A signal denoising method based on shape prior and iterative reweighted sparse reconstruction

Abstract

The present application belongs to the field of sensor and signal processing, and particularly relates to a signal denoising method based on shape prior and iterative reweighted sparse reconstruction, which comprises the following steps: obtaining a pretreatment signal by performing harmonic elimination on an abrasive particle induced voltage signal; constructing a multi-scale Gaussian first derivative template dictionary; constructing a non-convex variation optimization objective function containing a shape similarity regular term based on the pretreatment signal; calculating adaptive weights of each discrete point of the pretreatment signal based on the multi-scale Gaussian first derivative template dictionary; decoupling the structure coupling in the non-convex variation optimization objective function by using an iterative reweighted strategy, and converting it into a weighted LASSO sub-problem; solving by using an improved adaptive iterative shrinkage threshold method to obtain a multi-scale time domain characteristic spectrum; performing binary fusion processing on the multi-scale time domain characteristic spectrum to obtain a characteristic indication vector, and performing Hadamard product on the characteristic indication vector and the pretreatment signal to obtain a denoising signal; and the present application significantly improves the positioning accuracy and reconstruction quality of weak signals.

Description

Technical Field

[0001] This invention belongs to the field of sensors and signal processing, specifically relating to a signal denoising method based on shape prior and iterative reweighted sparse reconstruction. Background Technology

[0002] With the rapid development of modern industrial technology, high-end mechanical equipment places higher demands on the reliability and service life of transmission systems. Lubricating oil, as the "blood" of mechanical equipment, directly affects the operating efficiency and overall lifecycle performance of the equipment. Studies have shown that wear and tear on mechanical equipment can lead to metal particles mixing into the lubricating oil. If not monitored in time, this will further exacerbate wear and even cause serious malfunctions. Therefore, real-time monitoring of the state of metal particles in the lubricating oil is of great significance for early warning and intelligent diagnosis of mechanical faults.

[0003] Among various monitoring methods, the three-coil electromagnetic induction sensor has become a research hotspot in the field of online oil monitoring due to its ability to accurately capture the magnetic field distortion caused by the passage of abrasive particles and output a quantifiable voltage signal. Compared with optical and ultrasonic sensors, it has significant advantages in deployment cost, environmental adaptability, and detection sensitivity, providing high-quality raw input for subsequent signal analysis. However, in complex actual industrial monitoring scenarios, the weak abrasive particle characteristic signals output by the sensor are easily overwhelmed by mechanical vibration, electromagnetic interference, and background noise. Therefore, efficient noise reduction algorithms are crucial for improving signal reliability.

[0004] Currently, commonly used noise reduction methods mainly fall into two categories: time-frequency analysis and sparse representation. Time-frequency analysis methods, such as wavelet transform, empirical mode decomposition (EMD), and variational mode decomposition (VMD), can suppress noise to a certain extent, but their performance is heavily dependent on parameter settings such as the choice of basis functions and the number of decomposition layers. Under complex and non-stationary conditions, even small deviations in parameter settings can easily lead to signal distortion, and these methods have limited adaptive capabilities, making it difficult to guarantee the physical authenticity of the waveform. Methods based on sparse representation and regularization, such as dictionary learning and sparse coding, have shown potential in signal enhancement, but existing time-domain sparse methods often face the problem of high computational complexity, making it difficult to meet the real-time requirements of online monitoring. More importantly, excessive pursuit of sparsity can easily lead to waveform truncation, destroying the temporal integrity of the abrasive signal and affecting the accuracy of subsequent feature extraction and diagnosis.

[0005] In summary, existing technologies struggle to achieve a good balance between waveform integrity preservation, computational efficiency, and environmental adaptability. Therefore, there is an urgent need to develop a high-precision, low-complexity method for denoising abrasive signals that effectively avoids waveform truncation and distortion. This would enable robust extraction of subtle wear characteristics, supporting the further development of mechanical equipment condition monitoring and intelligent operation and maintenance. Summary of the Invention

[0006] To address the above problems, this invention provides a signal denoising method based on shape prior and iterative reweighted sparse reconstruction, comprising the following steps:

[0007] 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;

[0008] S2. Construct a multi-scale Gaussian first-order derivative template dictionary;

[0009] S3. Construct an estimated vector based on the preprocessed signal, and construct a non-convex variational optimization objective function that includes a shape similarity regularization term;

[0010] S4. Based on the multi-scale Gaussian first-derivative template dictionary, calculate the waveform similarity weight of each discrete point in the preprocessed signal and construct adaptive weights;

[0011] S5. Combining adaptive weights and adopting an iterative reweighting strategy, the structural coupling in the non-convex variational optimization objective function is decoupled and transformed into a series of weighted LASSO subproblems;

[0012] S6. An improved adaptive iterative shrinkage thresholding method is used to solve the weighted LASSO problem, and the multi-scale time-domain feature spectrum is obtained.

