Composite fault signal separation method based on adaptive spectral kurtosis deconvolution

Abstract

The invention discloses a composite fault signal separation method based on adaptive spectral kurtosis deconvolution. The method comprises the following steps: S1, carrying out noise reduction processing on an original composite fault signal; s2, separating the composite fault signal after noise reduction through Hilbert envelope demodulation; s3, optimizing a low-pass filter and a high-pass filter through a Bayesian objective function, and constructing a band-pass filter and a band elimination filter; and S4, carrying out iterative filtering on the composite fault signal after noise reduction through a band-pass filter and a band elimination filter, constructing a frequency-bandwidth fast spectral kurtosis graph according to a fast spectral kurtosis deconvolution method, obtaining a center frequency and bandwidth range corresponding to the maximum spectral kurtosis, and separating out the weak fault signal in the step S2. According to the method, a spectral kurtosis graph is constructed by combining a low-pass filter and a high-pass filter through a fast spectral kurtosis deconvolution method to determine the center frequency and the bandwidth range, targeted separation is carried out on composite fault signals, an initial filtering parameter range is provided for Bayesian optimization, and the fault separation efficiency and accuracy are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of gearbox fault diagnosis, and particularly relates to a composite fault signal separation method based on adaptive spectral kurtosis deconvolution. Background Art

[0002] Gearboxes are essential components for large-scale electromechanical equipment, such as mining excavators, wind turbines, and ships. Affected by the operating environment, gearboxes operate year-round under harsh conditions of varying loads, high loads, and high intensity. For economic reasons, gearbox components are usually not replaced immediately at the initial stage of a failure. However, the internal structure of a gearbox is complex, and the impact vibration of a single initial failure may induce other failures, ultimately leading to the coexistence of multiple failure modes. The vibration signals generated by these failures of different locations, forms, and degrees are superimposed on each other, and the various failure factors influence each other, increasing the difficulty of fault diagnosis. Early compound faults may have varying degrees of fault severity, and weaker fault characteristic signals may be masked by severe fault characteristic signals, making it difficult to significantly identify weak fault characteristics in early compound faults, resulting in missed diagnosis.

[0003] The gearbox composite fault diagnosis methods currently used and their corresponding defects or deficiencies are as follows: ① The fault diagnosis method based on specific signal analysis takes specific equipment as the research object, which limits the application scope and portability of the model; ② The fault diagnosis method based on blind source separation requires a high number of channels for the observation signal, which increases the cost of fault diagnosis; ③ The fault diagnosis method based on deconvolution lacks effective evaluation criteria for parameter selection, and the extracted features are easily affected by signal noise; ④ The fault diagnosis method based on deep learning has high requirements for the sample size of data. When the working conditions change, the repeatability and comparability of the data samples will decrease, which will affect the accuracy of the diagnosis results.

[0004] In addition, existing composite fault diagnosis methods usually treat composite faults as a new type of fault and use this composite fault as a label for classification and identification. However, it is difficult to effectively explain the coupling mechanism and contribution between the single faults in the composite fault. Under interference such as noise and transient impact, the classification results are easily confused with the single fault type. Summary of the Invention

[0005] The present invention aims to solve the problems existing in the prior art to at least a certain extent. In order to effectively separate composite fault signals and accurately extract weak fault features therein, and effectively overcome the adverse effects of composite fault coupling conditions on fault diagnosis accuracy, the present invention provides a composite fault signal separation method based on adaptive spectral kurtosis deconvolution, including the following specific technical solutions.

[0006] A composite fault signal separation method based on adaptive spectral kurtosis deconvolution comprises the following steps: S1, collects the original composite fault signal of the gearbox and performs noise reduction processing on it, and outputs the composite fault signal after noise reduction; S2, separating the noise-reduced composite fault signal through Hilbert envelope demodulation; S3, establishing a low-pass filter and a high-pass filter of normalized frequency, and optimizing the low-pass filter and the high-pass filter through a Bayesian objective function to construct a band-pass filter and a band-stop filter; S4, iteratively filtering the de-noised composite fault signal through the bandpass filter and the band-stop filter, constructing a frequency-bandwidth fast spectral kurtosis diagram of the de-noised composite fault signal according to the fast spectral kurtosis deconvolution method, obtaining the center frequency and bandwidth range corresponding to the maximum spectral kurtosis, and separating the fault signals that were not separated or identified in step S2.

