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

Abstract

The present 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 diagram. The method obtains a vibration signal, calculates the power spectrum density based on an autoregressive model, and uses an improved local maximum and minimum method to perform adaptive spectrum segmentation to generate an optimized spectrum boundary set. A hierarchical improved product envelope spectrum Gini coefficient ratio optimization diagram is then constructed. Fault characteristic frequencies are extracted through improved product envelope spectrum analysis optimized for frequency domain signal-to-noise ratio, and the optimal resonant frequency band is selected based on the Gini coefficient ratio to achieve fault diagnosis. The present invention effectively suppresses complex noise interference through Gaussian kernel smoothing, hierarchical spectrum segmentation, and frequency domain signal-to-noise ratio optimization, significantly improving the accuracy of identifying early fault features. The method is suitable for rolling bearing fault diagnosis under non-stationary working conditions and has high robustness and industrial application value.

Description

Technical Field

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

[0002] Rolling bearings, as key components in rotating machinery, are widely used in industrial equipment, fulfilling the core function of supporting and reducing friction. Because they often operate under harsh conditions such as high speeds and heavy loads, they are susceptible to multiple influences, including axial, radial, and impact loads. These can lead to localized failures, structural fatigue, and even cracks, which in turn affect the safety and reliability of mechanical systems. Therefore, early fault diagnosis of rolling bearings is crucial to preventing major mechanical failures and minimizing economic losses. However, rolling bearing fault signals are often accompanied by complex noise and interference, and exhibit characteristics such as non-stationarity, frequency modulation, and amplitude modulation. This makes it difficult for traditional spectrum analysis methods to effectively extract the fault characteristic frequencies.

[0003] Signal preprocessing is often required using feature enhancement techniques, such as signal decomposition, resonance demodulation, and blind deconvolution. Resonance demodulation is a common method for detecting rolling element bearing faults. It primarily filters the signal within the resonant frequency band using a bandpass filter, and then extracts fault features through envelope demodulation. The selection of the optimal ODFB is crucial in this process. Traditionally, methods such as the fast kurtogram (FK) and the logarithmic envelope spectrum Gini-efficient gram (LESGIRgram) have been used to select the optimal ODFB for the resonant frequency band.

[0004] However, because these methods use fixed frequency bands, they lack adaptive adjustment capabilities and are difficult to handle signal non-stationarity and local characteristics, potentially leading to inaccurate capture of fault-related frequency components. Consequently, adaptive frequency band division methods have been proposed, such as the adaptive harmonic product spectrum (AHPS). This method adaptively determines frequency band boundaries by analyzing local minima in the power spectral density (PSD) curve. Furthermore, the harmonic significance index (HSI) technique is used to lay out the spectrum plane, further enhancing the AHPS's ability to resist noise interference and random pulses.

[0005] After signal preprocessing, envelope analysis is often required to extract fault features. Common envelope analysis methods include envelope spectrum (ES), log-envelope spectrum (LES), and squared envelope spectrum (SES). ES and SES can effectively detect the fault characteristic frequency (FCF) of rolling bearings when interference noise is weak. However, these methods often perform poorly in environments with complex noise contamination. To address this, more effective analysis tools have been proposed, such as the improved envelope spectrum (IES). This method optimizes the diagnostic feature (DF) to select the optimal integration frequency band, effectively extracting fault features masked by strong signals and is suitable for fault diagnosis under non-stationary conditions. Furthermore, the generalized envelope spectrum (GES) analysis tool has been constructed using a simplified Box-Cox transform. Combining the advantages of different GES methods, the product envelope spectrum (PES) has been proposed. The construction of PES requires the selection of multiple GESs with different parameters. The choice of parameters has a significant impact on the final performance. Over-reliance on manual operations 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 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. To this end, the present invention provides a fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram.

[0008] A fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram, comprising the following steps:

[0009] a) Acquire vibration signals;

[0010] b) Analyze the vibration signal based on the autoregressive model, generate the power spectrum density, and determine the local maximum value set of the power spectrum density;

[0011] c) adaptively dividing the spectrum according to the local maximum value set to generate an optimized frequency band boundary set;

[0012] d) constructing a hierarchically improved product envelope spectrum Gini coefficient ratio optimization graph based on the boundary set;

[0013] e) obtaining the divided frequency bands in the hierarchically improved product envelope spectrum Gini coefficient ratio optimization diagram; determining the optimal resonant frequency band by an improved product envelope spectrum analysis method, and identifying the fault characteristic frequency.

