A Wavelet Kernel Scale Sensitivity-Guided Denoising Method for Abrasive Induced Voltage Signals

Abstract

This invention belongs to the field of sensors and signal processing, specifically relating to a wavelet kernel-scale sensitivity-guided denoising method for abrasive particle induced voltage signals. The method includes: acquiring abrasive particle induced voltage signals and performing harmonic cancellation to obtain a preprocessed signal; constructing a wavelet kernel function and calculating a kernel-scale guided spectrum using it and the preprocessed signal; constructing a sparse joint denoising model based on the kernel-scale guided spectrum; processing the sparse joint denoising model to obtain a convex optimization objective function; solving the convex optimization objective function using an adaptive step-size gradient descent method and an adaptive iterative shrinking threshold method to obtain a weight vector characterizing the distribution of abrasive particle characteristic signals; binarizing the weight vector characterizing the distribution of abrasive particle characteristic signals to obtain a feature indicator vector; performing a Hadamard product between the feature indicator vector and the preprocessed signal, followed by low-pass filtering to obtain a denoised signal. This invention can adaptively and non-destructively enhance and denoise abrasive particle characteristic signals under strong interference environments.

Description

Technical Field

[0001] This invention belongs to the field of sensors and signal processing, and specifically relates to a wavelet kernel scale sensitivity-guided method for noise reduction of abrasive induced voltage signals. Background Technology

[0002] When mechanical equipment is in operation, the friction between the contacting parts of its transmission device generates metal abrasive particles, which flow with the oil. As the wear process continues, the wear condition of each component intensifies, leading to an increase in the number of metal abrasive particles. If these particles are not detected in a timely manner, it will seriously affect the performance and service life of the mechanical equipment. Metal abrasive particles, as an important carrier reflecting the operating status of machinery, contain key information closely related to abnormal operating conditions of the equipment, and are of great significance for condition diagnosis and life prediction. Accurately obtaining the quantity, geometric characteristics, and material properties of metal abrasive particles has become an important requirement for efficient operation and maintenance and reliability assurance of industrial equipment.

[0003] The three-coil electromagnetic induction sensor, through a differential structure of "excitation + dual detection," accurately captures magnetic field distortion caused by abrasive particles and outputs a quantifiable voltage signal, providing high-quality input for subsequent signal processing. Compared to other sensors, the three-coil electromagnetic induction sensor has advantages in deployment cost, durability, and sensitivity; however, its accurate identification of weak abrasive particle features is still susceptible to various interferences. Therefore, noise reduction algorithms play a crucial role in weakening interference effects and improving the reliability of sensor signals. Currently, various noise reduction methods have emerged, such as wavelet and mode decomposition methods based on signal decomposition. While these methods can effectively suppress noise, their dependence on parameters leads to poor adaptability under complex and non-stationary conditions. Another example is filtering methods based on temporal feature correlation, which have a simple structure but are sensitive to key parameters, making it difficult to guarantee signal fidelity in low signal-to-noise ratio environments. In addition, there are feature extraction methods based on sparse representation, dictionary learning methods, and group lasso methods. The first two have high computational complexity, and while the third can enhance periodic pulses, it relies on the accuracy of the simulation model. Therefore, there is an urgent need for a high-precision, low-complexity, and environmentally adaptive method for denoising abrasive signals to extract weak features under complex monitoring environments and provide reliable condition monitoring and health assurance for critical equipment. Summary of the Invention

[0004] To address the above problems, this invention provides a wavelet kernel-scale sensitivity-guided method for denoising abrasive-induced voltage signals, comprising:

[0005] S1. Acquire the abrasive particle induced voltage signal through a three-coil electromagnetic induction sensor, and perform harmonic elimination on the abrasive particle induced voltage signal to obtain a preprocessed signal;

[0006] S2. Construct a wavelet kernel function and calculate the kernel-scale guided spectrum by combining it with the preprocessed signal;

