A rolling bearing signal denoising method based on adaptive window length time-frequency peak filtering

Abstract

The application provides a rolling bearing signal denoising method based on adaptive window length time-frequency peak filtering, which comprises the following steps: firstly, performing empirical wavelet decomposition on the vibration signal of the rolling bearing under variable working conditions to obtain different modal components with high to low frequency components; secondly, calculating the correlation coefficient of each modal component and the original signal, and screening out the fault-sensitive modal component; then, constructing a fault sensitivity index which fuses the correlation coefficient and kurtosis to adaptively adjust the window length of the time-frequency peak filtering method; using the adaptive window length peak filtering method to denoise the screened fault-sensitive modal component; finally, reconstructing the vibration signal through the denoised modal components and the reserved components to realize the rolling bearing vibration signal denoising. The application solves the problem that the traditional fixed window length time-frequency peak filtering method is difficult to perform wide frequency domain instantaneous frequency estimation, resulting in weak rolling bearing vibration signal denoising ability, and improves the rolling bearing denoising effect under strong noise.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of rolling bearing fault diagnosis, and particularly relates to a rolling bearing signal denoising method based on adaptive window length time-frequency peak filtering. BACKGROUND

[0002] Rolling bearings are key support components in rotating machinery equipment, and are complex in structure, variable in actual running speed and load. Signals generated by various excitation sources are coupled with each other, and are prone to faults, thereby affecting the running safety of the equipment. Impact features caused by rolling bearing faults are often submerged in strong background noise, and are accompanied by modulation phenomena of impact signals on system inherent vibration signals, so that it is very difficult to extract fault features. Therefore, it is of great significance for the safety of the equipment to study a method for denoising variable working condition vibration signals under strong noise interference and accurately extracting fault features.

[0003] Time-frequency peak filtering (TFPF) is an effective method for suppressing Gaussian noise in non-stationary deterministic band-limited signals, and has the advantages of strong adaptability and no need for additional information. TFPF has been successfully applied to fields such as earthquake monitoring, electroencephalogram signal enhancement, frequency hopping signal detection and mechanical fault diagnosis, and shows very good suppression effect on strong random noise. However, the selection of the filtering window length in the TFPF method is a difficulty, which directly affects the noise suppression ability and signal fidelity. A longer window length can effectively suppress noise, but will cause loss of the amplitude of effective signals at the same time. A shorter window length has poor suppression effect on noise, but can well protect the amplitude of effective signals. In order to solve the problem of window length selection of TFPF and achieve the balance between noise suppression and signal fidelity, some scholars make the vibration signal pass through ensemble empirical mode decomposition (EEMD) to obtain a series of IMFs from high frequency to low frequency, and denoising processing is performed on the IMFs in different frequency bands by using different window lengths. In addition, some scholars combine adaptive noise integrated empirical mode decomposition, permutation entropy and time-frequency peak filtering, use the algorithm to obtain the intrinsic mode function of the original signal to calculate the permutation entropy value of each IMF to determine whether the IMF needs to be filtered, and select different window lengths for filtering according to different IMFs, and good denoising effect is achieved.

[0004] However, the integrated empirical mode decomposition method and the adaptive noise integrated empirical mode decomposition method as the improved method of empirical mode decomposition (EMD) still retains the mode aliasing and end effect problems in the decomposition process. EEMD solves the mode aliasing problem to a certain extent by adding Gaussian white noise and taking the average result as the signal for decomposition, but the IMFs generated by decomposition often contain residual noise, which increases the complexity of the signal and is not conducive to the extraction of signal features. Compared with the EMD method, the empirical wavelet transform (EWT) can adaptively select the frequency band, overcome the mode aliasing problem caused by the discontinuity of the signal time-frequency scale, has a complete and reliable mathematical theoretical basis, has low computational complexity, and can also overcome the over-envelope and under-envelope problems in the EMD method. In summary, the traditional TFPF noise reduction method has the following problems:

[0005] 1. In the traditional TFPF algorithm, the selection of the window length will cause the contradiction between signal fidelity and noise suppression. A longer window length can effectively remove noise, but at the same time, it will cause the amplitude loss of the effective signal. A shorter window length can well protect the amplitude of the effective signal, but it is not enough in suppressing noise, and it is difficult to achieve a proper balance.

