that the period estimation method proposed by the present invention has better estimation accuracy.

[0060] In addition, it is worth noting that the AdaESPGL period estimation method needs to pre-calculate the bearing theoretical fault frequency before the period can be estimated, and the proposed AdaFP method can estimate the possible fault period without prior information, which has certain significance in practical engineering.

[0061] The present invention also proposes a bearing fault diagnosis system, including: A fault signal period acquisition module, configured to determine the estimated period value of the signal and obtain the fault period of the bearing by acquiring the spectrum information of the collected bearing fault signal and screening out the fault frequency; The fault signal sparse denoising module is used to determine the optimization objective function for the sparse representation of the bearing fault signal according to the fault period of the bearing; take the adaptive parameter in the optimization objective function as the optimization target, construct a comprehensive index, and determine the optimal adaptive parameter with the minimization of the comprehensive index as the goal; determine the optimal sparse representation optimization objective function according to the optimal adaptive parameter, and perform sparse denoising on the bearing fault signal; wherein, the comprehensive index is the ratio of the error between the sparse denoised signal and the noise-free original signal to the envelope spectrum peak factor, and is used to characterize the relationship between the adaptive parameter and the noise level; The fault signal enhancement module is used to construct a fitness function for the filter length and displacement number according to the bearing fault signal after sparse denoising through correlation kurtosis, obtain the parameter combination of the filter length and displacement number with the maximum correlation kurtosis, filter the bearing fault signal after sparse representation, and obtain the periodic fault component with enhanced signal; The fault signal diagnosis module is used to perform envelope spectrum analysis on the periodic fault component with enhanced signal to obtain the characteristic frequency and multiple frequency of the fault signal.

[0062] The bearing fault diagnosis method proposed by the present invention can achieve accurate diagnosis of bearing faults under strong noise.

[0063] Analog signal results Comparison results of different methods To verify the effectiveness of the method proposed by the present invention, the method proposed by the present invention was compared with three methods: (Periodic Group-Sparsity Learning, PGSL), (Basis Pursuit Denoising, BPD), and AdaESPGL.

[0064] Among them, the PGSL method belongs to a framework of sparse Bayesian learning, so no parameter adjustment is required. For the BPD method, the present invention k sets the sparse parameter to the true value. For the key parameter selection of AdaESPGL , the same number of iterations is set to observe the comparison effect . The relevant parameter settings in AdaSRMD are shown in Table 2. The results after processing the above analog signals by the above methods are as Figure 6 shown.

[0065] Table 2 AdaSRMD algorithm parameter settings

[0066] From Figure 6 (a), it can be seen that although the complete knowledge of k-sparsity is known, the fault pulse extraction performance of BPD is still the worst. Figure 6(b) It is observed that although PGSL has a certain accuracy for fault pulse extraction, it misjudges the fault extraction within the first 0.4 s. Figure 6 (c) It can be seen in (c) that AdaESPGL does not misjudge within 0.4 s, but its performance in maintaining the fault pulse amplitude is poor. Figure 6 (d) It can be seen in (d) that the proposed method performs well both in the accuracy of fault pulse extraction and the ability to maintain the fault pulse amplitude.

[0067] Robustness Evaluation of AdaSRMD Algorithm The estimation accuracy is evaluated by the RMSE index, and the envelope spectrum peak factor index is used to evaluate the fault feature detection ability. 100 groups of independent simulation experiments are carried out at each noise level, and the average value is calculated as the analysis result, and it is compared with the PGSL, BPD and AdaESPGL methods. The obtained results are as Figure 7 shown.

[0068] From Figure 7 (a), it can be seen that the RMSE values obtained by the four methods all increase with the increase of the noise level. However, the proposed method is better than the other methods in the ability to restore the amplitude of the fault signal. For AdaESPGL, when the noise level is small, the ability to maintain the amplitude is not much different from that of the proposed method, but as the noise increases, the proposed method has significantly better ability to maintain the amplitude after MCKD fault enhancement. From Figure 7 (b), it can be seen that the envelope spectrum peak factors of the AdaESPGL and BPD methods gradually decrease with the increase of the noise level, indicating that the anti-interference abilities of the two methods are weak.

