A Bearing Fault Diagnosis Method Based on Sparse Decomposition with Reweighted Stepwise Regularization

Abstract

A reweighted step-by-step regularized bearing fault diagnosis method based on sparse decomposition relates to bearing fault diagnosis. The method includes the following steps: 1) establishing a sparse decomposition problem model: by introducing a suitable penalty function to replace the 0 norm, and by means of regularization, transforming it into an unconstrained optimization problem; 2) constructing a substitute function so that the substitute function has an optimal solution close to the objective function; 3) optimizing the substitute function, by iteratively constructing and reducing the substitute function, the time index parameter gradually converges to the position where the actual impact occurs, and the sparse coefficient gradually approaches the true value; 4) updating the regularization parameter and eliminating redundant atoms, when the convergence error is less than the set convergence threshold, ending the iteration, and completing the reweighted step-by-step regularized bearing fault diagnosis. It can have both strong sparse promotion ability and high fitting accuracy, and has higher signal reconstruction accuracy, so as to provide more accurate bearing fault diagnosis results.

Description

Technical Field

[0001] The present invention relates to bearing fault diagnosis, and in particular to a reweighted stepwise regularization bearing fault diagnosis method based on sparse decomposition Background Art

[0002] Vibration monitoring is one of the most important methods for bearing fault diagnosis. However, the actually measured vibration signals usually contain a large amount of noise interference. Especially in the early stage of bearing faults, the impact signals are weak and the signal-to-noise ratio (SNR) is extremely low. How to accurately identify the characteristic parameters reflecting the bearing health state from the noisy signals is the key problem to be solved in bearing fault diagnosis based on vibration monitoring. Sparse decomposition is a powerful signal decomposition technique. By constructing a suitable sparse dictionary, the target components in the signal can be sparsely represented and accurately reconstructed by a few atoms in the dictionary, while the noise cannot be decomposed by the dictionary atoms. Therefore, sparse decomposition has extremely strong anti-noise ability. Among many methods based on sparse decomposition, the regularization method based on sparse constraints has been widely studied and adopted. L1-norm regularization is the earliest proposed sparse regularization method, which has the advantages of simple model and convenient calculation. However, the optimal solution of L1-norm regularization tends to underestimate the amplitude of transient impact signals, thus leading to an underestimation of the severity of bearing faults. To overcome this problem, the regularization method based on the generalized minimax-concave (GMC) penalty function has been proposed and applied to the field of bearing fault diagnosis, achieving remarkable performance improvement effects. However, whether it is GMC regularization or L1-norm regularization, a key problem that needs to be faced is the selection of the regularization parameter. The regularization parameter is an important parameter that balances the sparsity of the solution result and the fitting accuracy, and largely determines the reconstruction performance of the sparse regularization method.

[0003] Existing methods usually adopt an exhaustive method to select the optimal regularization parameter or artificially specify the sparsity through the K-sparse strategy. However, no matter how the selection of the regularization parameter is optimized, the optimal solution of the objective function will still be a compromise result between pursuing sparsity and fitting accuracy, that is, the existing sparse regularization is difficult to simultaneously have strong sparse promotion ability and high fitting accuracy, and the signal reconstruction performance is thus limited. Summary of the Invention

[0004] In view of the above-mentioned technical problems existing in the prior art, the present invention provides a bearing fault diagnosis method based on sparse decomposition and a reweighted stepwise regularization method (RSR) with sparse dictionary adaptation, which can have both strong sparsity promotion ability and high fitting accuracy. Compared with the existing mainstream sparse regularization methods, it has higher signal reconstruction accuracy, thereby providing more accurate bearing fault diagnosis results.