[0007] S3. Construct a sparse joint noise reduction model based on kernel-scale guided spectrum;

[0008] S4. Use the Majorization-Mi-nimization algorithm to process the sparse joint denoising model to obtain the convex optimization objective function;

[0009] S5. Combine the adaptive step-size gradient descent method and the adaptive iterative shrinkage threshold method to solve the convex optimization objective function and obtain the weight vector characterizing the distribution of wear grain feature signals;

[0010] S6. Binarize the weight vector representing the distribution of abrasive grain characteristic signals to obtain the feature indicator vector;

[0011] S7. Perform a Hadamard product between the feature indicator vector and the preprocessed signal, and then perform low-pass filtering to obtain the noise-reduced signal.

[0012] The beneficial effects of this invention are:

[0013] The method proposed in this invention can adaptively achieve rapid and accurate separation of noise segments and abrasive grain feature signals under strong interference environments. Specifically, the kernel-scale guided spectrum utilizes the guiding characteristics of the signal energy distribution after taking the scale derivative of the wavelet transform result to accurately capture the local energy change trend of the feature signal, thereby obtaining highly enhanced feature information in the multi-scale domain. The sparse joint denoising model significantly improves the positioning accuracy and enhancement effect of the abrasive grain feature signal by fusing multi-scale feature information and introducing local structured constraints, ensuring the accuracy and sparsity of the denoised signal.

[0014] This invention effectively avoids the over-reliance on precise parameter selection in traditional signal separation methods, exhibits stronger adaptability, and reduces the demand on users with complex expertise in signal processing. Simultaneously, this invention overcomes the shortcomings of existing methods in terms of reliability and practicality, providing strong support for feature extraction and noise reduction in abrasive particle induced voltage signals and other related fields. Attached Figure Description

[0015] Figure 1 This is a flowchart of a wavelet kernel-scale sensitivity-guided method for denoising abrasive particle induced voltage signals according to the present invention.

[0016] Figure 2 This refers to the abrasive grain induced voltage signal after harmonic elimination processing in an embodiment of the present invention.

[0017] Figure 3 This is a nuclear-scale steering spectrum according to an embodiment of the present invention;

[0018] Figure 4 This is a local time index set of abrasive grain feature signals at different scales in embodiments of the present invention;

[0019] Figure 5 This is a weight vector characterizing the distribution of abrasive grain feature signals in an embodiment of the present invention;

[0020] Figure 6 This is a feature indicator vector characterizing the distribution of abrasive grain feature signals in an embodiment of the present invention;

[0021] Figure 7 This is the noise reduction signal in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Figure 1 This is a flowchart of a wavelet kernel scale-sensitive denoising method for abrasive particle induced voltage signals, as shown in some embodiments of the present invention.

[0024] This invention provides a wavelet kernel-scale-sensitive-guided method for denoising abrasive particle-induced voltage signals in some embodiments, such as... Figure 1 As shown, it includes:

[0025] S1. The wear particle induced voltage signal is acquired by a three-coil electromagnetic induction sensor, and the harmonic elimination of the wear particle induced voltage signal is performed to obtain a preprocessed signal.

[0026] A three-coil electromagnetic induction sensor is a sensor used to detect abrasive particles in fluids (such as lubricating oil).

[0027] In some embodiments, at a preset sampling rate and sampling time, abrasive induced voltage signals are acquired by a three-coil electromagnetic induction sensor. The abrasive induced voltage signal is subjected to spectrum analysis to accurately estimate the frequency, amplitude, and phase of the main harmonic components of the abrasive induced voltage signal. The harmonic signal is reconstructed in the time domain based on the frequency, amplitude, and phase of the main harmonic components. The reconstructed harmonic signal is subtracted from the abrasive induced voltage signal to achieve harmonic elimination, thus obtaining a preprocessed signal.

[0028] In some embodiments, the sampling rate is set to 5000 and the sampling time is 10 seconds.

