Bearing fault diagnosis method and system based on parameterized time-frequency analysis

Abstract

The invention discloses a bearing fault diagnosis method and system based on parameterization time-frequency analysis, and belongs to the technical field of fault diagnos.The method comprises the steps that according to an obtained bearing fault signal, the optimal coefficient of a parameter transformation kernel is determined and serves as a kernel function parameter coefficient of GWT, then GWT operation is carried out to suppress time-frequency energy diffusion, and a fault diagnosis result is obtained; the initial time-frequency representation of the signal is obtained, and the problem of time-frequency energy diffusion of a traditional signal analysis method is solved. After the initial time frequency representation of the signal is obtained, an instantaneous frequency operator of STFT is replaced by an operator of GWT, time frequency energy is compressed from two directions of time and frequency, time frequency energy distribution of single-component signals in the two directions of time and frequency is obtained, the time frequency energy distribution of the single-component signals in the two directions of time and frequency is superposed, and the time frequency energy distribution of the single-component signals in the two directions of time and frequency is obtained. And obtaining the time-frequency energy distribution of the enhanced bearing fault signal. The time-frequency energy concentration degree and the TFR resolution are improved, and meanwhile the capability of coping with harmonic-like signals and pulse-like signals is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of fault diagnosis, and more particularly to a bearing fault diagnosis method and system based on parametric time-frequency analysis. Background Art

[0002] Rotating machinery plays a key role in industry and manufacturing, and its performance and reliability are crucial for preventing significant economic losses and avoiding catastrophic failures. Rolling bearings, as the core components of mechanical equipment, the monitoring and fault diagnosis of their operating states are particularly important. Traditional signal analysis methods are difficult to handle non-stationary signals, such as impulse-like signals generated by faulty bearings, harmonic-like signals generated by aero-engine faults, and modulated signals in communication systems.

[0003] Various signal processing methods, such as sparse representation, spectral kurtosis (SK), maximum correlated kurtosis deconvolution (MCKD), and time-frequency analysis (TFA), have been widely applied to mechanical fault diagnosis. Key information related to the health state of the equipment is contained in the vibration signal. Through the TFA technique, the sparsity of the signal can be realized, the dynamic characteristics of non-stationary signals can be revealed, and thus the identification and diagnosis of fault patterns can be improved, which plays a key role in the fault diagnosis process. Since the instantaneous frequency of non-stationary signals changes with time, how to extract the relationship between the instantaneous frequency of non-stationary signals and time, and extract fault features and compare them with fault frequencies becomes particularly important in the field of fault diagnosis. Researchers are committed to improving the time-frequency energy concentration of time-frequency analysis methods. High time-frequency energy concentration represents high time-frequency resolution, and a clearer time-frequency ridge line can accurately capture the signal time-frequency trajectory, which means that it is easier to identify fault features and sensitive frequency bands from the time-frequency representation of fault signals. Various time-frequency analysis methods have thus emerged.

[0004] At present, many scholars have proposed methods based on time-frequency analysis (TFA) to extract the time-varying features of non-stationary signals, including linear TFA methods and nonlinear TFA methods. Among them, linear TFA methods such as short-time Fourier transform (STFT), continuous wavelet transform (CWT), and S transform, etc., can transform the one-dimensional time-domain information of non-stationary signals into a distribution function in the two-dimensional TF plane considering time components and frequency components, revealing the fault characteristics of non-stationary signals. However, due to the existence of the Heisenberg uncertainty principle, they cannot simultaneously produce clear time and frequency resolutions, and there is a problem of time-frequency energy divergence. In order to overcome the energy divergence problem existing in linear TFA, many nonlinear TFA methods have emerged. The Wigner-Ville distribution (WVD) is one of the classic methods of nonlinear TFA, which provides a method to describe the distribution of signal energy in time and frequency, overcomes the problem of poor resolution of linear TFA, and improves the time-frequency resolution of non-stationary signals. However, the inherent cross-term interference problem limits its application. In order to solve the constraint between time and frequency of the basis function of the TFA method, researchers have studied the post-processing technology of TFA and obtained more accurate time-frequency representation results.

[0005] The reassignment method (RM) rearranges the TF coefficients of a signal in the time and frequency directions. Unfortunately, this method does not have the ability to reconstruct. To overcome this drawback, the synchrosqueezing transform method was proposed. Its main idea is to compress the scattered TF coefficients along the frequency axis onto the instantaneous frequency (IF) curve of the signal, thereby maintaining the reconstruction ability while ensuring TF resolution. However, SST can only handle weakly varying signals. Therefore, scholars have conducted research to improve SST in terms of order and dimension. The synchrosqueezing S transform (SSST) was proposed, extending SST to the second order. Subsequently, the parametric iterative synchrosqueezing transform, the iterative generalized IGSST, the high-order SST (HOSST), and the multiple synchrosqueezing transform (MSST) were proposed. This method greatly reduces the computational time through a fixed-point iteration strategy and improves the TF resolution of strongly time-varying signals. However, for impulse-like signals known for their wide bandwidth and rapid IF changes, the above-mentioned SST methods along the frequency direction cannot provide accurate time-frequency characteristics. Therefore, researchers proposed the time reassignment synchrosqueezing transform (TSST) to handle impulse signals. This method changes the reassignment direction to rearrangement along the time direction, the reassignment operator changes from the instantaneous frequency operator (IF) to the group delay (GD), and it has the reconstruction performance. Unfortunately, like SST, it can only handle weakly frequency-varying signals. Therefore, the time multiple synchrosqueezing transform (TMSST) and the second-order time synchrosqueezing transform (TSST2) were proposed to effectively handle the TF variation law of strongly frequency-varying signals by compressing the reassignment operator through an iterative algorithm. Although the existing synchrosqueezing transform (SST) and its time reassignment version (TSST) can effectively identify the changes in instantaneous frequency (IF) and group delay (GD) through post-processing techniques, in the face of complex and variable non-stationary signals, these techniques have not yet been able to achieve accurate estimation of both IF and GD simultaneously. To address this challenge, the time-frequency multiple compression transform (TFMST) was proposed. This method introduces a chirp rate (CR) discrimination criterion based on the Gaussian window in the short-time Fourier transform, clearly differentiates non-stationary signals containing harmonic and impulse characteristics, improves the time-frequency energy concentration of non-stationary signals, and achieves a comprehensive description of the signal while retaining the accurate reconstruction of the original signal. Although the methods introduced above have greatly improved the performance of post-processing techniques, there are still problems of cross-term interference and weak noise resistance when dealing with strong frequency modulation and amplitude modulation signals.

[0006] Parametric Time-Frequency Analysis (PTFA) is an advanced signal processing technique that combines the time-frequency characteristics of a signal with a specific parametric model to more accurately describe and analyze non-stationary signals, obtaining a Time-Frequency Representation (TFR) with high energy concentration and no cross-term interference. Existing technologies have proposed the Chirplet Transform, which approximates the time-frequency energy curve with a slanted line at any inclination angle on the time-frequency plane, but it is only applicable to processing Linear Frequency Modulation (LFM) signals. To handle non-linear frequency modulation signals, the proposed Polynomial Chirp Transform (PCT) and Spline Chirp Transform improve the energy diffusion phenomenon in the local part of the instantaneous frequency curve of PTFA. The proposed Generalized Wavelet Transform (GWT) uses a sine kernel function and adjusts its time-frequency resolution according to the local characteristics of the signal, which can effectively capture high-frequency oscillations. However, there is still a gap between GWT and the actual TF distribution, it is vulnerable to noise interference, and there is also the problem of low TFR resolution.