[0005] The present invention comprises the following steps:

[0006] 1) Establish a sparse decomposition problem model: by introducing a suitable penalty function to replace the zero norm, and with the help of regularization, it is transformed into an unconstrained optimization problem;

[0007] 2) Construct a substitute function so that the substitute function has an optimal solution close to the objective function;

[0008] 3) Optimize the substitution function. By iteratively constructing and reducing the substitution function, the time index parameter gradually converges to the location where the actual impact occurs, and the sparse coefficient gradually approaches the true value;

[0009] 4) Update the regularization parameters and eliminate redundant atoms. When the convergence error is less than the set convergence threshold, the iteration ends and the reweighted step-by-step regularized bearing fault diagnosis is completed.

[0010] In step 1), the specific steps of establishing the sparse decomposition problem model may be:

[0011] Introduce the logarithmic sum penalty function to replace the zero norm to construct the objective function to be optimized and solve the vibration signal y The sparse representation on the sparse dictionary A is described as:

[0012]

[0013] in, represents a sparse dictionary matrix, Represents a vector composed of sparse coefficients; n represents noise interference; τ represents the time index parameter, ε represents the tolerance, and ∈ is a positive parameter to ensure that the true value of the logarithmic function is greater than 0; by making the positive parameter ∈ approach 0 to ensure that the global optimal solution converges to the true value; with the help of regularization, the above formula is expressed as the following unconstrained objective function optimization problem:

[0014]

[0015] λ represents the regularization parameter, which is a parameter that varies with the iterative process. The value of λ determines the weight of the error term and the regularization term in the objective function, affecting the location of the global optimal solution. To solve the optimal solution of the above formula, a controlled minimization framework is adopted, and the objective function is indirectly optimized by optimizing an appropriate surrogate function.

[0016] In step 2), in the (i + 1)-th iteration, a surrogate function about the penalty function L(x) is constructed satisfying if and only if the equal sign holds:

[0017]

[0018] where and λ (i) respectively represent the sparse coefficient vector obtained in the i-th iteration and the selected regularization parameter. Thus, the above formula is rewritten in the following surrogate function form:

[0019]

[0020] According to the optimization process of the controlled minimization framework, the solution result close to the optimal solution of the objective function can be obtained by iteratively constructing and optimizing the surrogate function F.

[0021] In step 3), the specific steps for optimizing the surrogate function can be:

[0022] Remove the constant term in the surrogate function, and simplify it to an optimization problem for a single variable τ:

[0023]

[0024] Use the gradient descent method to solve the above formula to obtain a new estimated value of τ; by comparing the function values of R(τ) at the positions of multiples of adjacent T' after each optimization in the gradient descent method, the position corresponding to the minimum value is used as the result after this optimization to make τ n gradually converge to the position of the global optimal solution; solve the above formula to obtain a new estimated value The update process for each time index parameter is as follows:

[0025]

[0026] where g n is the result optimized by the gradient descent method, α is the step size, is the first-order partial derivative of R(τ) with respect to τ n K is the maximum period multiple for the quadratic search of the optimal solution, and the oscillation period f represents the natural frequency. After each optimization of τ nImmediately update the corresponding atom a in A(τ). n (τ n ), so as to utilize the optimized atom information when optimizing τ n+1 ; Ensure that the updated satisfies to obtain a new round of estimation of the sparse coefficient vector:

[0027]

[0028] By iteratively constructing and reducing the surrogate function, the time index parameter gradually converges to the position where the actual impact occurs, and the sparse coefficient vector is also estimated more accurately in this process.

[0029] In step 4), the specific steps for updating the regularization parameter and removing redundant atoms may be:

[0030] In the strong sparsity optimization stage, if the size of λ is set to the variance of the noise, it can better automatically balance the sparsity and fitting accuracy. The estimated value of the noise variance can be obtained by the following formula:

[0031]

[0032] Multiply by a fixed amplification factor μ as the value of λ in the next round of iteration to increase the weight of the regularization term:

[0033]

[0034] where the recommended value of μ is 4 - 7; preset the trimming threshold κ (set to 5% of the maximum amplitude of the vibration signal), and in each iteration, by removing the elements less than κ in and their corresponding atoms in the sparse dictionary, dynamically reduce the dimension of in real time, so that it gradually converges to the same sparsity as the actual impact signal, and at the same time shorten the calculation time required for updating