[0069] The of PGSL changes little with the increase of the noise level, proving that the PGSL method has a certain robustness. However, compared with AdaSRMD, it can be clearly seen that the proposed method has better fault extraction ability.

[0070] To sum up, it is proved that AdaSRMD has certain superiority compared with PGSL, BPD and AdaESPGL.

[0071] Case Analysis To verify the feasibility of the method proposed in the present invention, real bearing fault signals are used to verify the effectiveness of the method proposed in the present invention. The data sets are from the bearing fault data set of Case Western Reserve University and the bearing fault data collected personally.

[0072] Setting Data Set Experiments Data Source The rolling bearing fault simulation test bench at Case Western Reserve University in the United States mainly consists of components such as a motor, a torque sensor, a power tester, and an electronic controller.

[0073] Experimental environment The experimental bearing is electrically discharged to produce a single-point damage to simulate the fault states of the inner ring, outer ring, and rolling elements of the bearing. The diameter of the fault damage used in this experiment is 0.007 inches. The processed faulty bearing is installed in the test motor, and the vibration acceleration signal data is recorded when it operates under different loads. The signal is collected by a 16-channel data recorder, with a sampling frequency of 12 kHz and a motor speed of 1797 r / min.

[0074] Based on the various parameters of the bearing, the fault characteristic frequency of the inner ring of the bearing in the Case Western Reserve University bearing fault experiment is calculated as = 162.2 Hz, and the fault characteristic frequency of the outer ring is = 107.3 Hz. Since the k-sparsity parameter of BPD is unknown, it is set to 10% of the total number of coefficients, and the remaining parameters are the same as those set in the simulation experiment in Section 4. In this study, an NVIDIA GeForce RTX 4060 and a 3.4 GHz Gen Intel Core i7-13700K processor are equipped, and the calculation software is MATLAB 2024 a.

[0075] Analysis of experimental results As Figure 8 shown, it shows the extraction results of different strategies and their envelope spectra when the inner ring of the bearing fails. To reflect the proportion of the fault frequency and its harmonics, the amplitude of the envelope spectrum is normalized.

[0076] From Figure 8 (a) and Figure 8 (b), it is difficult to find effective fault information in the original vibration signal (the fault frequency is interfered by the sidebands). From Figure 8 (c), it can be seen that the time-domain signal after BPD processing performs poorly in fault information extraction and amplitude retention. Figure 8 (d), it can be seen that the BPD algorithm fails to effectively separate the fault frequency from its generated sidebands because it does not fully utilize the group sparsity and periodic structure of the fault pulses. Figure 8 (e), Figure 8 (f) and Figure 8 (g), Figure 8 (h) respectively show the results extracted by the PGSL algorithm and the AdaESPGL algorithm. It can be observed that both methods have good effects in fault information extraction, and the fault frequency and its harmonics can also be observed in the frequency domain. However, both methods have varying degrees of attenuation and loss in the extraction of time-domain fault information and do not retain the fault information to the greatest extent. Comparing Figure 8 (i) andFigure 8 (j) The method proposed in the present invention shows that AdaSRMD can completely extract the fault pulse components in the time domain. In the frequency domain, compared with the results extracted by the PGSL algorithm and the AdaESPGL algorithm, the fault information at [specific frequencies] is also highlighted by AdaSRMD, demonstrating the superiority of the proposed method.

[0077] To demonstrate the superiority of AdaSRMD, AdaSRMD and AdaSR were respectively used to process the inner race fault of the bearing. From Figure 9 (a) and Figure 9 (b), it can be observed that the results after sparse representation processing have the ability to extract fault pulses, but the restoration of fault information and the amplitude retention effect are quite different compared with Figure 9 (c) and Figure 9 (d) after being processed by AdaSRMD.