[0007] In summary, the parametric time-frequency analysis and synchrosqueezing transform-based bearing fault diagnosis methods in the existing technologies are vulnerable to the influence of noise and cross-term interference during the fault diagnosis process. There is still a gap between GWT and the time-frequency multiple synchrosqueezing transform operation and the actual TF distribution, with low time-frequency energy concentration and weak noise resistance, which affects the TFR resolution. Summary of the Invention

[0008] Aiming at the problems of low time-frequency energy concentration, poor noise resistance, and cross-term interference, the present invention proposes a bearing fault diagnosis method and system based on parametric time-frequency analysis to improve the defects of low time-frequency energy concentration and weak noise resistance and the phenomenon of cross-term interference. This method fully considers the frequency rotation and translation characteristics of parametric time-frequency analysis and the time-frequency compression characteristics of TFMST. Using the Fourier transform kernel as the transform kernel of PTFA and adopting Fourier spectrum parameter estimation enhances the flexibility of time-frequency analysis and time-frequency energy concentration. The time-frequency ridge line search method is used to extract fault features, and TFMST is used as post-processing to perform compression operations on the reassignment operator along both the time and frequency directions, further enhancing the time-frequency energy concentration, maintaining good noise resistance, and having the ability to process quasi-harmonic and quasi-pulse signals.

[0009] To solve the above technical problems, the present invention discloses a bearing fault diagnosis method based on parametric time-frequency analysis, including the following steps: Obtain the bearing fault signal; According to the obtained bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determine the optimal coefficient of the parametric transformation kernel and use it as the kernel function parameter coefficient of GWT; according to the kernel function parameter coefficient of GWT, by repositioning the frequency components of the signal in the TF plane, solve the cross-term interference, and then perform GWT operation to suppress the time-frequency energy diffusion to obtain the initial time-frequency representation of the signal; According to the initial time-frequency representation of the signal, a time-frequency ridge line search algorithm is used to extract the fault features of the signal and perform time-frequency multiple compression transformation. The instantaneous frequency operator of the STFT is replaced with the operator of the GWT, and the time-frequency energy is compressed in both the time and frequency directions to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions; The time-frequency energy distributions of the single-component signals are superimposed to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

[0010] Preferably, determining the optimal coefficient of the parameter transformation kernel and using it as the kernel function parameter coefficient of the GWT specifically includes: The time-frequency distribution of the bearing fault signal is generated through the kernel characteristic coefficients of the Fourier series, and the bearing fault signal is decomposed into the superposition of different frequency components. The signal is decomposed into multiple frequency components, and each component corresponds to a specific frequency; The position with the most concentrated energy is extracted by analyzing the generated TFR, and this position is used as the estimated instantaneous frequency: ; where and represent the sine and cosine coefficients, represents the harmonic coefficient, represents the length of the Gaussian window, represents the current moment, represents the current frequency point; According to the Fourier transforms of the estimated IF and , the Fourier spectrum of the instantaneous frequency IF is obtained through calculation: ; ; ; where represents the fundamental frequency, is an integer, represents 's Fourier transform, and are the obtained Fourier coefficients, represents the imaginary unit, represents when k =0, the Fourier coefficient; The calculation process of the Fourier spectrum is continuously repeated until the termination condition is reached, and the optimal coefficient of the parameter transformation kernel is output; The termination condition is: '; wherein, represents after the th iteration of IF , ' is a set threshold value.

[0011] Preferably, obtaining the initial time-frequency representation of the signal includes the following steps: Given a signal , the STFT of the signal is obtained as: ; wherein, is a window function moving with time, represents the initial signal, represents the imaginary symbol, represents the angular frequency, the radian value of the frequency; when it is a Gaussian window; The reassignment operator for obtaining the signal centroid is: ; ; wherein, is the partial derivative with respect to the variable , and through the reassignment operation, the time-frequency distribution of the signal is repositioned at the power centroid and of the signal; The most core step of TFMST is to construct a CR estimator for distinguishing the impulse-like components and harmonic-like components in the signal; The GD of the signal in the frequency domain model and the IF in the time domain model of the signal have a negative reciprocal relationship. In the second-order model, IF the CR estimator is constructed as: ; ; wherein, represents the instantaneous phase of the signal , represents the second derivative of the instantaneous phase , which is used to describe the frequency modulation characteristics of the signal. Due to IF the slope relationship with GD, there is no need to calculate the slope of GD anymore; is the TF window slope. By comparing the local CR estimation value of the signal with the specified boundary value , the STFT coefficients are divided into two parts, and the reassignment operations of MSST and TMSST are respectively used for the two parts of the coefficients: ; Among them, represents the time variable, represents the frequency variable, represents the short-time Fourier transform in the frequency direction, represents the short-time Fourier transform in the time direction, represents the time-frequency reassignment result in the time and frequency directions; By introducing the strategy of fixed-point iteration, the signal is made to be closer to the actual GD and IF , where the and are the number of iterations N under the compression result; The two reassignment operators are respectively: ; ; Among them, N is a constant, representing the number of iterations of the reassignment operation; Each TF point in the TFR has the ability to reconstruct, that is: ; Among them, represents the time vector, represents the time-frequency representation of frequency multiple compression, represents the time-frequency representation of time multiple compression.

[0012] Preferably, the fault feature of the extracted signal is extracted by the forward and backward ridge extraction algorithms.

[0013] Preferably, obtaining the time-frequency energy distribution of the enhanced bearing fault signal includes the following steps: Performing time-frequency multiple compression transformation is to replace the instantaneous frequency operator of the STFT of the signal with the operator of the GWT, and set the boundary threshold according to the CR estimator γ , the time-frequency coefficients of the initial TFR are divided into two parts, frequency and time, and the expression of the GTFST is: ; Among them, represents the parametric time-frequency analysis representation in the frequency direction, represents the parametric time-frequency analysis representation in the time direction; The compression operators GD corresponding to the time and frequency directions and IF are respectively: ; ; Among them,Re is the mathematical symbol for the real part of a complex number, is the derivative with respect to ; and are the partial derivatives with respect to and respectively; By taking the partial derivatives of and and and performing multiple iterative operations on the instantaneous frequency IF and the group delay GD, the expression of GTFMST is obtained: ; where represents the instantaneous frequency operator, represents the group delay operator; GTFMST integrates the two parts of the unidirectional compression in the frequency and time directions respectively, and the reconstructed signal is: ; where represents the time-frequency compression result in the frequency direction, represents the time-frequency compression result in the time direction; Through the TFMST operation, the time-frequency energy distributions of each single-component signal are superimposed to obtain an enhanced time-frequency energy distribution.