[0035] In the strong fitting optimization stage, there are no redundant atoms in and each atom corresponds to the actual impact one by one. The sparsity of the reconstructed signal is guaranteed by

[0036] Define as the convergence error of the (i + 1)-th iteration. Then, as the iteration result converges, Δ will converge to near 0; set the convergence threshold Δ1 = 10-3 and Δ2 = 10 -6 , respectively determine whether to enter the strong fitting optimization stage from the strong sparse optimization stage and whether to end the iteration by the conditions of whether Δ (i+1) is less than Δ1 and Δ2.

[0037] The present invention overcomes the problem that traditional sparse regularization methods are difficult to simultaneously have strong sparse promotion ability and high fitting accuracy, resulting in deterioration of signal reconstruction performance. Based on simulation and verification tests, its performance is analyzed. The results show that the present invention can have both strong sparse promotion ability and high fitting accuracy, and has higher signal reconstruction accuracy, so as to provide more accurate bearing fault diagnosis results. Brief Description of the Drawings

[0038] Figure 1 are the results of least squares fitting of impact signals using Laplace wavelets at different times.

[0039] Figure 2 is the variation law of the function R(τ) with the variable τ n .

[0040] Figure 3 are the simulation fault signals and the reconstruction results of different methods. Among them, (a) is the time-domain waveform of the fault signal, (b) is the L1-norm regularization, (c) is the GMC regularization, (d) is the reweighted stepwise regularization, and (e) is their envelope spectrum.

[0041] Figure 4 are the photos of the test site. Among them, (a) is the test bench and (b) is the faulty bearing;

[0042] Figure 5 are the measured fault signals and the reconstruction results of different methods in the test. Among them, (a) and (d) are the L1-norm regularization, (b) and (e) are the GMC regularization, and (c) and (f) are the reweighted stepwise regularization. Detailed Embodiment

[0043] The following embodiments will further illustrate the present invention in conjunction with the drawings.

[0044] The embodiments of the present invention include the following steps:

[0045] Step 1: Establish a sparse decomposition problem model

[0046] When a bearing running at a constant speed fails, the actually measured vibration signal usually contains noise interference in addition to periodic transient impact components. Therefore, the vibration signal can be expressed as follows:

[0047] y = y0 + n (1)

[0048] Among them, represents the bearing fault signal, n represents the noise interference, which is usually white noise with a Gaussian distribution. y0 can be decomposed by a suitable sparse dictionary into a series of sparse coefficients with most elements being 0, that is

[0049] y0 = Ax (2)

[0050] Among them, represents the sparse dictionary matrix, represents the vector composed of sparse coefficients. Solving the sparse representation of the vibration signal y on the sparse dictionary A can be described as the following problem

[0051]

[0052] where ||·|| p represents the p-norm, and ε represents the tolerance. The above problem is an NP-hard problem and is difficult to solve directly. By introducing a suitable penalty function to replace the 0-norm and with the help of regularization, the above problem can be further transformed into the following unconstrained optimization problem, so as to use the optimization algorithm for solution

[0053]

[0054] Among them, λ represents the regularization parameter, and its value determines the weight of the error term and the regularization term in the objective function, thus affecting the location of the global optimal solution. P(x) represents the penalty function, which has the ability to promote sparsity. Typical penalty functions include the L1 norm and the GMC function, etc.