[0006] 2. The traditional noise reduction method combining EMD method with TFPF still retains the mode aliasing and end effect problems in the decomposition process. EEMD solves the mode aliasing problem to a certain extent by adding Gaussian white noise and taking the average result as the signal for decomposition, but the IMFs generated by decomposition often contain residual noise, which increases the complexity of the signal and is not conducive to the extraction of signal features.

[0007] 3. The adaptive method of the traditional TFPF method sets different filter window lengths according to the threshold of the judgment index, but the selection of the window length is still limited to a few fixed values determined by experience, and it does not have a quantitative description and complete adaptability. SUMMARY

[0008] The purpose of the present application is to provide a rolling bearing signal denoising method based on adaptive window length time-frequency peak value filtering to realize effective denoising of rolling bearing variable working condition fault signals under strong noise.

[0009] Technical scheme: The present application provides a rolling bearing signal denoising method based on adaptive window length time-frequency peak value filtering, which specifically comprises the following steps:

[0010] (1) Collect the vibration signal of rolling bearing under variable speed condition with strong noise at a fixed sampling frequency, and record the change relationship between the rotation frequency and time in the signal segment;

[0011] (2) Perform empirical wavelet decomposition on the fault signal of rolling bearing to obtain different signal components with high to low frequency components;

[0012] (3) Calculate the correlation coefficient between each signal component in step (2) and the original signal, and the standard deviation between the components;

[0013] (4) Screen the fault sensitive modal components by comparing the correlation coefficient and the standard deviation, that is, the signal component with a correlation coefficient greater than the standard deviation is taken as the object of subsequent noise reduction processing, and the signal component with a correlation coefficient less than the standard deviation is retained without processing;

[0014] (5) Calculate the kurtosis value of the component selected in step (4) that needs to be processed, construct a fault sensitivity index integrating the correlation coefficient and the kurtosis, and adaptively adjust the window length of the time-frequency peak value filtering method according to the index, and thus perform adaptive window length time-frequency peak value filtering processing;

[0015] (6) Reconstruct the vibration signal by the modal components after noise reduction and the retained components to realize the noise reduction of rolling bearing vibration signal.

[0016] Further, the step (2) is implemented as follows:

[0017] (21) Fourier spectrum band division: obtain the Fourier spectrum of the signal by fast Fourier transform, standardize the spectrum in [0, π] based on Shannon criterion, and divide it into N continuous unequal width band intervals, then the range of each band is represented as:

[0018] Λ n = [ω n-1 ,ω n ] (n = 1, 2, …, N) (1)

[0019] In the formula, ω n is the midpoint of adjacent maximum points Ψ n of the Fourier spectrum of the signal; a transition section is defined with each support boundary ω n as the center, and the width is:

[0020] T n = 2τ (2)

[0021] In the formula,

[0022] (22) Construct filter bank based on band boundary coordinates: construct the empirical wavelet scale function and the wavelet function ψ n (w) are respectively:

[0023]

[0024]

[0025] where the function β(x) = x 4 (35 - 84x + 70x 2 - 20x 3 ), τ n = γω n ,

[0026] (23) Component signals are obtained by wavelet basis function filtering: the empirical wavelet transform detail coefficients and approximation coefficients are constructed according to the construction method of classical wavelet transform, the detail coefficients and the approximation coefficients represent the high frequency component and the low frequency component of the signal respectively:

[0027]

[0028]

[0029] where <·> is the inner product operation; ψ n and φ1are the empirical wavelet function and the scaling function respectively; and are the Fourier transform of ψ n and φ1(ω) respectively, and are the conjugate complex of ψ n and φ1(ω) respectively; the original signal is reconstructed as:

[0030]

[0031] where * represents convolution, and represent the Fourier transform of and respectively.

[0032] Further, the correlation coefficient in step (3) is realized by the following formula:

[0033]

[0034] R x (τ) = E[x(t)x(t+τ)] (9)

[0035]

[0036] where represents the cross-correlation value of each IMF component and the original signal; R x (τ) represents the autocorrelation of the original signal itself, x(t) represents the original signal, c j (t) represents the jth IMF component; the IMF component containing fault information has a larger correlation with the original signal, and if it is a false component, the correlation is smaller.

