A bearing fault diagnosis method based on SGMD and an optimized CNN model

Abstract

The application discloses a bearing fault diagnosis method based on SGMD and an optimized CNN model. According to the vibration signal characteristics of the bearing, the bearing signal is decomposed by using symplectic geometry modal decomposition to obtain a series of symplectic geometry modal components, the symplectic geometry modal components are selected based on the Pearson correlation coefficient index, and the fuzzy scatter entropy is calculated. The fuzzy scatter entropy is used as a characteristic vector to construct a characteristic sample set of the vibration signal. A CNN-LSTM model is constructed by fusing a convolutional neural network and a long short-term memory network model, and the trained model is obtained by adjusting the convolution kernel and other parameters by using the training sample set. The least square support vector machine is used to replace the normalized exponential function layer of the trained CNN-LSTM model, and the least square support vector machine parameters are optimized based on the electric eel foraging optimization algorithm. Finally, the test sample set is input into the improved CNN-LSTM model for fault identification and classification. The method has higher accuracy in bearing fault diagnosis in a small sample noise environment.

Description

TECHNICAL FIELD

[0001] The application relates to a bearing fault diagnosis method based on an SGMD and an optimized CNN model, which is used for bearing fault feature extraction and classification under multiple faults and belongs to the technical field of signal processing. BACKGROUND

[0002] Rolling bearings, as key components of rotating machinery, are prone to fatigue fracture and other faults under various loads in different working conditions. Studies have shown that more than 45% of rotating machinery equipment failures are caused by bearing damage, so effective diagnosis of bearings is crucial to ensure system safety and economy. However, during data acquisition, environmental noise interferes with bearing signals, making traditional machine learning less sensitive to local features of bearing signals, and the signals are non-Gaussian and non-stationary, causing low diagnostic rates. The academic community has proposed various methods for processing bearing data, including ensemble empirical mode decomposition, empirical wavelet decomposition, and variational mode decomposition. Among them, ensemble empirical mode decomposition eliminates mode mixing by adding white noise, but it takes a long time to calculate long time series. Variational mode decomposition requires manual selection of mode number and regularization parameter, and improper selection can easily lead to over-decomposition. These methods cannot well extract the features of the signal.

[0003] Deep learning is a research hotspot in machine learning in recent years, which has certain improvement compared with traditional methods. Convolutional neural network, as one of its important algorithms, can perform supervised learning and has strong feature learning and representation ability, and can automatically learn features from data, so many scholars apply it to fault diagnosis. However, the convolutional neural network is not very sensitive to local features when processing bearing signals, so it is necessary to enhance the capture of local features of the signal. In addition, most of the current fault diagnosis methods based on convolutional neural network use normalized exponential function for classification, and the fault type is determined by calculating the class probability. This method has limited effect when dealing with complex boundaries, especially when dealing with loss functions using cross-entropy. Therefore, it is necessary to redesign the classifier to improve the classification performance. SUMMARY

[0004] In order to overcome the deficiencies of the prior art, the application provides a bearing fault diagnosis method based on an SGMD and an optimized CNN model, which can solve the problem of inaccurate extraction of bearing fault signal features in a small sample noisy environment.

[0005] To achieve the above objectives, this invention uses symplectic geometric mode decomposition to decompose the bearing signal, obtaining a series of symplectic geometric mode components. Based on the Pearson correlation coefficient, appropriate components are selected, and the fuzzy spread entropy of each component is calculated. The fuzzy spread entropy is then used as a feature vector to construct a feature sample set of the vibration signal. A CNN-LSTM model is constructed by fusing convolutional neural networks and long short-term memory networks to better capture the local features of the signal. The normalized exponential function layer of the CNN-LSTM model is replaced with a least-squares support vector machine optimized based on the electric eel foraging algorithm to help the model handle complex boundary problems and achieve accurate bearing fault identification and classification. This method includes the following steps:

[0006] (1) Collect bearing fault diagnosis signals under different working conditions and preprocess them;

[0007] (2) Perform symplectic geometric mode decomposition (SGMD) on vibration signals under different working conditions to obtain a series of symplectic geometric mode components (SGC). Select appropriate SGC based on Pearson correlation coefficient index and calculate the fuzzy spread entropy (FDE) of each SGC. Use FDE as feature vector to construct a feature sample set of vibration signals.