[0055] The sparse dictionary is usually constructed artificially according to prior knowledge. The matching degree between the preset atoms in the sparse dictionary and the actual transient impact signal greatly affects the signal reconstruction performance of the sparse regularization method. For the transient impact signal caused by bearing faults, the most commonly used dictionary at present is the Laplace wavelet dictionary. Its form is constructed as follows

[0056]

[0057] Among them, f represents the natural frequency, ζ ∈ [0, 1) represents the damping ratio, τ represents the time index parameter, and W s represents the wavelet support interval. The relevant filtering method can be used to obtain reliable estimated values of the natural frequency f and the damping ratio ζ. The specific method is to calculate the inner product of the wavelet sequence and the vibration signal by traversing all discrete points in the feasible domain of the parameters, and the parameters corresponding to the maximum value are the estimated values. The value of τ determines the position of the preset atom on the time axis. Traditional sparse regularization usually discretizes a series of different τ values on the time axis at intervals of the sampling period, and constructing Laplace wavelet atoms at these positions forms the atom library of the sparse dictionary A, that is, A = [a1, a2,... aN , where represents the nth column of A, and t is the column vector composed of all sampling moments.

[0058] In the present invention, the time index parameter is defined as a variable. Therefore, the sparse dictionary is no longer a constant matrix but becomes a function of the time index τ, A(τ) = [a1(τ1), a2(τ2),... a N (τ N ), where represents the nth column of A(τ). Therefore, Equation (3) correspondingly becomes

[0059]

[0060] To solve the above problem and obtain a better sparse promotion ability, a logarithmic sum penalty function is introduced to replace the 0 norm to construct the objective function to be optimized. Then, Equation (6) can be rewritten as

[0061]

[0062] where ∈ is a positive parameter, which can ensure that the argument of the logarithmic function is greater than 0. In addition, by making ∈ approach 0, it can be ensured that the global optimal solution of Equation (7) converges to the vicinity of the true value. With the help of regularization, Equation (7) can be further expressed as the following unconstrained optimization problem

[0063]

[0064] In the present invention, λ is set as a parameter that changes with the iterative process, and its specific selection method will be described in the following part. Since the optimal solution of Equation (8) is difficult to directly solve, a controlled minimization framework is used to indirectly optimize the objective function by optimizing a suitable surrogate function.

[0065] Step 2: Construct a surrogate function

[0066] Use and λ (i) to represent the sparse coefficient vector obtained in the i-th iteration and the selected regularization parameter respectively. In the (i + 1)-th iteration, construct a surrogate function about L(x) satisfying (equal sign holds if and only if ). Where

[0067]

[0068] Thus, Equation (8) can be rewritten as the following surrogate function form

[0069]

[0070] According to the optimization process of the controlled minimization framework, the solution result close to the optimal solution of Equation (8) can be obtained by iteratively constructing and optimizing the surrogate function F.

[0071] Step 3: Optimize the surrogate function

[0072] First, remove the constant term in Equation (10) and simplify it to

[0073]

[0074]

[0075] where, diag{·} represents a diagonal matrix. Fix τ, and the optimal solution of Equation (11) with respect to x can be obtained by the method of Lagrange multipliers as

[0076]

[0077] Substitute back into Equation (11), then the problem is further simplified to an optimization problem of a single variable τ

[0078]

[0079] Since the object of optimization is the surrogate function, it is not necessary to find the optimal solution that makes Equation (14) take the minimum value. It is only necessary to find a sub-optimal solution that makes it take a smaller value. Therefore, it is easy to solve Equation (14) by the gradient descent method to obtain a new estimate value of τ. However, due to the periodic oscillation characteristic of the transient impact signal, R(τ) does not monotonically decrease as τ gradually approaches the true value. Assume that a certain impact in the fault signal occurs at time τ0. When optimizing the corresponding element τ n in the τ vector, then R(τ) can take the minimum value if and only if τ n is a multiple of half the oscillation period away from τ0. Figure 1 Give an example to show the least squares fitting results of the impact signal using the Laplace wavelet when τ n is different multiples of half the oscillation period away from τ0. Figure 2 shows the variation law of R(τ) near τ0 with respect to τ n . It is usually very difficult to solve the global optimal solution for a function with many extreme points because it is easy to be trapped in a local optimal solution and end the iteration. Fortunately, R(τ) oscillates with τ n at a specific period, that is . By virtue of this characteristic, by comparing the function values of R(τ) at positions of multiples of adjacent T' after each optimization in the gradient descent method, and taking the position corresponding to the minimum value as the result of this optimization, τn Gradually converge to the position of the global optimal solution. That is, as long as the local optimal solution is found, the global optimal solution can be found. The new round of estimated values is obtained by solving (14) through the above method The update process for each time index parameter is as follows