[0078] As Figure 10 shown, the extraction results and their envelope spectra of different strategies when the outer race of the bearing fails are presented. To demonstrate the strong noise background, Gaussian white noise ( ) was added to the original signal.

[0079] Figure 10 (a) and Figure 10 (b) are the original vibration signals when the outer race of the bearing fails. From Figure 10 (c) and Figure 10 (d), it can be seen that BPD shows a significant performance degradation because the sparse structure of the pulse is almost masked by the strong background noise. Figure 10 (e) and Figure 10 (f) show the results extracted by the PGSL algorithm. Since PGSL has a certain robustness, the extraction of fault information is relatively complete. However, compared with the proposed method, the AdaSRMD algorithm has different degrees of improvement in , , , . From Figure 10 (g) and Figure 10 (h) are the extraction results of AdaESPGL. Due to the strong noise background, there are varying degrees of attenuation and missing at the fault frequency and its multiples, and the fault information is not retained to the greatest extent. Figure 10 (i) and Figure 10 (j) are the methods proposed in the present invention. It can be seen that when the outer race of the bearing fails, AdaSRMD can completely extract the fault pulse components in the time domain.

[0080] TYS1-8 Bearing Vibration Dataset Data Source This experiment verified the effectiveness of the method of the present invention using a private dataset. In the experiment, a Lion Precision B06A00 uniaxial acceleration sensor was installed on the vertical axis of the test bearing housing, and the sensor was installed in a magnetic adsorption manner.

[0081] Experimental environment To simulate the actual working environment of the bearing, a load of 2.5 kN was applied radially to the test bearing housing, and a load of 5 kN was applied axially to the test bearing housing. The data acquisition card used a PXIe-69529 dynamic signal acquisition module, and the sampling frequency was 12 kHz. The experimental faulty bearing used a rolling bearing SKF 6206-2Z, and the bearing-related parameters are shown in Table 3.

[0082] Table 3 Main parameters of the bearing

[0083] Artificially machined cracks were introduced on the inner and outer rings of the bearing, and the fault size was 1.0×1.0 mm. According to the theoretical fault frequency calculation formula, the fault characteristic frequency of the bearing inner ring can be obtained as , and the fault characteristic frequency of the outer ring is Hz.

[0084] Analysis of experimental results As Figure 11 shown, it shows the extraction results and their envelope spectra of different strategies when a fault occurs in the inner ring of the bearing based on the TYS1-8 bearing vibration dataset. Figure 11 (a) and Figure 11 (b) are the original vibration signals when a fault occurs in the inner ring of the bearing. It can be seen from Figure 11 that the fault pulse signal of the inner ring fault is masked by strong background noise. In this case, it can be seen from Figure 11 (c) and Figure 11 (d) that the extraction effect of the BPD algorithm is always the worst. It can be seen from Figure 11 (e) and Figure 11 (f) that the PGSL algorithm performs better in extracting faults, but there are gaps in both the time domain and the frequency domain compared with the proposed algorithm. It can be seen from Figure 11 (g) and Figure 11 (h) that AdaESPGL captured some important pulses, but the key periodic pulses corresponding to the inner ring fault of the bearing were ignored, which was caused by the error between the fault period value obtained by the AdaESPGL method and the theoretical value. Figure 11 (i) and Figure 11 (j) is the method proposed in the present invention. It can be seen that when a fault occurs in the inner ring of the bearing, AdaSRMD completely extracts the fault pulse component in the time domain.

[0085] As Figure 12As shown, the update curve of the period estimation with the number of iterations is presented. For the method proposed in the present invention, namely the AdaFP period estimation method, the estimation error is close to 2, while the error between the convergence value of the AdaESPGL method and the theoretical value reaches 6, further demonstrating the superiority of the method proposed in the present invention.