[0029] Figure 2 It is a preprocessed signal as shown in some embodiments of the present invention.

[0030] For example, with a sampling rate of 5000 and a sampling time of 10 seconds, the wear particle induced voltage signal is acquired by a three-coil electromagnetic induction sensor, and after harmonic elimination, a preprocessed signal is obtained as follows: Figure 2 As shown.

[0031] S2. Construct a wavelet kernel function and calculate the kernel-scale guided spectrum by combining it with the preprocessed signal.

[0032] In some embodiments, step S2 includes:

[0033] S21. Select the first-order Gaussian derivative of the optimal matching preprocessed signal as the wavelet kernel function.

[0034] Specifically, the wavelet kernel function ψ a for:

[0035]

[0036] In the formula, ψ a (k) represents the wavelet kernel function value under variable k, and a represents the wavelet scaling parameter. This represents the normalization parameter.

[0037] S22. The preprocessed signal u is convolved with the wavelet kernel function in the multi-scale domain. Then, the derivative of the convolution result with respect to the wavelet scale parameter is calculated, and the square of the derivative result is taken to finally obtain the kernel scale steering spectrum.

[0038] Specifically, the abrasive particle induced voltage signal is a discrete-time signal. This invention utilizes the sensitivity of each element in its discrete sequence to changes in the wavelet kernel scale to establish a kernel scale steering spectrum. The specific construction process is as follows: the preprocessed signal u is coupled with the wavelet kernel function ψ in a multi-scale domain. a Performing a convolution operation yields the wavelet transform result, i.e., u*ψ. a Take the derivative of the wavelet transform result with respect to the wavelet scale parameter a, i.e. Then to Taking the square, the final nuclear-scale steering spectrum is expressed as:

[0039]

[0040]

[0041] In the formula, y a (n) represents the spectral density of the preprocessed signal at time index point n under small-scale parameter a; M represents the length of the finite wavelet kernel window. Represents the wavelet kernel function ψ a The partial derivative of the small-scale parameter a with respect to the variable k∈[-M,M].

[0042] In some embodiments, the finite wavelet kernel window length M is 200.

[0043] In some embodiments, the small-scale parameter a takes the values ​​20, 21, 22, and 23.

[0044] Figure 3 It is a nuclear-scale guided spectrum as shown in some embodiments of the present invention.

[0045] For example, targeting Figure 2 The preprocessed signal shown is submerged in noise, and in this embodiment of the invention, within a finite wavelet kernel window length M=200 and a multi-scale domain [20,21,22,23], the preprocessed signal is compared with the wavelet kernel function ψ. a After performing convolution, differentiation, and squaring, the final kernel-scale steering spectrum is as follows: Figure 3 As shown, three distinct energy salient points can be observed.

[0046] S3. Construct a sparse joint noise reduction model based on kernel-scale guided spectrum.

[0047] In some embodiments, step S3 utilizes the sparsity of the wear grain feature signals in the kernel-scale guided spectrum to construct a sparse joint noise reduction model, including:

[0048] S31. Form a local time index set C by combining all time index points in the significant peak region of the nuclear scale guided spectrum, and construct a structured penalty term G(x) based on the local time index set C.

[0049] The significant peak regions of a kernel-scale guided spectrum refer to the local maxima regions in a multi-scale Gaussian first-derived convolution spectrum where the signal and kernel function produce strong responses at specific scales and time indices. These regions typically correspond to edges, abrupt changes, or structural features in the signal.

[0050] Figure 4 It is a local time index set of abrasive grain feature signals at different scales as shown in some embodiments of the present invention.

[0051] For example, for Figure 3 The nuclear-scale guided spectrum is shown, and a two-dimensional multi-scale energy map is constructed, as follows. Figure 4 As shown, a suitable local time index set is obtained.