[0080]

[0081] where g n is the result optimized by the gradient descent method, and α is the step size. In this embodiment, α = 1 is taken is the first-order partial derivative of R(τ) with respect to τ n K is the maximum period multiple for the quadratic search of the optimal solution. In this embodiment, K = 5 is taken. Here, after each optimization of τ n it is necessary to immediately update the corresponding atom a n (τ n ) in A(τ), so as to utilize the optimized atom information when optimizing τ n+1 . Through the above optimization process, it can be ensured that the updated satisfies

[0082]

[0083] Substitute back into Equation (13) to obtain a new round of estimation of the sparse coefficient vector

[0084]

[0085] By iteratively constructing and reducing the surrogate function, the time index parameter gradually converges to the position where the actual impact occurs, and the sparse coefficient vector is also estimated more accurately in this process

[0086] Step 4: Update the regularization parameter and eliminate redundant atoms

[0087] In order to obtain strong sparsity and high fitting accuracy simultaneously during the iteration process, different strategies are adopted to select the regularization parameter λ at different iteration stages, so as to achieve strong sparse optimization and strong fitting optimization step by step. First, in the strong sparse optimization stage, if the magnitude of λ is set to the variance of the noise, it can better automatically balance the sparsity and fitting accuracy. The estimated value of the noise variance can be obtained through the following formula

[0088]

[0089] In order to emphasize the sparse promotion ability of the algorithm in this stage, based on Equation (18), Multiply it by a fixed amplification factor μ to obtain the value of λ in the next round of iteration, so as to increase the weight of the regularization term

[0090]

[0091] Among them, the recommended value of μ is 4 to 7. In order to maintain the sparsity obtained in this stage in the optimization of the next stage and achieve the purpose of reducing the computational complexity, a preset trimming threshold κ (set to 5% of the maximum amplitude of the vibration signal) is used. In each iteration, by removing the elements less than κ in and the corresponding atoms in the sparse dictionary, the dimension of can be dynamically reduced in real time, so that it gradually converges to the same sparsity as the actual impact signal, while shortening the calculation time required for updating .

[0092] And in the strong fitting optimization stage, since has almost converged to the actual impact occurrence time, at this time there are no redundant atoms and each atom corresponds to an actual impact one by one. Therefore, the sparsity of the reconstructed signal can be guaranteed by , and there is no need to sacrifice the fitting accuracy for sparsity. By simply setting λ = 0 to remove the regularization term, that is, the least squares method can be used to obtain the best fitting result for the impact signal.

[0093] Define as the convergence error of the (i + 1)-th iteration. Then, as the iteration result converges, Δ will converge to near 0. Set the convergence thresholds Δ1 = 10 -3 and Δ2 = 10 -6 . Respectively, judge whether to enter the strong fitting optimization stage from the strong sparsity optimization stage and whether to end the iteration by whether Δ (i+1) is less than Δ1 and Δ2. The specific solution steps of the reweighted stepwise regularization algorithm are as follows:

[0094]

[0095] Among them, the fixed parameter λ (0) = 20, and the initial number of atoms N only needs to be greater than the number of impacts in the signal segment to ensure the signal reconstruction performance of the reweighted stepwise regularization.

[0096] To verify the accuracy of the present invention and explore the performance improvement by comparison, a bearing fault diagnosis simulation is carried out based on MATLAB software programming. Construct a noisy bearing fault signal y(t) according to the following formula.