[0013] S7. Perform binarization fusion processing on the multi-scale time-domain feature spectrum to obtain the feature indicator vector, and perform Hadamard product on the feature indicator vector and the preprocessed signal to obtain the noise-reduced signal.

[0014] The beneficial effects of this invention are:

[0015] The method proposed in this invention can significantly improve the localization accuracy and reconstruction quality of weak signals in high-noise environments. Specifically, this invention constructs a non-convex variational optimization objective function that includes a shape similarity regularization term, calculates adaptive weights, and employs an iterative reweighting strategy to decouple the structural coupling in the non-convex variational optimization objective function. The solution from the previous iteration is used to fix the current regularization weights, and an improved adaptive iterative shrinkage threshold method is combined for rapid solution, avoiding highly complex computations. By introducing multi-scale shape priors, targeted extraction of weak abrasive grain features is achieved. This method, while ensuring the sparsity of the denoised signal, effectively overcomes the signal distortion and missed detection problems easily caused by traditional methods in extremely low signal-to-noise ratio environments, significantly improving the accuracy and reliability of the detection results.

[0016] This invention, while ensuring high accuracy, also boasts low computational cost, meeting the requirements for rapid sensor signal processing. Furthermore, this method effectively overcomes the limitations of existing solutions in terms of reliability and practicality, providing strong technical support for feature extraction and noise reduction in abrasive particle induced voltage signals and other related fields. Attached Figure Description

[0017] Figure 1 This is a flowchart of a signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to the present invention.

[0018] Figure 2 This refers to the abrasive grain induced voltage signal after harmonic elimination processing in an embodiment of the present invention.

[0019] Figure 3 This is a heatmap of the multi-scale time-domain feature spectrum after binarization processing according to an embodiment of the present invention.

[0020] Figure 4 This is a feature indicator vector characterizing the distribution of abrasive grain feature signals in an embodiment of the present invention;

[0021] Figure 5 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] Please see Figure 1 This invention provides a signal denoising method based on shape prior and iterative reweighted sparse reconstruction, comprising the following steps:

[0024] 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.

[0025] A three-coil electromagnetic induction sensor is a sensor used to detect abrasive particles in fluids (such as lubricating oil).

[0026] 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.

[0027] S2. Construct a multi-scale Gaussian first-order derivative template dictionary.

[0028] In some embodiments, a multi-scale Gaussian first-order derivative template dictionary is constructed. N represents the length of the first-order Gaussian steering at a given scale, and n represents the number of scales. The expression for the first-order Gaussian derivative atom at the i-th scale is:

[0029] ,

[0030] In the formula, Indicates the independent variable. This indicates the width and scaling factor of the control waveform.

[0031] S3. Construct an estimated vector based on the preprocessed signal, and construct a non-convex variational optimization objective function that includes a shape similarity regularization term.

[0032] In some embodiments, the nonconvex variational optimization objective function is expressed as:

[0033] ,

[0034] In the formula, Indicates preprocessed signal, Let argmin represent the estimation vector, and let argmin represent the independent variable that minimizes the objective function. This indicates a waveform similarity penalty term. , This represents the adaptive weight corresponding to the m-th data point in the estimation vector. This represents the m-th data point in the estimation vector. This represents the regularization parameter.

[0035] S4. Based on the multi-scale Gaussian first-order derivative template dictionary, calculate the waveform similarity weight of each discrete point (data point) in the preprocessed signal, and construct adaptive weights.

[0036] In some embodiments, step S4 includes:

[0037] S41. Padding the estimated vector x with zeros at the beginning and end yields a zero-padded estimated vector. , Let represent the neighborhood parameters, and M represent the length of the preprocessed signal. Zero-padding ensures that the length of the local observation vector is consistent with the length of the Gaussian first-order derivative template vector during weight calculation. When extracting the elements at the beginning and end of the estimated vector x, zero-padding is used to align the lengths, thus meeting the requirements of subsequent calculations.