[0086] As Figure 13 shown, the extraction results and their envelope spectra of different strategies when a fault occurs in the outer ring of the bearing based on the TYS1-8 bearing vibration dataset are presented. Figure 13 (a) and Figure 13 (b) are the original vibration signals when a fault occurs in the outer ring of the bearing. As can be seen from Figure 13 (c) and Figure 13 (d), it can be seen that the ability of BPD to extract faults in the presence of strong noise background is still the worst. As can be seen from Figure 13 (g) and Figure 13 (h), the AdaESPGL algorithm shows poor denoising ability in the time domain and can only extract and in the frequency domain. Figure 13 (e) and Figure 13 (f) of PGSL can achieve good performance in this case. However, it should be noted that the AdaSRMD method can provide the fault frequency more clearly. Figure 13 (i) and Figure 13 (j) are the methods proposed in the present invention. It can be seen that when a fault occurs in the outer ring of the bearing, the AdaSRMD can completely extract the fault pulse components in the time domain.

[0087] Table 4 Comparison results of different methods

[0088] From Table 4, the processing results of different methods for the TYS1-8 platform dataset can be seen. BPD fails in the extraction of inner ring faults and also has poor extraction effect for outer ring faults. The extraction effect of AdaESPGL is not good due to the excessive error between the period estimation value and the theoretical value. The AdaSRMD and PGSL methods have better extraction ability compared with other methods. However, it should be noted that the AdaSRMD has stronger ability to restore faults.

[0089] In summary, the AdaSRMD bearing fault detection method proposed by the present invention. First, according to the characteristics of the fault signal, without any information about the faulty bearing, the possible fault period in the fault signal is dynamically estimated and constructed into a binary vector and embedded into the penalty function to promote the intra-group and inter-group sparsity of the fault signal, realizing the denoising of the fault signal. Then, the denoised signal is enhanced for fault information through the MCKD algorithm, effectively combining the advantages of pulse extraction of the adaptive sparse cycle group lasso and pulse feature enhancement of the MCKD algorithm, making it have good anti-noise performance and fault feature extraction ability for vibration signals. Finally, the effectiveness and applicability of the method are demonstrated through a simulation study and two experimental cases. By comparing with the BPD, PGSL, and AdaESPGL methods, the effectiveness of the bearing fault diagnosis method proposed by the present invention is further verified.

[0090] As described above, the above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

[0091] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In case of conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A bearing fault diagnosis method, characterized in that, It includes the following steps: According to the collected bearing fault signals, by obtaining the spectral information of the signals and screening out the fault frequencies, determine the estimated period value of the signals, and obtain the fault period of the bearing; According to the fault period of the bearing, determine the optimization objective function for the sparse representation of the bearing fault signals; take the adaptive parameter in the optimization objective function as the optimization target, construct a comprehensive index, and take the minimization of the comprehensive index as the goal to determine the optimal adaptive parameter; according to the optimal adaptive parameter, determine the optimal sparse representation optimization objective function, and perform sparse denoising on the bearing fault signals; where the comprehensive index is the ratio of the error between the sparse denoised signal and the noiseless original signal to the envelope spectrum peak factor, and is used to characterize the relationship between the adaptive parameter and the noise level; According to the bearing fault signals after sparse denoising, construct a fitness function for the filter length and displacement number through the relevant kurtosis, obtain the parameter combination of the filter length and displacement number with the maximum relevant kurtosis, filter the bearing fault signals after sparse representation, and obtain the enhanced periodic fault components of the signals; Perform envelope spectrum analysis on the enhanced periodic fault components of the signals to obtain the characteristic frequencies and multiple frequencies of the fault signals.