[0014] Preferably, it also includes a quantitative evaluation of the enhanced time-frequency energy distribution, specifically including: Using the root mean square error RMSE to quantitatively evaluate the signal reconstruction ability, RMSE and its calculation formula is: ; where is the reconstructed signal, is the original time-domain signal.

[0015] Preferably, it also includes using the Rényi entropy as a quantitative evaluation index for energy aggregation, and the expression of the Rényi entropy is: ; where , , is 's probability density, q the entropy is the Shannon entropy, changing the q value to obtain the probability distribution characteristics, and ; where the smaller the Rényi entropy, the higher the time-frequency energy aggregation degree of the signal.

[0016] Preferably, it further includes a bearing fault diagnosis system based on parametric time-frequency analysis, including: A signal acquisition module for acquiring bearing fault signals; A parametric time-frequency analysis module for, according to the acquired bearing fault signals, determining the optimal coefficients of the parametric transformation kernel by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signals and using them as the kernel function parameter coefficients of the GWT; according to the kernel function parameter coefficients of the GWT, relocating the frequency components of the signals in the TF plane to solve the cross-term interference, then performing the GWT operation to suppress the time-frequency energy diffusion, and obtaining the initial time-frequency representation of the signals; A time-frequency energy compression module for, according to the initial time-frequency representation of the signals, extracting the fault features of the signals by using the time-frequency ridge line search algorithm and performing time-frequency multiple compression transformation, replacing the instantaneous frequency operator of the STFT with the operator of the GWT, and compressing the time-frequency energy in both the time and frequency directions respectively to obtain the time-frequency energy distribution of the single-component signals in both the time and frequency directions; A signal enhancement module for superimposing the time-frequency energy distributions of the single-component signals to obtain the time-frequency energy distribution of the enhanced bearing fault signals.

[0017] Preferably, it further includes a computer device, the computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the following steps: Acquire bearing fault signals; According to the acquired bearing fault signals, determining the optimal coefficients of the parametric transformation kernel by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signals and using them as the kernel function parameter coefficients of the GWT; according to the kernel function parameter coefficients of the GWT, relocating the frequency components of the signals in the TF plane to solve the cross-term interference, then performing the GWT operation to suppress the time-frequency energy diffusion, and obtaining the initial time-frequency representation of the signals; According to the initial time-frequency representation of the signals, extracting the fault features of the signals by using the time-frequency ridge line search algorithm and performing time-frequency multiple compression transformation, replacing the instantaneous frequency operator of the STFT with the operator of the GWT, and compressing the time-frequency energy in both the time and frequency directions respectively to obtain the time-frequency energy distribution of the single-component signals in both the time and frequency directions; Superimpose the time-frequency energy distributions of the single-component signals to obtain the time-frequency energy distribution of the enhanced bearing fault signals.

[0018] Preferably, it further includes a computer-readable storage medium, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor performs the following steps: Obtain the bearing fault signal; According to the obtained bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determine the optimal coefficient of the parameter transformation kernel and use it as the kernel function parameter coefficient of the GWT; according to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane to solve the cross-term interference, and then perform the GWT operation to suppress the time-frequency energy diffusion to obtain the initial time-frequency representation of the signal; According to the initial time-frequency representation of the signal, adopt the time-frequency ridge line search algorithm to extract the fault features of the signal and perform the time-frequency multiple compression transformation. Replace the instantaneous frequency operator of the STFT with the operator of the GWT, and compress the time-frequency energy in both the time and frequency directions to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions; Superimpose the time-frequency energy distributions of each single-component signal to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

[0019] Compared with the prior art, the present invention has the following beneficial effects: The bearing fault diagnosis method based on parametric time-frequency analysis proposed by the present invention, by determining the optimal coefficient of the parameter transformation kernel, parametric time-frequency analysis uses the frequency rotation factor and the frequency shift operator to reposition the frequency components of the signal in the TF plane, solves the problem of cross-term interference, and then performs the GWT to suppress the time-frequency energy diffusion. Parametric time-frequency analysis can effectively improve the energy concentration of non-stationary signals and solve the problem of GWT suppressing time-frequency energy diffusion of traditional signal analysis methods. After obtaining the initial time-frequency representation of the signal, adopt the time-frequency ridge line search algorithm to extract the fault features of the signal, perform the time-frequency multiple compression transformation on the extracted signal fault features, compress the time-frequency energy in both the time and frequency directions, and obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions, which can process both harmonic-like signals and impulse-like signals simultaneously, improve the time-frequency energy concentration and the TFR resolution. Finally, obtain the time-frequency result of the fault signal without cross-term interference and with high time-frequency resolution. Description of the Drawings

[0020] Figure 1 It is the flowchart of the GTFMST method proposed by the present invention; Figure 2 It is the time domain of the simulated signal of the present invention; Figure 3 It is the frequency domain of the simulated signal of the present invention; Figure 4 It is the multi-component ridge line extraction of the simulated signal of the present invention; Figure 5 It is the time-frequency representation obtained by the GTFMST method proposed by the present invention through the simulated signal experiment; Figure 6 Time-domain comparison of the reconstructed signal and the original signal provided for the analysis of the embodiments of the present invention; Figure 7 Error between the reconstructed signal and the original signal provided for the analysis of the embodiments of the present invention; Figure 8 Time-frequency representation of STFT provided for the analysis of the embodiments of the present invention; Figure 9 Time-frequency representation of SST provided for the analysis of the embodiments of the present invention; Figure 10 Time-frequency representation of IMSST provided for the analysis of the embodiments of the present invention; Figure 11 Time-frequency representation of GTMSST provided for the analysis of the embodiments of the present invention; Figure 12 Time-frequency representation of TFMST provided for the analysis of the embodiments of the present invention; Figure 13 Time-frequency representation of GTFMST provided for the analysis of the embodiments of the present invention; Figure 14 Noise immunity tests of six methods, namely STFT, SST, IMSST, GTMSST, TFMST, and GTFMST, under different signal-to-noise ratios provided for the analysis of the embodiments of the present invention; Figure 15 TFR comparison of STFT for ball fault provided in Embodiment 1 of the present invention; Figure 16 TFR comparison of SST for ball fault provided in Embodiment 1 of the present invention; Figure 17 TFR comparison of IMSST for ball fault provided in Embodiment 1 of the present invention; Figure 18 TFR comparison of GTMSST for ball fault provided in Embodiment 1 of the present invention; Figure 19 TFR comparison of TFMST for ball fault provided in Embodiment 1 of the present invention; Figure 20 TFR comparison of GTFMST for ball fault provided in Embodiment 1 of the present invention; Figure 21 TFR comparison of STFT for inner race fault provided in Embodiment 1 of the present invention; Figure 22 TFR comparison of SST for inner race fault provided in Embodiment 1 of the present invention; Figure 23 TFR comparison of IMSST for inner race fault provided in Embodiment 1 of the present invention; Figure 24TFR comparison of the GTMSST with inner race fault provided in Embodiment 1 of the present invention; Figure 25 TFR comparison of the TFMST with inner race fault provided in Embodiment 1 of the present invention; Figure 26 TFR comparison of the GTFMST with inner race fault provided in Embodiment 1 of the present invention; Figure 27 TFR comparison of the STFT with inner race fault between shafts provided in Embodiment 2 of the present invention; Figure 28 TFR comparison of the SST with inner race fault between shafts provided in Embodiment 2 of the present invention; Figure 29 TFR comparison of the IMSST with inner race fault between shafts provided in Embodiment 2 of the present invention; Figure 30 TFR comparison of the GTMSST with inner race fault between shafts provided in Embodiment 2 of the present invention; Figure 31 TFR comparison of the TFMST with inner race fault between shafts provided in Embodiment 2 of the present invention; Figure 32 TFR comparison of the GTFMST with inner race fault between shafts provided in Embodiment 2 of the present invention. Detailed implementation manners