[0052] Specifically, the structured penalty term G(x) is a dimensionless ratio used to constrain and describe the local signal segment energy to the global energy, expressed as:

[0053]

[0054] In the formula, k represents a variable whose value range is the local time index set C; ε represents the neighborhood width. This represents the vector obtained by filling x with zeros. , express The nth element in the sequence, where n corresponds to the time index point of the preprocessed signal.

[0055] In some embodiments, the neighborhood width ε is 75.

[0056] S32. Construct a data fidelity term in the multi-scale domain and combine it with a regularization term that includes a structured penalty term to construct the objective function of the sparse joint denoising model.

[0057] Specifically, the objective function is expressed as:

[0058]

[0059] In the formula, y a Let g represent the kernel-scale guided spectrum, x represent the weight vector, a represent the wavelet scale parameter, J represent the wavelet scale transform range (i.e., the multi-scale domain), and g = |J|. -1 λ represents the regularization parameter. max represents the maximum operation, n represents the time index point of the preprocessed signal, and G(x) represents the structured penalty term; Let L0 denote the square of the L-2 norm, ||·||1 denote the sum of the absolute values ​​of all elements in the vector, and argmin denote the independent variable that minimizes the objective function.

[0060] The weight vector x is fitted to the kernel scale steering spectrum y over the multiscale domain J. a Obtain data fidelity items Combined with nonconvex regularization terms sparse terms To promote the sparsity of the weight vector x, the structured penalty term G(x) introduces a local structure constraint, ensuring that the weight vector x has energy concentration in the local time neighborhood.

[0061] In some embodiments, the multi-scale domain J takes the value [20, 21, 22, 23].

[0062] S4. Use the Majorization-Mi-nimization algorithm to process the sparse joint denoising model and obtain the convex optimization objective function.

[0063] In some embodiments, for the non-convex regularization term of the sparse joint denoising model, the Majorization-Mi-nimization algorithm is used to achieve local convexity of the problem, including:

[0064] S41. Construct an upper bound alternative convex function for the structured penalty term using the Majorization-Mi-nimization algorithm. .

[0065] Majorization-Minimization (MM) is a general iterative optimization framework. Its core is to transform non-convex, non-smooth, or complex objective functions into easily solvable approximate problems by using upper bound approximation (Majorization) and minimization (Minimization), and iteratively approximate the optimal solution. It is particularly suitable for scenarios such as signal denoising and multi-scale feature extraction.

[0066] Specifically, the nonconvexity of the structured penalty term G(x) stems from the variable to be determined in the denominator. Based on the idea of ​​the MM algorithm, in the tth iteration, a constant is used to replace the variable to be calculated in the denominator, thereby constructing an upper bound substitution convex function. , represented as:

[0067]

[0068] In the formula, S (t) = x (t) This represents the weight vector after t iterations.

[0069] In some embodiments, the maximum number of iterations is 20.

[0070] S42. Using an upper bound to replace a convex function By replacing the structured penalty term, we obtain the convex optimization objective function Q(x).

[0071] Specifically, the structured penalty term G(x) in the objective function is replaced with an upper bound substitution convex function. This forms a local convex optimization problem for each iteration, resulting in the convex optimization objective function Q(x) expressed as:

[0072]

[0073] In the formula, N represents the length of the preprocessed signal sequence, and x(n) represents the nth element in x.

[0074] In some embodiments, N is 50000.

[0075] S5. Combine the adaptive step-size gradient descent method and the adaptive iterative shrinkage threshold method to solve the convex optimization objective function and obtain the weight vector characterizing the distribution of abrasive grain feature signals.

[0076] In some embodiments, step S5 includes:

[0077] S51. Take the derivative of the data fidelity term and the upper bound substitution convex function in the convex optimization objective function to obtain the gradient of the convex optimization objective function.

