Variable-speed bearing fault diagnosis method based on Pareto frontier

Abstract

The invention relates to the technical field of fault diagnosis, and discloses a variable speed bearing fault diagnosis method based on Pareto leading edge, and the method comprises the steps: obtaining a basic data set, carrying out the improved calculation order analysis based on segmented cubic Hermite interpolation on the basic data set, and obtaining an angular domain vibration signal; for a domain vibration signal, creating an initial population by using a chaotic mapping initialization method; performing variational mode decomposition based on the angular domain vibration signal, the sampling frequency and the initial population, calculating an envelope spectrum peak factor and an average envelope spectrum kurtosis of each IMF component, and selecting the IMF component corresponding to the weighted highest value as an optimal mode to establish a target function; performing iterative optimization on the target function by using a multi-target grey wolf algorithm to determine an optimal variational mode decomposition parameter; and for the angular domain vibration signal, variational mode decomposition is carried out based on the corresponding optimal variational mode decomposition parameter to obtain an optimal mode, so that iterative training is carried out on the variable-speed bearing fault diagnosis model.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of fault diagnosis, and in particular to a variable speed bearing fault diagnosis method based on Pareto front. Background Art

[0002] Rolling bearings are crucial components in the mechanical field, widely used in rotating machinery such as aircraft, wind turbines, and automobiles. Variable-speed rolling bearings (such as ball bearings and cylindrical roller bearings) must adapt to large or rapid changes in speed during operation. They are commonly used in equipment such as wind turbines, automotive transmissions, and aircraft engines. During operation, rolling bearings often suffer from pitting, wear, adhesion, and deformation, which can lead to safety accidents. Therefore, developing effective bearing fault diagnosis methods is crucial.

[0003] When diagnosing faults in variable-speed bearings, the signal characteristics are time-varying due to the changing bearing speed. These fault characteristics are easily lost in the signal, making them difficult to accurately extract. This significantly reduces the accuracy of fault diagnosis. Researchers have discovered that computational order analysis can eliminate the influence of speed, and performing variational modal decomposition on the signal processed by computational order analysis can yield the optimal mode for characterizing the fault characteristics.

[0004] Computational order analysis is an order tracking method that uses a data interpolation algorithm and an external speed sensor to reconstruct the rotational speed signal in the angle domain. Its basic principle and process are as follows: First, the original vibration, rotational speed, and other signals are sampled simultaneously at equal sampling frequencies using multiple sensors or multiple channels. The angle domain resampling time points are calculated according to a formula. Next, the original signal is interpolated based on the calculated resampling time points to obtain the required equal-angle resampling sequence. Signal processing methods such as the Fast Fourier Transform (FFT) are then used to obtain the order spectrum for further analysis. Classic computational order analysis has low interpolation accuracy and may produce large errors in areas of drastic signal changes. Furthermore, when performing FFT analysis on the resampled signal, the interpolation algorithm may introduce spectral leakage.

[0005] Variational Mode Decomposition (VMD) decomposes the input signal into multiple intrinsic mode functions (IMFs) with different center frequencies and limited bandwidths. In variable-speed bearing fault diagnosis, adaptive decomposition of complex vibration signals can be achieved by constructing a variational model and iteratively optimizing the parameters of each modal component. In previous studies, the number of modal decompositions and the penalty factor were typically optimized as variables in the optimization of VMD, with one of the parameters, such as the envelope spectrum peak factor, the average envelope spectrum kurtosis, and the full modal correlation coefficient, being selected as a single optimization objective. However, a single optimization metric cannot fully reveal the characteristics of the fault, which makes some fault characteristics hidden in other modes and difficult to fully characterize.

[0006] In summary, the classic variable speed bearing fault diagnosis method has technical problems such as difficulty in fault feature extraction and low fault diagnosis accuracy. This is because the classic computational order analysis is not accurate enough and the single-objective optimization variational modal decomposition is not capable of extracting fault features. Summary of the Invention

[0007] In order to solve the above technical problems, the embodiment of the present application proposes a variable speed bearing fault diagnosis method based on the Pareto front, introduces a more accurate piecewise cubic Hermite interpolation method to improve the calculation order analysis, and expands the single optimization objective in the variational modal decomposition to multiple objectives, so that the obtained optimal modal decomposition number can maximize the characterization of the fault characteristics, thereby effectively improving the accuracy and efficiency of variable speed bearing fault diagnosis.

[0008] In order to achieve the above-mentioned purpose, an embodiment of the present application proposes a variable speed bearing fault diagnosis method based on Pareto front, and the method includes the following steps: obtaining a basic data set containing n types of faults and each fault has m groups of data, each group of data includes time domain vibration signals and speed signals with the same sampling frequency and sampling time, performing improved computational order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals; for the i-th group of angular domain vibration signals, determining the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor, setting the built-in parameters of the multi-objective grey wolf algorithm to the default values, determining the objective function, population size, number of iterations and number of archives, and creating an initial population using a chaotic mapping initialization method; performing variational modal decomposition based on the i-th group of angular domain vibration signals, sampling frequency and initial population to obtain several IMF components, calculating the envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component, and selecting The IMF component corresponding to the weighted highest value is taken as the optimal mode, and the objective function is established based on the envelope spectrum peak factor and the average envelope spectrum kurtosis; the objective function is iteratively optimized using the multi-objective grey wolf algorithm, and after completing M iterations, the Pareto front of the variational modal decomposition parameters of a single signal is obtained, the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference, and the set of variational modal decomposition parameters with the smallest reference is selected as the optimal variational modal decomposition parameters; for n×m groups of angular domain vibration signals, variational modal decomposition is performed based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, the optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set according to a preset ratio, so as to iteratively train the pre-constructed variable speed bearing fault diagnosis model to obtain a trained variable speed bearing fault diagnosis model, thereby realizing variable speed bearing fault diagnosis.