[0097]

[0098] Among them, A = 2 is the amplitude parameter, damping ratio ζ = 0.08, natural frequency f = 2000Hz, time index τ0 = 0.005s, fault period T = 0.01s. The sampling rate is 25600Hz, and the signal length is 0.1s. The noise n(t) obeys Gaussian distribution The standard deviation σ = 0.75, so the SNR of the simulated signal can be calculated to be -7.78dB. Its time domain waveform is as follows: Figure 3 In order to compare and analyze the improvement effect of reweighted step-by-step regularization on signal reconstruction accuracy, the simulated signal was imaged after L1 norm regularization, GMC regularization and reweighted step-by-step regularization respectively, and the envelope spectra of the reconstructed signal obtained by the three methods were compared. The results are shown in Figure 2. Figure 3 (b), (c), (d), and (e). From the simulation results, it can be seen that L1 norm regularization and GMC regularization reconstruct false impact signals at some non-impact positions, while reweighted step-by-step regularization can reconstruct a more "clean" fault signal. From the envelope spectrum, it can be seen that the three methods can accurately extract the fault characteristic frequency and its frequency harmonic components. Among them, the amplitude fidelity of the fault signal of the reweighted step-by-step regularization is better than that of the other two methods. In summary, the signal reconstruction result of the reweighted step-by-step regularization has both the best sparsity and the lowest amplitude error. According to the RMSE value, the signal reconstruction accuracy of the reweighted step-by-step regularization is improved by 81.5% and 31.8% compared with the L1 norm regularization and GMC regularization, respectively. In order to verify the correctness of the simulation conclusions, a vibration test experiment of a prefabricated fault bearing was carried out on the test bench. As shown Figure 4 As shown in (a), the test device includes a drive motor, a speed sensor, a support shaft, a test bearing, an acceleration sensor and a loaded pulley. Figure 4 As shown in (b), the outer ring fault in the early stage is simulated by artificially processing the outer ring pitting. The sampling frequency of the signal is 10.24kHz, and a data segment with a length of 0.2s is intercepted for analysis. Among them, the AC motor rotates at a constant speed of 2100r / min, and the fault characteristic frequency of the bearing can be calculated to be f1=90Hz. The reconstruction results of the fault signal and its envelope spectrum of the three methods are shown in Figure 5 As shown. Figure 5 It can be seen that the transient impulse signals extracted by the three methods can all indicate the fault characteristic frequency f1 and its frequency multiple components, but both the reconstructed signal and the envelope spectrum show that the reweighted step-by-step regularization has the highest fault signal reconstruction amplitude. The experimental results are also consistent with the simulation, proving that the signal reconstruction accuracy of the present invention is better than that of the other two methods.

Claims

1. A bearing fault diagnosis method based on sparse decomposition with reweighted stepwise regularization, characterized in that The following steps are involved: 1) Establish a sparse decomposition problem model: by introducing a suitable penalty function to replace the zero norm, and using regularization, transform it into an unconstrained optimization problem; The specific steps of establishing the sparse decomposition problem model are: The logarithmic sum penalty function is introduced to replace the zero norm to construct the objective function to be optimized. The sparse representation of the vibration signal y on the sparse dictionary A is described as: Among them, represents a sparse dictionary matrix, represents a vector composed of sparse coefficients; n represents noise interference; τ represents a time index parameter, ε represents a tolerance, ∈ is a positive parameter to ensure that the argument of the logarithmic function is greater than 0; by making the positive parameter ∈ approach 0, the global optimal solution is ensured to converge near the true value; with the help of regularization, the above formula is expressed as the following unconstrained optimization problem: λ represents the regularization parameter, which changes with the iterative process. The value of λ determines the weight of the error term and the regularization term in the objective function, and affects the location of the global optimal solution. The optimal solution of the above equation adopts the controlled minimization framework, and the objective function is indirectly optimized by optimizing the appropriate surrogate function. 2) Construct a substitute function so that the substitute function has an optimal solution close to the objective function; 3) Optimize the substitution function. By iteratively constructing and reducing the substitution function, the time index parameter gradually converges to the location where the actual impact occurs, and the sparse coefficient gradually approaches the true value; 4) Update the regularization parameters and eliminate redundant atoms. When the convergence error is less than the set convergence threshold, the iteration ends and the reweighted step-by-step regularized bearing fault diagnosis is completed.