[0014] Furthermore, step a) includes collecting vibration signal data and setting the modal number according to the signal characteristics;

[0015] The vibration signal includes a fault signal and a healthy signal.

[0016] Furthermore, step b) comprises the following steps:

[0017] Establish an autoregressive model and solve the model parameters based on the autocorrelation function and Yule-Walker equation;

[0018] The Akaike Information Criterion was used to determine the optimal order of the autoregressive model;

[0019] The power spectrum density is calculated based on the autoregressive model of the optimal order, and a set of local maximum values ​​of the power spectrum density is extracted.

[0020] Furthermore, step c) includes the following steps:

[0021] Set the minimum distance between adjacent local maxima and filter the local maximum set, which is determined based on the fault signal length and control parameters;

[0022] Determine the initial boundary based on the filtered local maximum value set;

[0023] The final set of band boundaries is generated through iterative optimization based on the variance calculation of the band energies.

[0024] Furthermore, the iterative optimization step includes:

[0025] Discard the boundaries in the initial boundary set one by one, and define the upper and lower limits of the boundary set to generate a new boundary set;

[0026] Divide the spectrum based on the new boundary set and calculate the energy variance of each interval;

[0027] The boundary position is iteratively adjusted until the energy variance is minimized, the spectrum segmentation boundary is determined, and the final boundary set is generated.

[0028] Furthermore, step d) comprises the following steps:

[0029] d1) Applying a Gaussian kernel function to the power spectrum density for convolution smoothing to generate a smoothed power spectrum density;

[0030] Repeat steps b) to d1) until the number of partition intervals no longer changes with iteration; sort all boundary sets generated by the iteration in ascending order to form a boundary set;

[0031] Based on the smoothed power spectral density and boundary set, a hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph is constructed.

[0032] Furthermore, in step d), constructing the hierarchical improved product envelope spectrum Gini coefficient ratio optimization map includes: selecting a predetermined number of boundary sets from the boundary set, forming a hierarchical structure together with the initial boundary, and constructing the hierarchical improved product envelope spectrum Gini coefficient ratio optimization map.

[0033] Furthermore, step e) comprises the following steps:

[0034] Applying a bandpass filter to each frequency band interval in the hierarchically improved product envelope spectrum Gini coefficient ratio optimization map to generate a filtered signal;

[0035] Based on the frequency domain signal-to-noise ratio optimization, the generalized envelope spectrum is selected to construct an improved product envelope spectrum;

[0036] The value of the improved product envelope spectrum Gini coefficient ratio of each frequency band interval is calculated based on the filtered signal, the optimal resonance frequency band is determined, and the fault characteristic frequency is identified through the improved product envelope spectrum.

[0037] Furthermore, the calculation formula of the frequency domain signal-to-noise ratio FDSNR based on the product envelope spectrum is as follows:

[0038]

[0039]

[0040]

[0041]

[0042] in, is the number of harmonics of the fault characteristic frequency FCF, is set to , Represents the frequency value; The first A small frequency band consisting of the sub-resonant frequency and multiple spectrum frequencies on both sides; express Frequency value in ; is in the interval the number of mid-spectral frequencies; Represent different forms of generalized envelope signals; Indicates the construction of the product envelope spectrum PES The parameters corresponding to the generalized envelope spectrum GES ; is a generalized envelope based on the simplified Box-Cox transformation; represents fast Fourier transform; For signal envelope.

[0043] Furthermore, 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 difference between the two, combined with the sequence norm and sorting operation, the optimal resonant frequency band is determined; the value of the improved product envelope spectrum Gini coefficient ratio IPESGIR is defined as follows:

[0044]

[0045]

[0046] in, A modified product envelope spectrum representing a signal; Indicates the length of the product envelope spectrum; Representation sequence Sort in ascending order; Representation sequence of norm; IPESGI indicating a fault signal; IPESGI representing the health signal.

[0047] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0048] 1. Improved 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 ability to identify fault characteristic frequencies is effectively enhanced, overcoming the limitation of the traditional envelope spectrum method in poor feature extraction in strong noise environments.