[0078] Specifically, the gradient calculation of the convex optimization objective function Q(x) is performed only on the differentiable part of the convex optimization objective function, excluding the data fidelity term. Find the partial derivative with respect to x(n), and substitute the convex function with respect to the upper bound. Find the partial derivatives with respect to x(n), including:

[0079] When n∈C, the gradient of the convex optimization objective function Represented as:

[0080]

[0081] When n∉C, the gradient of the convex optimization objective function Represented as:

[0082]

[0083] In the formula, n represents the time index point of the preprocessed signal, C represents the local time index set, and λ represents the regularization parameter. max represents the maximum operation, g = |J| -1 J represents the wavelet scaling range, y a Represents the nuclear-scale guided spectrum, S (t) = x (t) This represents the weight vector after t iterations; l represents the local neighborhood length, l = 2ε + 1, where ε represents the neighborhood width. This represents the vector obtained by filling x with zeros. express The nth element in; x (t) This represents the weight vector after t iterations.

[0084] When n∉C, the location of the time index point n is assumed to be noise or a non-feature region. The sparse joint denoising model aims to recover the sparse weight vector x. Therefore, when n∉C, the corresponding weight vector x(n) should theoretically be 0. Hence, this invention defines the gradient when n∉C. Setting it to 0 avoids unnecessary gradient calculations and improves computational efficiency.

[0085] S52. Gradient descent update is performed using an adaptive step size α to obtain the intermediate solution z. (t) (n).

[0086] Specifically, to ensure the convergence and stability of the algorithm, the adaptive step size α is based on the global energy of the previous iteration. The Lipschitz condition is determined, and expressed as:

[0087]

[0088] In the formula, δ represents the protection coefficient.

[0089] In some embodiments, the protection factor δ is 0.01.

[0090] Specifically, after adopting an adaptive step size α, the data fidelity term of the convex optimization objective function is adjusted. Perform gradient descent to obtain the intermediate solution z. (t) (n) is represented as:

[0091]

[0092] In the formula, x (t) (n) represents the nth element in the weight vector after t iterations. This represents the gradient of the objective function Q(x) at the nth element x(n) of the weight vector.

[0093] S53. For the intermediate solution z (t) (n) The adaptive iterative shrinkage threshold method is executed to iteratively solve for the weight vector characterizing the distribution of wear particle feature signals. Specifically, the intermediate solution z is obtained. (t) After (n), the adaptive iterative shrinking threshold method is executed to process the sparse terms in the convex optimization objective function. The unconstrained term x(n) ≥ 0 is expressed as:

[0094]

[0095]

[0096] In the formula, η represents the adaptive threshold, N represents the length of the preprocessed signal sequence, φ represents the marginal parameter, Std() represents the standard deviation, and sign() represents the sign function. x represents the reciprocal of the infinity norm. (0) This represents the initial iteration value of the weight vector.

[0097] In some embodiments, the marginal parameter φ is 3.5.

[0098] Figure 5 It is a weight vector characterizing the distribution of abrasive grain feature signals, as shown in some embodiments of the present invention.

[0099] For example, targeting Figure 2-4The corresponding signal is given by a neighborhood width of 75, N = 50000, a protection coefficient δ = 0.01, a multi-scale domain J = [20, 21, 22, 23], and a marginal parameter φ = 3.5. A sparse joint denoising model is established. For the non-convex regularization term of the sparse joint denoising model, the MM algorithm is used to achieve local convexity of the problem. An adaptive gradient descent method with an adaptive step size α is adopted, combined with an adaptive iterative shrinkage threshold method, to obtain the weight vector characterizing the distribution of the wear particle feature signal, as shown below. Figure 5 As shown.

[0100] S6. Binarize the weight vector representing the distribution of abrasive grain characteristic signals to obtain the feature indicator vector.

