Fault diagnosis method based on improved Gini coefficient ratio optimization diagram of product envelope spectrum

Abstract

The invention relates to the field of fault diagnosis, and discloses a fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization graph, and the method comprises the steps: obtaining a vibration signal, calculating the power spectrum density based on an autoregression model, carrying out the adaptive spectrum segmentation through employing an improved local maximum and minimum method, and generating an optimized spectrum boundary set; and constructing a Gini coefficient ratio optimization graph of the hierarchical improved product envelope spectrum, analyzing and extracting a fault characteristic frequency through the improved product envelope spectrum optimized by a frequency domain signal-to-noise ratio, and selecting an optimal resonance frequency band based on a Gini coefficient ratio to realize fault diagnosis. Through Gaussian kernel smoothing, hierarchical spectrum segmentation and frequency domain signal-to-noise ratio optimization, complex noise interference is effectively suppressed, the identification precision of early fault features is remarkably improved, and the method is suitable for rolling bearing fault diagnosis under the non-stationary working condition and has high robustness and industrial application value.

Description

Technical Field

[0001] The present invention relates to the field of fault diagnosis, and particularly to a fault diagnosis method based on an improved product envelope spectrum Ginicoefficient ratio optimization graph. Background Art

[0002] As a key component in rotating machinery, rolling bearings are widely used in industrial equipment and undertake the core functions of supporting and reducing friction. Since they often operate under harsh conditions such as high speed and heavy load, they are easily affected by multiple factors such as axial, radial loads and impact loads, resulting in local faults, structural fatigue and even cracks, thus affecting the safety and reliability of the mechanical system. Therefore, the early fault diagnosis of rolling bearings is crucial for preventing major mechanical failures and reducing economic losses. However, the fault signals of rolling bearings are usually accompanied by complex noises and interferences, and exhibit characteristics such as non-stationarity, frequency modulation and amplitude modulation, which makes it difficult for traditional spectrum analysis methods to effectively extract fault characteristic frequencies.

[0003] Usually, it is necessary to preprocess the signal by means of feature enhancement techniques, such as signal decomposition, resonance demodulation and blind deconvolution. Among them, resonance demodulation technology is a commonly used means for detecting rolling bearing faults. It mainly filters the signals in the resonance frequency band through a band-pass filter, and then extracts the fault characteristics through envelope demodulation. In this process, the selection of ODFB is crucial. For the selection of the optimal resonance frequency band ODFB, the fast kurtogram (FK) method and the logarithmic envelope spectrum Ginicoefficient gram (LESGIRgram) method have been used in the past.

[0004] However, due to the above methods using a fixed frequency band division method and lacking the ability of adaptive adjustment, it is difficult to cope with the non-stationarity and local characteristics of the signals, which may lead to inaccurate capture of fault-related frequency components. Therefore, some adaptive frequency band division methods have been proposed, such as the adaptive harmonic product spectrum (AHPS) method. This method adaptively determines the frequency band division boundary by analyzing the local minimum points in the power spectral density (PSD) curve. At the same time, the harmonic significance index (HSI) technology is used to lay the spectrum plane, further enhancing the ability of AHPS in anti-noise interference and random pulses.

[0005] After signal preprocessing, envelope analysis is usually required to extract fault features. Common envelope analysis methods include envelope spectrum (ES), log-envelope spectrum (LES), and squared envelope spectrum (SES). In the case of weak interference noise, ES and SES can effectively detect the fault characteristic frequency (FCF) of rolling bearings; however, in an environment with complex noise pollution, the effects of these methods are usually not ideal. In response, more effective analysis tools have been proposed, such as the improved envelope spectrum (IES), which selects the optimal integration frequency band by optimizing the diagnostic feature (DF), thereby effectively extracting the fault features masked by strong signals and being applicable to fault diagnosis under non-stationary working conditions. And a generalized envelope spectrum (GES) analysis tool is constructed using a simplified Box-Cox transform, and combining the advantages of different GESs, a product envelope spectrum (PES) is proposed. The construction of PES requires the selection of multiple GESs with different parameters, and the selection of parameters has a significant impact on the final performance. Over-reliance on manual operation may lead to instability and deviation of the results.