[0009] In order to achieve the above-mentioned purpose, the embodiment of the present application also proposes a variable speed bearing fault diagnosis system based on the Pareto front, including: an improved computational order analysis module for obtaining a basic data set containing n types of faults and each type of fault has m groups of data, each group of data includes a time domain vibration signal and a speed signal with the same sampling frequency and sampling time, and performing an improved computational order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals, where n and m are both integers greater than 1; an initial population creation module for determining the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor for the i-th group of angular domain vibration signals, setting the built-in parameters of the multi-objective grey wolf algorithm to the default values, determining the objective function, the number of populations, the number of iterations and the number of archives, and creating the initial population using the chaotic mapping initialization method; an objective function establishment module for performing variational modal decomposition based on the i-th group of angular domain vibration signals, the sampling frequency and the initial population to obtain several IMF components, and calculating the envelope spectrum peak factor and average of each IMF component respectively. Envelope spectrum kurtosis, select the IMF component corresponding to the weighted highest value as the optimal mode, and establish the objective function based on the envelope spectrum peak factor and the average envelope spectrum kurtosis; the iterative optimization module is used to iteratively optimize the objective function using the multi-objective grey wolf algorithm. After completing M iterations, the Pareto front of the variational modal decomposition parameters of a single signal is obtained, and the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, and the set of variational modal decomposition parameters with the smallest reference quantity is selected as the optimal variational modal decomposition parameter; the variable speed bearing fault diagnosis model training module is used to perform variational modal decomposition based on the corresponding optimal variational modal decomposition parameters for n×m groups of angular domain vibration signals to obtain the optimal mode, use the optimal mode as the signal feature, and divide the signal feature and the corresponding label into a training set and a test set according to a preset ratio to iteratively train the pre-constructed variable speed bearing fault diagnosis model to obtain a trained variable speed bearing fault diagnosis model, thereby realizing variable speed bearing fault diagnosis.

[0010] In order to achieve the above-mentioned purpose, an embodiment of the present application also proposes an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a variable speed bearing fault diagnosis method based on Pareto front as described above.

[0011] In order to achieve the above objectives, an embodiment of the present application further proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the variable speed bearing fault diagnosis method based on Pareto front as described above.

[0012] This application proposes a variable speed bearing fault diagnosis method based on the Pareto front. Considering that the linear interpolation accuracy used in the classic computational order analysis algorithm is low and the smoothness of the fitting curve is insufficient, which leads to poor results, the computational order analysis is improved and a piecewise cubic Hermite interpolation method is introduced to effectively improve the interpolation accuracy, thereby improving the accuracy of variable speed bearing fault diagnosis. At the same time, the previous single-objective optimization variational modal decomposition modal decomposition modal decomposition number and penalty factor, the optimal mode obtained cannot well represent the fault information. Therefore, a multi-objective grey wolf variational modal decomposition method is introduced, and the envelope spectrum peak factor and average envelope spectrum kurtosis of the optimal mode are used as two optimization objectives. The obtained Pareto front will simultaneously meet the two optimization objectives, and then the parameter set corresponding to the Pareto front is re-introduced into the variational modal decomposition, the correlation coefficient of all modes is calculated, and the parameter group with the smallest correlation coefficient is used as the final selected parameter group. Such a signal reconstruction method enables the obtained optimal modal decomposition number to maximize the characterization of the fault characteristics, thereby effectively improving the accuracy and efficiency of variable speed bearing fault diagnosis.

[0013] In some optional embodiments, assuming that the sampling frequency is s, the sampling time is f, the time domain vibration signal is S, and the speed signal is V, an improved computational order analysis based on piecewise cubic Hermite interpolation is performed on all time domain vibration signals to obtain n×m groups of angular domain vibration signals, which is achieved by the following formula:

[0014] s_theta=pchip(theta_t,s,theta);

[0015] Where s represents the signal value of the time domain vibration signal S, theta_t represents the original angle coordinate, theta represents the target angle coordinate, pchip(·) represents the piecewise cubic Hermite interpolation, and s_theta represents the signal value after interpolation, which corresponds to the angular domain vibration signal S * .

[0016] In some optional embodiments, the lower bound of the modal decomposition number is determined to be 5, the upper bound is determined to be 10, the lower bound of the penalty factor is determined to be 500, the upper bound is determined to be 2000, the population size N is determined to be 30, the number of iterations M is determined to be 50, and the number of archives A is determined to be 50;

[0017] The initial population is created using the chaotic map initialization method, which is achieved through the following formula:

[0018] mu=4;

[0019] x i =rand(1,nVar);

[0020] x i(r+1) =mu×x ir ×(1-x ir );

[0021] r=1,2,…,R;

[0022] GreyWolves(i),Position(1,j)=lb(j)+[ub(j)-lb(j)]×x(j);

[0023] Among them, mu is the parameter of the Logistic mapping, mu = 4 means the system is in a chaotic state, nVar = 2, which represents the number of independent variables, i.e. the modal decomposition number and penalty factor, x i represents the chaotic variable of the i-th individual. After the chaotic variable is iterated R times, the system enters a chaotic state. ir represents the chaotic variable of the i-th individual in the r-th iteration, GreyWolves(i),Position(1,j) represents the position of the i-th individual in the j-th dimension, lb(j) and ub(j) represent the lower bound and upper bound of the position of the j-th dimension, respectively.

[0024] In some optional embodiments, variational mode decomposition is performed based on the i-th group of angular domain vibration signals, the sampling frequency, and the initial population to obtain a plurality of IMF components, and the envelope spectrum peak factor and the average envelope spectrum kurtosis of each IMF component are calculated, including:

[0025] Input the modal decomposition number K corresponding to the initial population, the penalty factor α corresponding to the initial population, and the angular domain vibration signal S * and sampling frequency fs, the modal decomposition number K and penalty factor α are used as optimization variables;

[0026] The modal decomposition number K, penalty factor α, and angular domain vibration signal S * The sampling frequency fs is brought into the classical variational mode decomposition algorithm to perform variational mode decomposition and obtain K IMF components with different center frequencies;

[0027] The Hilbert transform of the k-th IMF component is performed using the following formula to obtain the analytical signal corresponding to the k-th IMF component:

[0028] Hx1(:,k)=hilbert{imf(:,k)-mean[imf(:,k)]};

[0029] Where imf(:,k) represents the k-th IMF component, mean(·) represents the mean, hilbert(·) represents the Hilbert transform, and Hx1(:,k) represents the analytical signal corresponding to the k-th IMF component.