[0007] Furthermore, the original composite fault signal described in step S1 is subjected to noise reduction processing by an adaptive wavelet threshold denoising algorithm, and the expression is as follows: , Where, is the new wavelet coefficient; is a symbolic function; is the frequency domain wavelet coefficient of the composite fault signal; y To adjust the parameters; K is a threshold parameter that has been selected and determined.

[0008] Furthermore, in step S2, the specific steps of separating the noise-reduced composite fault signal by Hilbert envelope demodulation are as follows: I. Define the composite fault signal after noise reduction as , perform Hilbert transform on it and get the analytical signal , the process is as follows: , Where, To analyze the signal; is the composite fault signal after noise reduction; j is an imaginary unit; is the Hilbert transform; II. Define the expression of analytical signal as: , Where, To analyze the signal; is the phase of the signal; e is a natural constant; j is an imaginary unit; is the envelope of the signal; where It is obtained by calculating the modulus length of the analytical signal, that is: , Where, is the composite fault signal after noise reduction; is the Hilbert transform; III, Envelope Perform Fourier transform to obtain the Hilbert envelope spectrum, which is expressed as: , Where, is the Hilbert envelope spectrum, is the Fourier transform, f is the normalized frequency variable.

[0009] Furthermore, the expressions of the low-pass filter and high-pass filter of the normalized frequency are as follows: , Where, is a low-pass filter; is a high-pass filter; for FIR The filter has an order of 16 and a cutoff frequency of 0.4; n is the discrete time index; j is an imaginary unit; f is the normalized frequency variable; e is a natural constant; π is pi.

[0010] Furthermore, based on the SPSE theory, the Bayesian objective function is changed and expressed as follows: , Where, is the power spectrum entropy of the signal; is the kurtosis of the signal.

[0011] Furthermore, the specific steps to establish the objective function based on SPSE theory are as follows: Ⅰ, the power spectrum calculation formula is: , Where, is the power spectrum;L is the signal length; is the discrete Fourier transform of the original composite fault signal; π is pi; II. Normalize the power spectrum to obtain the power spectrum probability density function, which is calculated as follows: , Where, for Power density of the component; for Power spectrum value of the component; N is the number of frequency components of the discrete Fourier transform; l The frequency component index currently being calculated; q Temporary index for summing; For temporary index q The original power spectrum value of the corresponding frequency; III. The calculation formula of power spectrum entropy is: , Where, is the power spectrum entropy of the signal; N is the number of frequency components of the discrete Fourier transform; l The frequency component index currently being calculated; for Power density of the component; IV, the kurtosis expression is: , Where, is the kurtosis of the signal; E is the mathematical expectation operator; x is the original signal sequence; is the standard deviation of the signal; μ is the average value of the signal.

[0012] Furthermore, the method of constructing the frequency-bandwidth fast spectral kurtosis diagram of the composite fault signal after noise reduction is as follows: through a series of filtered signals in different frequency bands, that is, after decomposing each layer, the complex envelope frequency band signal is obtained. , that is, the signal at the center frequency and bandwidth The time-frequency complex envelope at , calculate each The kurtosis of the frequency band signal is calculated and the results are presented in the form of a binary grid to form a frequency-bandwidth fast spectral kurtosis diagram; The following formulas are used to calculate the entire The spectral kurtosis value of each node in the plane is expressed as follows: , Where, is the spectral kurtosis value of each node; is the complex envelope frequency band signal; i is the subband index; k is the number of decomposition layers; n is a discrete time index.

[0013] Furthermore, due to the complex envelope frequency band signal After each decomposition, the length of the next layer of complex envelope frequency band signal will be halved. To prevent excessive decomposition, the signal length R and decomposition layers k The following formula requirements must be met: , where k is the number of decomposition layers, R is the signal length, l The frequency component index currently being calculated.

