Bearing electrostatic signal noise reduction method based on VMD-OMP

Abstract

The invention discloses a bearing electrostatic signal noise reduction method based on VMD-OMP. In order to solve the problem that early fault features are difficult to extract due to the fact that bearing electrostatic signals are easily affected by power frequency interference and environmental noise, a noise reduction technology based on combination of VMD (variational mode decomposition) and OMP (orthogonal matching pursuit) is provided. The method comprises the following steps of: firstly, performing automatic optimization on a modal number and a secondary penalty factor of VMD decomposition by taking an envelope entropy as a fitness function through a grey wolf optimization algorithm to realize adaptive decomposition; and then, screening effective modal components according to the cross correlation coefficient and the kurtosis, determining the optimal sparseness by adopting a saturation value method, respectively reconstructing the components through an OMP algorithm, and finally, directly adding reconstructed signals to obtain a noise reduction result. According to the method, power frequency noise and broadband interference in the bearing electrostatic signal can be effectively suppressed, and the feature definition and the fault recognition capability of the electrostatic signal are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a bearing electrostatic signal noise reduction method based on VMD-OMP. Background Art

[0002] With the continuous advancement of industrial technology and the increasing demand for equipment reliability, the demand for bearing fault prediction and diagnosis is growing, and electrostatic signal monitoring has gradually become a key fault diagnosis tool. Traditional fault detection methods, such as vibration monitoring and temperature monitoring, can provide certain fault information, but often suffer from issues such as inability to accurately locate early faults, high costs, and poor real-time performance. Electrostatic signals, as a physical quantity that can be monitored in real time using simple sensors, offer advantages such as high sensitivity and rapid response. Continuous monitoring of bearing electrostatic signals can identify early abnormalities. Electrostatic monitoring not only reduces the risk of failure and extends equipment life, but also effectively improves equipment operating efficiency, reduces downtime and maintenance costs, and significantly optimizes equipment maintenance and management.

[0003] However, natural bearing electrostatic signals are very weak and easily affected by external factors such as electromagnetic interference, mechanical vibration, and temperature fluctuations, resulting in high signal noise. This noise can mask actual fault signals, limiting the accuracy and reliability of monitoring results. Especially in high-frequency, high-speed equipment, power frequency interference and background broadband noise can interfere with the acquisition and analysis of electrostatic signals. Summary of the Invention

[0004] To overcome the existing problems and defects, the present invention proposes a bearing electrostatic signal noise reduction method based on VMD-OMP, comprising the following steps:

[0005] S1. The original bearing electrostatic signal collected by the electrostatic sensor is decomposed using the variational mode decomposition (VMD) method. During the decomposition process, an optimization algorithm is used to automatically optimize the number of VMD modal components K and the quadratic penalty factor α to obtain the optimal parameter combination, thereby optimizing the decomposition effect and obtaining multiple modal components.

[0006] S2. For each modal component decomposed in step S1, calculate its mutual correlation coefficient and kurtosis with the original bearing electrostatic signal, and select the effective signal component according to the preset standard;

[0007] S3. Based on the screened modal component signals, the saturation value method is used to determine the optimal sparsity of signal reconstruction;

[0008] S4. Reconstruct the effective modal components and optimal sparsity after processing in steps S2 and S3 using the orthogonal matching pursuit (OMP) algorithm, and finally merge them to obtain the denoised bearing electrostatic signal.

[0009] 2. The bearing electrostatic signal denoising method based on VMD-OMP according to claim 1 is characterized in that: the VMD decomposition process includes constructing a constrained variational problem and converting it into an unconstrained variational problem containing a quadratic penalty factor α and a Lagrange multiplier λ, and sequentially updating the center frequency and component signal of each modal component in an iterative manner until the termination condition is met.