[0030] Calculate the amplitude of Hx1(:,k) and obtain the envelope signal of imf(:,k), which can be expressed as follows:

[0031] f2(:,k)=abs[Hx1(:,k)];

[0032] Where f2(:,k) represents the envelope signal of imf(:,k), and abs(·) represents the absolute value.

[0033] Perform zero mean processing on f2(:,k) and remove the DC component in f2(:,k) to obtain f3(:,k). The f3(:,k) corresponding to the K IMF components form a matrix f3. Perform FFT transformation of length L on f3 to obtain the matrix Y1. Each column in Y1 corresponds to the frequency domain representation of an IMF component. Y1 is expressed by the formula:

[0034] Y1=FFT(f3,L);

[0035] Wherein, FFT(·) indicates FFT transformation;

[0036] Calculate the amplitude of Y1 and perform normalization to obtain the bilateral amplitude spectrum P2. Then extract the first L / 2+1 points of the bilateral amplitude spectrum P2 to obtain the unilateral amplitude spectrum P1.

[0037] Multiply all points except the first and last points in the single-sided amplitude spectrum P1 by 2 to compensate for the discarded second half of the double-sided amplitude spectrum P2, and obtain the envelope spectrum P(:,k) corresponding to the k-th IMF component;

[0038] Based on the envelope spectrum P(:,k), the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component are calculated respectively.

[0039] In some optional embodiments, the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the k-th IMF component are calculated based on the envelope spectrum P(:,k), respectively, and are implemented by the following formula:

[0040] a1(k)={<(max[P(:,k)]-min[P(:,k)])> / rms[P(:,k)]};

[0041] a2(k)=kurtosis[P(:,k)];

[0042] Among them, max(·), min(·), and rms(·) respectively represent the maximum value, minimum value, and root mean square value, and kurtosis(·) represents the kurtosis.

[0043] The IMF component corresponding to the highest weighted value is selected as the best mode, including:

[0044] The envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component are normalized to the maximum and minimum values ​​respectively, and the weighted value a(k) is calculated. The calculation process of the weighted value a(k) is expressed by the formula:

[0045] a(k)=a1′(k)+a2′(k);

[0046] a1′(k)=[a1(k)-a1 min ] / [a1 max -a1(k)];

[0047] a2′(k)=[a2(k)-a2 min ] / [a2 max -a2(k)];

[0048] Among them, a1 min Indicates the minimum value of the envelope spectrum peak factor corresponding to the K IMF components, a1 max represents the maximum value of the envelope spectrum peak factor corresponding to the K IMF components, a2 min represents the minimum value of the average envelope spectrum kurtosis corresponding to the K IMF components, a2 max Indicates the maximum value of the average envelope spectrum kurtosis corresponding to K IMF components;

[0049] The largest corresponding IMF component is selected from the weighted values ​​corresponding to the K IMF components as the optimal mode.

[0050] In some optional embodiments, the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, which is expressed by the formula:

[0051]

[0052] ρ ij =Cov(u i ,u j ) / (σ i σ j );

[0053] i≠j;

[0054] Among them, Cov(u i ,uj ) represents any two modal components u i (t) and u j The covariance between (t), σ i Indicates u i The standard deviation of (t), σ j Indicates u j The standard deviation of (t), ρ ij Indicates u i (t) and u j (t), and δ represents the reference value.

[0055] In some optional embodiments, for n×m groups of angular domain vibration signals, variational modal decomposition is performed based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, the optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set according to a preset ratio, so as to iteratively train the pre-built variable speed bearing fault diagnosis model, including: based on the i-th group of angular domain vibration signals, the sampling frequency, the optimal modal decomposition number K * and the optimal penalty factor α * Perform variational mode decomposition and obtain K * In this paper, the variable speed bearing fault diagnosis model composed of a convolutional neural network and a softmax classifier is iteratively trained. The optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set in a ratio of 8:2. The optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set ... optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set in a ratio of 8:2. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. The optimal mode is used as the signal feature, and the optimal mode is used as the signal feature. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the following is a brief introduction to the drawings required for use in the embodiments of the present application or the description of the related technologies. The following drawings are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. The drawings described here are only used to explain the present application and are not used to limit the present application.

[0057] Figure 1 This is a flow chart of a variable speed bearing fault diagnosis method based on Pareto front provided in one embodiment of the present application;

[0058] Figure 2 This is a detailed flow chart of a variable speed bearing fault diagnosis method based on Pareto front provided in one embodiment of the present application;

[0059] Figure 3is a structural diagram of a variable speed bearing fault diagnosis system based on Pareto front provided in another embodiment of the present application;

[0060] Figure 4 This is a structural diagram of an electronic device provided by another embodiment of the present application. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will appreciate that in the embodiments of the present application, many technical details are provided to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is only for the convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined with each other and referenced to each other under the premise of no contradiction.

[0062] One embodiment of the present application proposes a Pareto front-based variable speed bearing fault diagnosis method, which is applied to an electronic device, where the electronic device can be a terminal or a server. In this embodiment and the following embodiments, the electronic device is described using a server as an example. The following describes the implementation details of the Pareto front-based variable speed bearing fault diagnosis method proposed in this embodiment. The following content is merely provided for ease of understanding and is not required for the implementation of this solution.