[0014] Based on the above technical solution, the method described in the present invention has the following beneficial effects: 1. The method described in the present invention adopts an adaptive wavelet threshold denoising algorithm combined with Hilbert envelope demodulation. By optimizing the wavelet threshold function, the noise of the original signal of the gearbox in a strong noise environment is effectively removed, and the weak fault impulse signal is retained, thus solving the problem that Hilbert envelope demodulation has difficulty in identifying weak outer race fault characteristics.

[0015] 2. The method described in the present invention uses a fast spectral kurtosis deconvolution method, combined with the design of low-pass and high-pass filters to construct a spectral kurtosis diagram to determine the center frequency and bandwidth range, retain the targeted separation of composite fault signals, provide an initial filtering parameter range for Bayesian optimization, and improve the efficiency and accuracy of fault separation.

[0016] 3. The method described in the present invention proposes an adaptive spectral kurtosis deconvolution algorithm based on spectral kurtosis and power spectrum entropy to eliminate the influence of noise, construct an impact-sensitive objective function to accurately extract multiple local spectral kurtosis maxima, effectively separate complex fault features, and identify weak fault feature frequencies.

[0017] 4. The method described in the present invention combines the kurtosis index with the power spectrum entropy to construct an objective function based on the SPSE theory. The power spectrum entropy is used to characterize and quantify the complex and uncertain frequency domain energy in the signal. It is a feature extraction method based on the frequency domain spatial energy distribution of the vibration signal, which can describe the frequency distribution of the signal. However, if the power spectrum entropy is used as the only objective function, it is very easy for the decomposed signal to be a simple harmonic wave after optimization. This is because the extreme pursuit of spectrum distribution concentration leads to over-decomposition in the signal decomposition and serious energy loss. The kurtosis index is sensitive to pulse signals and is often used to measure the number of impacts in vibration signals. The introduction of kurtosis can improve the over-decomposition phenomenon of power spectrum entropy. Kurtosis is a statistic that reflects the distribution characteristics of random variables, that is, the normalized fourth-order central moment, a dimensionless parameter that describes the peak degree of the waveform, and is sensitive to impact signals. Therefore, the objective function based on the SPSE theory constructed by this method can find the most suitable filter parameters for adaptive search. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the overall process of the method of the present invention; Figure 2 Schematic diagram of the time domain and frequency domain of the original composite fault signal of the gearbox; Figure 3 This is a frequency domain diagram of the composite fault signal after noise reduction; Figure 4 Schematic diagram of the Hilbert envelope spectrum of the composite fault signal after noise reduction; Figure 5 This is a schematic diagram of the spectral kurtosis diagram after fast spectral kurtosis deconvolution; Figure 6 Schematic diagram of the envelope spectrum of gear fault and bearing outer ring fault; Figure 7 SPSE results for Bayesian optimization; Figure 8 Schematic diagram of the envelope spectrum of gear fault and bearing outer race fault after Bayesian optimization; Figure 9 Schematic diagram for low-pass and high-pass filter calculation; Figure 10 Schematic diagram of filter decomposition tree structure; Figure 11 is a frequency-bandwidth fast spectral kurtosis plot. DETAILED DESCRIPTION

[0019] Before describing the specific embodiments, the following explanations or glossaries are required: 1. Certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that they may use different terms to refer to the same component. This specification and claims do not distinguish components based on differences in terms, but rather on differences in their functions. Unless otherwise defined, technical or scientific terms used in this disclosure should have the ordinary meanings understood by persons of ordinary skill in the art to which this disclosure pertains.

[0020] 2. Bayesian Optimization algorithm, also known as Bayesian Optimization, abbreviated as BO, is a method for solving unknown objective functions. The global optimization algorithm of extreme values ​​mainly includes the probabilistic surrogate model and Bayesian theorem. The probabilistic surrogate model and the acquisition function are the core of the BO algorithm. The probabilistic surrogate model is used to simulate the distribution of the objective function, and the acquisition function estimates the optimal value based on the posterior distribution. BO uses the probabilistic surrogate model to replace the initial optimization stage. The most commonly used model is the Gaussian Processes (GP) function, which is widely used in nonlinear data fitting, regression and clustering problems. The expression is as follows: , , , Where, for The mathematical expectation of for x The covariance function of is the mean function; E is the expectation mathematical operator.