[0008] (3) Integrate the Convolutional Neural Network (CNN) and Long Short-Term Memory Network (LSTM) models to construct a CNN-LSTM model. Train the CNN-LSTM model using the training sample set, and adjust the number of convolutional layers, kernel size, epoch, learning rate, number of LSTM layers and hidden units to obtain the trained CNN-LSTM model;

[0009] (4) Replace the normalized exponential function layer (Softmax) in the trained CNN-LSTM model with a least squares support vector machine (LSSVM);

[0010] (5) The electric eel foraging optimization algorithm (EEFO) was used to optimize the parameters of LSSVM;

[0011] (6) Input the test sample set into the improved CNN-LSTM model to obtain the fault diagnosis results.

[0012] The symplectic geometric mode decomposition steps of the vibration signal in step (2) are as follows:

[0013] Assume a one-dimensional vibration signal x = (x1, x2, ..., x...) n According to Takens' embedding theorem, the time-series delay topological equivalence method is used to map x into a multidimensional signal, obtaining the trajectory matrix X:

[0014]

[0015] where d is the embedding dimension, τ is the delay time, and m = n - (d - 1)τ.

[0016] A covariance matrix A is constructed using the trajectory matrix X, A = X T X.

[0017] The trajectory matrix X is reconstructed, and the reconstructed trajectory matrix Z is constructed by a series of initial single-component matrices Z i (i = 1, 2, …, d), that is, Z = Z1+ Z2+ L + Z d . Wherein, Z i = Q i S i , Q i is the eigenvector of matrix A, S i is the transformation coefficient matrix,

[0018] The elements in the initial single-component matrix Z i are z ij , 1≤i≤d, 1≤j≤m. The initial single-component matrix Z i is converted into a one-dimensional time series signal with a length of n by using the diagonal average conversion, and the diagonal average expression is

[0019]

[0020] where d * = min(m, d), m * = max(m, d), when m < d, otherwise

[0021] The one-dimensional single-component signal Y i corresponding to the single-component matrix Z i = (y1, y2, …, y n ) is calculated using the above formula, and the diagonal average is performed on each single-component matrix in turn to obtain d single-component signals, that is, Y = Y1+ Y2+ L + Y d .

[0022] Based on the periodic similarity evaluation index, the components of the d single-component signals are reorganized. First, Y1 and the remaining components are compared in terms of periodic similarity, and the single-component signals with high similarity are superimposed to obtain SGC1. Then, SGC1 is separated from Y, and the first single-component signal after separation of Y and the remaining components are compared in terms of periodic similarity to obtain SGC2. After h iterations, SGC h is obtained, and the sum of the remaining components is obtained to obtain the residual term g h of the signal. The normalized mean square error (NMSE) between the residual signal after h iterations and the original signal is

[0023]

[0024] When the NMSE h is less than a threshold, the entire decomposition process is ended, otherwise the iterative decomposition is continued until the iteration termination condition is satisfied.

[0025] The final decomposition result is represented as

[0026]

[0027] In the formula, N represents the number of SGCs.

[0028] In the step (2), when the feature sample set is constructed, three SGCs with larger correlation coefficients are selected from each preprocessed signal segment, and the FDE corresponding to the SCG is calculated to obtain a three-dimensional feature vector [e1, e2, e3], which is used as the feature sample set.

[0029] The feature sample set in the step (2) is divided into a training feature sample set and a test feature sample set.

[0030] The LSSVM in the step (4) is an improved support vector machine based on statistical theory, which can convert the solution of a quadratic optimization problem into the solution of a linear equation system, and the expression of the linear equation system is

[0031]

[0032] In the formula, γ is a regularization parameter used to determine the trade-off between model complexity and accuracy, b represents a bias term, E is a column vector with elements of 1, α represents a Lagrange multiplier vector, y represents output data, and Ω is a kernel function symmetric matrix of input data. The elements in the kernel function matrix adopt a radial basis function, and the expression of the radial basis function is

[0033]

[0034] In the formula, σ represents the bandwidth of the kernel function, and σ>0.

[0035] In the step (5), the EEFO is used to optimize the parameters of the LSSVM, and the two parameters γ and σ in the LSSVM are optimized. The specific optimization process of the EEFO is as follows:

[0036] The number of individuals in the population n and the maximum number of iterations T are set, and the eel population x is randomly initialized i (i=1,…,n), the fitness of the candidate position of the eel individual is evaluated fit(x i ), the position vector x prey of the optimal individual in this stage is obtained. Whether x prey satisfies the convergence condition is judged, and if the convergence condition is satisfied, xprey i.e. optimized γ and σ.