[0037] Further, the step (4) is implemented as follows:

[0038] The correlation coefficient of the IMF component and the original signal is greater than the standard deviation, and the similarity is greater. The window length threshold coefficient is:

[0039]

[0040] Where σ is the average value of the standard deviation of all signal components; when the correlation coefficient of the signal is greater than σ, the window length coefficient is 1, and it needs to be denoised; when the correlation coefficient of the signal is less than σ, it is indicated that the signal is determined to have no impact component, and the fault sensitivity is too low, and it is not used as an effective signal for denoising.

[0041] Further, the step (5) is implemented as follows:

[0042] (51) Calculate the kurtosis value of the screened component, and the calculation formula of kurtosis is as follows:

[0043]

[0044] In the formula, x is a discrete signal; is the signal mean value; N is the sampling length; σ is the standard deviation of the signal;

[0045] (52) Construct a fault sensitivity index κ of the fusion correlation coefficient and kurtosis:

[0046]

[0047] In the formula, K j is the kurtosis value of the jth component;

[0048] According to κ, the window length of the time-frequency peak filtering method is adaptively adjusted, and the formula of the adaptive window length KL is defined as:

[0049]

[0050] Where f s is the sampling frequency, f d is the main frequency of the signal segment;

[0051] (53) The TFPF adaptive window length adjustment formula based on kurtosis value, according to the impact signal and noise intensity in the component to adaptively adjust the window length; wherein the window length coefficient γ is the threshold of the segmented effective component, when γ = 0, the window length is 0, indicating that the component does not need to be processed; when γ ≠ 0, the window length is determined according to the signal main frequency, the higher the main frequency, the smaller the window length; according to the sensitivity index κ Item, which indicates that the window length is inversely proportional to the kurtosis; the lower the kurtosis, the greater the proportion of noise components, the longer the window length, and the more obvious the random noise suppression effect; since the amplitude of the signal after wavelet decomposition decreases with the increase of the scale, therefore The larger the denominator part log(j+2) of the item, the smaller the window length, which prevents the filter window length from being too large for low amplitude components, resulting in excessive suppression;

[0052] (54) Adaptive TFPF based on kurtosis value, for the noisy signal s(t), the frequency modulation is changed to the analytical signal:

[0053]

[0054] Wherein, μ is the scaling coefficient of z(t) phase; then solve the pseudo Wigner-Ville distribution of the analytical signal:

[0055]

[0056] Finally, the instantaneous frequency at the peak of the pseudo Wigner-Ville distribution is taken as the estimation of the effective signal x(t):

[0057]

[0058] Further, the step (6) is implemented as follows:

[0059] The vibration signal is reconstructed by the denoised modal components and the remaining components, wherein the denoised modal components are the components processed by the adaptive window length TFPF in step (5), and the remaining modal components are the signal components in step (4) whose correlation coefficient with the original signal in the EWT component is less than the standard deviation, finally realizing the denoising of the rolling bearing vibration signal.

[0060] Beneficial effects: compared with the prior art, the beneficial effects of the present application: the present application introduces EWT signal decomposition method as the pretreatment method of signal denoising, and the adaptive window length TFPF denoising is carried out on each component after EWT decomposition, which overcomes the problems of mode aliasing when the existing TFPF denoising with EMD type decomposition method as pretreatment, and the decomposition error is large and the noise robustness is not strong when the recursive decomposition method is affected by the sampling frequency; the present application constructs a fault sensitivity index based on correlation coefficient and kurtosis, and proposes an adaptive adjustment method of window length based on the index, which improves the denoising effect of rolling bearing under strong noise, and solves the problem that the existing adaptive method determines the window length according to experience, resulting in low accuracy; thus, the problem that the traditional fixed window length time-frequency peak filtering method is difficult to estimate the wide frequency domain instantaneous frequency, resulting in weak denoising ability of rolling bearing vibration signal is solved; the present application can effectively retain the fault impact component, significantly improve the signal-to-noise ratio, and realize the denoising of rolling bearing variable working condition vibration signal under strong noise. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 the flow chart of the method of the present application;

[0062] Figure 2 the physical diagram of the rolling bearing fault vibration test equipment in the embodiment of the present application;

[0063] Figure 3 the rotational speed curve diagram of the test signal analysis section of the present application;

[0064] Figure 4 the first four EWT components of the original signal of the present application;

[0065] Figure 5 the first four EWT components after filtering of the present application;

[0066] Figure 6 the time domain diagram of the original signal, fixed window length TFPF and adaptive time-frequency peak filtering processing of the present application;

[0067] Figure 7 the envelope spectrum diagram of the test original signal of the present application;

[0068] Figure 8 the envelope spectrum diagram after adaptive window length time-frequency peak filtering processing of the present application;

[0069] Figure 9 the short-time Fourier transform diagram of the original signal of the present application;

[0070] Figure 10 the short-time Fourier transform diagram after fixed window length TFPF processing of the present application;

[0071] Figure 11The short-time Fourier transform diagram after adaptive window length time-frequency peak filtering noise reduction of the application. DETAILED DESCRIPTION

[0072] The application will be further described in detail below with reference to the accompanying drawings.