[0021] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. It should be understood that the terms described in the present invention are only used to describe specific embodiments and are not intended to limit the present invention. Figures 1 - 32

[0022] The optimal General Warblet Transform (GWT) can handle any highly oscillatory signal through the displacement characteristics of the frequency shift operator and the rotation operator, and avoid the interference of cross terms. The Time-Frequency multisqueezing Transform (TFMST) can compress the time-frequency energy along the time and frequency directions and can handle both quasi-harmonic and quasi-impulse components simultaneously. The present invention makes full use of the advantages of both and proposes a parametric time-frequency multisqueezing transform method (Generalized Time-Frequency multisqueezing Transform, GTFMST).

[0023] ​The present invention proposes a bearing fault diagnosis method based on parametric time-frequency analysis. First, the optimal parameters are found through the Fourier spectrum of the instantaneous frequency IF of the signal to be obtained, and the optimal coefficients of the parametric transformation kernel are determined. PTFA uses the frequency rotation factor and frequency shift operator to relocate the frequency components of the signal in the TF plane to solve the cross-term interference, and then performs GWT to suppress the time-frequency energy diffusion. After the initial time-frequency representation of the signal obtained preliminarily, the fault features of the signal are extracted from the result of GWT using the forward and backward ridge extraction algorithms. Finally, the TFMST operation is performed on the extracted signal to obtain an enhanced time-frequency energy representation. The specific steps of GTFMST are as Figure 1 shown, including the following steps: S1: Obtain the bearing fault signal; S2: According to the obtained bearing fault signal, determine the optimal coefficients of the parametric transformation kernel by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, and use them as the kernel function parameter coefficients of GWT; according to the kernel function parameter coefficients of GWT, relocate the frequency components of the signal in the TF plane to solve the cross-term interference, and then perform the GWT operation to suppress the time-frequency energy diffusion to obtain the initial time-frequency representation of the signal; S3: According to the initial time-frequency representation of the signal, use the time-frequency ridge search algorithm to extract the fault features of the signal and perform the time-frequency multiple compression transformation. Replace the instantaneous frequency operator of STFT with the operator of GWT, and compress the time-frequency energy in both the time and frequency directions respectively to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions; S4: Superimpose the time-frequency energy distributions of each single-component signal to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

[0024] Specifically, determining the optimal coefficients of the parametric transformation kernel and using them as the kernel function parameter coefficients of GWT specifically includes: In signal analysis, the instantaneous frequency of non-periodic or high-frequency oscillatory periodic signals IF is difficult to estimate. The generalized Warblet transform using Fourier series to replace the original parametric transformation kernel can effectively handle such signals through the rotation operator and frequency shift operator.

[0025] The most important step in parametric time-frequency analysis is to construct the parametric transformation kernel. The general expression of GWT is: ; where is the window sliding function of the short-time Fourier transform STFT , usually a Gaussian window, defined as a symmetric normalized real window; The calculation formula of ; Among them, is the order of the Fourier series, and are the sine coefficient and cosine coefficient respectively, is the frequency of the corresponding harmonic component.

[0026] Generate the time-frequency distribution of the bearing fault signal through the kernel characteristic coefficients of the Fourier series, decompose the bearing fault signal into the superposition of different frequency components, and reveal the frequency characteristics of the signal. In this process, the signal is decomposed into multiple frequency components, and each component corresponds to a specific frequency.

[0027] Extract the position with the most concentrated energy from the generated TFR. This position usually corresponds to the main frequency component of the signal, and use this position as the estimated instantaneous frequency: ; Among them, and represent the sine and cosine coefficients, represents the harmonic coefficient, represents the length of the Gaussian window; represents the current moment, represents the current frequency point.

[0028] According to the Fourier transform of the estimated IF and , calculate the Fourier spectrum of the instantaneous frequency IF : ; ; ; Among them, represents the fundamental frequency, is an integer, represents 's Fourier transform, and are the obtained Fourier coefficients, represents the imaginary unit, represents when k = 0, the Fourier coefficient.

[0029] Repeat the calculation process of the Fourier spectrum continuously until the termination condition is reached, and output the optimal coefficients of the determined parameter transformation kernel.

[0030] Termination condition is: '; Among them, represents after the th iteration of IF , is a set threshold value.

[0031] Improving the time-frequency energy concentration of non-stationary signals is the key to fault diagnosis. Group Delay (GD) is an important concept in the field of signal processing, which describes the delay time of different frequency components of a signal passing through a system. The instantaneous frequency IF is the frequency estimation of a signal at a specific time point, which describes the rate of change of the signal phase with time; both GD and IF are key characteristic parameters in time-frequency analysis. TFMST compresses the operations on two reassignment operators of the instantaneous frequency IF and the group delay GD, simultaneously processes the quasi-harmonic and quasi-impulse components, and improves the time-frequency energy concentration and TF resolution.

[0032] As is well known, the impulse component and the quasi-harmonic component are both important characteristics existing in non-stationary signals. TFMST solves the defect that the synchrosqueezing transform (SST) and the time-reassigned synchrosqueezing transform (TSST) cannot simultaneously process the quasi-impulse and quasi-harmonic components, and at the same time maintains the ability to restore the original signal.

[0033] Given a signal , the STFT of the signal is: ; Among them, is the window function moving with time, represents the original signal, represents the imaginary symbol, represents the angular frequency, which is the radian value of the frequency; when it is a Gaussian window.

[0034] The reassignment operator for obtaining the signal centroid is: ; ; Among them, is the partial derivative of the variable . Through the reassignment operation, the time-frequency distribution of the signal can be repositioned at the power centroid and of the signal; The most core step of the time-frequency multiple synchrosqueezing transform (TFMST) is to construct a CR estimator to distinguish the quasi-impulse component and the quasi-harmonic component in the signal, the GD of the signal in the frequency domain model and theIF show a negative reciprocal relationship. Under the second-order model, IF the CR estimator of ; ; where represents the instantaneous phase of the signal , denotes the second derivative of the instantaneous phase used to describe the frequency modulation characteristics of the signal. Since IF the slope relationship between and GD, there is no need to calculate the slope of GD anymore; is the TF window slope. By comparing the local CR estimation value of the signal with the specified boundary value ; where represents the time variable, represents the frequency variable, represents the short-time Fourier transform in the frequency direction, represents the short-time Fourier transform in the time direction, represents the time-frequency reassignment result in the time and frequency directions.