[0021] The core idea of ​​Bayes' theorem is to use the prior probability distribution of the probabilistic proxy model and the known observation set obtained by random sampling to calculate the posterior probability distribution, select the next more reasonable sampling point based on the posterior probability distribution, and finally approach the extreme point by correcting the probabilistic proxy model through multiple iterations of Bayes' theorem. Its expression is as follows: , Where, f is the unknown objective function; is a known observation set, where is the decision variable, is the observed value, is the observation error; for f The posterior probability distribution of ; for y The likelihood distribution of for f The prior probability distribution of ; for f The marginal likelihood distribution of .

[0022] like Figures 1-11 As shown, this embodiment describes a composite fault signal separation method based on adaptive spectral kurtosis deconvolution. Figure 1 The flowchart of the method of this embodiment is shown, which specifically includes the following steps.

[0023] S1, collects the original composite fault signal of the gearbox and performs noise reduction processing on it.

[0024] As preferred: ① This example uses a gearbox fault simulation test bench to collect the uniform-speed composite fault signal of the gearbox gear and rolling bearing outer ring. The signal sampling frequency is set to 5000 Hz, the sample length is 20,000 sampling points, the time interval is 4 seconds, the motor speed is 1600 rpm, the gear fault characteristic frequency is 30 Hz, and the rolling bearing outer ring fault characteristic frequency is 65 Hz.

[0025] ② Based on the collected composite fault signal output such as Figure 2 (a) shows the signal time domain diagram and Figure 2 From the frequency domain diagram shown in (b), we can see that the signal time domain diagram under the composite fault state has obvious periodic impact, but due to the influence of noise, some spectrum peaks in the frequency domain diagram are submerged.

[0026] In order to reduce the impact of noise on the subsequent fault signal separation algorithm, it is necessary to perform noise reduction processing on the original composite fault signal to obtain the composite fault signal after noise reduction. In this embodiment, an adaptive wavelet threshold denoising algorithm is used to perform noise reduction processing on the original composite fault signal. The expression is as follows: , Where, is the new wavelet coefficient; is a symbolic function; is the frequency domain wavelet coefficient of the composite fault signal; y To adjust the parameters; K It is a threshold parameter that is selected and determined to control the denoising strength, smoothing strength and sensitivity.

[0027] S2, analyze the frequency domain diagram of the composite fault signal after noise reduction obtained in step S1, as shown in Figure 3As shown in the figure, it can be seen that there are abundant resonant peak components in the spectrum, but the peaks in the frequency domain diagram do not have a periodic pattern, but different fault features are coupled together. In this step, the noise-reduced composite fault signal is separated by Hilbert envelope demodulation to obtain the following: Figure 4 The Hilbert envelope spectrum diagram shown in the figure is as follows: S201, define the composite fault signal after noise reduction as , perform Hilbert transform on it and get the analytical signal , the process is as follows: , Where, To analyze the signal; is the composite fault signal after noise reduction; j is an imaginary unit; is the Hilbert transform.

[0028] S202, define the analytical signal The expression is: , Where, To analyze the signal; is the phase of the signal; j is an imaginary unit; is the envelope of the signal.

[0029] in, It is obtained by calculating the modulus length of the analytical signal, that is: , Where, is the composite fault signal after noise reduction; is the Hilbert transform; Envelope Perform Fourier transform to obtain the Hilbert envelope spectrum: , Where, is the Fourier transform, f is the normalized frequency variable.

[0030] S3. Analyzing the Hilbert envelope spectrum obtained in step S2, it can be seen that since the amplitude of the impact signal generated by the gearbox bearing outer ring fault is much smaller than that of the gear fault, the Hilbert envelope demodulation can only distinguish the gearbox rotational frequency and the gear fault characteristic frequency, while the weak outer ring fault feature is submerged in the noise and difficult to identify.