[0006] The market urgently needs a fault diagnosis method that can solve the problems of over-decomposition and boundary concentration in the traditional Locmaxmin method, effectively suppress noise interference, and significantly improve the signal identification accuracy. Summary of the Invention

[0007] The present invention aims to solve at least one of the technical problems existing in the related art. For this reason, the present invention provides a fault diagnosis method based on an optimized graph of the Gini coefficient ratio of the improved product envelope spectrum.

[0008] A fault diagnosis method based on an optimized graph of the Gini coefficient ratio of the improved product envelope spectrum, the steps include: a) Obtain vibration signals; b) Analyze the vibration signals based on an autoregressive model to generate a power spectral density, and determine the set of local maxima of the power spectral density; c) Adaptively divide the frequency spectrum according to the set of local maxima to generate a set of boundaries of the optimized frequency band; d) Construct a hierarchical improved optimized graph of the Gini coefficient ratio of the product envelope spectrum based on the set of boundaries; e) Obtain the divided frequency bands in the optimized graph of the product envelope spectrum Gini coefficient ratio with hierarchical improvement; determine the optimal resonance frequency band through the improved product envelope spectrum analysis method, and identify the fault characteristic frequencies.

[0009] Further, step a) includes collecting vibration signal data and setting the number of modes according to the signal characteristics; The vibration signals include fault signals and healthy signals.

[0010] Further, step b) includes the following steps: Establish an autoregressive model and solve the model parameters based on the autocorrelation function and the Yule-Walker equation; Use the Akaike information criterion to determine the optimal order of the autoregressive model; Calculate the power spectral density based on the autoregressive model of the optimal order, and extract the set of local maxima of the power spectral density.

[0011] Further, step c) includes the following steps: Set the minimum distance between adjacent local maxima, and screen the set of local maxima, which is determined based on the fault signal length and control parameters; Determine the initial boundary according to the screened set of local maxima; Through iterative optimization, generate the final frequency band boundary set based on the calculation of the variance of the frequency band energy.

[0012] Further, the steps of the iterative optimization include: Discard the boundaries in the initial boundary set in turn, and limit the upper and lower limits of the boundary set to generate a new boundary set; Divide the frequency spectrum based on the new boundary set, and calculate the energy variance of each interval; Iteratively adjust the boundary positions until the energy variance is minimized, determine the frequency spectrum segmentation boundary, and generate the final boundary set.

[0013] Further, step d) includes the following steps: d1) Apply a Gaussian kernel function to the power spectral density for convolution smoothing to generate a smoothed power spectral density; Repeat steps b) to d1) until the number of divided intervals no longer changes with iteration; sort all the boundary sets generated by iteration in ascending order to form a boundary set; Based on the smoothed power spectral density and the boundary set, construct an optimized graph of the product envelope spectrum Gini coefficient ratio with hierarchical improvement.

[0014] Further, in step d), the construction of the stratified improved product envelope spectrum Gini coefficient ratio optimization graph includes: selecting a predetermined number of boundary sets from the boundary set, jointly constituting a hierarchical structure with the initial boundary, and constructing a stratified improved product envelope spectrum Gini coefficient ratio optimization graph.

[0015] Further, step e) includes the following steps: Using a band-pass filter for each frequency band interval in the stratified improved product envelope spectrum Gini coefficient ratio optimization graph to generate a filtered signal; Based on the frequency domain signal-to-noise ratio optimization, select the generalized envelope spectrum and construct an improved product envelope spectrum; Calculate the value of the improved product envelope spectrum Gini coefficient ratio for each frequency band interval based on the filtered signal, determine the optimal resonance frequency band, and identify the fault characteristic frequency through the improved product envelope spectrum.