[0035] By introducing the strategy of fixed-point iteration, the signal can be made closer to the actual GD and IF , where and are the compression results under the iteration times N respectively.

[0036] The two reassignment operators are respectively: ; ; where N is a constant representing the iteration times of the reassignment operation; each TF point in the TFR has the reconstruction ability, that is: ; where v represents the time vector, represents the time-frequency representation of frequency multiple compression, represents the time-frequency representation of time multiple compression.

[0037] For a single-component signal, once the required parameterized transformation kernel is determined, the TFMST operation can be performed. By replacing the instantaneous frequency operator of the STFT of the original signal with the operator of the GWT, the expression of the GTFST is: ; Among them, represents the parametric time-frequency analysis representation in the frequency direction, represents the parametric time-frequency analysis representation in the time direction.

[0038] Among them, IF and the expressions of GD are as follows: ; ; Among them, Re is the mathematical symbol for the real part of a complex number, is the derivative of with respect to and are respectively the partial derivatives of with respect to and with respect to

[0039] By obtaining the partial derivatives of and and performing multiple iterative operations on the instantaneous frequency IF and the group delay GD, the expression of GTFMST is obtained: ; Among them, represents the instantaneous frequency operator, represents the group delay operator.

[0040] GTFMST still has the performance of reconstructing the signal. By integrating the two parts of the unidirectional compression in the frequency and time directions respectively, the reconstructed original signal is: ; Among them, represents the time-frequency compression result in the frequency direction, represents the time-frequency compression result in the time direction.

[0041] Through the TFMST operation, the time-frequency energy distributions of each single-component signal are superimposed to obtain an enhanced time-frequency energy distribution.

[0042] The present invention also proposes a bearing fault diagnosis system based on parametric time-frequency analysis, including: A signal acquisition module for acquiring bearing fault signals; The parametric time-frequency analysis module is used to determine the optimal coefficient of the parametric transformation kernel as the kernel function parameter coefficient of the GWT by calculating the Fourier spectrum of the instantaneous frequency IF of the acquired bearing fault signal; according to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane to solve the cross-term interference, and then performing the GWT operation to suppress the time-frequency energy diffusion, the initial time-frequency representation of the signal is obtained; The time-frequency energy compression module is used to extract the fault features of the signal and perform time-frequency multiple compression transformation by using the time-frequency ridge line search algorithm according to the initial time-frequency representation of the signal, replace the instantaneous frequency operator of the STFT with the operator of the GWT, compress the time-frequency energy in both the time and frequency directions respectively, and obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions; The signal enhancement module is used to superimpose the time-frequency energy distributions of each single-component signal to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

[0043] The method proposed by the present invention can compress the time-frequency energy in both the time and frequency directions, can process both quasi-harmonic signals and quasi-impulse signals simultaneously, improves the time-frequency energy concentration and TF resolution, and avoids the influence of cross-term interference.

[0044] Numerical simulation To prove the effectiveness of the proposed GTFMST method in processing non-stationary signals, the present invention selects a group of two-component polynomial frequency-modulated simulation signals as experimental signals. The sampling points of the signal are set to 1000, and the sampling frequency is set to 1000 Hz. The description of the signal is as follows: ; Component simulation signal is a non-stationary signal, and the instantaneous frequency varies with time The two components are composed of the polynomial fast frequency-modulated signal simulation signal and . The time domain and frequency domain diagrams of Figure 2 and Figure 3 are shown as follows. Among them, Figure 2 is the time domain of the analog signal, Figure 3 is the frequency domain of the analog signal.

[0045] Due to 's non-balance, GTFMST is used to process the multi-component signal.

[0046] First, the optimal parameters of the parametric transformation kernel are estimated by the Fourier spectral kernel parameter estimation algorithm, and the signal is repositioned for GWT. After obtaining the preliminary TFR, the time-frequency characteristics are enhanced. The time-frequency ridges of the signal are extracted using the ridge detection algorithm, and the extraction results of the ridges are as shown in Figure 4 . The processed signal is subjected to the TFMST operation to superimpose the time-frequency energy distributions of each single-component signal, obtaining the enhanced time-frequency energy distribution. The final time-frequency representation obtained by the GTFMST method is as shown in Figure 5 .

[0047] It can be seen from Figure 4 that the time-frequency representation extracted by the GTFMST method has a high energy concentration degree, the time-frequency energies of each component do not interfere with each other, the frequency components of the polynomial signal are close, and the amplitude modulation and frequency modulation characteristics are good.

[0048] The signal reconstruction ability is an important characteristic of time-frequency analysis methods. To further verify the signal reconstruction ability of GTFMST, the root mean square error RMSE is used for quantitative evaluation when evaluating the reconstruction effect. RMSE The calculation formula of is as follows: where is the reconstructed signal, and is the original time-domain signal.

[0049] The time-domain comparison between the reconstructed signal and the original signal (true signal) is as shown in Figure 6 , and the reconstruction error between the reconstructed signal and the original signal is as shown in Figure 7 . It can be seen that the overall reconstruction performance of GTFMST is good, and it can remove the cross-term interference in the multi-component signal to reconstruct the signal. Through analysis Figure 7 it can be known that the reconstruction error of the signal is small within 0.034 s to 0.957 s, and the error is only large at the two endpoints, but it does not exceed the limit of 0.05. The root mean square error of the reconstructed signal is 2.1036e-07.

[0050] The experimental results show that the GTFMST method proposed by the present invention has good reconstruction performance.

[0051] To further prove the effectiveness of GTFMST, the present invention selects five methods, namely STFT, SST, IMSST, GTMSST, and TFMST, to compare with GTFMST. The five methods all select the same parameter settings and are all experimented under the condition of no noise interference. The TFR of the simulated signal is as shown in Figures 8 - 13 , where Figure 8 is the time-frequency representation of STFT, Figure 9 is the time-frequency representation of SST, Figure 10is the time-frequency representation of IMSST, Figure 11 is the time-frequency representation of GTMSST, Figure 12 is the time-frequency representation of TFMST, Figure 13 is the time-frequency representation of GTFMST.

[0052] From Figures 8 - 13 's TFR, it can be seen that Figure 8 the TFR obtained by the STFT of has the lowest aggregation degree and is interfered by cross terms. The SST obtains the TFR through the synchrosqueezing operation as shown in Figure 9 . The time-frequency energy aggregation degree is better than that of the STFT, but the anti-noise ability is very poor and the time-frequency ridge line is almost submerged by noise. It is still interfered by cross terms at the endpoints. From Figure 10 and Figure 11 , it can be seen that both IMSST and TFMST obtain clear time-frequency representations. The iterative algorithm enhances the anti-noise performance of the method, and the energy aggregation degree of the signal is very high. However, the time-frequency energy near 0-1.15 s and 0.95-1 s is lower than the true amplitude. This is because the time-frequency ridge line in this part is more similar to the impulse part, and the frequency-direction compression cannot fully represent the amplitude modulation characteristics of Sig(t). Figure 12 GTMSST uses the time-frequency displacement characteristic of the GWT. Although it avoids the problem of cross-term interference and the obtained TFR representation has a very high energy aggregation degree, there is an energy diffusion phenomenon at the time-frequency ridge peaks of 0.28 s and 0.72 s, and it is not suitable for processing quasi-harmonic components. Figure 13 This is the GTFMST method proposed by the present invention. It uses the rotation and frequency shift operators of the GWT to avoid the problem of cross-term interference and accurately locate the instantaneous frequency. And TFMST further compresses and iterates the reassignment operator along both the time and frequency directions. The obtained time-frequency energy aggregation degree is the best, and the obtained time-frequency spectrum is more accurate. Therefore, GTFMST can effectively extract the time-frequency characteristics of unstable signals.