[0037] If the convergence condition is not satisfied, the energy factor E(t) = 4sin(l-t / T)xl n(l / r7) is calculated, where r7is a random number in (0, 1). When E > 1, the population implements the interaction behavior, the expression of which is

[0038]

[0039] where p1and p2are random numbers in (0, 1), x i is the randomly selected electric eel position in the current population, x r (t) = Low + r x (Up - Low), Up and Low represent the upper limit and the lower limit respectively, and r is a random vector in (0, 1).

[0040] When E≤1 and r7<1 / 3, the population implements the rest behavior, the expression of which is

[0041] v i (t+1) = R i (t+1) + n2(R i (t+1) round(rand) x i (t)

[0042] where n2: N(0, 1), R i (t+1) = Z(t) + a |Z(t) - x prey (t) | represents the rest region, and a is the rest region ratio.

[0043] When E≤1 and r7>2 / 3, the population implements the migration behavior, the expression of which is

[0044] v i (t+1) = -r5R i (t+1) + r6H r (t+1) - L(H r (t+1) - x i (t)

[0045] where r5and r6are random numbers in (0, 1), L is the Levy flight function, represents any position in the hunting region, and β is the hunting region ratio.

[0046] In the remaining cases, the population implements the hunting behavior, the expression of which is

[0047] v i (t+1) = H prey (t+1) + η(H prey(t+1)-round(rand)x i (t))

[0048] wherein, η is a curl factor, represents a hunting area.

[0049] After the population is calculated according to the requirements of interaction, rest, migration and hunting, the fitness of the population individuals fit(x i is evaluated, and the position vector x prey of the optimal individual is obtained again. It is judged whether x prey satisfies the convergence condition, if the convergence condition is still not satisfied, the population position is updated, and the population position updating expression is

[0050]

[0051] After the population position is updated, the iterative calculation of the interaction, rest, migration and hunting behavior is carried out according to the energy factor and the random number condition, then the fitness of the population individuals is evaluated, the position vector of the optimal individual is formed, it is judged whether the convergence condition is satisfied, if the convergence condition is not satisfied, the population position is updated and the iterative calculation is continued. The cycle is repeated until the position vector x prey of the optimal individual of the converged population is obtained, and the optimization parameters γ and σ are output.

[0052] The beneficial effects of the present application are: the present application proposes a bearing fault diagnosis method based on SGMD and optimized CNN model, the method introduces vibration signal data under different working conditions, uses correlation coefficient to determine the selection of SGC, effectively removes the components with low correlation, and improves the reliability of the results. The corresponding fuzzy scatter entropy of each component can be obtained, and a three-dimensional feature vector [e1, e2, e3] is obtained, which is used as a feature sample set to provide features that can distinguish bearing faults for the following deep learning algorithm. The long short-term memory network is combined with the convolutional neural network, which enhances the sensitivity to local signals and can accurately extract the features of bearing fault signals in a noisy environment. The least square support vector machine is used to replace the normalization exponential function layer in the trained CNN-LSTM model, which effectively improves the ability to handle complex boundaries. The electric eel foraging optimization algorithm is used to optimize the parameters of LSSVM, which effectively improves the fault recognition accuracy and reduces the cost. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The bearing fault diagnosis flowchart of the present application.

[0054] Figure 2 The bearing vibration signal example diagram of the present application.

[0055] Figure 3 The time domain diagram of the vibration signal after the present application is decomposed by the symplectic geometry modal decomposition.

[0056] Figure 4 The frequency domain graph of the vibration signal after the decomposition of the invention in the symplectic geometry mode.

[0057] Figure 5 The structure diagram of the CNN-LSTM model of the invention.

[0058] Figure 6 The EEFO optimization convergence curve diagram of the invention.

[0059] Figure 7 The model classification result diagram after the optimization of the invention. DETAILED DESCRIPTION

[0060] The invention will be further described below in combination with the drawings and specific embodiments.

[0061] As Figure 1 shown, the bearing fault diagnosis method based on SGMD and optimized CNN model of the embodiment includes the following steps:

[0062] (1) Collect bearing fault diagnosis signals under different working conditions, and pretreat them, which include normal, inner ring, outer ring and rolling body bearing fault signals. The data used is acceleration signal, and the vibration signal instance graph is as shown in Figure 2 .