[0016] Further, the calculation formula of the frequency domain signal-to-noise ratio FDSNR based on the product envelope spectrum is as follows: Where, is the number of harmonics of the fault characteristic frequency FCF, is set to , represents the frequency value; represents the th resonance frequency of the fault characteristic frequency FCF and a small frequency band composed of multiple spectrum frequencies on both sides; represents the frequency value in; is the number of spectrum frequencies in the interval ; represents different forms of the generalized envelope signal; represents the th generalized envelope spectrum GES corresponding parameter for constructing the product envelope spectrum PES ; is the generalized envelope based on the simplified Box-Cox transformation; represents the fast Fourier transform; is the envelope of the signal .

[0017] Furthermore, the calculation of the value of the improved product envelope spectrum Gini coefficient ratio is achieved by comparing the improved product envelope spectra of the fault signal and the healthy signal. By comparing the differences between the two and combining sequence norm and sorting operations, the optimal resonance frequency band is determined. The definition of the value of the improved product envelope spectrum Gini coefficient ratio IPESGIR is as follows: Wherein, represents the improved product envelope spectrum of the signal; represents the length of the product envelope spectrum; represents the sequence sorted in ascending order; represents the sequence of norm; represents the IPESGI of the fault signal; represents the IPESGI of the healthy signal.

[0018] One or more of the above technical solutions in the embodiments of the present invention have at least one of the following technical effects: 1. Improve the accuracy of fault feature extraction: By introducing the frequency domain signal-to-noise ratio (FDSNR) to optimize the generalized envelope spectrum parameters and constructing the improved product envelope spectrum (IPES), the identification ability of fault feature frequencies is effectively enhanced, overcoming the limitation of poor feature extraction effect of traditional envelope spectrum methods in strong noise environments.

[0019] 2. Enhance the anti-noise interference ability: The power spectral density is smoothed by using the Gaussian kernel function, and the improved local maximum and minimum method is combined to achieve adaptive spectrum segmentation, significantly reducing the interference of complex noise and random pulses on signal analysis, and is applicable to fault diagnosis under non-stationary working conditions.

[0020] 3. Optimize the accuracy of spectrum segmentation: By iteratively optimizing the spectrum boundary set with the goal of minimizing the energy variance, the problems of over-segmentation and boundary concentration in the traditional local maximum and minimum method are solved, the generated spectrum boundary distribution is more uniform, and the capture of fault-related frequencies is more accurate.

[0021] 4. Achieve the flexibility of multi-scale analysis: By constructing a hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph (IPESGIRgram), a multi-scale frequency band analysis framework is provided, enhancing the adaptability of the method to different fault features and improving the robustness of diagnosis.

[0022] 5. Improved early fault diagnosis ability: By using the improved product envelope spectrum Gini coefficient ratio (IPESGIR) as the optimal resonant frequency band selection index, and analyzing the non-uniformity of feature distribution, faults and healthy states can be clearly distinguished, significantly improving the detection accuracy of early faults in rolling bearings.

[0023] 6. Has broad industrial application value: This method shows good stability and reliability under complex working conditions, is applicable to the fault diagnosis of rotating machinery in fields such as aviation, railway, and wind power, can effectively prevent major mechanical faults, and reduce economic losses.

[0024] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. Brief Description of the Drawings

[0025] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0026] Figure 1 Flow chart of the fault diagnosis method based on the optimized graph of the improved product envelope spectrum Gini coefficient ratio according to the present invention; Figure 2 Time domain diagram of the inner ring signal; Figure 3 Spectrum of the inner ring fault signal; Figure 4 AIC value of the inner ring fault signal; Figure 5 PSD and spectrum of the inner ring fault signal; Figure 6 Spectrum segmentation result of traditional Locmaxmin; Figure 7 Spectrum segmentation result of the improved Locmaxmin; Figure 8 FDSNR values of different generalized envelope spectra of the inner ring fault signal; Figure 9 IPES of the inner ring fault signal; Figure 10 Segmentation map and spectrogram generated by the FDMKgram analysis method for the inner ring fault signal; Figure 11 Segmentation map and spectrogram generated by the ACCUgram analysis method for the inner ring fault signal; Figure 12The segmentation map and spectrogram generated by the IESCFFOgram analysis method for the inner ring fault signal; Figure 13 The segmentation map and spectrogram generated by the IPESGIRgram analysis method for the inner ring fault signal. Detailed implementation manner

[0027] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts fall within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention but cannot be used to limit the scope of the present invention.