[0053] The calculation efficiency and calculation error of the analog signal experiment are shown in Tables 1 and 2.

[0054] Table 1 Calculation efficiency (s) of analog signal experiment

[0055] Table 2 Calculation error (%) of other methods compared with GTFMST

[0056] As can be seen from Table 1, the shortest calculation time of STFT is 0.1380 s. SST requires synchronous compression operation, and the time is 0.1460 s. Both GTMSST and IMSST need to calculate and iterate synchronous compression operations, and the running times are 0.1820 s and 0.2080 s respectively. Since TFMST needs to compress in both time and frequency directions, the calculation time is slightly longer at 0.3690 s. GTFMST needs to estimate the transform kernel coefficients, and the running time is 0.5750 s. Although the running time of GTFMST is the longest, it is still less than 0.6 s. Therefore GTFMST an accurate time-frequency feature curve can be obtained within a short time.

[0057] Table 2 shows the calculation errors between various methods and GTFMST. It is found through comparison that there are certain calculation errors in several methods, but the calculation error of the GTFMST method proposed by the present invention is the smallest.

[0058] In order to compare the energy concentration degree and sharpness, the present invention uses Rényi entropy as a quantitative evaluation index for energy concentration. The expression of Rényi entropy is: ; where , , is the probability density of q the entropy is Shannon entropy, changing q the value to obtain the probability distribution characteristics, and ; among them, the smaller the Rényi entropy, the higher the time-frequency energy concentration degree of the signal.

[0059] The Rényi entropies of several methods selected in the simulation signal experiment of the present invention are shown in Table 3.

[0060] Table 3 Rényi entropy values

[0061] As can be seen from Table 3, in the case of no noise interference, the Rényi entropy values of STFT, SST, IMSST, TFMST and GTMSST are 16.1838, 12.9710, 11.3354, 11.1700 and 10.9804 respectively. Comparing them with the Rényi entropy value of GTFMST, it is obtained that the Rényi entropy value of GTFMST is the smallest, which is 10.7384.

[0062] The experimental results show that in the case of no noise interference, the time-frequency energy obtained by GTFMST proposed by the present invention is sharper and the energy concentration degree is the best.

[0063] To prove that the GTFMST method proposed in the present invention can still process non-stationary signals in the presence of noise interference, Gaussian white noise with a signal-to-noise ratio of 0 to 30 dB is added to the signal. Six methods are used to process the noise signal respectively, and the corresponding Rényi entropy under different signal-to-noise ratios is obtained, as Figure 14 shown.

[0064] It can be seen from Figure 14 that the Rényi entropy of the six methods shows a decreasing trend with the increase of the signal-to-noise ratio, and the energy concentration degree also gradually increases. Among these methods, STFT and SST have poor robustness. Due to the compression iteration strategies of IMSST, TFMSF, and GTMSST, the noise resistance is improved. In contrast, GTFMST has the best robustness and significantly improved noise resistance.

[0065] The experimental results show that under strong noise interference, GTFMST can also obtain a time-frequency energy representation with high concentration.

[0066] Example analysis Example 1

[0067] To evaluate the performance of GTFMST, the present invention selects the vibration data of the inner race fault (BPFI) and ball fault (BSF) on the QPZZ-II bearing test rig for experimental analysis.

[0068] The bearing of QPZZ-II is driven by a motor, and the speed regulation is adjusted by an AC frequency conversion controller. The rotational speed of the test bench is 1000 r / min, and a frequency of 12 kHz is adopted under the no-load condition.

[0069] To verify the effectiveness of the GTFMST method proposed in the present invention, STFT, SST, IMSST, TFMST, and GTMSST are selected for comparative analysis. The same parameters are set for several methods, and the experiments are all carried out under the condition of 1000 r / min. The TFRs of the rolling element fault (ball fault) and inner race fault are obtained as Figures 15 - 20 and Figures 21 - 26 shown, and the Rényi entropy is marked on each time-frequency diagram.

[0070] Figure 15 is the TFR of the ball fault STFT, Figure 16 is the TFR of the ball fault SST, Figure 17 is the TFR of the ball fault IMSST, Figure 18 is the TFR of the ball fault TFMST, Figure 19 is the TFR of the ball fault GTMSST, Figure 20 is the TFR of the ball fault GTFMST.

[0071] Figure 21is the TFR of the inner race fault STFT, Figure 22 is the TFR of the inner race fault SST, Figure 23 is the TFR of the inner race fault IMSST, Figure 24 is the TFR of the inner race fault TFMST, Figure 25 is the TFR of the inner race fault GTMSST, Figure 26 is the TFR of the inner race fault GTFMST.

[0072] From Figures 15 - 26 it can be seen that for the rolling element fault signal and the inner race fault signal, due to the window function being affected by the Heisenberg uncertainty principle, the STFT has the most blurred time-frequency energy distribution and the largest Rényi entropy value. Compared with the STFT, the SST enhances the energy concentration, but there are still noise components in the time-frequency energy. Through the iterative operation of the instantaneous frequency operator, the IMSST has highly concentrated time-frequency energy. However, since the compression direction is the frequency method, it cannot accurately capture the fault occurrence moment. In addition, observing the enlarged view on the right, there is local low-energy time-frequency interference at the energy center of the frequency band. The TFMST and GTMSST suppress the energy diffusion, have smaller Rényi entropy values, and the time-frequency energy shows sharp vertical ridges, which can capture the fault occurrence moment. However, through the enlarged view on the right, it can be observed that there is a problem of local time-frequency energy interference at the energy center of the vertical ridges for both methods. Finally, by comparing at the red arrow in the figure, the GTFMST shows the most concentrated time-frequency energy. Looking from the time direction, there is no local low-energy time-frequency interference at the energy center of the ridge line, suppressing the local time-frequency interference, having the thinnest vertical ridge while accurately positioning the instantaneous frequency moment, and also showing a frequency band with high-energy concentration in the frequency direction. The comparison shows that the RE value of the GTFMST is the smallest among several methods.

[0073] The comparison shows that the Rényi entropy value of the GTFMST method proposed by the present invention is the smallest among several methods.

[0074] In order to verify that the GTFMST can still effectively extract fault information under variable working conditions, the rotational speeds of the inner race fault and the rolling element fault are changed, and several methods are set with the same parameters for experiments. The rotational speeds are set to 1250 r / min and 1500 r / min respectively. The experimental results are shown in Table 4.