[0049] 2. Enhanced anti-noise interference capability: Gaussian kernel function is used to smooth the power spectrum density, and the improved local maximum and minimum method is combined to achieve adaptive spectrum segmentation, which significantly reduces the interference of complex noise and random pulses on signal analysis, making it suitable for fault diagnosis under non-stationary working conditions.

[0050] 3. Optimized the accuracy of spectrum segmentation: By iteratively optimizing the spectrum boundary set and minimizing the energy variance, the problems of over-decomposition and boundary concentration in the traditional local maximum and minimum methods are solved. The generated spectrum boundary distribution is more uniform, and the fault-related frequencies are captured more accurately.

[0051] 4. Achieved flexibility in multi-scale analysis: By constructing a hierarchical improved product envelope spectral Gini coefficient ratio optimization graph (IPESGIRgram), a multi-scale frequency band analysis framework is provided, which enhances the adaptability of the method to different fault characteristics and improves the robustness of diagnosis.

[0052] 5. Improved early fault diagnosis capabilities: Using the improved product envelope spectrum Gini coefficient ratio (IPESGIR) as the optimal resonant frequency band selection indicator, by analyzing the unevenness of feature distribution, clearly distinguishing between faults and healthy states, significantly improving the detection accuracy of early rolling bearing faults.

[0053] 6. It has extensive industrial application value: This method shows good stability and reliability under complex working conditions. It is suitable for rotating machinery fault diagnosis in aviation, railways, wind power and other fields. It can effectively prevent major mechanical failures and reduce economic losses.

[0054] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0056] Figure 1 Flowchart of the fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram of the present invention;

[0057] Figure 2 is the time domain diagram of the inner circle signal;

[0058] Figure 3 is the spectrum of the inner race fault signal;

[0059] Figure 4 is the AIC value of the inner ring fault signal;

[0060] Figure 5 is the PSD and spectrum of the inner race fault signal;

[0061] Figure 6 is the spectrum segmentation result of traditional Locmaxmin;

[0062] Figure 7 The spectrum segmentation result of the improved Locmaxmin;

[0063] Figure 8 is the FDSNR value of different generalized envelope spectra of the inner race fault signal;

[0064] Figure 9 IPES for inner race fault signal;

[0065] Figure 10 The segmentation graph and spectrum generated by the FDMKgram analysis method for the inner race fault signal;

[0066] Figure 11 Segmentation graph and spectrum generated by ACCUgram analysis method for inner race fault signal;

[0067] Figure 12 The segmentation map and spectrum generated by the IESCFFOgram analysis method for the inner race fault signal;

[0068] Figure 13 The segmentation map and spectrum generated by the IPESGIRgram analysis method for the inner race fault signal. DETAILED DESCRIPTION

[0069] To make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0070] The English abbreviations used in this invention are defined as follows:

[0071] PSD: power spectral density;

[0072] ODFB: optimal resonance frequency band;

[0073] FDSNR: frequency domain signal-to-noise ratio;

[0074] FCF: fault characteristic frequency;

[0075] GES: generalized envelope spectrum;

[0076] PES: Product Envelope Spectrum;

[0077] IPES: Improved Product Envelope Spectrum;

[0078] IPESGI: Improved Product Envelope Spectral Gini Index;

[0079] IPESGIR: Improved Product Envelope Spectral Gini Ratio;

[0080] IPESGIRgram: Improved Product Envelope Spectral Gini Ratio Optimization Graph.

[0081] In response to the current problems in bearing fault diagnosis, this paper introduces the frequency domain signal-to-noise ratio to improve PES, proposes an IPES analysis method, and creates an adaptive spectrum segmentation method based on autoregressive power spectral density and an improved Locmaxmin method to solve the problems of over-decomposition and boundary concentration in the traditional Locmaxmin method. The IPESGIRgram method is used in early fault diagnosis to effectively suppress noise interference and significantly improve signal identification accuracy.

[0082] The following combination Figure 1 The process shown in FIG. 1 is used to describe in detail the fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram of the present invention. The specific steps include:

[0083] Step 1: Get the rolling bearing signal and set the modal number , ;

[0084] S is a calculation parameter used for iterative assignment in subsequent calculations.

[0085] This example uses the bearing test data published by CWRU, Case Western Reserve University, USA, as an example. The fault diameter is 0.1778mm, the motor speed is 1797rpm, and the load is 0HP. The sampling frequency of the signal is 12kHz and the duration is 1 second. The theoretical FCF of the selected inner race fault signal is 162.19Hz, and the rotation frequency is 0.1778mm. is 29.95Hz. The result is as follows Figure 2 、 Figure 3 As shown, Figure 2 Represents the healthy signal and fault signal of the inner circle time domain, Figure 3 The spectrum of the inner race fault signal.