[0073] The application proposes a rolling bearing signal noise reduction method based on adaptive window length time-frequency peak filtering, as shown in the formula: Figure 1 Specifically, the method comprises the following steps:

[0074] Step 1: Collect the vibration signal of the rolling bearing under strong noise and variable speed conditions at a fixed sampling frequency Fs, and record the change relationship between the rotation frequency and time in the collected signal segment.

[0075] Step 2: Perform EWT decomposition on the rolling bearing fault signal obtained in step 1 to obtain different signal components IMFs with high to low frequency components.

[0076] First, Fourier spectrum band division is performed. The Fourier spectrum of the signal is obtained by FFT, the spectrum is standardized to [0, π] based on the Shannon criterion, and it is divided into N continuous unequal width band intervals, then the range of each band can be expressed as:

[0077] Λ n = [ω n-1 ,ω n ](n = 1, 2, …, N) (1)

[0078] In the formula, ω n is the midpoint of adjacent maximum points Ψ n of the Fourier spectrum of the signal. A transition section is defined with each support boundary ω n as the center, and the width is:

[0079] T n = 2τ (2)

[0080] In the formula, τ n = γω n ,

[0081] Then, the filter bank is constructed based on the band boundary coordinates. According to the construction method of Meyer wavelet, the scale function and the wavelet function ψ n (w) constructed by experience are respectively:

[0082]

[0083]

[0084] In the formula, the function β(x) = x 4(35-84x+70x 2 -20x 3 ), τ n = gω n ,

[0085] Next, the component signals are obtained by wavelet basis function filtering. The empirical wavelet transform detail coefficients and approximation coefficients are constructed according to the construction method of the classical wavelet transform. The detail coefficients and approximation coefficients represent the frequency components and low frequency components of the signal respectively.

[0086]

[0087]

[0088] where, · is the inner product operation; ψ n and φ1 are the empirical wavelet function and scale function respectively; and are the Fourier transforms of ψ n and φ1(ω) respectively, and are the conjugate complex numbers of ψ n and φ1(ω) respectively. The original signal is reconstructed as:

[0089]

[0090] where, * represents convolution, and represent the Fourier transforms of and respectively.

[0091] Step 3: Calculate the correlation coefficient values between each signal component in step 2 and the original signal and the standard deviation between the components.

[0092] After the EWT decomposition of the noisy signal, a series of different IMFs with high to low frequency components are obtained. With the increase of the decomposition layer number, the impact components contained in the signal component are less and less, and the signal presents completely random noise, so a threshold needs to be set to determine whether it is necessary to denoise. The correlation coefficient is used to represent the correlation degree between two signals, that is, if the correlation coefficient of the IMF component is large, the correlation is large, and vice versa. The correlation of the IMF component containing fault information with the original signal is relatively large, and the correlation of the false component, i.e. the pseudo component, is relatively small. The calculation formula of the correlation coefficient is as follows:

[0093]

[0094] R x (τ) = E[x(t)x(t+τ)] (9)

[0095]

[0096] wherein, represents the cross-correlation value of each IMF component and the original signal; R x represents the autocorrelation of the original signal itself, x(t) represents the original signal, c j (t) represents the jth IMF component.

[0097] Step 4: The correlation coefficient and the standard deviation obtained by step 3 are compared to screen out the fault-sensitive modal components, that is, the signal component with the correlation coefficient greater than the standard deviation is taken as the object of subsequent noise reduction processing, and the signal component with the correlation coefficient less than the standard deviation is retained without processing.

[0098] According to the correlation coefficient and the standard deviation value obtained by step 3, the components that need to be processed are screened out. For the relationship between the component and the original signal, it is generally considered that the IMF component with the correlation coefficient greater than the standard deviation has a relatively large degree of similarity with the original signal. Therefore, the following formula is proposed to calculate the window length threshold coefficient:

[0099]

[0100] wherein, σ is the average value of the standard deviation of all signal components.