[0028] The interpretations of the English abbreviations used in the present invention are as follows: PSD: Power spectral density; ODFB: Optimal resonance frequency band; FDSNR: Frequency domain signal-to-noise ratio; FCF: Fault characteristic frequency; GES: Generalized envelope spectrum; PES: Product envelope spectrum; IPES: Improved product envelope spectrum; IPESGI: Improved product envelope spectrum Gini coefficient; IPESGIR: Improved product envelope spectrum Gini coefficient ratio; IPESGIRgram: Improved product envelope spectrum Gini coefficient ratio optimization graph.

[0029] Aiming at the problems existing in the current bearing fault diagnosis, the present invention improves PES by introducing the frequency domain signal-to-noise ratio, proposes an IPES analysis method, and creates an adaptive spectrum segmentation method based on the autoregressive power spectral density and the improved Locmaxmin method to solve the problems of over-decomposition and boundary concentration existing in the traditional Locmaxmin method, and applies the IPESGIRgram method to early fault diagnosis, effectively suppressing noise interference and significantly improving the signal identification accuracy.

[0030] The following combines Figure 1 The flow shown to detail the fault diagnosis method of the present invention based on the improved product envelope spectrum Gini coefficient ratio optimization graph. The specific steps include: Step 1: Obtain the rolling bearing signal and set the number of modes , ; S is a calculation parameter for iterative assignment in subsequent calculations.

[0031] In this example, the bearing test data publicly disclosed by Case Western Reserve University (CWRU) in the United States is used. The fault diameter is 0.1778 mm, the motor speed is 1797 rpm, and the load is 0 HP. The fault signal of the inner ring of the drive-end rolling bearing is selected. The sampling frequency of the signal is 12 kHz, and the duration is 1 second. The theoretical FCF of the selected inner ring fault signal is 162.19 Hz, and the rotational frequency is 29.95 Hz. The results are as Figure 2 , Figure 3 shown, Figure 2 representing the healthy signal and the fault signal in the time domain of the inner ring, Figure 3 representing the spectrum of the inner ring fault signal.

[0032] Step 2: Calculate the power spectral density (PSD) using the AR model and obtain the set of local maxima of the PSD; Step 2.1: Given an -order AR model, its difference equation is as follows: where is the random signal for model solution, are the model parameters, and ; is a white noise sequence with a mean of zero and a variance of . This model can be regarded as the output response of a system driven by a white noise input.

[0033] For the above AR model, its autocorrelation function satisfies the following relationship: where is 's autocorrelation function, represents the lag order, is the rd model parameter.

[0034] Step 2.2: Construct the Yule-Walker equation based on the autocorrelation function to solve for the model parameters , and the system of equations for solving is as follows: By solving this system of equations, the parameters of the AR model can be obtained, and then all the autocorrelation function values of the random signal can be determined.

[0035] Step 2.3: Calculate the PSD of the AR model. The PSD describes the distribution of the signal in the frequency domain and helps analyze the spectral characteristics of the signal. As Figure 5 shown, by combining the PSD with the spectrum, it can be seen that the trend of the PSD is basically the same as that of the spectrum, and the PSD can effectively capture the change trend of the spectral amplitude while reducing the influence of noise and other interference factors. The best single-step linear predictor of the AR model aims to minimize the prediction error. The process is as follows: Step 2.3.1: Derive the power spectrum formula. In a single-step predictor at a point, the predicted value of the signal is: The prediction error is defined as: where ; is the signal value predicted based on the current and past values. represents the th observation value before the current value, The system function of the order prediction error filter can be expressed as: where is the autocorrelation function, are the prediction error filter coefficients, is the minimum mean square value of the prediction error. Let , , then there is a relational expression: Then The order PSD result of the AR model is: where represents the frequency value.