[0010] Furthermore, the method for automatically optimizing the VMD parameters K and α is specifically as follows: using the gray wolf algorithm to initialize the parameters of the GWO algorithm, including the number of wolves, the number of iterations, the parameter range, etc.; using the VMD penalty factor α and the modal decomposition number K as optimization variables, and using the envelope entropy as the fitness function, and using the GWO algorithm for optimization; according to the update rule of the GWO algorithm, updating the position and speed of each wolf, and calculating the fitness value of each wolf; finally, updating the optimal solution, suboptimal solution and general solution according to the fitness value; until the maximum number of iterations is reached or the fitness value converges, the penalty factor α and modal decomposition number K corresponding to the optimal solution are output.

[0011] Furthermore, the calculation methods of the mutual correlation coefficient and kurtosis between each modal component and the original bearing electrostatic signal are respectively:

[0012]

[0013]

[0014] in, represents the correlation coefficient, m represents the length of the original bearing electrostatic signal, represents the average value of a modal component IMF=(x1,x2,...,xm), represents the average value of the original bearing electrostatic signal x(t) = (y1, y2, ..., ym); xi represents the i-th observation value of the original bearing electrostatic signal, yi represents the i-th observation value of a modal component IMF; N is the total number of observations; represents the kurtosis, Represents standard deviation.

[0015] Furthermore, the preset criteria for screening out effective signal components include: modal components with a cross-correlation coefficient higher than a self-set threshold and a kurtosis of not less than 3 are retained, and the remaining components are removed as noise components.

[0016] Furthermore, the saturation value method is used to determine the optimal sparsity of signal reconstruction as follows:

[0017] When the sparsity is gradually increased, the signal reconstruction error is monitored as it changes with the sparsity. When the error decrease rate is lower than the preset threshold or the error no longer decreases significantly, the corresponding sparsity is determined to be the optimal sparsity.

[0018] Beneficial effects of the present invention:

[0019] The present invention provides a bearing electrostatic signal denoising method based on improved variational modal decomposition, and an adaptive method for determining the modal number based on kurtosis and mutual correlation coefficients, to achieve adaptive separation of the modal components and noise components in the signal. The objective function is optimized by constructing a quadratic penalty factor based on saturation values ​​to quantify the modal aliasing between the electrostatic components of the structure. The quadratic penalty factor and the number of modal decomposition layers are optimized and solved based on the Grey Wolf Optimization Algorithm to obtain the optimal parameters of the VMD algorithm, which are then used to process the bearing electrostatic signal. Based on the adaptively obtained structural modal number, the method of the present invention uses an algorithm to seek the optimal solution for the quadratic penalty factor, effectively filtering out power frequency noise in the electrostatic signal and suppressing the modal aliasing of the components, thus providing a new approach for bearing electrostatic signal denoising during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0021] Figure 1 This is a flow chart of a bearing electrostatic signal noise reduction method based on VMD-OMP in an embodiment of the present invention;

[0022] Figure 2 is a time domain diagram of the original electrostatic signal in an embodiment of the present invention;

[0023] Figure 3 is a frequency domain schematic diagram of the original electrostatic signal in an embodiment of the present invention;

[0024] Figure 4 is a time domain schematic diagram of VMD decomposition of modal components in an embodiment of the present invention;

[0025] Figure 5 is a time domain schematic diagram of the residual modal component after reconstruction in an embodiment of the present invention;

[0026] Figure 6 is a time domain schematic diagram of reconstructed signals after merging in an embodiment of the present invention;

[0027] Figure 7 is a schematic diagram of the time-frequency domain after the reconstructed signals are merged in an embodiment of the present invention;

[0028] Figure 8 This is a schematic diagram of the time-frequency domain in which only variational mode decomposition is performed and then merging is completed in an embodiment of the present invention;

[0029] Figure 9 It is a working experimental platform for hardware equipment in the embodiment of the present invention. DETAILED DESCRIPTION

[0030] The present application is described below with reference to specific embodiments:

[0031] Example 1:

[0032] In order to effectively remove noise interference and maximize the preservation of the original fault characteristics of the electrostatic monitoring signal, this embodiment provides the following Figure 1 The following figure shows a bearing electrostatic signal noise reduction method based on VMD-OMP. This method can effectively remove the noise interference of the electrostatic signal during the acquisition process, greatly improving the quality of the bearing electrostatic signal. The specific steps are as follows:

[0033] S1. The original bearing electrostatic signal collected by the electrostatic sensor is decomposed using the variational mode decomposition (VMD) method. During the decomposition process, an optimization algorithm is used to automatically optimize the number of VMD modal components K and the quadratic penalty factor α to obtain the optimal parameter combination, thereby optimizing the decomposition effect and obtaining multiple modal components.

[0034] S11. Constructing variational problems

[0035] The original bearing electrostatic signal is decomposed into a finite number of intrinsic modal components. Its essence is to construct and solve the variational problem. The constrained variational problem can be expressed as follows:

[0036]

[0037] Wherein, {uk}={u1,u2…,uK} represents the K modal component signals obtained by decomposing the original bearing electrostatic signal, {ωk}={ω1,ω2…,ωK} represents the center frequency of each of the K modal components, x(t) is the original bearing electrostatic signal, and δ(t) represents the Dirac function; Indicates the derivative of the function with respect to time t, * indicates convolution, and j indicates the imaginary unit;

[0038] S12. Transform into an unconstrained variational problem

[0039] By introducing the quadratic penalty coefficient α and the Lagrange multiplication operator λ, the constrained variational problem is transformed into an unconstrained variational problem, thereby obtaining the optimal solution of the variational problem:

[0040]

[0041] Where K represents the number of modal components; x(t) is the original bearing electrostatic signal; α is the quadratic penalty factor; <> represents the inner product operation;

[0042] S13. Iterative update, the solution becomes an unconstrained variational problem

[0043] Update through iteration 、 、 To seek the optimal solution of the constrained variational problem and find the minimum point of the expression of the unconstrained variational problem;

[0044] Among them, The updated expression is:

[0045]

[0046] right The expression for center frequency update is:

[0047]

[0048] right The updated expression is:

[0049]

[0050] in, represents the fidelity coefficient, λ(t) represents the Lagrange multiplication operator, Represents the given discrimination accuracy, n represents the number of iterations, 、 、 Respectively represent the n+1th iteration 、 、 The Fourier transform of represents the center frequency;

[0051] The iteration is terminated until the constraint conditions are met. The iteration stopping condition is defined as follows:

[0052]

[0053] Among them, it means At the nth iteration Fourier transform of

[0054] In the embodiment, the specific implementation process of the above variational mode decomposition algorithm is as follows: Figure 1 As shown. First, it is necessary to preset the modal number K and set the quadratic penalty factor α according to the empirical value; then initialize the update calculation uk, ωk, and increment the variables n and k to determine whether the value of k reaches the preset value, and then obtain After that, it is determined whether the iteration stop condition is met. When the condition is met, K modal components are finally obtained.

[0055] Specifically, in the embodiment, an electrostatic sensor is used to collect the electrostatic signal of the bearing, and the signal is converted into the time-frequency domain, which can more accurately show the degree of interference of the signal. For details, see Figure 2 and Figure 3 Schematic diagram of the time domain and time-frequency domain of the original electrostatic signal.

[0056] After decomposing the above-mentioned simulation signal using the variational mode decomposition method (VMD), the individuals in the gray wolf group are initialized through the gray wolf algorithm, and the fitness of each gray wolf's parameter combination (k, α) is evaluated. According to the corresponding function value, the individuals in the gray wolf group are sorted by merit, and the position of the gray wolf is gradually updated until the maximum number of iterations is reached or the stopping condition is met. The final position of the wolf is the optimal parameter combination (k, α) of VMD.