[0101] When the correlation coefficient of the signal is greater than σ, the window length coefficient is 1, and it needs to be processed for noise reduction; when the correlation coefficient of the signal is less than σ, it is indicated that the signal is almost free of impact components, and the fault sensitivity is too low, so it is not taken as an effective signal for noise reduction.

[0102] Step 5: The kurtosis value of the component screened out in step 4 is calculated, a fault sensitivity index fusing the correlation coefficient and the kurtosis is constructed, and the window length of the time-frequency peak filtering method is adaptively adjusted according to the index, so as to perform adaptive window length TFPF processing;

[0103] (5.1) The kurtosis value of the screened component is calculated, and the calculation formula of the kurtosis is as follows:

[0104]

[0105] wherein, x is a discrete signal; is the signal mean value; N is the sampling length; and σ is the standard deviation of the signal.

[0106] In the normal operation process of the bearing, the amplitude distribution of the vibration signal is close to the normal distribution, and the kurtosis value is about 3. If the bearing fails, the amplitude distribution of the vibration signal will deviate from the normal distribution, and the greater the kurtosis value, the greater the impact.

[0107] (5.2) Constructing the fault sensitivity index κ of the fusion correlation coefficient and kurtosis,

[0108]

[0109] In the formula, K j is the kurtosis value of the jth component.

[0110] According to the index, the window length of the time-frequency peak filtering method is adaptively adjusted, and the formula of the adaptive window length KL is defined as:

[0111]

[0112] In formula (14), f s is the sampling frequency, f d is the main frequency of the signal segment (i.e., the frequency at the peak of the spectrum).

[0113] (5.3) The TFPF adaptive window length adjustment formula based on kurtosis value, which adaptively adjusts the time window length according to the intensity of the impact signal and noise in the component. The window length coefficient γ is used as the threshold for segmenting effective components. When γ = 0, the window length is 0, indicating that the component does not need to be processed. When γ ≠ 0, the time window length is determined according to the main frequency, and the higher the main frequency, the smaller the time window length; according to the term of the sensitivity index κ, it is indicated that the time window length is inversely proportional to the kurtosis. The lower the kurtosis, the greater the proportion of noise components, and the longer the time window length, the more obvious the random noise suppression effect. Since the amplitude of the signal decreases with the increase of the scale after wavelet decomposition, the larger the denominator part log(j+2) of the term, the smaller the window length, which prevents the filter window length from being too large for low-amplitude components, resulting in excessive suppression.

[0114] (5.4) TFPF adaptive filtering based on kurtosis value, the principle is:

[0115] For the noisy signal s(t), frequency modulation is performed to become the analytical signal

[0116]

[0117] Where μ is the scaling factor of the phase of z(t). Then solve the PWVD of the analytical signal:

[0118]

[0119] Finally, the instantaneous frequency at the peak of the PWVD is taken as the estimation of the effective signal x(t), that is:

[0120]

[0121] Step 6: Reconstruct the vibration signal by the denoised modal components and the reserved components to realize the denoising of the rolling bearing vibration signal.

[0122] Reconstruct the vibration signal by the denoised modal components and the reserved components to realize the denoising of the rolling bearing vibration signal. The denoised modal component is the component processed by the adaptive window length TFPF in step 5, and the remaining modal component is the signal component with a correlation coefficient less than the standard deviation between the original signal and the signal decomposed in step 4.

[0123] The present application adopts the test data of the fault bearing to process the signal denoising. The test equipment is shown in the physical diagram as Figure 2 The test equipment is shown in the physical diagram as Figure 3 The test equipment is shown in the physical diagram as

[0124] Table 1: Parameters of the test rolling bearing

[0125] Bearing model Pitch diameter D Rolling element diameter d Number of rollers N ER16K 38.52 mm 7.94 mm 9 Fault location Pressure angle a Inner ring fault coefficient Outer ring fault coefficient Inner ring 0 5.43 3.57

[0126] The collected variable working condition signal has strong noise, and the variable speed fault characteristics of the signal cannot be identified according to the time domain and frequency domain graphs, so the original signal is first decomposed by EWT to obtain 10 IMF components. After decomposition, the correlation coefficient and kurtosis of the 10 IMF components are calculated to calculate the IMF components that need to be denoised and the window length of denoising selection, and the calculation results are shown in Table 2.