[0036] Step 2.3.2: Adopt the AIC criterion to select the order that minimizes the AIC, which is defined as follows: where is the number of samples; is the mean square error of the residuals; is the order of the AR model.

[0037] When , repeat steps 2.1 - 2.3.1 and select the order , indicating that this order is the optimal order of the AR model. Through the optimal order, the PSD of the AR model is further obtained, and a set of local maxima of the PSD is obtained.

[0038] Through the above operations, the AIC values of different orders can be obtained and plotted, as Figure 4 shown. It can be concluded from the figure that: When the order reaches 148, the AIC is at the minimum value, and as the order increases, the change of the AIC value gradually becomes flat, indicating that this order is the optimal order of the AR model. Thus, the order for solving the PSD is determined to be 148.

[0039] Step 3: Require that the distance between adjacent extrema is not less than L to obtain a new set of maxima; To reduce the number of local maxima in the spectrum, a minimum peak distance is set and defined as: where is a control parameter, and is the length of the fault signal.

[0040] When the value is too large, the local maxima in the PSD will be overly reduced, resulting in under-decomposition of the spectrum. On the contrary, when the value is too small, there will be too many local maxima, resulting in over-decomposition of the spectrum. Through experimental analysis of various fault signals in the Case Western Reserve University Bearing Data Center, is finally selected.

[0041] Step 4: Obtain a boundary set; Step 4.1: Find the position of the minimum value between two adjacent maxima as the boundary to obtain an initial boundary set , and let .

[0042] Step 4.2: Discard in the initial boundary set , and define , , to obtain a new boundary set .

[0043] Step 5: Iteratively optimize the boundary set and use energy variance calculation to confirm the final boundary set; Step 5.1: Divide the spectrum according to the new boundary set, calculate the energy of each interval, and then find the variance to obtain the energy variance . Let .

[0044] Step 5.2: Repeat steps 4.2 - 5.1 until an energy variance set is obtained and the one corresponding to the minimum energy variance is the final boundary set. In each iteration, the boundary position is adjusted according to the difference in band energy, thereby optimizing the spectral division. Then, the final boundary set is determined by solving the minimum energy variance, avoiding the problems of over - decomposition or inaccurate segmentation.

[0045] In the above steps 3 - 5, the fault signal is spectrally segmented by using the improved Locmaxmin method. Comparing Figure 6 with Figure 7 it can be seen that, as can be seen from Figure 6 most of the boundaries are concentrated in the frequency band interval, resulting in an overly concentrated frequency band, which may cause over - decomposition problems. In contrast, Figure 7 the boundaries in are more evenly distributed, avoiding the phenomena of over - decomposition and under - decomposition.

[0046] Step 6: Construct a hierarchical IPESGIRgram; If , then perform a convolution operation on the PSD and the Gaussian kernel function, that is, smooth the PSD curve by using the Gaussian kernel function and let . Repeat all the specified steps in 2 - 5 above until the number of divided intervals no longer changes with iteration; otherwise, sort all the boundary sets generated by iteration in ascending order to form a boundary set, select the first boundary sets, and construct a - layer IPESGIRgram together with the initial boundary . The definition of the Gaussian kernel function is as follows: where is the size of the Gaussian kernel; is the standard deviation of the Gaussian kernel; is the PSD with different smoothness degrees, is the initially estimated PSD; represents the convolution operation.

[0047] Step 7: Analyze the ODFB using the IPES analysis method to identify the FCF.

[0048] Step 7.1: Filter each frequency band interval using a band - pass filter to obtain the filtered signal.