[0063] The specific process of the variable speed bearing fault diagnosis method based on Pareto front proposed in this embodiment can be as follows: Figure 1 As shown, the detailed flow chart can be as follows Figure 2 As shown, the method includes:

[0064] Step 11: Obtain a basic data set containing n types of faults, each of which has m groups of data. Each group of data includes time-domain vibration signals and speed signals with the same sampling frequency and sampling time. Perform an improved computational order analysis based on piecewise cubic Hermite interpolation on all time-domain vibration signals to obtain n×m groups of angular-domain vibration signals.

[0065] In the specific implementation, the first thing that needs to be performed is the improved computational order analysis in variable speed bearing fault diagnosis. The server obtains a basic data set containing n types of faults and m groups of data for each fault. There are n×m groups of data in the basic data set. Each group of data includes time domain vibration signals and speed signals with the same sampling frequency and sampling time. The server needs to perform an improved computational order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals.

[0066] In one example,

[0067] Assume that the sampling frequency is fs, the sampling time is t, the time domain vibration signal is S, and the speed signal is V. Perform an improved computational order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals. This can be achieved using the following formula:

[0068] s_theta=pchip(theta_t,s,theta);

[0069] Where s represents the signal value of the time domain vibration signal S, theta_t represents the original angle coordinate, theta represents the target angle coordinate, pchip(·) represents the piecewise cubic Hermite interpolation, and s_theta represents the signal value after interpolation, which corresponds to the angular domain vibration signal S * .

[0070] Step 12: For the i-th group of angular domain vibration signals, determine the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor, set the built-in parameters of the multi-objective grey wolf algorithm to the default values, determine the objective function, population size, number of iterations, and number of archives, and create the initial population using the chaotic map initialization method.

[0071] In the specific implementation, after the server completes the conversion of the angular domain vibration signal, it can start applying the multi-objective gray wolf algorithm for variational modal decomposition. For the i-th group of angular domain vibration signals, the server needs to determine the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor, set the built-in parameters of the multi-objective gray wolf algorithm to the default values, determine the objective function, population size, number of iterations and number of archives, and use the chaotic map initialization method to create the initial population.

[0072] In one example, the server determines that the lower bound of the modal decomposition number is 5 and the upper bound is 10, the lower bound of the penalty factor is 500 and the upper bound is 2000, the population size N is set to 30, the number of iterations M is set to 50, and the number of archives A is set to 50.

[0073] In one example, the server uses a chaotic map initialization method to create an initial population, which can be achieved by the following formula:

[0074] mu=4;

[0075] x i =rand(1,nVar);

[0076] x i(r+1) =mu×x ir ×(1-x ir );

[0077] r=1,2,…,R;

[0078] GreyWolves(i),Position(1,j)=lb(j)+[ub(j)-lb(j)]×x(j);

[0079] Among them, mu is the parameter of the Logistic mapping, mu = 4 means the system is in a chaotic state, nVar = 2, which represents the number of independent variables, i.e. the modal decomposition number and penalty factor, x i represents the chaotic variable of the i-th individual. After the chaotic variable is iterated R times, the system enters a chaotic state. ir represents the chaotic variable of the i-th individual in the r-th iteration, GreyWolves(i),Position(1,j) represents the position of the i-th individual in the j-th dimension, lb(j) and ub(j) represent the lower bound and upper bound of the position of the j-th dimension, respectively.

[0080] Step 13: Perform variational modal decomposition based on the i-th group of angular domain vibration signals, sampling frequency, and initial population to obtain several IMF components. Calculate the envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component, select the IMF component corresponding to the weighted highest value as the optimal mode, and establish an objective function based on the envelope spectrum peak factor and average envelope spectrum kurtosis.

[0081] In the specific implementation, after completing the creation of the initial population, the server will start the position update, selection and archiving of the multi-objective gray wolf algorithm. Compared with the traditional single-objective gray wolf algorithm, only the objective function is changed. The server performs variational modal decomposition based on the i-th group of angular domain vibration signals, sampling frequency and initial population to obtain several IMF components, calculates the envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component, selects the IMF component corresponding to the weighted highest value as the optimal mode, and establishes the objective function based on the envelope spectrum peak factor and average envelope spectrum kurtosis.

[0082] In an example, the modal decomposition number K corresponding to the initial population, the penalty factor α corresponding to the initial population, and the angular domain vibration signal S are input. * and sampling frequency fs, and takes the modal decomposition number K and penalty factor α as optimization independent variables. The server takes the modal decomposition number K, penalty factor α, angular domain vibration signal S * The sampling frequency fs is brought into the classical variational mode decomposition algorithm to perform variational mode decomposition and obtain K IMF components with different center frequencies.

[0083] Next, the Hilbert transform of the k-th IMF component is performed using the following formula to obtain the analytical signal corresponding to the k-th IMF component:

[0084] Hx1(:,k)=hilbert{imf(:,k)-mean[imf(:,k)]};

[0085] Here, imf(:,k) represents the k-th IMF component, mean(·) represents the mean, hilbert(·) represents the Hilbert transform, and Hx1(:,k) represents the analytical signal corresponding to the k-th IMF component.

[0086] Then, the amplitude of Hx1(:,k) is calculated to obtain the envelope signal of imf(:,k), which is expressed as follows:

[0087] f2(:,k)=abs[Hx1(:,k)];

[0088] Where f2(:,k) represents the envelope signal of imf(:,k), and abs(·) represents the absolute value.

[0089] Then, f2(:,k) is zero-mean processed to remove the DC component in f2(:,k) to obtain f3(:,k). f3(:,k) is expressed by the formula:

[0090] f3(:,k)=f2(:,k)-mean[f2(:,k)].

[0091] The f3(:,k) corresponding to the K IMF components form a matrix f3. The FFT transformation of f3 with a length of L is performed to obtain the matrix Y1. Each column in Y1 corresponds to the frequency domain representation of an IMF component. Y1 is expressed by the formula:

[0092] Y1=FFT(f3,L);

[0093] Here, FFT(·) indicates that FFT transformation is performed.