[0127] Table 2: Kurtosis and correlation coefficient of each component

[0128] IMFs Kurtosis Correlation coefficient IMFs Kurtosis Correlation coefficient IMF1 12.247 0.7459 IMF2 2.3028 0.4099 IMF3 2.8077 0.0490 IMF4 3.2046 0.0173 IMF5 2.8093 0.0060 IMF6 2.4869 0.0017 IMF7 2.8603 0.0016 IMF8 2.6061 0.0015 IMF9 3.2545 0.0003 IMF10 2.9484 0.0001

[0129] The standard deviation of all EWT components is 0.0112, and the window length coefficient is calculated according to According to Table 2, the correlation coefficient of the 5th component sharply decreases and is less than the standard deviation, and the window length threshold coefficient is 0, so only the first four modes are denoised, and the remaining components are reserved. According to the kurtosis of each component in Table 2 and the adaptive window length formula, the window length suitable for each component is calculated, and TFPF processing is performed. The results before and after processing of the first four components are shown in Figure 4 and 5The denoised modal components are finally combined with the modal components without denoising to reconstruct the final adaptive time-frequency peak filtering result. The time-domain waveform diagrams of the three results are shown in Figure 6 The envelope spectrum of the original signal is shown in Figure 7 It is found that there are high-frequency components showing frequency multiplication relationship in the envelope spectrum of the original signal, but the frequency characteristics of the variable speed signal cannot be observed obviously, and there are high-amplitude interference components and a large amount of high-frequency noise. However, in the envelope spectrum after adaptive denoising Figure 8 , there are three groups of high-amplitude frequency components increasing, which are found to be the fault frequencies by comparing with the theoretical fault frequencies. The three groups of frequencies show frequency multiplication relationship and meet the characteristics of linear increase in speed, and the diagram does not contain irrelevant high-amplitude interference components, and the high-frequency noise is significantly reduced. It is thus illustrated that the adaptive time-frequency peak filtering method combined with EWT has good denoising effect.

[0130] Further, the original test signal, the signal after fixed window length TFPF processing and the signal after adaptive window length time-frequency peak filtering processing are respectively subjected to short-time Fourier transform, and the results are shown in Figure 9 , Figure 10 and Figure 11 . The results show that after adaptive denoising processing, more sharpened and higher energy concentration time-frequency ridge lines can be identified, and the time-frequency resolution is obviously higher than that of the signal before denoising. It is illustrated that the high-frequency noise components in the signal are significantly reduced, the impact characteristic components are effectively retained, and the characteristics of the signal are more prominent, which embodies that the method has good denoising effect.

[0131] The above only describes the preferred embodiments of the present application, and it should be noted that for ordinary skilled persons in the art, several improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering, characterized in that, Includes the following steps: (1) The vibration signal of the rolling bearing under strong noise and variable speed is collected at a fixed sampling frequency, and the relationship between the rotational frequency and time within the collected signal segment is recorded. (2) Perform empirical wavelet decomposition on the rolling bearing fault signal to obtain different signal components with high to low frequency components; (3) Calculate the correlation coefficient between each signal component and the original signal in step (2) and the standard deviation between the components; (4) By comparing the correlation coefficient with the standard deviation, the fault-sensitive modal components are selected. The signal components with a correlation coefficient greater than the standard deviation are used as the objects of subsequent noise reduction processing, while the signal components with a correlation coefficient less than the standard deviation are retained without processing. (5) Calculate the kurtosis value of the components that need to be denoised in step (4), construct a fault sensitivity index that integrates correlation coefficient and kurtosis, and adaptively adjust the window length of the time-frequency peak filtering method based on the index, thereby performing time-frequency peak filtering with adaptive window length. (6) The vibration signal is reconstructed by the noise-reduced modal components and the retained components to achieve noise reduction of the rolling bearing vibration signal.