[0038] For each data point in the estimation vector x Construct a local observation vector centered on it. Local shape similarity is calculated based on a multi-scale Gaussian first-order derivative template dictionary; the formula for calculating local shape similarity is:

[0039] ,

[0040] In the formula, Represents the local observation vector Local similarity, Let represent the first Gaussian derivative atom at the i-th scale, <·> represent the inner product, and ||·||2 represent the L-2 norm.

[0041] S42. Construct each data point based on local shape similarity. The original weights are expressed as:

[0042] ,

[0043] In the formula, Representing data points The original weights, This represents a very small positive value to prevent the denominator from being 0.

[0044] S43. A moving minimum filter is introduced to smooth the original weights. When high similarity points exist in a local region, morphological erosion is used to expand the signal protection range, thereby effectively preventing the pulse edges from being mistakenly cut off, generating adaptive weights, expressed as:

[0045] ,

[0046] In the formula, Representing data points The adaptive weight vector, min represents finding the minimum value. Represents the discrete index points of the signal. This represents the smooth window length.

[0047] S5. Combining adaptive weights, an iterative reweighting strategy is adopted to decouple the structural coupling in the non-convex variational optimization objective function, and the solution of the previous iteration is used to fix the current regularization weights, transforming it into a series of weighted LASSO subproblems.

[0048] In some embodiments, step S5 includes:

[0049] S51. An iterative reweighting strategy is adopted to construct a decoupled linear weighted penalty term for the variable coupling structure existing in the waveform similarity penalty term. :

[0050] ,

[0051] In the formula, This represents the estimated vector value after the t-th iteration. This represents the estimated vector value based on the (t-1)th iteration. The adaptive weights of the m-th data point in the calculated estimation vector are as follows: Let M represent the element value of the m-th data point in the estimated vector after the t-th iteration, where M represents the length of the preprocessed signal and λ represents the regularization parameter.

[0052] S52. Replace the waveform similarity penalty term with a linear weighted penalty term, transforming it into a weighted LASSO problem, thus obtaining a convex optimization objective function, expressed as:

[0053] ,

[0054] In the formula, Indicates preprocessed signal, Let represent the absolute value of the m-th data point in the estimated vector x, M represent the length of the preprocessed signal, ||·||2 represents the L-2 norm, and argmin represents the independent variable that minimizes the objective function.

[0055] S6. An improved adaptive iterative shrinkage thresholding method is used to solve the weighted LASSO problem, and the multi-scale time-domain feature spectrum is obtained.

[0056] In some embodiments, step S6 includes:

[0057] S61. Construct a normalized symbol threshold operator to shrink and truncate the signal amplitude, thereby obtaining an intermediate sparse solution. The normalized symbol threshold operator is expressed as:

[0058] ,

[0059] In the formula, It represents the Hadamah accumulation. Represents a symbolic function. This indicates taking the maximum value. Indicates preprocessed signal, This represents the estimated vector value based on the (t-1)th iteration. The calculated adaptive weight vector, This represents the regularization parameter.

[0060] The symbolic function is represented as:

[0061]

[0062] In the formula, 'a' represents the independent variable.

[0063] S62. Perform inertial damped relaxation update on the intermediate sparse solution, that is: weight the intermediate sparse solution with the update solution of the previous round to obtain the current round update solution after smoothing numerical oscillation, expressed as:

[0064] ,

[0065] In the formula, α represents the relaxation iteration factor. This is the updated solution for the current round t. This represents the intermediate sparse solution in the current round t. This represents the updated solution from the previous round t-1;

[0066] S63. Calculate the convergence residual R using the updated solution from the current round and the updated solution from the previous round, expressed as:

[0067] ,

[0068] S64. If the convergence residual R is less than or equal to the convergence threshold δ, the algorithm is considered to have converged globally. No inertial damping relaxation update is performed, and the time-domain feature spectrum at the current i-th scale is calculated. Otherwise, let t = t + 1 and return to step S61.

[0069] S65. Iteratively execute steps S61-S64, applying them to Gaussian first-order derivative atoms at all scales to obtain the corresponding time-domain feature spectra at each scale; then, splice the time-domain feature spectra at all scales to finally obtain the multi-scale time-domain feature spectra.

[0070] Multi-scale temporal feature spectrum It can be represented as:

[0071] ,

[0072] Row indexes represent scales, and column indexes represent sampling points.