[0031] For the weak fault signals that are not separated or identified in step S2, the fault signals are divided into the gear fault characteristic frequency of 30Hz and the amplitude range of 0-350; the bearing outer race fault characteristic frequency of 65Hz and the amplitude range of 0-100. The low amplitude signal of the bearing outer race signal is drowned by the high amplitude signal of the gear, such as Figure 4 This step is based on the fast spectral kurtosis deconvolution algorithm, so as to obtain the fast spectral kurtosis diagram of the composite fault signal after noise reduction, as shown in Figure 5 The specific steps are as follows: S301, establish a low-pass filter and a high-pass filter of normalized frequency, the expressions are as follows: , Where, is a low-pass filter; is a high-pass filter; It is an FIR filter with an order of 16 and a cutoff frequency of 0.4; n is the discrete time index; j is an imaginary unit; f is the normalized frequency variable; e is a natural constant; π is pi.

[0032] S302, iteratively filtering the denoised composite fault signal through a low-pass filter and a high-pass filter to obtain a series of filtered signals in different frequency bands, constructing a frequency-bandwidth fast spectral kurtosis diagram to obtain the center frequency and bandwidth range corresponding to the maximum spectral kurtosis.

[0033] like Figure 9 As shown, the low-pass filter of the normalized frequency and high-pass filter The process or method of decomposing the composite fault signal is: Signal First, input to the low-pass filter and high-pass filter middle; The low-pass filter is used to retain the low-frequency components in the signal and filter out the high-frequency components. Its output signal is downsampled (represented by ↓2) to obtain the filtered signal; The high-pass filter is used to retain the high-frequency components in the signal and filter out the low-frequency components. Multiplication is used to correct the frequency band misalignment, and then the downsampling operation is also performed to obtain the filtered signal, where There is no band misalignment factor.

[0034] Use the low-pass filter and high-pass filter of normalized frequency to decompose and filter the composite fault signal after noise reduction layer by layer. k When the layer is formed, the decomposed signal is subjected to short-time Fourier transform, and the transformed coefficients are used as the first k+1 The input of the layer continues to be filtered and decomposed until the decomposition is completed. Figure 10 A schematic diagram of the filter decomposition tree structure is shown.

[0035] S303, through a series of filtered signals in different frequency bands, calculate the kurtosis of each frequency band signal and present the result in the form of a binary grid, forming the following Figure 11 A quick spectral kurtosis plot of frequency versus bandwidth is shown.

[0036] After decomposition of each layer, the complex envelope frequency band signal is obtained , that is, the signal is at the center frequency and bandwidth The time-frequency complex envelope at .

[0037] Calculate the entire Spectral kurtosis value of each node in the plane , the expression is as follows: , Where, is the spectral kurtosis value of each node; is the complex envelope frequency band signal; i is the subband index; k is the number of decomposition layers; n is a discrete time index.

[0038] Since the complex envelope frequency band signal After each decomposition, the length of the next layer of complex envelope frequency band signal will be halved. To prevent excessive decomposition, the signal length R and decomposition layers k The following formula requirements must be met: , Where, k is the number of decomposition layers; R is the signal length.

[0039] S304 , obtaining a fast spectral kurtosis graph of the composite fault signal after noise reduction according to a fast spectral kurtosis deconvolution method, and finding the center frequency and bandwidth range corresponding to the maximum spectral kurtosis according to the graph.

[0040] S4. In the gearbox composite fault scenario, there are often multiple local maxima in the fast spectral kurtosis diagram of the composite fault signal after noise reduction, which makes it difficult to directly determine the single optimal center frequency and bandwidth range based on the maximum spectral kurtosis, and it is difficult to effectively separate different fault characteristics.

[0041] According to the kurtosis graph, the bandpass and bandstop filters are constructed, and the separation results are as follows: Figure 6 (a) and Figure 6 As shown in (b), Figure 6 (a) is the envelope spectrum of gear fault, Figure 6 Figure (b) shows the envelope spectrum of a bearing outer race fault. As can be seen from the figure, the composite fault signal has been separated. However, due to the mutual interference and overlap between the different fault features in the composite fault signal, the separation effect is poor. The presence of other frequency components makes the peak of the fault feature frequency less prominent, and some fault features may be obscured by other frequency components, making them difficult to clearly identify.