[0049] Step 7.2: Improve the product envelope spectrum IPES to enhance the identification accuracy of fault characteristics. The explanation of IPES in this process is as follows: Since the product envelope spectrum PES is constructed by multiplying multiple generalized envelope spectra GES, in traditional methods, due to fixed relevant parameters, the accuracy of the analysis results decreases. Therefore, the FDSNR evaluation index is introduced to optimize the selection of GES. By selecting GES that meet the requirements to construct PES, the error introduced by human operation can be effectively reduced, and the identification accuracy of fault characteristics can be improved, that is, the improved product envelope spectrum IPES. The FDSNR based on PES is defined as follows: Where, is the number of harmonics of the FCF, is set to , which ensures that the FCF and its two resonant frequencies are considered; represents the frequency value; s represents the th resonant frequency of the FCF and the small frequency band composed of 3 spectral frequencies on both sides; represents the frequency value in; is the number of spectral frequencies in the interval ; represents different forms of the generalized envelope signal; represents the th parameter corresponding to the GES used to construct PES ; is the generalized envelope based on the simplified Box-Cox transform; represents the fast Fourier transform (FFT); is the envelope of the signal .

[0050] The above operations are as Figure 8 shown. The figure shows the FDSNR values of from 1 to 5, every 0.1. Select the corresponding top 4 maximum GES to construct IPES. As Figure 9 shown, the FCF and its resonant frequencies can be clearly observed.

[0051] Step 7.3: Calculate the IPESGIR value for each interval and determine the ODFB. In this step, the definition of the IPESGIR value is as follows: Among them, represents the improved product envelope spectrum of the signal; represents the length of the PES product envelope spectrum; represents the sequence in ascending order; represents the sequence of norm; represents the IPESGI of the bearing fault signal; represents the IPESGI of the bearing healthy signal. The IPESGIR index shows strong advantages in fault diagnosis by combining IPES and GI.

[0052] First of all, it can effectively identify changes in the state of mechanical equipment, especially in the initial stage of a fault. By analyzing the non-uniformity of the feature distribution, it can clearly distinguish between fault and healthy states. Secondly, IPESGI shows good robustness in dealing with noise interference and can operate stably in a complex working environment. In addition, IPESGI has strong adaptability and can provide accurate fault diagnosis results under different fault modes and working conditions, thereby improving the accuracy and reliability of diagnosis.

[0053] Figure 10 - Figure 13 shows the processing results of 4 methods, Figure 10 is FDMKgram and SES, Figure 11 is ACCUgram and SES, Figure 12 is IESCFFOgram and IES, Figure 13 is IPESGIRgram and IPES; First of all, the FDMKgram and ACCUgram methods selected the same frequency band for demodulation analysis. It can be observed from SES that both of these methods successfully identified the FCF and its three resonant frequencies. However, there are still a small number of interference frequencies that could not be effectively suppressed. Secondly, the IESCFFOgram method selected a frequency band for demodulation analysis. Although the FCF and its three resonant frequencies were successfully identified in IES, compared with the previous two methods, the prominence of these frequencies is relatively poor and the identification effect is relatively limited. The method proposed in the present invention selected a frequency band for demodulation analysis. The FCF and its three resonant frequencies were clearly presented in IPES, and the identification of these frequencies is more prominent than that of the previous three methods, showing a significant enhancement effect Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault diagnosis method based on an optimized graph of the ratio of the improved product envelope spectrum Gini coefficient, characterized in that the steps Including: a) Obtain vibration signals; b) Analyze the vibration signals based on an autoregressive model, generate a power spectral density, and determine a set of local maxima of the power spectral density; c) Adaptively divide the frequency spectrum according to the set of local maxima, and generate a set of boundaries of the optimized frequency bands; d) Construct a hierarchical improved product envelope spectrum Gini coefficient ratio optimization diagram based on the set of boundaries; e) Obtain the divided frequency bands in the hierarchical improved product envelope spectrum Gini coefficient ratio optimization diagram; Determine the optimal resonance frequency band through an improved product envelope spectrum analysis method and identify the fault characteristic frequencies.

2. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1, characterized in that: Step a) includes collecting vibration signal data and setting the number of modes according to the signal characteristics; The vibration signals include fault signals and healthy signals.

3. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1, characterized in that: Step b) includes the following steps: Establish an autoregressive model and solve the model parameters based on the autocorrelation function and the Yule-Walker equation; Use the Akaike information criterion to determine the optimal order of the autoregressive model; Calculate the power spectral density based on the autoregressive model of the optimal order and extract the set of local maxima of the power spectral density.

4. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1, characterized in that: Step c) includes the following steps: Set the minimum distance between adjacent local maxima, screen the set of local maxima, which is determined based on the fault signal length and control parameters; Determine the initial boundaries according to the screened set of local maxima; Through iterative optimization, generate the final frequency band boundary set based on the calculation of the variance of the frequency band energy.

5. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 4, characterized in that: The steps of the iterative optimization include: Discard the boundaries in the initial boundary set in turn, and limit the upper and lower limits of the boundary set to generate a new boundary set; Divide the frequency spectrum based on the new boundary set and calculate the energy variance of each interval; Iteratively adjust the boundary positions until the energy variance is minimized, determine the frequency spectrum segmentation boundary, and generate the final boundary set.

6. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1, characterized in that: Step d) includes the following steps: d1) Apply a Gaussian kernel function to the power spectral density for convolution smoothing to generate a smoothed power spectral density; Repeat steps b) to d1) until the number of divided intervals no longer changes with iteration; sort all the boundary sets generated by iteration in ascending order to form a boundary set; Construct a hierarchical improved product envelope spectrum Gini coefficient ratio optimization diagram based on the smoothed power spectral density and the boundary set.

7. The fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 6, characterized in that: In step d), the construction of the hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph includes: selecting a predetermined number of boundary sets from the boundary set, jointly forming a hierarchical structure with the initial boundary, and constructing a hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph.

8. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization graph according to claim 1, characterized in that Step e) includes the following steps: Using a band-pass filter for each frequency band interval in the hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph to generate a filtered signal; Based on the frequency-domain signal-to-noise ratio optimization, select the generalized envelope spectrum and construct an improved product envelope spectrum; Calculate the value of the improved product envelope spectrum Gini coefficient ratio for each frequency band interval based on the filtered signal, determine the optimal resonance frequency band, and identify the fault characteristic frequency through the improved product envelope spectrum.

9. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization graph according to claim 8, characterized in that The calculation formula of the frequency-domain signal-to-noise ratio FDSNR based on the product envelope spectrum is as follows: Among them, is the number of harmonics of the fault characteristic frequency FCF, is set to , representing a frequency value; represents the small frequency band composed of the th resonance frequency of the fault characteristic frequency FCF and multiple spectral frequencies on both sides; represents the frequency value in; is the number of spectral frequencies in the interval ; represents different forms of the generalized envelope signal; represents the parameter corresponding to the th generalized envelope spectrum GES for constructing the product envelope spectrum PES; is the generalized envelope based on the simplified Box-Cox transform; represents the fast Fourier transform; is the envelope of the signal .

10. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization graph according to claim 9, characterized in that The value of the improved product envelope spectrum Gini coefficient ratio is calculated by comparing the improved product envelope spectrum Gini coefficients of the fault signal and the healthy signal. By comparing the differences between the two and combining the sequence norm and sorting operation, the optimal resonance frequency band is determined; the definition of the improved product envelope spectrum Gini coefficient ratio IPESGIR is as follows: Among them, represents the improved product envelope spectrum of the signal; represents the length of the product envelope spectrum; represents the sequence arranged in ascending order; represents the sequence of norm; represents the IPESGI of the fault signal; represents the IPESGI of the healthy signal.

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