2. The method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering according to claim 1, characterized in that, The implementation process of step (2) is as follows: (21) Fourier spectrum band division: The Fourier spectrum of the signal is obtained through Fast Fourier Transform. Based on the Shannon criterion, the spectrum is normalized to [0,π] and divided into N continuous frequency bands of unequal width. The range of each frequency band is then expressed as: L n =[ω n-1 ,oh n ](n=1,2,…,N) (1) In the formula, ω n Ψ is the adjacent maximum point of the Fourier spectrum of the signal. n The midpoint; with each supporting boundary ω n Define a transition segment at the center with a width of: T n =2τ (2) In the formula, (22) Constructing a filter bank based on frequency band boundary coordinates: constructing an empirical wavelet scaling function based on the Meyer wavelet construction method. and wavelet function ψ n (w) are respectively: In the formula, the function β(x) = x 4 (35-84x+70x 2 -20x 3 ), τ n =γω n , (23) Obtain component signals through wavelet basis function filtering: Construct empirical wavelet transform detail coefficients and approximation coefficients according to the construction method of classical wavelet transform. Detail coefficients and approximation coefficients These represent the high-frequency and low-frequency components of the signal, respectively. In the formula, <·> represents the inner product operation; ψ n φ1 and φ2 are the empirical wavelet function and the scaling function, respectively; and ψ n Fourier transform of φ1(ω), and ψ n The complex conjugate of φ1(ω); the original signal is reconstructed as: In the formula, * denotes convolution. and They represent and Fourier transform.

3. The method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering according to claim 1, characterized in that, The correlation coefficient mentioned in step (3) is achieved through the following formula: R x (τ)=E[x(t)x(t+τ)] (9) In the formula, R represents the cross-correlation value between each IMF component and the original signal; x (τ) represents the autocorrelation of the original signal itself, x(t) represents the original signal, and c j (t) represents the j-th IMF component; the IMF component containing fault information has a relatively high correlation with the original signal, while the correlation of a false component is relatively low.

4. The method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering according to claim 1, characterized in that, The implementation process of step (4) is as follows: IMF components with correlation coefficients greater than the standard deviation are more similar to the original signal. Calculate the window length threshold coefficient: Where σ is the average of the standard deviations of all signal components; when the correlation coefficient of the signal is greater than σ, the window length coefficient is 1, and noise reduction processing is required; when the correlation coefficient of the signal is less than σ, it indicates that the signal is determined to have no impact component, the fault sensitivity is too low, and it is not used as an effective signal for noise reduction.

5. A method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering according to claim 1, characterized in that, The implementation process of step (5) is as follows: (51) Calculate the kurtosis value of the filtered components. The formula for calculating kurtosis is as follows: In the formula, x is a discrete signal; σ is the signal mean; N is the sampling length; σ is the standard deviation of the signal. (52) Construct a fault sensitivity index κ that combines correlation coefficient and kurtosis: In the formula, K j Let be the kurtosis value of the j-th component; Based on κ, the window length of the time-frequency peak filtering method is adaptively adjusted, and the formula for the adaptive window length KL is defined as follows: Among them, f s f is the sampling frequency. d The main frequency of the signal band; (53) The TFPF adaptive window length adjustment formula based on kurtosis value adaptively adjusts the window length according to the impulse signal and noise intensity in the component; where the window length coefficient γ is used as the threshold for segmenting the effective component. When γ = 0, the window length is 0, indicating that the component does not need to be processed; when γ ≠ 0, the window length is determined according to the signal dominant frequency. The higher the dominant frequency, the smaller the window length; according to the sensitivity index κ The term indicates that the time window length is inversely proportional to the kurtosis; the lower the kurtosis, the greater the proportion of noise components, and the longer the time window length, the more significant the random noise suppression effect; since the amplitude of the signal after wavelet decomposition decreases with increasing scale, therefore... The larger the denominator log(j+2) of the term, the smaller its window length, to prevent the filtering window length from being too large for low-amplitude components, which would lead to excessive suppression. (54) Based on kurtosis-based TFPF adaptive filtering, for a noisy signal s(t), frequency modulation is applied to convert it into an analytic signal: Where μ is the scaling factor of the z(t) phase; then, the pseudo-Wigner-Ville distribution of the analytic signal is obtained: Finally, the instantaneous frequency at the peak of the pseudo-Wigner-Ville distribution is used as an estimate of the effective signal x(t):

6. The method for denoising rolling bearing signals based on adaptive window length time-frequency peak filtering according to claim 1, characterized in that, The implementation process of step (6) is as follows: The vibration signal is reconstructed by the noise-reduced modal components and the retained components. The noise-reduced modal components are the components processed by the adaptive window length TFPF in step (5), and the remaining modal components are the signal components in step (4) whose correlation coefficient with the original signal is less than the standard deviation with the EWT component. Finally, the noise reduction of the rolling bearing vibration signal is achieved.

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