[0073] S7. Perform binarization fusion processing on the multi-scale time-domain feature spectrum to obtain the feature indicator vector, and perform Hadamard product on the feature indicator vector and the preprocessed signal to obtain the noise-reduced signal.

[0074] In some embodiments, a feature indicator vector is obtained by binarizing and fusing the multi-scale time-domain feature spectrum. , represented as:

[0075] ,

[0076] in, Represents a symbolic function. This represents the i-th row vector of the multi-scale temporal feature spectrum, where n represents the number of scales;

[0077] Use feature indicator vectors The Hadamard product is performed with the preprocessed signal y, and then low-pass filtered to obtain the noise-reduced signal, which is expressed as:

[0078] ,

[0079] In the formula, Indicates the noise reduction signal. represents the Hadamard product, and LPF{·} represents low-pass filtering.

[0080] In one specific embodiment, the present invention sets the sampling rate to 5000 and the sampling time to 10 seconds. The abrasive particle induced voltage signal is acquired using a three-coil electromagnetic induction sensor, and harmonic cancellation is performed on the abrasive particle induced voltage signal to obtain a preprocessed signal, such as... Figure 2 As shown, the abrasive grain characteristic signal is overwhelmed by noise.

[0081] Construct a multi-scale Gaussian first-order derivative template dictionary, setting the number of scales n to 9, and the width and scale factor... Starting from 1, gradually increase by 0.25, that is... ;make ,but The center of the waveform is the vector The center.

[0082] set up =0.85, construct a non-convex variational optimization objective function including a shape similarity regularization term. Set M=50000, μ=100, and calculate adaptive weights. Adaptive reweighting strategy is adopted to decouple the structural coupling in the objective function. The solution of the previous iteration is used to fix the current regularization weights, transforming it into a weighted LASSO problem. Improve the adaptive iterative shrinking threshold method to solve it, where the first iteration is set as the preprocessed signal, ε=0.0001, α=0.6, δ=0.00001.

[0083] The preprocessed signal is input into the model to obtain the multi-scale time-domain feature spectrum. Figure 3 The multi-scale time-domain characteristic spectrum heatmap after binarization is displayed, from which the discrimination of discrete points at each scale can be observed intuitively. Figure 4 The feature indicator vector obtained by multi-scale fusion can clearly identify the location of segments with abrasive grain features in the signal. Figure 5Even under noise, the proposed feature extraction method for the denoised signal still causes almost no distortion of signal features, maintaining high accuracy while also possessing good feature protection capabilities.

[0084] In summary, this invention first constructs a multi-scale Gaussian first-order derivative template dictionary, utilizes waveform similarity to build adaptive penalty weights, and transforms the non-convex variational optimization problem involving shape priors into a weighted LASSO problem through an iterative reweighting strategy. A multi-scale time-domain feature spectrum is obtained by solving an improved adaptive iterative shrinkage threshold method, and finally, the feature spectrum is subjected to multi-scale fusion binarization processing to generate accurate feature indicator vectors. The proposed method can achieve targeted extraction and high-fidelity reconstruction of weak transient abrasive signals under strong background noise interference, effectively solving the waveform distortion and truncation problems existing in traditional methods, and significantly improving the robustness and accuracy of signal detection while maintaining low computational complexity.

[0085] 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 signal denoising method based on shape prior and iterative reweighted sparse reconstruction, characterized in that, Includes the following steps: 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 multi-scale Gaussian first-order derivative template dictionary; S3. Construct an estimated vector based on the preprocessed signal, and construct a non-convex variational optimization objective function that includes a shape similarity regularization term; S4. Based on the multi-scale Gaussian first-derivative template dictionary, calculate the waveform similarity weight of each discrete point in the preprocessed signal and construct adaptive weights; S5. Combining adaptive weights and adopting an iterative reweighting strategy, the structural coupling in the non-convex variational optimization objective function is decoupled and transformed into a series of weighted LASSO subproblems; S6. An improved adaptive iterative shrinkage thresholding method is used to solve the weighted LASSO problem, and the multi-scale time-domain feature spectrum is obtained. S7. Perform binarization fusion processing on the multi-scale time-domain feature spectrum to obtain the feature indicator vector, and perform Hadamard product on the feature indicator vector and the preprocessed signal to obtain the noise-reduced signal.

2. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, Constructing a multi-scale Gaussian first-order derivative template dictionary N represents the length of the first-order Gaussian steering at a given scale, and n represents the number of scales. The expression for the first-order Gaussian derivative atom at the i-th scale is: ， In the formula, Indicates the independent variable. This indicates the width and scaling factor of the control waveform.

3. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, The nonconvex variational optimization objective function is expressed as: ， In the formula, Indicates preprocessed signal, Let argmin represent the estimation vector, and let argmin represent the independent variable that minimizes the objective function. This indicates a waveform similarity penalty term. , This represents the adaptive weight corresponding to the m-th data point in the estimation vector. This represents the m-th data point in the estimation vector. This represents the regularization parameter.

4. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, Step S4 includes: S41. Padding the estimated vector x with zeros at the beginning and end yields a zero-padded estimated vector. For each data point in the estimation vector x Construct a local observation vector centered on it. , Represent the neighborhood parameters; and calculate the local shape similarity based on the multi-scale Gaussian first-order derivative template dictionary; the formula for calculating the local shape similarity is: ， In the formula, Represents the local observation vector Local similarity, Let represent the Gaussian first derivative atom at the i-th scale, <·> denote the inner product, and ||·||2 denote the L-2 norm; S42. Construct each data point based on local shape similarity. The original weights are expressed as: ， In the formula, Representing data points The original weights, To represent a very small positive value, to prevent the denominator from being 0; S43. Perform morphological smoothing on the original weights to generate adaptive weights, represented as follows: ， In the formula, Representing data points The adaptive weight vector, min represents finding the minimum value. Represents the discrete index points of the signal. This represents the smooth window length.

5. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, Step S5 includes: S51. An iterative reweighting strategy is adopted to construct a decoupled linear weighted penalty term for the variable coupling structure existing in the waveform similarity penalty term. : ， In the formula, This represents the estimated vector value after the t-th iteration. This represents the estimated vector value based on the (t-1)th iteration. The adaptive weights of the m-th data point in the calculated estimation vector are as follows: Let M represent the element value of the m-th data point in the estimated vector after the t-th iteration, where M represents the length of the preprocessed signal and λ represents the regularization parameter. S52. Replace the waveform similarity penalty term with a linear weighted penalty term, transforming it into a weighted LASSO problem, expressed as: ， In the formula, Indicates preprocessed signal, Let M represent the absolute value of the m-th data point in the estimated vector x, M represent the length of the preprocessed signal, and ||·||2 represent the L-2 norm.

6. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, Step S6 includes: S61. Construct a normalized symbol threshold operator to shrink and truncate the signal amplitude, thereby obtaining an intermediate sparse solution; the normalized symbol threshold operator is expressed as: ， In the formula, It represents the Hadamah accumulation. Represents a symbolic function. This indicates taking the maximum value. Indicates preprocessed signal, This represents the estimated vector value based on the (t-1)th iteration. The calculated adaptive weight vector, Represents the regularization parameter; S62. The intermediate sparse solution is weighted and combined with the updated solution from the previous round to obtain the updated solution for the current round after smoothing numerical oscillations, as follows: ， In the formula, α represents the relaxation iteration factor. This is the updated solution for the current round t. This represents the intermediate sparse solution in the current round t. This represents the updated solution from the previous round t-1; S63. Calculate the convergence residual R using the updated solution from the current round and the updated solution from the previous round, expressed as: ， S64. If the convergence residual R is less than or equal to the convergence threshold δ, then the algorithm is determined to be globally converged, and the temporal feature spectrum at the current i-th scale is calculated. Otherwise, let t = t + 1 and return to step S61. S65. Iteratively execute steps S61-S64, applying them to Gaussian first-order derivative atoms at all scales to obtain the time-domain feature spectra corresponding to each scale; subsequently, splice the time-domain feature spectra of all scales to obtain the multi-scale time-domain feature spectra.

7. The signal denoising method based on shape prior and iterative reweighted sparse reconstruction according to claim 1, characterized in that, The feature indicator vector is obtained by binarizing and fusing the multi-scale time-domain feature spectra. , represented as: ， in, Represents a symbolic function. This represents the i-th row vector of the multi-scale temporal feature spectrum, where n represents the number of scales; Use feature indicator vectors The Hadamard product is performed with the preprocessed signal y, and then low-pass filtered to obtain the noise-reduced signal, which is expressed as: ， In the formula, Indicates the noise reduction signal. represents the Hadamard product, and LPF{·} represents low-pass filtering.

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