2. The method for bearing fault diagnosis based on sparse decomposition and reweighted stepwise regularization according to claim 1, wherein In step 2), in the (i + 1)-th iteration, construct a surrogate function for the objective function L(x). Satisfy If and only if the equality holds when Among them, and λ (i) respectively represent the sparse coefficient vector obtained in the i-th iteration and the selected regularization parameter; thus, the above formula is rewritten into the following surrogate function form: According to the optimization process of the controlled minimization framework, the solution close to the optimal solution of the objective function is obtained by iteratively constructing and optimizing the substitute function F.

3. The method for bearing fault diagnosis based on sparse decomposition and reweighted stepwise regularization as claimed in claim 1, wherein In step 3), the specific steps of optimizing the substitution function are: Removing the constant term in the substitution function simplifies it to an optimization problem for a single variable τ: The gradient descent method is used to solve the above equation to obtain a new round of estimated values ​​for τ; By comparing the function values of \(R(\tau)\) at the positions of multiples of adjacent \(T'\) after each optimization of the gradient descent method, and taking the position corresponding to the minimum value as the result after this optimization to make \(\tau\) n gradually converge to the position of the global optimal solution; solve the above formula to obtain a new round of estimated values The update process for each time index parameter is as follows: Among them, g n is the result optimized by the gradient descent method, α is the step size, is the first-order partial derivative of R(τ) with respect to τ n , K is the maximum period multiple of the optimal solution of the quadratic search, and the oscillation period f represents the natural frequency. After each optimization of τ n , the corresponding atom a in A(τ) is immediately updated n (τ n ), so that the optimized atom information is utilized when optimizing τ n+1 ; through the above optimization process of the time index parameter, it is ensured that the updated satisfies to obtain a new round of estimation of the sparse coefficient vector: By iteratively constructing and reducing the surrogate function, the time index parameter gradually converges to the location where the actual impact occurs, and the sparse coefficient vector is also estimated more accurately in this process.

4. The method for bearing fault diagnosis based on sparse decomposition and reweighted stepwise regularization according to claim 1, wherein In step 4), the specific steps of updating the regularization parameter and removing redundant atoms are: In the strong sparse optimization stage, if the size of λ is set to the variance of the noise, the sparsity and fitting accuracy can be better automatically balanced; the estimated value of the noise variance is obtained by the following formula: Multiply by a fixed amplification factor μ to obtain the value of λ in the next iteration, thereby increasing the weight of the regularization term: Among them, the recommended value of μ is 4 to 7; a preset trimming threshold κ is set to 5% of the maximum amplitude of the vibration signal, and in each iteration, by removing the elements less than κ in and their corresponding atoms in the sparse dictionary, the dimension of is dynamically reduced in real time, so that it gradually converges to the same sparsity as the actual impact signal, while shortening the calculation time required for updating; In the strong fitting optimization stage, there are no redundant atoms and each atom corresponds to an actual impact one by one. The sparsity of the reconstructed signal is ensured by By simply setting λ = 0 to remove the regularization term, that is, the least squares method is used to obtain the best fitting result for the impact signal; Definition Let it be the convergence error of the (i + 1)-th iteration. Then, as the iteration result converges, Δ will converge to around 0. Set the convergence thresholds Δ1 = 10 -3 and Δ2 = 10 -6 , and determine whether to enter the strong fitting optimization stage from the strong sparse optimization stage and whether to end the iteration by the conditions that Δ (i+1) is less than Δ1 and Δ2 respectively.

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