2. The bearing fault diagnosis method according to claim 1, wherein The obtaining of the fault period of the bearing specifically includes: For the signal perform a first-order difference operation to obtain , and calculate the analytic signal of the signal through Hilbert transform : ； For perform FFT to obtain spectral information. The obtained frequency-domain information is symmetric about the left and right. Only select the right half of it to obtain the frequency index after descending sorting of the spectral energy information; Select the top 20 largest frequencies as the active frequency set according to the sorted index : ； Among them, f s is the sampling frequency, f c is the fault frequency, n is the index of the fault frequency set; Obtain the active frequency set in which the frequency intervals less than for the frequency individuals are removed, and update the current active frequency set ; Loop through each element in the updated current active frequency set to calculate the multiple relationships between them, and filter out the active frequencies with multiple relationships from the active frequency set ​ Perform a weighted average on the active frequencies with a multiple relationship that are screened out, and calculate the fault frequency with the highest occurrence probability ; According to the failure frequency , determine the estimated period value of the signal P .

3. The bearing fault diagnosis method according to claim 2, characterized in that, The determination of the optimization objective function for the sparse representation of the bearing fault signals includes the following steps: The mathematical expression for obtaining the dictionary-free sparse representation of the signals is: ； Among them, is the original signal without noise, is the sparse denoised signal, is the adaptive parameter, P ( x ) is the penalty function; Obtain a binary weight vector : ； Among them, is the estimated length of a fault impulse pulse, is the interval length between adjacent fault impulses, is the group size, is the number of complete fault impulses contained in each group, is the length occupied by each complete fault impulse, that is, the estimated period value of the signal; According to the sampling frequency and the fault frequency , the parameter P satisfies the equation: ； According to the binary weight vector , penalty function and the mathematical expression of dictionary-free sparse representation, the optimization objective function for the sparse representation of bearing fault signals is obtained as follows: ； Among them, i is the group indexing coefficient, is the set indexing, is the sparsity penalty function, , is the constant value for controlling the non-convexity degree of the penalty, is the balance parameter, is the reweighted l penalty of 1; ， ； Among them, is a diagonal matrix, and the diagonal elements contain , is defined as: ； wherein, is a small positive constant for avoiding division by zero; When and then is convex.

4. The bearing fault diagnosis method according to claim 3, characterized in that The determination of the optimal adaptive parameter includes the following steps: The adaptive parameter in the optimization objective function for sparsely representing the bearing fault signal , is used as the optimization objective; Based on the adaptive parameter , construct a comprehensive index to characterize the relationship between the adaptive parameter and the noise level; The more the number of periodic impulses in the vibration signal, the greater the peak value at the impulse occurrence frequency in the signal envelope spectrum ; the ratio of the maximum value to the effective value of the filtered signal envelope spectrum within the range of is taken as the envelope spectrum peak factor , which is expressed as: ； Among them, is the rotation frequency; The larger the value, the higher the signal-to-noise ratio and the greater the energy of the signal, and the stronger the periodic impact component; the envelope spectrum peak factor is used as a measure of the impact component in the signal; The error between the sparse denoised signal and the noiseless original signal is: ； RMSE The smaller it is, the better the fitting degree between the denoised signal and the original noise-free signal, indicating that the model is more accurate in estimation; Place and RMSE in the denominator and numerator of the fraction respectively to construct a comprehensive index : ； Comprehensive index It is used to simultaneously reflect the denoising ability and estimation accuracy of the model; Comprehensive index The smaller the value is, the closer the denoised signal is to the original fault pulse; when the value reaches the minimum, it indicates that the adaptive parameter is optimal; Using comprehensive indicators Minimize to determine the optimal adaptive parameters , and determine the best through linear fitting curves at different noise levels to obtain the relationship between 5. The bearing fault diagnosis method according to claim 4, wherein The sparse denoising of the bearing fault signals specifically includes: Substitute the optimal adaptive parameters into the optimization objective function for the sparse representation of the bearing fault signal to obtain the optimal sparse representation optimization objective function; Adopt the iterative optimization process of the MM algorithm to solve the optimal sparse representation optimization objective function, and obtain the bearing fault signals after sparse denoising.