[0057] In this paper, the minimum envelope entropy is selected as the fitness function, and the algorithm parameters are set as follows: the iteration range of k is (3, 10); the iteration range of α is (1000, 5000), the number of optimization variables is 2, the maximum number of iterations is 20, and the population size is 20. That is, through the adaptive optimization of GWO optimized VMD, the optimal parameter modal number K and penalty factor α are 8 and 2000 respectively. Figure 1 The variational mode decomposition algorithm described in Figure 2 The noisy signal is decomposed into 8 modal component signals, and the waveform in the time domain is as follows Figure 4 shown.

[0058] S2. For each modal component decomposed in step S1, calculate its mutual correlation coefficient and kurtosis with the original bearing electrostatic signal, and screen out effective signal components according to preset standards.

[0059] The process of using kurtosis and cross-correlation coefficients to screen categorical modal components is as follows:

[0060] Based on the K modal component signals decomposed in step S1, the cross-correlation coefficient and kurtosis of each modal component signal and the original bearing electrostatic signal are calculated to obtain the correlation coefficient and kurtosis of each modal component. The correlation coefficient and kurtosis calculation method of each modal component signal IMF = (x1, x2, ..., xm) and the original bearing electrostatic signal x(t) = (y1, y2, ..., ym) are as follows:

[0061]

[0062]

[0063] in, represents the correlation coefficient, m represents the length of the original bearing electrostatic signal, represents the average value of a modal component IMF=(x1,x2,...,xm), represents the average value of the original bearing electrostatic signal x(t)=(y1,y2,...,ym), The larger the value of , the more components of the original electrostatic signal are contained in the modal component signal. By comparing the correlation coefficients calculated for each modal component, the modal component signal with the smallest correlation coefficient with the original electrostatic signal is selected and treated as a noise component for removal. xi represents the i-th observation value of the original bearing electrostatic signal, yi represents the i-th observation value of a modal component IMF; N is the total number of observations. represents the kurtosis, Represents the standard deviation. When the kurtosis is 3, the distribution of the signal is the standard value of the normal distribution. That is, the kurtosis of the normal distribution is usually set to 3. If the kurtosis of the modal component signal is less than 3, it means that the peak of the component is relatively gentle and lacks strong impact characteristics. Therefore, the electrostatic signal component with a kurtosis less than 3 is removed and the remaining modal component signals are retained.

[0064] In this embodiment, according to the definition of correlation coefficient, the Figure 4 The 8 modal components and Figure 3 The correlation coefficient of the noisy signal in is shown in Table 1.

[0065] Table 1 Calculated values ​​of correlation coefficients of each modal component

[0066] IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 Correlation coefficient 0.876 0.798 0.775 0.688 0.654 0.382 0.776 0.215

[0067] It can be seen from the table that the correlation coefficients of IMF6 and IMF8 with the original signal are small. Figure 4The decomposed modal components also show that the IMF6 and IMF8 components contain fewer components from the original signal, and the frequency band amplitude of the fault information is lower. Based on step (S2), in this embodiment, the IMF6 and IMF8 modal components are directly treated as noise modal components, removed, and the remaining six modal components are retained as valid component signals. The other six decomposed modal components contain a lot of noise interference, which will be processed in steps (S3) and (S4).

[0068] S3. Based on the screened modal component signals, the saturation value method is used to determine the optimal sparsity of signal reconstruction.

[0069] The core of this step is to find the saturation point in the curve of electrostatic signal quality changing with sparsity. The sparsity coefficient decreases continuously with the increase of sparsity. When it reaches a certain value, it tends to saturation and the electrostatic signal quality no longer improves significantly. That is, this value can be considered as the optimal sparsity of the electrostatic signal. Assume that the signal Can be in the dictionary The following expression is:

[0070]

[0071] in, is the coefficient vector, That is the sparsity of the signal. When using the saturation value method, the dictionary The number of elements in the array increases gradually from small to large until it reaches a certain threshold. , at this time the error No longer decreases significantly. At this point, the sparsity of the signal can be roughly considered to be: ;

[0072] S4. Reconstruct the effective modal components and optimal sparsity after processing in steps S2 and S3 using the orthogonal matching pursuit (OMP) algorithm, and finally merge them to obtain the denoised bearing electrostatic signal.