[0075] Table 4 Rényi entropy values (bits)

[0076] In order to analyze the differences in the calculation errors and calculation efficiencies of various methods, they are corresponding as shown in Table 5 and Table 6.

[0077] Table 5 Calculation errors of other methods compared with the GTFMST (%)

[0078] Table 6 Computational efficiency (s)

[0079] By comparing the Rényi entropy values under different rotational speed experiments, it can be seen from Table 4 that the Rényi entropy value of the GTFMST method proposed in the present invention is the smallest under different working conditions, indicating that GTFMST is the most effective among all methods and has the best time-frequency energy aggregation and anti-noise performance in practical applications.

[0080] It can be seen from Table 5 that compared with GTFMST, there are calculation errors for several methods under different working conditions, and the calculation error of the GTFMST method is the smallest. Due to the influence of the uncertainty criterion and noise interference, the calculation errors of STFT and SST are the largest, exceeding 80%.

[0081] It can be seen from Table 6 that the calculation time of all methods is less than 2 s, meeting the requirements of actual engineering.

[0082] Example 2 The aircraft rolling bearing is a crucial component. The HIT test bench is established based on a real aero-engine, and the test environment and conditions are closer to the complex operating environment of the aero-engine. The rotor speed of the dataset includes the high-pressure rotational speed (HP) and the low-pressure rotational speed (LP), and the sampling frequency is 25 kHz under the no-load condition.

[0083] To verify the effectiveness of GTFMST, STFT, SST, IMSST, TFMST, and GTMSST are selected for comparison. These methods are set with the same parameters as GTFMST, and experiments are carried out under the working conditions where the low-pressure rotational speed LP and the high-pressure rotational speed HP are 1000 r / min and 1200 r / min respectively, and the TFR of the inner race fault between shafts is obtained as Figures 27 - 32 shown, and the Rényi entropy is marked on each time-frequency diagram.

[0084] Figure 27 is the TFR of STFT for the inner race fault between shafts, Figure 28 is the TFR of SST for the inner race fault between shafts, Figure 29 is the TFR of IMSST for the inner race fault between shafts, Figure 30 is the TFR of TFMST for the inner race fault between shafts, Figure 31 is the TFR of GTMSST for the inner race fault between shafts, Figure 32 is the TFR of GTFMST for the inner race fault between shafts.

[0085] The time-frequency characteristics of the vibration signal are pointed to by the arrow, Figure 27 the time-frequency energy diffusion of the STFT of is the largest, and the Rényi entropy value is also the largest. Figure 28The energy concentration degree of the SST has been improved, but the time-frequency resolution is still blurred. Figure 29 The IMSST has a high time-frequency energy concentration degree. However, by only compressing the reassignment operator in the frequency direction, the instantaneous frequency cannot be accurately located. Figure 30 Although the time-frequency energy of the GTMSST is sharp, there is a phenomenon of local time-frequency interference. Figure 31 The Rényi entropy value of the TFMST has been improved, but affected by noise interference, the time-frequency vertical ridges are blurred. Only Figure 32 The GTFMST can suppress the interference of local time-frequency, and has the highest time-frequency energy concentration degree and the smallest Rényi entropy value, and can realize the fault characteristics under complex working conditions.

[0086] During the actual operation of an aero-engine, the intermediate shaft speed often encounters variable speed conditions. To verify that the GTFMST is still effective under variable working conditions, two examples of high and low pressure speeds are selected, and the experimental results are shown in Table 7, and the errors and calculation efficiencies are shown in Tables 8 and 9.

[0087] Table 7 Comparison of Rényi entropy of various methods under variable working conditions

[0088] Table 8 Calculation errors (%) of various methods compared with GTFMST

[0089] Table 9 Calculation time (s) of various methods

[0090] Through experimental comparison, it can be seen from Table 7 that as the speed increases, the Rényi entropy values of all methods have increased. Among several methods, the Rényi entropy value of the GTFMST is the smallest, indicating that the GTFMST is still effective under variable working conditions.

[0091] It can be seen from Table 8 that the error of the STFT is the largest, and the Rényi entropy value is also the largest. The errors of the STFT, SST, IMSST, GTMSST, and TFMST have all decreased, but there are calculation errors compared with the GTFMS.

[0092] It can be seen from Table 9 that the calculation time of all methods is less than 2 s, meeting the actual engineering requirements of the aero-engine operating environment.

[0093] The analysis results of the embodiments show that, compared with the STFT, SST, IMSST, GTMSST, and TFMST time-frequency analysis methods, there are certain calculation errors between these methods and the GTFMST method proposed in the present invention. The Rényi entropy of GTFMST is the smallest among these methods, and the calculation efficiency of GTFMST in the experiments of simulated signals and actual bearing signals is also less than 2 s, which meets the engineering practice. Therefore, GTFMST can better capture the time-frequency characteristics of signals, retain sharper time-frequency energy, and have more accurate time-frequency resolution. While maintaining the signal reconstruction characteristics, GTFMST has a high time-frequency energy concentration degree and has good effects under different noise levels and working conditions.

[0094] In summary, the parametric time-frequency multiple compression transform method GTFMST proposed in the present invention fully utilizes the advantages of GWT and TFMST, extracts the time-frequency characteristics of signals, obtains a more accurate time-frequency spectrum, and diagnoses faults for non-stationary signals by obtaining time-frequency energy with a high energy concentration degree. Using the Rényi entropy, calculation error, and calculation efficiency as evaluation indicators, the effectiveness of GTFMST is verified with numerical simulation signals and actual bearing fault signals.

[0095] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution of the present invention and its inventive concept, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

[0096] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In case of conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A bearing fault diagnosis method based on parametric time-frequency analysis, characterized in that, It includes the following steps: Obtain the bearing fault signal; According to the obtained bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determine the optimal coefficient of the parameter transformation kernel and use it as the kernel function parameter coefficient of the GWT; according to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane, solve the cross-term interference, and then perform the GWT operation to suppress the time-frequency energy diffusion to obtain the initial time-frequency representation of the signal; According to the initial time-frequency representation of the signal, adopt the time-frequency ridge line search algorithm to extract the fault features of the signal and perform the time-frequency multiple compression transformation. Replace the instantaneous frequency operator of the STFT with the operator of the GWT, and compress the time-frequency energy in both the time and frequency directions respectively to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions; Superimpose the time-frequency energy distributions of each single-component signal to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

2. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 1, characterized in that The determination of the optimal coefficient of the parameter transformation kernel and using it as the kernel function parameter coefficient of the GWT specifically includes: Generate the time-frequency distribution of the bearing fault signal through the kernel characteristic coefficient of the Fourier series, decompose the bearing fault signal into the superposition of different frequency components, the signal is decomposed into multiple frequency components, and each component corresponds to a specific frequency; Extract the position with the most concentrated energy from the generated TFR and use this position as the estimated instantaneous frequency: ； Among them, and represent the sine and cosine coefficients, represent the harmonic coefficients, represents the length of the Gaussian window, represents the current moment, represents the current frequency point; According to the estimated IF and Fourier transform, the instantaneous frequency is obtained by calculation IF Fourier spectrum of: ； ； ； Among them, represents the fundamental frequency, is an integer, represents the Fourier transform of, and are the obtained Fourier coefficients, represents the imaginary unit, represents when k = 0, the Fourier coefficient; The calculation process of the Fourier spectrum is continuously repeated until the termination condition is reached , and the optimal coefficients of the determined parameter transformation kernel are output; Termination condition is as follows: '； Among them, represents after the th iteration of IF , ' is the set threshold.

3. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 2, wherein The obtaining of the initial time-frequency representation of the signal includes the following steps: Given a signal , the STFT of the signal is obtained as follows: ； Among them, is a window function that moves with time, represents the initial signal, represents the imaginary symbol, represents the angular frequency, which is the radian value of the frequency; when it is a Gaussian window; Obtain the reassignment operator of the signal centroid as: ； ； Among them, is the partial derivative with respect to the variable . Through the operation of reallocation, the time-frequency distribution of the signal is repositioned at the energy centroid and of the signal; The most core step of TFMST is to construct a CR estimator for distinguishing the impulse-like components and harmonic-like components in the signal; The GD of the signal in the frequency - domain model and the IF are in a negative reciprocal relationship. In the second - order model, IF the CR estimator is constructed as: ； ； Among them, represents the instantaneous phase of the signal , and represents the second derivative of the instantaneous phase , which is used to describe the frequency modulation characteristics of the signal. Since IF there is a slope relationship with GD, there is no need to calculate the slope of GD anymore; is the TF window slope. By comparing the local CR estimation value of the signal with the specified boundary value , the coefficients of the STFT are divided into two parts, and the MSST and TMSST are respectively used for the reassignment operation on the two parts of the coefficients: ； Among them, represents a time variable, represents a frequency variable, represents the short-time Fourier transform in the frequency direction, represents the short-time Fourier transform in the time direction, represents the time-frequency reassignment result in the time and frequency directions; By introducing the strategy of fixed-point iteration, the signal is made to be closer to the actual GD and IF , where the and are the number of iterations N The compression result under; The two reassignment operators are respectively: ； ； Among them, N is a constant representing the number of iterations of the reassignment operation; each TF point in the TFR has the ability to be reconstructed, that is: ； Among them, v represents a time vector, represents a time-frequency representation of frequency multiplex compression, represents a time-frequency representation of time multiplex compression.

4. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 1, wherein The extraction of the fault features of the signal is performed by the forward and backward ridge line extraction algorithms.

5. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 4, characterized in that The obtaining of the time-frequency energy distribution of the enhanced bearing fault signal includes the following steps: Performing time-frequency multiple compression transformation is to replace the instantaneous frequency operator of the STFT of the signal with the operator of the GWT, and set the boundary threshold according to the CR estimator. γ , the time-frequency coefficients of the initial TFR are divided into two parts: frequency and time. The expression of the GTFST is as follows: ； Among them, represents the time-frequency analysis representation of the parameter in the frequency direction, represents the time-frequency analysis representation of the parameter in the time direction; The compression operators GD corresponding to the two directions of time and frequency and IF are respectively as follows: ； ； Among them, Re is the mathematical symbol for the real part of a complex number, is the derivative of ; and are the partial derivatives of with respect to and respectively; By obtaining the and partial derivatives of, after performing multiple iterative operations on the instantaneous frequency IF and the group delay GD, the expression of GTFMST is obtained: ； Among them, represents the instantaneous frequency operator, represents the group delay operator; GTFMST integrates the two parts of the unidirectional compression in the frequency and time directions respectively to obtain the reconstructed signal as: ； Among them, represents the time-frequency compression result in the frequency direction, represents the time-frequency compression result in the time direction; Through the TFMST operation, superimpose the time-frequency energy distributions of each single-component signal to obtain the enhanced time-frequency energy distribution.

6. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 5, characterized in that It also includes the quantitative evaluation of the enhanced time-frequency energy distribution, specifically including: The root mean square error is adopted RMSE to quantitatively evaluate the signal reconstruction ability, RMSE and its calculation formula is as follows: ； Among them, is the reconstructed signal, is the original time-domain signal.

7. The bearing fault diagnosis method based on parametric time-frequency analysis according to claim 6, wherein It also includes using the Rényi entropy as the quantitative evaluation index of energy aggregation, and the expression of the Rényi entropy is: ； Among them, , , is the probability density of, q the entropy is the Shannon entropy, changing the q value to obtain the probability distribution characteristics, and ; among them, the smaller the Rényi entropy, the higher the time-frequency energy concentration degree of the signal.

8. A bearing fault diagnosis system based on parametric time-frequency analysis, characterized in that It includes: A signal acquisition module for acquiring the bearing fault signal; A parametric time-frequency analysis module for, according to the acquired bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determining the optimal coefficient of the parameter transformation kernel and using it as the kernel function parameter coefficient of the GWT; according to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane, solving the cross-term interference, and then performing the GWT operation to suppress the time-frequency energy diffusion to obtain the initial time-frequency representation of the signal; A time-frequency energy compression module, which is used to extract the fault features of a signal according to the initial time-frequency representation of the signal and perform time-frequency multiple compression transformation. It replaces the instantaneous frequency operator of the STFT with the operator of the GWT, and compresses the time-frequency energy in both the time and frequency directions to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions. A signal enhancement module, which is used to superimpose the time-frequency energy distributions of the single-component signals to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

9. A computer device, characterized in that, The computer device includes a memory and a processor. When the computer program stored in the memory is executed by the processor, the processor performs the following steps: Obtain a bearing fault signal. According to the obtained bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determine the optimal coefficient of the parameter transformation kernel and use it as the kernel function parameter coefficient of the GWT. According to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane to solve the cross-term interference, and then performing the GWT operation to suppress the time-frequency energy diffusion, obtain the initial time-frequency representation of the signal. According to the initial time-frequency representation of the signal, adopt the time-frequency ridge line search algorithm to extract the fault features of the signal and perform time-frequency multiple compression transformation. Replace the instantaneous frequency operator of the STFT with the operator of the GWT, and compress the time-frequency energy in both the time and frequency directions to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions. Superimpose the time-frequency energy distributions of the single-component signals to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the processor performs the following steps: Obtain a bearing fault signal. According to the obtained bearing fault signal, by calculating the Fourier spectrum of the instantaneous frequency IF of the bearing fault signal, determine the optimal coefficient of the parameter transformation kernel and use it as the kernel function parameter coefficient of the GWT. According to the kernel function parameter coefficient of the GWT, by repositioning the frequency components of the signal in the TF plane to solve the cross-term interference, and then performing the GWT operation to suppress the time-frequency energy diffusion, obtain the initial time-frequency representation of the signal. According to the initial time-frequency representation of the signal, adopt the time-frequency ridge line search algorithm to extract the fault features of the signal and perform time-frequency multiple compression transformation. Replace the instantaneous frequency operator of the STFT with the operator of the GWT, and compress the time-frequency energy in both the time and frequency directions to obtain the time-frequency energy distribution of the single-component signal in both the time and frequency directions. Superimpose the time-frequency energy distributions of the single-component signals to obtain the time-frequency energy distribution of the enhanced bearing fault signal.

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