[0094] Finally, the amplitude of Y1 is calculated and normalized to obtain the bilateral amplitude spectrum P2. The first L / 2+1 points of the bilateral amplitude spectrum P2 are then extracted to obtain the unilateral amplitude spectrum P1. All points in the unilateral amplitude spectrum P1 except the first and last points are multiplied by 2 to compensate for the discarded second half of the bilateral amplitude spectrum P2. The envelope spectrum P(:, k) corresponding to the k-th IMF component can be obtained. The server needs to calculate the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the k-th IMF component based on the envelope spectrum P(:, k).

[0095] In an example, the server calculates the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component based on the envelope spectrum P(:,k), which can be achieved by the following formula:

[0096] a1(k)={<(max[P(:,k)]-min[P(:,k)])> / rms[P(:,k)]};

[0097] a2(k)=kurtosis[P(:,k)];

[0098] Among them, max(·), min(·), and rms(·) respectively represent the maximum value, minimum value, and root mean square value, and kurtosis(·) represents the kurtosis.

[0099] In one example, when the server selects the IMF component corresponding to the highest weighted value as the optimal mode, it needs to perform maximum and minimum normalization processing on the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component, and calculate the weighted value a(k).

[0100] The calculation process of the weighted value a(k) is expressed by the formula:

[0101] a(k)=a1′(k)+a2′(k);

[0102] a1′(k)=[a1(k)-a1 min ] / [a1 max -a1(k)];

[0103] a2′(k)=[a2(k)-a2 min ] / [a2 max -a2(k)];

[0104] Among them, a1 min represents the minimum value of the envelope spectrum peak factor corresponding to k IMF components, a1 max represents the maximum value of the envelope spectrum peak factor corresponding to the K IMF components, a2 min represents the minimum value of the average envelope spectrum kurtosis corresponding to the K IMF components, a2 max It represents the maximum value of the average envelope spectrum kurtosis corresponding to K IMF components.

[0105] Finally, the server selects the IMF component corresponding to the largest weighted value among the weighted values ​​corresponding to the K IMF components as the optimal mode.

[0106] Step 14, use the multi-objective grey wolf algorithm to iteratively optimize the objective function. After completing M iterations, obtain the Pareto front of the variational modal decomposition parameters of a single signal, calculate the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front as a reference quantity, and select the set of variational modal decomposition parameters with the smallest reference quantity as the optimal variational modal decomposition parameters.

[0107] In the specific implementation, the server uses the multi-objective grey wolf algorithm to iteratively optimize the objective function. After completing M iterations, the Pareto front of the variational modal decomposition parameters of a single signal can be obtained. The server needs to calculate the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front as a reference quantity, and select the set of variational modal decomposition parameters with the smallest reference quantity as the optimal variational modal decomposition parameters.

[0108] In one example, the server calculates the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front as a reference quantity, which can be expressed by the formula:

[0109]

[0110] ρ ij =Cov(u i ,u j ) / (σ i σ j );

[0111] i≠j;

[0112] Among them, Cov(u i ,u j ) represents any two modal components u i (t) and u j The covariance between (t), σ i Indicates u i The standard deviation of (t), σ j Indicates u j The standard deviation of (t), ρ ij Indicates u i (t) and u j (t), and δ represents the reference value.

[0113] After obtaining the reference quantity corresponding to each set of variational modal decomposition parameters, the server will determine the minimum value of the reference quantity and use the set of variational modal decomposition parameters corresponding to the minimum value of the reference quantity as the optimal variational modal decomposition parameters.

[0114] Step 15: For n×m groups of angular domain vibration signals, variational modal decomposition is performed based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, the optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set according to a preset ratio, so as to iteratively train the pre-built variable speed bearing fault diagnosis model to obtain a trained variable speed bearing fault diagnosis model, thereby realizing variable speed bearing fault diagnosis.

[0115] In the specific implementation, for n×m groups of angular domain vibration signals, the server will perform variational modal decomposition based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, and then use the optimal mode as the signal feature and divide the signal feature and the corresponding label into training set and test set according to the preset ratio, so as to iteratively train the pre-built variable speed bearing fault diagnosis model to obtain the trained variable speed bearing fault diagnosis model, thereby realizing the fault diagnosis of the variable speed bearing.

[0116] In one example, the server is based on the i-th group of angular domain vibration signals, sampling frequency, and optimal modal decomposition number K * and the optimal penalty factor α * Perform variational mode decomposition and obtain K * The authors used a pre-built variable speed bearing fault diagnosis model consisting of a convolutional neural network and a softmax classifier to iteratively train and test the model. The model was trained to diagnose variable speed bearing faults, ultimately completing the fault diagnosis of variable speed bearings.

[0117] This embodiment proposes a variable speed bearing fault diagnosis method based on the Pareto front. Considering that the linear interpolation accuracy used in the classic computational order analysis algorithm is low and the smoothness of the fitting curve is insufficient, which can lead to poor results, the computational order analysis is improved by introducing a piecewise cubic Hermite interpolation method, which effectively improves the interpolation accuracy and thus enhances the accuracy of variable speed bearing fault diagnosis. At the same time, the previous single-objective optimization variational modal decomposition modal decomposition modal decomposition number and penalty factor, the optimal mode obtained cannot well represent the fault information. Therefore, a multi-objective Grey Wolf variational modal decomposition method is introduced. The envelope spectrum peak factor and average envelope spectrum kurtosis of the optimal mode are used as two optimization objectives. The resulting Pareto front will simultaneously meet both optimization objectives. The parameter set corresponding to the Pareto front is then re-introduced into the variational modal decomposition, the correlation coefficients of all modes are calculated, and the parameter group with the smallest correlation coefficient is selected as the final parameter group. This signal reconstruction method largely enables the obtained optimal modal decomposition number to maximize the representation of fault characteristics, thereby effectively improving the accuracy and efficiency of variable speed bearing fault diagnosis.