[0073] Based on the definition of the constrained variational problem described in step S11, the sum of all decomposed modal components constitutes the original input signal, which can be expressed as follows:

[0074]

[0075] Where {uk} = {u1, u2..., uK} decomposes the original signal into K modal components, and x(t) is the original input signal. In step S2, the modal components of the interfering noise are identified using the correlation coefficient method and removed. In steps S3 and S4, the component signals are reconstructed using the sparsity determined by the saturation value method. The sum of the remaining modal component signals after the reconstruction is defined as follows:

[0076]

[0077] Among them, IMF is the remaining modal component after screening and reconstruction. Since two noise modal components are taken out in step S2, the number of remaining modal components becomes K-2, and Out(t) is the output signal after the noise reduction process, that is, the reconstructed noise reduction signal.

[0078] In this embodiment, Figure 4 The six modal component signals that have been screened are reconstructed to obtain Figure 5 Reconstruct the noise reduction signal from Figure 5 It can be seen that the algorithm processing effectively removes the power frequency noise interference, greatly improving the data quality of the bearing electrostatic signal.

[0079] By merging the reconstructed electrostatic signal components, the effective information of multiple components can be integrated, thereby significantly enhancing the characteristic performance of the electrostatic signal and effectively improving its time domain resolution. The time domain diagram of the merged reconstructed signal is as follows: Figure 6 As shown in the figure, it can be clearly seen that the peak pulses of the electrostatic signal have a certain regularity and show periodic changes.

[0080] Table 2 Performance comparison of different noise reduction methods for bearing electrostatic signals

[0081] parameter SNR STD MSE VMD 9.713 0.527 0.228 VMD-OMPP 14.427 0.332 0.106

[0082] Table 2 shows the performance comparison of the results obtained by using the orthogonal matching pursuit algorithm to process the bearing electrostatic signal. The comparison of the processing results of the two methods in the time-frequency domain is shown in Table 2. Figure 7 and Figure 8 As shown in Figure 2, the signal-to-noise ratio (SNR), standard deviation (STD), and mean square error (MSE) are used as evaluation indicators for the algorithm performance.

[0083] As shown in the table, the VMD-OMP algorithm demonstrates significant advantages in noise reduction performance compared to the VMD algorithm alone. Specifically, its signal-to-noise ratio (SNR) improved by approximately 4.7 dB, while the standard deviation and mean square error (MSE) decreased by 19.5% and 12.2%, respectively. This demonstrates that the VMD-OMP algorithm not only effectively reduces noise but also maximizes the preservation of the original characteristics of the electrostatic anomaly signal. Therefore, as an efficient and reliable method for electrostatic signal noise reduction, the VMD-OMP algorithm provides new insights and approaches for monitoring anomaly electrostatic signals in rolling element bearings.

[0084] In addition to the above algorithm, this embodiment also provides an experimental platform for implementing the above algorithm, such as Figure 9 As shown, the test bench includes, from left to right, key components such as the motor, soundproof enclosure, drive shaft, fixture, electrostatic sensor, bearing housing, and magnetic powder brake. In addition, there is a drive belt, coupling, and monitoring area. The electrostatic sensor is installed near the monitoring area and performs online condition monitoring of the rolling bearing within the bearing housing, enabling real-time acquisition of electrostatic signals generated during bearing operation. This test bench structure helps verify the effectiveness of electrostatic sensors in rolling bearing condition monitoring.