[0101] In some embodiments, a weight vector x characterizing the distribution of abrasive grain feature signals is obtained. o Then, binarization is performed to obtain the feature indicator vector. Each element in the feature indicator vector takes only 0 or 1 and does not carry other amplitude information, accurately indicating the time position of the abrasive grain feature signal, as shown below:

[0102]

[0103] In the formula, h(k) represents the feature indicator vector, x o (n) represents the weight vector x that characterizes the distribution of abrasive grain feature signals. o The nth element in the expression, k∈N, represents a variable; ε represents the neighborhood width.

[0104] Figure 6 It is a feature indicator vector characterizing the distribution of abrasive grain feature signals, as shown in some embodiments of the present invention.

[0105] For example, targeting Figure 5 Binarization is performed to obtain the feature indicator vector, such as Figure 6 As shown.

[0106] S7. Perform a Hadamard product between the feature indicator vector and the preprocessed signal, and then perform low-pass filtering to obtain the noise-reduced signal.

[0107] In some embodiments, after obtaining the feature indicator vector, a Hadamard product is performed with the preprocessed signal to effectively suppress interference in non-feature regions, while non-destructively preserving the wear particle feature signal components. A low-pass filter is then applied to obtain the denoised signal, expressed as:

[0108]

[0109] in, Let LPF{·} represent the noise-reduced signal, LPF{·} represent low-pass filtering with a cutoff frequency of 30Hz, and u(n) represent the preprocessed signal.

[0110] Figure 7It is a noise-reduced signal as shown in some embodiments of the present invention.

[0111] For example, targeting Figure 2-6 The feature indicator vector is multiplied by the preprocessed signal using a Hadamard product, and then low-pass filtered to obtain the denoised signal, as shown below. Figure 7 As shown.

[0112] Under strong noise, the signal denoising method proposed in this invention can non-destructively preserve the waveform structure and time-domain characteristics of the original abrasive feature signal. Moreover, it can accurately locate the local time-domain support set of the abrasive feature signal and accurately denoise under different conditions, thus possessing adaptability.

[0113] The method proposed in this invention can adaptively reduce the noise of abrasive induced voltage signals under strong noise, providing reliable support for feature signal identification and analysis.

[0114] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0115] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A wavelet kernel-scale sensitivity-guided method for denoising abrasive particle-induced voltage signals, characterized in that, include: S1. Acquire the abrasive particle induced voltage signal through a three-coil electromagnetic induction sensor, and perform harmonic elimination on the abrasive particle induced voltage signal to obtain a preprocessed signal; S2. Construct a wavelet kernel function and calculate the kernel-scale guided spectrum by combining it with the preprocessed signal; S3. Construct a sparse joint noise reduction model based on kernel-scale guided spectrum; The construction process of the sparse joint denoising model includes: S31. Form a local time index set C by including all time index points within the significant peak region of the kernel-scale guided spectrum, and construct a structured penalty term G(x) based on the local time index set C, expressed as: In the formula, k represents a variable whose value range is the local time index set C; ε represents the neighborhood width. This represents the vector obtained by filling x with zeros. express The nth element in the sequence, where n corresponds to the time index point of the preprocessed signal; S32. Construct a data fidelity term in the multi-scale domain, and combine it with a regularization term that includes a structured penalty term to construct the objective function of the sparse joint denoising model, expressed as: In the formula, y a Let g represent the kernel-scale guided spectrum, x represent the weight vector, a represent the wavelet scaling parameter, J represent the wavelet scaling range, and g = |J|. -1 λ represents the regularization parameter. max represents the maximum operation, n represents the time index point of the preprocessed signal, and G(x) represents the structured penalty term; Let L0 denote the square of the L-2 norm, ||·||1 denote the sum of the absolute values ​​of all elements in the vector, and argmin denote the independent variable that minimizes the objective function. S4. Use the Majorization-Mi-nimization algorithm to process the sparse joint denoising model to obtain the convex optimization objective function; S5. Combine the adaptive step-size gradient descent method and the adaptive iterative shrinkage threshold method to solve the convex optimization objective function and obtain the weight vector characterizing the distribution of wear grain feature signals; S6. Binarize the weight vector representing the distribution of abrasive grain characteristic signals to obtain the feature indicator vector; S7. Perform a Hadamard product between the feature indicator vector and the preprocessed signal, and then perform low-pass filtering to obtain the noise-reduced signal.