[0118] The steps of the various methods described above are divided for clarity of description only. During implementation, they can be combined into a single step, or some steps can be split into multiple steps. As long as they contain the same logical relationships, they are all within the scope of protection of this application. Insignificant modifications or designs added to the algorithm or process that do not change the core design of the algorithm or process are also within the scope of protection of this application.

[0119] In one embodiment, in order to demonstrate the effectiveness of the variable speed bearing fault diagnosis method based on Pareto front proposed in this application, we conducted relevant simulation experiments.

[0120] In the simulation experiment, we used the Ottawa variable-speed bearing dataset and the speed-up bearing dataset. The fault types were healthy, inner race fault, and outer race fault. The sampling frequency was 200 kHz. There were three types of faults in total, and each fault had 200 sets of data. Each set of data had 1000 sampling points. Each set of data included time-domain vibration signals and speed signals with the same sampling frequency and sampling time. The initial data volume was 3 × 200 × 2 × 1000.

[0121] About algorithm parameter settings.

[0122] To ensure fairness in the experiment, we first needed to determine the optimal parameter settings for each algorithm for this problem. We set the population size to 30, the maximum number of iterations to 50, the number of Pareto archives to 50, the upper and lower limits of the variational mode decomposition mode number to 5 to 10, and the upper and lower limits of the penalty factor to 500 to 2000. All other algorithm parameters were left to their default values.

[0123] On improving computational order analysis.

[0124] The improved computational order analysis method and the classical computational order analysis method are applied to the initial data to obtain two sets of angular domain signals for subsequent fault feature extraction and classification.

[0125] On improving the variational mode decomposition parameters for multi-objective grey wolf optimization.

[0126] Two sets of signal processing were performed. In the first, the signals processed using the improved order analysis method were fed into the improved multi-objective Grey Wolf variational modal decomposition algorithm. In the second, the signals processed using the classic order analysis method were fed into the single-objective Grey Wolf variational modal decomposition algorithm. The single objective was the envelope spectrum peak factor. The second set used the classic variable speed bearing fault diagnosis method.

[0127] On Convolutional Neural Network Fault Classification.

[0128] The two sets of data, processed using different data processing methods, were fed into a convolutional neural network for feature extraction and classification, yielding the final diagnostic results. The fault diagnosis accuracy for the first test set was 93.3%, while the second test set achieved an accuracy of 87.5%. This accuracy was approximately 5.8% higher than the second, demonstrating that the proposed fault diagnosis method can effectively improve diagnostic accuracy.

[0129] Another embodiment of the present application proposes a variable speed bearing fault diagnosis system based on the Pareto front. The implementation details of the variable speed bearing fault diagnosis system based on the Pareto front proposed in this embodiment are described in detail below. The following content is only the implementation details provided for the convenience of understanding and is not necessary for the implementation of this solution.

[0130] The specific structure of the variable speed bearing fault diagnosis system based on Pareto front proposed in this embodiment can be as follows: Figure 3 As shown, it includes: an improved calculation order analysis module 21, an initial population creation module 22, an objective function establishment module 23, an iterative optimization module 24 and a variable speed bearing fault diagnosis model training module 25.

[0131] The improved calculation order analysis module 21 is used to obtain a basic data set containing n types of faults and each fault has m groups of data, each group of data includes a time domain vibration signal and a speed signal with the same sampling frequency and sampling time, and perform an improved calculation order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals, where n and m are both integers greater than 1.

[0132] The initial population creation module 22 is used to determine the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor for the i-th group of angular domain vibration signals, set the built-in parameters of the multi-objective grey wolf algorithm to default values, determine the objective function, population size, number of iterations and number of archives, and create the initial population using the chaotic map initialization method.

[0133] The objective function establishment module 23 is used to perform variational modal decomposition based on the i-th group of angular domain vibration signals, the sampling frequency and the initial population to obtain several IMF components, calculate the envelope spectrum peak factor and the average envelope spectrum kurtosis of each IMF component respectively, select the IMF component corresponding to the weighted highest value as the optimal mode, and establish the objective function based on the envelope spectrum peak factor and the average envelope spectrum kurtosis.

[0134] The iterative optimization module 24 is used to iteratively optimize the objective function using the multi-objective grey wolf algorithm. After completing M iterations, the Pareto front of the variational modal decomposition parameters of the single signal is obtained, the sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, and the set of variational modal decomposition parameters with the smallest reference quantity is selected as the optimal variational modal decomposition parameters.

[0135] The variable speed bearing fault diagnosis model training module 25 is used to perform variational modal decomposition on n×m groups of angular domain vibration signals based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, use the optimal mode as the signal feature, and divide the signal feature and the corresponding label into a training set and a test set according to a preset ratio, so as to iteratively train the pre-built variable speed bearing fault diagnosis model to obtain a trained variable speed bearing fault diagnosis model, thereby realizing fault diagnosis of the variable speed bearing.

[0136] It is worth mentioning that all modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, to highlight the innovation of this application, this embodiment does not include units that are not closely related to solving the technical problem proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0137] It is not difficult to find that this embodiment is a system embodiment corresponding to the above-mentioned method embodiment. This embodiment can be implemented in conjunction with the above-mentioned method embodiment. The relevant technical details and technical effects mentioned in the above-mentioned method embodiment are still valid in this embodiment. In order to reduce repetition, they will not be repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned method embodiment.

[0138] Another embodiment of the present application provides an electronic device, which can be specifically structured as follows: Figure 4 As shown, it includes: at least one processor 31; and a memory 32 that is communicatively connected to the at least one processor 31; wherein the memory 32 stores instructions that can be executed by the at least one processor 31, and the instructions are executed by the at least one processor 31 so that the at least one processor 31 can execute a variable speed bearing fault diagnosis method based on Pareto front as described in the above method embodiment.

[0139] The memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, which connect various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be further described in this application. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on a wireless medium via an antenna. Furthermore, the antenna also receives data and transmits the data to the processor.

[0140] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0141] Another embodiment of the present application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a variable speed bearing fault diagnosis method based on Pareto front as described in the above method embodiment.