[0042] Although the center frequency and bandwidth range of the filter can be determined based on the fast spectral kurtosis plot, the optimal filter order, center frequency and bandwidth range need to be determined based on the Bayesian optimization algorithm. In order to adaptively find the most appropriate filter parameters, the objective function of BO needs to be changed.

[0043] In order to adaptively find the most appropriate filter parameters, this embodiment combines the kurtosis index with the power spectrum entropy to construct an objective function based on the SPSE theory, which is expressed as follows: , Where, is the power spectrum entropy of the signal; is the kurtosis of the signal.

[0044] The objective function is sensitive to shock signals, namely, the numerator power spectrum entropy promotes the optimization to favor signals with more concentrated frequency energy distribution, which usually corresponds to periodic shocks; while the denominator kurtosis avoids excessive energy concentration leading to the loss of shock features and degeneration into simple harmonics, thus achieving a balance between extracting shock features and avoiding over-decomposition, and better expressing the significance and uniform distribution characteristics of periodic pulses. Figure 7 A schematic diagram of the SPSE results of Bayesian optimization is given.

[0045] The process of establishing the objective function based on SPSE theory is as follows: S401, the power spectrum calculation formula is: , Where, is the power spectrum; L is the signal length; is the discrete Fourier transform of the original composite fault signal; π is pi.

[0046] S402, normalize the power spectrum to obtain the power spectrum probability density function, which is calculated as follows: , Where, for Power density of the component; for Power spectrum value of the component; N is the number of frequency components of the discrete Fourier transform; l The frequency component index currently being calculated; q Temporary index for summing; For index q The original power spectrum value corresponding to the frequency.

[0047] S403, the calculation formula of power spectrum entropy is: , Where, is the power spectrum entropy of the signal; N is the number of frequency components of the discrete Fourier transform; l is the index of the frequency component; for The power density of the component.

[0048] S404, the kurtosis expression is: , Where, is the kurtosis of the signal; E is the expectation mathematical operator; x is the original signal sequence; is the standard deviation of the signal; μ is the average value of the signal.

[0049] S5, constructs a bandpass filter and a bandstop filter according to the optimal filter parameters obtained after Bayesian optimization. Through the coordinated processing of the bandpass filter and the bandstop filter, the effective separation and extraction of fault features of different impact intensities in the composite fault signal after noise reduction are achieved.

[0050] Right now: Use bandpass filters to extract fault characteristic components with strong impact energy, that is, corresponding to the maximum value area of ​​the fast spectrum kurtosis diagram, for example, extract gear faults with severe impact, and calculate the gear fault envelope spectrum. Figure 8 As shown in (a); The band-stop filter is used to suppress the frequency band corresponding to the strong impact component, thereby highlighting another fault characteristic component with weak impact energy that is masked in the remaining signal. For example, the bearing outer ring fault with weak impact is extracted and the bearing outer ring fault envelope spectrum is calculated, such as Figure 8 As shown in (b).

[0051] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention as claimed.

Claims

1. A composite fault signal separation method based on adaptive spectral kurtosis deconvolution, characterized in that: The following steps are involved: S1, collects the original composite fault signal of the gearbox and performs noise reduction processing on it, and outputs the composite fault signal after noise reduction; S2, separating the noise-reduced composite fault signal through Hilbert envelope demodulation; S3, establishing a low-pass filter and a high-pass filter of normalized frequency, and optimizing the low-pass filter and the high-pass filter through a Bayesian objective function to construct a band-pass filter and a band-stop filter; S4, iteratively filtering the de-noised composite fault signal through the bandpass filter and the band-stop filter, constructing a frequency-bandwidth fast spectral kurtosis diagram of the de-noised composite fault signal according to the fast spectral kurtosis deconvolution method, obtaining the center frequency and bandwidth range corresponding to the maximum spectral kurtosis, and separating the fault signals that were not separated or identified in step S2.

2. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 1, characterized in that: The original composite fault signal described in step S1 is subjected to noise reduction processing by the adaptive wavelet threshold denoising algorithm, and the expression is as follows: ， Where, is the new wavelet coefficient; is a symbolic function; Frequency domain wavelet coefficients of composite fault signal; y To adjust the parameters; K is a threshold parameter that has been selected and determined.

3. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 1, characterized in that: In step S2, the specific steps of separating the noise-reduced composite fault signal by Hilbert envelope demodulation are as follows: I. Define the composite fault signal after noise reduction as , perform Hilbert transform on it and get the analytical signal , the process is as follows: ， Where, To analyze the signal; is the composite fault signal after noise reduction; j is the imaginary unit; is the Hilbert transform; is the Hilbert transform; II. Define the analytical signal The expression is: ， Where, To analyze the signal; is the phase of the signal; e is a natural constant; j is an imaginary unit; is the envelope of the signal; where It is obtained by calculating the modulus length of the analytical signal, that is: ， Where, is the composite fault signal after noise reduction; is the Hilbert transform; III, Envelope Perform Fourier transform to obtain the Hilbert envelope spectrum, which is expressed as: ， Where, is the Hilbert envelope spectrum, is the Fourier transform, f is the normalized frequency variable.

4. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 1, characterized in that: The low-pass filter and high-pass filter expressions of normalized frequency are as follows: ， Where, is a low-pass filter; is a high-pass filter; for FIR The filter has an order of 16 and a cutoff frequency of 0.4; n is the discrete time index; j is an imaginary unit; f is the normalized frequency variable; e is a natural constant; π is pi.

5. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 4, characterized in that: Based on the SPSE theory, the Bayesian objective function is changed and the expression is as follows: ， Where, is the power spectrum entropy of the signal; is the kurtosis of the signal.

6. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 5, characterized in that: The specific steps to establish the objective function based on SPSE theory are as follows: Ⅰ, the power spectrum calculation formula is: ， Where, is the power spectrum; L is the signal length; is the discrete Fourier transform of the original composite fault signal; π is pi; II. Normalize the power spectrum to obtain the power spectrum probability density function, which is calculated as follows: ， Where, for Power density of the component; for Power spectrum value of the component; N is the number of frequency components of the discrete Fourier transform; l The frequency component index currently being calculated; q Temporary index for summing; For temporary index q The original power spectrum value of the corresponding frequency; III. The calculation formula of power spectrum entropy is: ， Where, is the power spectrum entropy of the signal; N is the number of frequency components of the discrete Fourier transform; l The frequency component index currently being calculated; for Power density of the component; IV, the kurtosis expression is: ， Where, is the kurtosis of the signal; E is the mathematical expectation operator; x is the original signal sequence; is the standard deviation of the signal; μ is the average value of the signal.

7. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 1, characterized in that: The method of constructing the frequency-bandwidth fast spectral kurtosis diagram of the composite fault signal after noise reduction is as follows: through a series of filtered signals in different frequency bands, that is, after decomposing each layer, the complex envelope frequency band signal is obtained. , that is, the signal at the center frequency and bandwidth The time-frequency complex envelope at , calculate each The kurtosis of the frequency band signal is calculated and the results are presented in the form of a binary grid to form a frequency-bandwidth fast spectral kurtosis diagram; The following formulas are used to calculate the entire The spectral kurtosis value of each node in the plane is expressed as follows: ， Where, is the spectral kurtosis value of each node; is the complex envelope frequency band signal; i is the subband index; k is the number of decomposition layers; n is a discrete time index.

8. The method for separating composite fault signals based on adaptive spectral kurtosis deconvolution according to claim 1, characterized in that: Since the complex envelope frequency band signal After each decomposition, the length of the next layer of complex envelope frequency band signal will be halved. To prevent excessive decomposition, the signal length R and decomposition layers k The following formula requirements must be met: , where k is the number of decomposition layers, R is the signal length, l The frequency component index currently being calculated.

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