2. The wavelet kernel scale-sensitive guided noise reduction method for abrasive particle induced voltage signals according to claim 1, characterized in that, Step S2 includes: S21. Construct the wavelet kernel function ψ a for: In the formula, ψ a (k) represents the wavelet kernel function value under variable k, and a represents the wavelet scaling parameter. Indicates the normalization parameter; S22. The preprocessed signal u is convolved with a wavelet kernel function in the multi-scale domain. Then, the derivative of the convolution result with respect to the wavelet scale parameters is calculated, and the square of the derivative is taken to obtain the kernel scale steering spectrum, which is expressed as: In the formula, y a (n) represents the spectral density of the preprocessed signal at time index point n under small-scale parameter a; k∈[-M,M], where M represents the length of the finite wavelet kernel window.

3. The wavelet kernel scale-sensitive guided noise reduction method for abrasive particle induced voltage signals according to claim 1, characterized in that, By processing the structured penalty term in the sparse joint denoising model, the convex optimization objective function is obtained, including: S41. Construct an upper bound alternative convex function for the structured penalty term using the Majorization-Mi-nimization algorithm. , represented as: In the formula, S (t) = x (t) This represents the weight vector after t iterations; S42. Using an upper bound to replace a convex function Replacing the structured penalty term yields the convex optimization objective function Q(x), expressed as: In the formula, N represents the length of the preprocessed signal sequence, and x(n) represents the nth element in x.

4. The wavelet kernel scale-sensitive guided noise reduction method for abrasive particle induced voltage signals according to claim 1, characterized in that, Step S5 includes: S51. Differentiate the data fidelity term and the upper bound substitution convex function in the convex optimization objective function to obtain the gradient of the convex optimization objective function, including: When n∈C, the gradient of the convex optimization objective function Represented as: When n∉C, the gradient of the convex optimization objective function Represented as: In the formula, n represents the time index point of the preprocessed signal, C represents the local time index set, and λ represents the regularization parameter. max represents the maximum operation, g = |J| -1 J represents the wavelet scaling range, y a Represents the nuclear-scale guided spectrum, S (t) = x (t) This represents the weight vector after t iterations; l represents the local neighborhood length, l = 2ε + 1, where ε represents the neighborhood width. This represents the vector obtained by filling x with zeros. express The nth element in; x (t) This represents the weight vector after t iterations; S52. Gradient descent update is performed using an adaptive step size α to obtain the intermediate solution z. (t) (n), represented as: In the formula, x (t) (n) represents the nth element in the weight vector after t iterations. This represents the gradient of the convex optimization objective function Q(x) at the nth element of the weight vector; S53. For the intermediate solution z (t) (n) The adaptive iterative shrinkage threshold method is executed to iteratively solve for the weight vector characterizing the distribution of wear grain feature signals, which is expressed as: In the formula, η represents the adaptive threshold, N represents the length of the preprocessed signal sequence, φ represents the marginal parameter, Std() represents the standard deviation, and sign() represents the sign function. x represents the reciprocal of the infinity norm. (0) This represents the initial iteration value of the weight vector.

5. The wavelet kernel scale-sensitive guided noise reduction method for abrasive particle induced voltage signals according to claim 4, characterized in that, The adaptive step size α is: In the formula, δ represents the protection coefficient.

6. The wavelet kernel scale-sensitive guided noise reduction method for abrasive particle induced voltage signals according to claim 1, characterized in that, Step S6 includes: In the formula, h(k) represents the feature indicator vector, x o (n) represents the weight vector x that characterizes the distribution of abrasive grain feature signals. o The nth element in the expression, k∈N, represents a variable; ε represents the neighborhood width.

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