[0142] That is, those skilled in the art will understand that all or part of the steps in the above-mentioned method embodiments can be implemented by instructing the relevant hardware through a program, which is stored in a storage medium and includes a number of instructions for causing a device (such as a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the Pareto front-based variable speed bearing fault diagnosis method described in the method embodiments of this application. The aforementioned storage medium includes: a USB flash drive, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc., various media that can store program code.

[0143] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and that in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A variable speed bearing fault diagnosis method based on Pareto front, characterized in that: include: A basic data set containing n faults, each with m data sets, is obtained. Each data set includes time-domain vibration signals and speed signals with the same sampling frequency and time. An improved computational order analysis based on piecewise cubic Hermite interpolation is performed on all time-domain vibration signals to obtain n×m groups of angular-domain vibration signals. For the i-th group of angular domain vibration signals, determine the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor, set the built-in parameters of the multi-objective grey wolf algorithm to their default values, determine the objective function, population size, number of iterations, and number of archives, and create the initial population using the chaotic map initialization method; Based on the i-th group of angular domain vibration signals, sampling frequency and initial population, variational modal decomposition is performed to obtain several IMF components. The envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component are calculated. The IMF component corresponding to the highest weighted value is selected as the optimal mode, and the objective function is established based on the envelope spectrum peak factor and average envelope spectrum kurtosis. The objective function is iteratively optimized using the multi-objective Grey Wolf Algorithm. After completing M iterations, the Pareto front of the variational modal decomposition parameters of a single signal is obtained. The sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, and the set of variational modal decomposition parameters with the smallest reference quantity is selected as the optimal variational modal decomposition parameters. For n×m groups of angular domain vibration signals, variational modal decomposition is performed based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode. The optimal mode is used as the signal feature, and the signal features and the corresponding labels are divided into training sets and test sets according to a preset ratio. The pre-built variable speed bearing fault diagnosis model is iteratively trained to obtain the trained variable speed bearing fault diagnosis model, thereby realizing variable speed bearing fault diagnosis.

2. The variable speed bearing fault diagnosis method based on Pareto front according to claim 1 is characterized in that: Assume that the sampling frequency is fs, the sampling time is t, the time domain vibration signal is S, and the speed signal is V. Perform an improved computational order analysis based on piecewise cubic Hermite interpolation on all time domain vibration signals to obtain n×m groups of angular domain vibration signals, which is achieved by the following formula: s_theta=pchip(theta_t,s,theta); Where s represents the signal value of the time domain vibration signal S, theta_t represents the original angle coordinate, theta represents the target angle coordinate, pchip(·) represents the piecewise cubic Hermite interpolation, and s_theta represents the signal value after interpolation, which corresponds to the angular domain vibration signal S * .

3. The variable speed bearing fault diagnosis method based on Pareto front according to claim 1 is characterized in that: The lower bound of the modal decomposition number is determined to be 5, the upper bound is determined to be 10, the lower bound of the penalty factor is determined to be 500, the upper bound is determined to be 2000, the population size N is determined to be 30, the number of iterations M is determined to be 50, and the number of archives A is determined to be 50; The initial population is created using the chaotic map initialization method, which is achieved through the following formula: mu=4; x i =rand(1,nVar); x u(r+1) =mu×x ir ×(1-x ir ); r＝1,2,…,R； GreyWolves(i),Position(1,j)=lb(j)+[ub(j)-lb(j)]×x(j); Among them, mu is the parameter of the Logistic mapping, mu = 4 means the system is in a chaotic state, nVar = 2, which represents the number of independent variables, i.e. the modal decomposition number and penalty factor, x i represents the chaotic variable of the i-th individual. After the chaotic variable is iterated R times, the system enters a chaotic state. ir represents the chaotic variable of the i-th individual in the r-th iteration, GreyWolves(i),Position(1,j) represents the position of the i-th individual in the j-th dimension, lb(j) and ub(j) represent the lower bound and upper bound of the position of the j-th dimension, respectively.

4. The variable speed bearing fault diagnosis method based on Pareto front according to claim 3 is characterized in that: Based on the i-th group of angular domain vibration signals, sampling frequency and initial population, variational mode decomposition is performed to obtain several IMF components. The envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component are calculated, including: Input the modal decomposition number K corresponding to the initial population, the penalty factor α corresponding to the initial population, and the angular domain vibration signal S * and sampling frequency fs, the modal decomposition number K and penalty factor α are used as optimization variables; The modal decomposition number K, penalty factor α, and angular domain vibration signal S * The sampling frequency fs is brought into the classical variational mode decomposition algorithm to perform variational mode decomposition and obtain K IMF components with different center frequencies; The Hilbert transform of the k-th IMF component is performed using the following formula to obtain the analytical signal corresponding to the k-th IMF component: Hx1(:,k)=hilbert{imf(:,k)-mean[imf(:,k)]}; Where imf(:,k) represents the k-th IMF component, mean(·) represents the mean, hilbert(·) represents the Hilbert transform, and Hx1(:,k) represents the analytical signal corresponding to the k-th IMF component. Calculate the amplitude of Hx1(:,k) and obtain the envelope signal of imf(:,k), which can be expressed as follows: f2(:,k)=abs[Hx1(:,k)]; Where f2(:,k) represents the envelope signal of imf(:,k), and abs(·) represents the absolute value. Perform zero mean processing on f2(:,k) and remove the DC component in f2(:,k) to obtain f3(:,k). The f3(:,k) corresponding to the K IMF components form a matrix f3. Perform FFT transformation of length L on f3 to obtain the matrix Y1. Each column in Y1 corresponds to the frequency domain representation of an IMF component. Y1 is expressed by the formula: Y1=FFT(f3,L); Wherein, FFT(·) indicates FFT transformation; Calculate the amplitude of Y1 and perform normalization to obtain the bilateral amplitude spectrum P2. Then extract the first L / 2+1 points of the bilateral amplitude spectrum P2 to obtain the unilateral amplitude spectrum P1. Multiply all points except the first and last points in the single-sided amplitude spectrum P1 by 2 to compensate for the discarded second half of the double-sided amplitude spectrum P2, and obtain the envelope spectrum P(:,k) corresponding to the k-th IMF component; Based on the envelope spectrum P(:,k), the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component are calculated respectively.