6. The bearing fault diagnosis method according to claim 5, characterized in that, The obtaining of the enhanced periodic fault components of the signals includes the following steps: With the condition that the relevant kurtosis value of the bearing fault signals after sparse denoising is the largest, filter the fault signals to extract the fault characteristics; The essence of the MCKD algorithm is to find a FIR filter to recover the continuous impact signal submerged by noise; through correlation kurtosis, the signal is filtered, and when the correlation kurtosis is the maximum, the signal recovered by the solved filter satisfies the periodic impact characteristic; Correlation kurtosis The expression is as follows: ； The condition for maximizing the relevant kurtosis is: ； Calculate the filter coefficients: ； Among them, is the deconvolution period, is the shift number, m ∈ [0, M , is the filter length; Each coefficient in the formula is: ； ； ； ； For the filter length L and the displacement number M , construct the fitness function of the filter length and the displacement number through the relevant kurtosis; Through the grid search method, search for the parameter combination of the filter length and displacement number that maximizes the relevant kurtosis, and obtain the optimized filter length, displacement number, and deconvolution period. The optimized filter length, displacement number, and deconvolution period are the enhanced periodic fault components of the signals.

7. The bearing fault diagnosis method according to claim 6, characterized in that The specific steps for obtaining the optimized filter length, displacement number, and deconvolution period include: Determine the filter length L and the displacement number M of the search range and the search step size; Initialize the parameter filter length according to the search range L and the displacement number M ; assign a value to the deconvolution period T according to the period estimation result According to the initialized parameter filter length L , displacement number M and the deconvolution period assigned according to the period estimation result T , calculate the corresponding correlation kurtosis as the correlation kurtosis A ; Update the parameters according to the search step size, and calculate the relevant kurtosis corresponding to the updated parameters as the relevant kurtosis B ; Compare the relevant kurtosis B with the relevant kurtosis A When the relevant kurtosis B is less than the relevant kurtosis A , retain the relevant kurtosis B ; When the relevant kurtosis B is greater than the relevant kurtosis A , retain the relevant kurtosis A ; After the search is completed, the parameters corresponding to the relevant kurtosis finally retained are output as the optimal filter length L , the number of displacements M and the deconvolution period T .

8. The bearing fault diagnosis method according to claim 7, wherein The obtaining of the characteristic frequencies and multiple frequencies of the fault signals specifically includes: According to the optimized filter length, displacement number, and deconvolution period, perform fault feature enhancement on the bearing fault signals after sparse denoising through the MCKD algorithm, and perform envelope spectrum analysis on the enhanced results to obtain the extraction and diagnosis results of the characteristic frequencies and multiple frequencies of the bearing faults under strong noise.

9. A bearing fault diagnosis system, characterized in that, It includes: A fault signal period acquisition module, which is used to determine the estimated period value of the signals and obtain the fault period of the bearing according to the collected bearing fault signals by obtaining the spectral information of the signals and screening out the fault frequencies; A fault signal sparse denoising module, which is used to determine an optimization objective function for the sparse representation of the bearing fault signal according to the fault period of the bearing; take the adaptive parameter in the optimization objective function as the optimization objective, construct a comprehensive index, and determine the optimal adaptive parameter with the minimization of the comprehensive index as the goal; according to the optimal adaptive parameter, determine the optimal sparse representation optimization objective function, and perform sparse denoising on the bearing fault signal; wherein, the comprehensive index is the ratio of the error between the sparse denoised signal and the noise-free original signal to the envelope spectrum peak factor, and is used to characterize the relationship between the adaptive parameter and the noise level; A fault signal enhancement module, which is used to construct a fitness function of the filter length and the displacement number according to the sparse denoised bearing fault signal through the correlation kurtosis, obtain the parameter combination of the filter length and the displacement number with the maximum correlation kurtosis, filter the sparse represented bearing fault signal, and obtain the periodic fault component with enhanced signal; A fault signal diagnosis module, which is used to perform envelope spectrum analysis on the periodic fault component with enhanced signal to obtain the characteristic frequency and multiple frequency of the fault signal.

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