[0086] Step 2: Calculate the power spectral density (PSD) using the AR model and obtain the set of local maximum values ​​of the PSD.

[0087] Step 2.1: Given a The difference equation of the AR model is as follows:

[0088]

[0089] in, is the random signal for which the model is solved, are model parameters, and ; is zero in mean and has a variance of The model can be viewed as the output response of a system driven by white noise input.

[0090] For the above AR model, its autocorrelation function Satisfies the following relationship:

[0091]

[0092] in yes The autocorrelation function of represents the lag order, That is the model parameters.

[0093] Step 2.2: Construct the Yule-Walker equation based on the autocorrelation function to solve the model parameters , the set of equations to be solved is as follows:

[0094]

[0095] By solving this set of equations, the parameters of the AR model can be obtained , and then determine the random signal All autocorrelation function values ​​of .

[0096] Step 2.3: Calculate the PSD of the AR model. PSD describes the distribution of the signal in the frequency domain and helps to analyze the spectral characteristics of the signal. Figure 5 As shown in Figure 2, combining the PSD with the spectrum shows that the PSD and spectrum trends are basically consistent, and the PSD can effectively capture the changing trend of the spectrum amplitude while reducing the impact of noise and other interference factors. The optimal single-step linear predictor of the AR model aims to minimize the prediction error. The process is as follows:

[0097] Step 2.3.1: Derive the power spectrum formula. In the single-step predictor at a point, the predicted value of the signal is:

[0098]

[0099] The prediction error is defined as:

[0100]

[0101] in, ; It is the signal value that is predicted based on current and past values. Represents the value before the current value The observation value of times, Order prediction error filter system function It can be expressed as:

[0102]

[0103] in for The autocorrelation function of are the prediction error filter coefficients, is the minimum prediction error mean square value. Let , , then there is a relationship:

[0104]

[0105] but of The results of the PSD of the first-order AR model are:

[0106]

[0107] in Represents the frequency value.

[0108] Step 2.3.2: Use the AIC criterion and select the order that minimizes AIC , which is defined as follows:

[0109]

[0110] in is the sample size; is the mean square error of the residual; is the order of the AR model.

[0111] when Repeat steps 2.1-2.3.1 and select the order that minimizes AIC , indicating that this order is the optimal order of the AR model. The PSD of the AR model is obtained through the optimal order, and the set of local maximum values ​​of PSD is obtained.

[0112] Through the above operations, we can get the AIC values ​​of different orders and plot them, such as Figure 4 As shown, it can be concluded from the figure:

[0113] When the order When it reaches 148, AIC is at its minimum value, and as the order increases, the change of AIC value gradually tends to be flat, which indicates that this order is the optimal order of AR model. The order of solving PSD is also determined from this. It is 148.

[0114] Step 3: The distance between adjacent extreme values ​​must not be less than L, and a new maximum value set is obtained;

[0115] In order to reduce the number of local maxima in the spectrum, set the minimum peak distance , defined as:

[0116]

[0117] in is the control parameter, is the length of the fault signal.

[0118] when When the value is too large, the local maximum in the PSD will be excessively reduced, resulting in under-resolved spectrum. If the value is too small, there will be too many local maxima, which will lead to over-decomposition of the spectrum. .

[0119] Step 4: Get the boundary set;

[0120] Step 4.1: Find the minimum value between two adjacent maxima as the boundary and obtain the initial boundary set ,set up .

[0121] Step 4.2: Discard the initial boundary set in , and define , , and obtain a new boundary set .

[0122] Step 5: Iteratively optimize the boundary set and use energy variance calculation to confirm the final boundary set;

[0123] 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 .make .

[0124] Step 5.2: Repeat steps 4.2-5.1 until . Get the energy variance set , the minimum energy variance corresponds to This is the final boundary set. In each iteration, the boundary positions are adjusted based on the energy differences between the frequency bands, thereby optimizing the spectrum partitioning. The final boundary set is then determined by solving the minimum energy variance, avoiding over-decomposition or inaccurate segmentation.