[0085] It should be noted that the above embodiments can be freely combined as needed. The above are only preferred embodiments of the present invention. It should be pointed out that ordinary relevant personnel in this technical field can make several improvements and modifications without departing from the principles of the present invention. Such improvements and modifications should also be considered as the scope of protection of the present invention.

[0086] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

Claims

1. A bearing electrostatic signal noise reduction method based on VMD-OMP, characterized in that: The steps include: S1. The original bearing electrostatic signal is decomposed using the variational mode decomposition (VMD) method. During the decomposition process, an optimization algorithm is used to automatically optimize the number of VMD modal components K and the quadratic penalty factor α to obtain the optimal parameter combination, thereby optimizing the decomposition effect and obtaining multiple modal components. S2. For each modal component decomposed in step S1, calculate its mutual correlation coefficient and kurtosis with the original bearing electrostatic signal, and select the effective signal component according to the preset standard; S3. Based on the screened modal component signals, the saturation value method is used to determine the optimal sparsity of signal reconstruction; S4. Reconstruct the effective modal components and optimal sparsity after processing in steps S2 and S3 using the orthogonal matching pursuit (OMP) algorithm, and finally merge them to obtain the denoised bearing electrostatic signal.

2. The bearing electrostatic signal noise reduction method based on VMD-OMP according to claim 1 is characterized in that: The VMD decomposition process includes constructing a constrained variational problem and converting it into an unconstrained variational problem containing a quadratic penalty factor α and a Lagrange multiplier λ, and sequentially updating the center frequency and component signal of each modal component in an iterative manner until a termination condition is met.

3. The bearing electrostatic signal noise reduction method based on VMD-OMP according to claim 2 is characterized in that: The method for automatically optimizing the VMD parameters K and α is as follows: using the Grey Wolf Algorithm (GWO) with envelope entropy as the fitness function, continuously updating the parameter combination through hunting behavior simulation, minimizing the sum of the envelope entropy of all modal component decompositions, and ultimately obtaining the global optimal parameters. The specific steps include: Initialize the parameters of the GWO algorithm, including the number of wolves, number of iterations, and parameter range; use the VMD penalty factor α and the modal decomposition number K as optimization variables, and the envelope entropy as the fitness function, and use the GWO algorithm for optimization; according to the update rule of the GWO algorithm, update the position and velocity of each wolf and calculate the fitness value of each wolf; based on the fitness value, update the optimal solution, suboptimal solution, and general solution; until the maximum number of iterations is reached or the fitness value converges, then output the penalty factor α and modal decomposition number K corresponding to the optimal solution.

4. The bearing electrostatic signal noise reduction method based on VMD-OMP according to claim 1 is characterized in that: The calculation methods of the mutual correlation coefficient and kurtosis of each modal component and the original bearing electrostatic signal are: ； ； in, represents the correlation coefficient, m represents the length of the original bearing electrostatic signal, represents the average value of a modal component IMF=(x1,x2,...,xm), represents the average value of the original bearing electrostatic signal x(t) = (y1, y2, ..., ym); xi represents the i-th observation value of the original bearing electrostatic signal, yi represents the i-th observation value of a modal component IMF; N is the total number of observations; represents the kurtosis, Represents standard deviation.

5. The bearing electrostatic signal noise reduction method based on VMD-OMP according to claim 4 is characterized in that: The preset criteria for selecting effective signal components include: modal components with a correlation coefficient higher than a self-set threshold and a kurtosis of not less than 3 are retained, and the remaining components are removed as noise components.

6. The bearing electrostatic signal noise reduction method based on VMD-OMP according to claim 1 is characterized in that: The optimal sparsity of signal reconstruction determined by the saturation value method is specifically as follows: When the sparsity is gradually increased, the signal reconstruction error is monitored as it changes with the sparsity. When the error decrease rate is lower than the preset threshold or the error no longer decreases significantly, the corresponding sparsity is determined to be the optimal sparsity.

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