5. The variable speed bearing fault diagnosis method based on Pareto front according to claim 4 is characterized in that: Based on the envelope spectrum P(:,k), the envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component are calculated respectively, which is achieved by the following formula: a1(k)={<(max[P(:,k)]-min[P(:,k)])> / rms[P(:,k)]}; a2(k)=kurtosis[P(:,k)]; Among them, max(·), min(·), and rms(·) respectively represent the maximum value, minimum value, and root mean square value, and kurtosis(·) represents the kurtosis. The IMF component corresponding to the highest weighted value is selected as the best mode, including: The envelope spectrum peak factor a1(k) and the average envelope spectrum kurtosis a2(k) corresponding to the kth IMF component are normalized to the maximum and minimum values ​​respectively, and the weighted value a(k) is calculated. The calculation process of the weighted value a(k) is expressed by the formula: a(k)=a1′(k)+a2′(k); a1′(k)=[a1(k)-a1 min ] / [a1 max -a1(k)]; <h2 style=";text-align:left;direction:ltr">a2′(k) = [a2(k) - a2<h2 style=";text-align:left;direction:ltr"> min <h2 style=";text-align:left;direction:ltr"> ] / [a2<h2 style=";text-align:left;direction:ltr"> max <h2 style=";text-align:left;direction:ltr"> -a2(k)]; Among them, a1 min Indicates the minimum value of the envelope spectrum peak factor corresponding to the K IMF components, a1 max represents the maximum value of the envelope spectrum peak factor corresponding to the K IMF components, a2 min represents the minimum value of the average envelope spectrum kurtosis corresponding to the K IMF components, a2 max Indicates the maximum value of the average envelope spectrum kurtosis corresponding to K IMF components; The largest corresponding IMF component is selected from the weighted values ​​corresponding to the K IMF components as the optimal mode.

6. The variable speed bearing fault diagnosis method based on Pareto front according to claim 1, characterized in that: The sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, which is expressed by the formula: r ij =Cov(u i ,u j ) / (s i s j ); i≠j; Among them, Cov(u i ,u j ) represents any two modal components u i (t) and u j The covariance between (t), σ i Indicates u i The standard deviation of (t), σ j Indicates u j The standard deviation of (t), ρ ij Indicates u i (t) and u j (t), and δ represents the reference value.

7. A variable speed bearing fault diagnosis method based on Pareto front according to any one of claims 1 to 6, characterized in that: For n×m groups of angular domain vibration signals, variational modal decomposition is performed based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode. The optimal mode is used as the signal feature, and the signal features and corresponding labels are divided into training and test sets according to a preset ratio to iteratively train the pre-built variable speed bearing fault diagnosis model, including: Based on the i-th group of angular domain vibration signals, sampling frequency, and optimal modal decomposition number K * and the optimal penalty factor α * Perform variational mode decomposition and obtain K * IMF components, calculate the envelope spectrum peak factor and average envelope spectrum kurtosis of each IMF component, and select the IMF component corresponding to the highest value after weighting as the best mode; The optimal mode is used as the signal feature, and the signal feature and the corresponding label are divided into a training set and a test set in a ratio of 8:2 to iteratively train the pre-built variable speed bearing fault diagnosis model consisting of a convolutional neural network and a Softmax classifier.

8. A variable speed bearing fault diagnosis system based on Pareto front, characterized in that: include: An improved computational order analysis module is used to obtain a basic data set containing n types of faults, each with m sets of data. Each set of data includes time-domain vibration signals and speed signals with the same sampling frequency and sampling time. An improved computational order analysis based on piecewise cubic Hermite interpolation is performed on all time-domain vibration signals to obtain n×m sets of angular-domain vibration signals, where n and m are both integers greater than 1. The initial population creation module is used to determine the upper and lower bounds of the modal decomposition number and the upper and lower bounds of the penalty factor for the i-th group of angular domain vibration signals, set the built-in parameters of the multi-objective grey wolf algorithm to their default values, determine the objective function, population size, number of iterations, and number of archives, and create the initial population using the chaotic map initialization method; An objective function establishment module is used to perform variational modal decomposition based on the i-th group of angular domain vibration signals, the sampling frequency, and the initial population to obtain several IMF components, calculate the envelope spectrum peak factor and the average envelope spectrum kurtosis of each IMF component, select the IMF component corresponding to the highest weighted value as the optimal mode, and establish an objective function based on the envelope spectrum peak factor and the average envelope spectrum kurtosis; An iterative optimization module is used to iteratively optimize the objective function using a multi-objective grey wolf algorithm. After completing M iterations, the Pareto front of the variational modal decomposition parameters of a single signal is obtained. The sum of the absolute values ​​of the correlation coefficients between all modal components corresponding to each set of variational modal decomposition parameters in the Pareto front is calculated as a reference quantity, and the set of variational modal decomposition parameters with the smallest reference quantity is selected as the optimal variational modal decomposition parameters. The variable speed bearing fault diagnosis model training module is used to perform variational modal decomposition on n×m groups of angular domain vibration signals based on the corresponding optimal variational modal decomposition parameters to obtain the optimal mode, use the optimal mode as the signal feature, and divide the signal feature and the corresponding label into a training set and a test set according to a preset ratio, so as to iteratively train the pre-built variable speed bearing fault diagnosis model to obtain the trained variable speed bearing fault diagnosis model, thereby realizing variable speed bearing fault diagnosis.

9. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute a variable speed bearing fault diagnosis method based on Pareto front as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can implement a variable speed bearing fault diagnosis method based on Pareto front as described in any one of claims 1 to 7.

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