[0125] The above steps 3-5 use the improved Locmaxmin method to perform spectrum segmentation on the fault signal. Figure 6 and Figure 7By comparison, it can be seen that Figure 6 It can be seen that most of the boundaries are concentrated in The frequency band interval results in the frequency band being too concentrated, which may cause the problem of over-decomposition. In contrast, Figure 7 The boundary distribution in the model is relatively uniform, avoiding the phenomenon of over-decomposition and under-decomposition.

[0126] Step 6: Construct hierarchical IPESGIRgram;

[0127] if , then the PSD is convolved with the Gaussian kernel function, that is, the PSD curve is smoothed by using the Gaussian kernel function, and Repeat all the steps 2-5 above until the number of partition intervals no longer changes with iterations; otherwise, sort all the boundary sets generated by the iteration in ascending order to form a boundary set, and select the first boundary set. boundary set, and the initial boundary Build together Layer IPESGIRgram. The Gaussian kernel function is defined as follows:

[0128]

[0129]

[0130] in is the size of the Gaussian kernel; is the standard deviation of the Gaussian kernel; For PSDs with different smoothness, is the initial estimated PSD; Represents the convolution operation.

[0131] Step 7: Use IPES analysis method to analyze ODFB and identify FCF.

[0132] Step 7.1: Use a bandpass filter to filter each frequency band interval to obtain a filtered signal.

[0133] Step 7.2: Improve the product envelope spectrum (IPES) to improve the accuracy of fault feature identification. The interpretation of IPES in this process is as follows:

[0134] Since the product envelope spectrum (PES) is constructed by multiplying multiple generalized envelope spectra (GES), the accuracy of the analysis results decreases in traditional methods due to the fixed related parameters. Therefore, the FDSNR evaluation index is introduced to optimize the selection of GES. By selecting GESs that meet the requirements to construct the PES, the errors introduced by human operation can be effectively reduced and the identification accuracy of fault characteristics can be improved. This is the improved product envelope spectrum (IPES). The FDSNR based on the PES is defined as follows:

[0135]

[0136]

[0137]

[0138]

[0139] in, is the number of harmonics in the FCF, is set to , which ensures that the FCF and its two resonant frequencies are considered; Represents the frequency value; Indicates the first A small frequency band consisting of the sub-resonant frequency and three spectrum frequencies on both sides; express Frequency value in ; is in the interval the number of mid-spectral frequencies; Represent different forms of generalized envelope signals; Indicates the construction of PES Parameters corresponding to GES ; is a generalized envelope based on the simplified Box-Cox transformation; Represents fast Fourier transform (FFT); For signal envelope.

[0140] The above operation is as follows Figure 8 As shown in the figure, The value ranges from 1 to 5. Every 0.1 FDSNR value, the corresponding first 4 maximum GESs are selected to construct IPES, such as Figure 9 As shown, the FCF and its resonant frequency can be clearly observed.

[0141] Step 7.3: Calculate the IPESGIR value for each interval and determine the ODFB. In this step, the IPESGIR value is defined as follows:

[0142]

[0143]

[0144] in, A modified product envelope spectrum representing a signal; Indicates the length of the PES product envelope spectrum; Representation sequence Sort in ascending order; Representation sequence of norm; IPESGI indicating bearing fault signal; IPESGI, which represents the bearing health signal. The IPESGIR indicator shows strong advantages in fault diagnosis by combining IPES and GI.

[0145] First, it can effectively identify changes in the state of mechanical equipment, especially in the early stages of a fault. By analyzing the unevenness of feature distribution, it can clearly distinguish between faulty and healthy states. Second, IPESGI demonstrates good robustness when dealing with noise interference and can operate stably in complex operating environments. Furthermore, IPESGI is highly adaptable and can provide accurate fault diagnosis results under different fault modes and operating conditions, thereby improving diagnostic accuracy and reliability.

[0146] Figure 10 - Figure 13 The processing results of four methods are shown. Figure 10 For FDMKgram and SES, Figure 11 For ACCUgram and SES, Figure 12 For IESCFFOgram and IES, Figure 13 For IPESGIRgram and IPES; first, FDMKgram and ACCUgram methods were selected The same frequency band is demodulated and analyzed. From SES, it can be observed that both methods successfully identify the FCF and its three resonant frequencies. However, there are still a few interference frequencies that cannot be effectively suppressed. Secondly, the IESCFFOgram method selects The demodulation analysis of the frequency band was performed. Although the FCF and its three resonant frequencies were successfully identified in IES, the prominence of these frequencies was poorer than that of the previous two methods, and the identification effect was relatively limited. The FCF and its three resonant frequencies are clearly presented in IPES, and the identification of these frequencies is more prominent than the previous three methods, showing a significant enhancement effect.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A fault diagnosis method based on an improved product envelope spectrum Gini coefficient ratio optimization diagram, characterized in that the steps include: a) Acquire vibration signals; b) Analyze the vibration signal based on the autoregressive model, generate the power spectrum density, and determine the local maximum value set of the power spectrum density; c) adaptively dividing the spectrum according to the local maximum value set to generate an optimized frequency band boundary set; d) constructing a hierarchically improved product envelope spectrum Gini coefficient ratio optimization graph based on the boundary set; Step d) comprises the following steps: d1) Applying a Gaussian kernel function to the power spectrum density for convolution smoothing to generate a smoothed power spectrum density; Repeat steps b) to d1) until the number of partition intervals no longer changes with iteration; sort all boundary sets generated by the iteration in ascending order to form a boundary set; Based on the smoothed power spectrum density and boundary set, a hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph is constructed; 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, forming a hierarchical structure together with the initial boundary, and constructing the hierarchical improved product envelope spectrum Gini coefficient ratio optimization graph; e) obtaining the divided frequency bands in the hierarchically improved product envelope spectrum Gini coefficient ratio optimization diagram; determining the optimal resonant frequency band by an improved product envelope spectrum analysis method, and identifying the fault characteristic frequency; Step e) comprises the following steps: Applying a bandpass filter to each frequency band interval in the hierarchically improved product envelope spectrum Gini coefficient ratio optimization map to generate a filtered signal; Based on the frequency domain signal-to-noise ratio optimization, the generalized envelope spectrum is selected to construct an improved product envelope spectrum; The value of the improved product envelope spectrum Gini coefficient ratio of each frequency band interval is calculated based on the filtered signal to determine the optimal resonant frequency band, and the fault characteristic frequency is identified by the improved product envelope spectrum; 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, and the optimal resonant frequency band is determined by comparing the difference between the two, combining the sequence norm and the sorting operation; the value of the improved product envelope spectrum Gini coefficient ratio IPESGIR is defined as follows: in, A modified product envelope spectrum representing a signal; Indicates the length of the product envelope spectrum; Representation sequence Sort in ascending order; Representation sequence of norm; IPESGI indicating a fault signal; IPESGI representing the health signal.

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

3. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1 is characterized in that: Step b) comprises the following steps: Establish an autoregressive model and solve the model parameters based on the autocorrelation function and Yule-Walker equation; The Akaike Information Criterion was used to determine the optimal order of the autoregressive model; The power spectrum density is calculated based on the autoregressive model of the optimal order, and a set of local maximum values ​​of the power spectrum density is extracted.

4. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1 is characterized in that: Step c) comprises the following steps: Set the minimum distance between adjacent local maxima and filter the local maximum set, which is determined based on the fault signal length and control parameters; Determine the initial boundary based on the filtered local maximum value set; The final set of band boundaries is generated through iterative optimization based on the variance calculation of the band energies.

5. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 4 is characterized in that: The steps of iterative optimization include: Discard the boundaries in the initial boundary set one by one, and define the upper and lower limits of the boundary set to generate a new boundary set; Divide the spectrum based on the new boundary set and calculate the energy variance of each interval; The boundary position is iteratively adjusted until the energy variance is minimized, the spectrum segmentation boundary is determined, and the final boundary set is generated.

6. The fault diagnosis method based on the improved product envelope spectrum Gini coefficient ratio optimization diagram according to claim 1 is characterized in that: The calculation formula of the frequency domain signal-to-noise ratio FDSNR based on the product envelope spectrum is as follows: in, is the number of harmonics of the fault characteristic frequency FCF, is set to , Represents the frequency value; The first A small frequency band consisting of the sub-resonant frequency and multiple spectrum frequencies on both sides; express Frequency value in ; is in the interval the number of mid-spectral frequencies; Represent different forms of generalized envelope signals; Indicates the construction of the product envelope spectrum PES The parameters corresponding to the generalized envelope spectrum GES ; is a generalized envelope based on the simplified Box-Cox transformation; represents fast Fourier transform; For signal envelope.

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