[0063] (2) Perform symplectic geometry modal decomposition (SGMD) on the vibration signals under different working conditions to obtain a series of symplectic geometry modal components (SGC). Select appropriate SGC based on the Pearson correlation coefficient index, and calculate the fuzzy scatter entropy (FDE) of each SGC. Take the FDE as a feature vector to construct a feature sample set of the vibration signal.

[0064] The steps of symplectic geometry modal decomposition in step (2) are as follows:

[0065] Suppose a one-dimensional vibration signal x=(x1,x2,…,x n n), according to the Takens embedding theorem, map x to a multi-dimensional signal by using time series delay topology equivalence method to obtain a trajectory matrix X:

[0066]

[0067] Wherein, d is the embedding dimension, τ is the delay time, and m=n-(d-1)τ.

[0068] Use the trajectory matrix X to construct a covariance matrix A, A=X T X.

[0069] Reconstruct the trajectory matrix X, and the reconstructed trajectory matrix Z is obtained through a series of initial single-component matrices Z i(Constructed for \(i = 1, 2, \ldots, d\)), that is, \(Z = Z_1+Z_2+\cdots+Z\) d . Among them, \(Z\) i =Q i S i , \(Q\) i is the eigenvector of matrix \(A\), and \(S\) i is the transformation coefficient matrix.

[0070] Define the elements in the initial single-component matrix \(Z\) i as \(z\) ij , where \(1\leq i\leq d\) and \(1\leq j\leq m\). Use diagonal averaging transformation to transform the initial single-component matrix \(Z\) i into a one-dimensional time series signal with length \(n\). The diagonal averaging expression is

[0071]

[0072] where \(d\) * =\(\min(m, d)\), \(m\) * =\(\max(m, d)\). When \(m < d\), Otherwise

[0073] Calculate the one-dimensional single-component signal \(Y\) i corresponding to the single-component matrix \(Z\) using the above formula i =(y1, y2, \ldots, y n ). Perform diagonal averaging on each single-component matrix in turn to obtain \(d\) single-component signals, that is, \(Y = Y_1+Y_2+\cdots+Y\) d .

[0074] Based on the periodic similarity evaluation index, perform component recombination on the \(d\) single-component signals. First, compare the periodic similarity of \(Y_1\) with the other components, and superimpose the single-component signals with high similarity to obtain SGC1. Then, separate SGC1 from \(Y\), and compare the periodic similarity of the first single-component signal after \(Y\) is separated with the remaining components to obtain SGC2. After \(h\) iterations, SGC h can be obtained. Finally, sum the remaining components to obtain the residual term \(g\) of the signal h . Construct the normalized mean square error (NMSE) between the residual signal and the original signal after \(h\) iterations as

[0075]

[0076] When NMSE h is less than the threshold, end the entire decomposition process; otherwise, continue the iterative decomposition until the iterative termination condition is satisfied.

[0077] The final decomposition result is expressed as

[0078]

[0079] In the formula, N represents the number of SGCs.

[0080] The selection of appropriate SGCs in step (2) is determined by calculating the Pearson correlation coefficient, and the results are shown in Table 1. By observing the correlation coefficient of each SGC component and the original signal in the table, it can be seen that the four SGCs of the inner ring fault have good correlation with the original signal, but the normal, outer ring and rolling body faults have little correlation with the original signal from SGC4.

[0081] Table 1 Correlation coefficient of SGC under different faults

[0082]

[0083] Because the number of SGCs obtained by decomposing different vibration signals is different, in order to facilitate subsequent processing, the feature dimension extracted from each vibration signal is consistent, and three components with larger correlation are selected from each group of decomposed SGCs for calculation of fuzzy scatter entropy. The results of singular geometric modal decomposition of the outer ring raceway fault vibration signal and the spectrum graphs of each modal component are shown in Figs. 1 and 2. Figure 3 and Figure 4 .

[0084] In step (2), the corresponding fuzzy scatter entropy of each component can be obtained, and a three-dimensional feature vector [e1, e2, e3] is obtained as a feature sample set.

[0085] (3) Fuse the convolutional neural network (CNN) and the long short-term memory network (LSTM) model to construct a CNN-LSTM model. Train the CNN-LSTM model using the training sample set, adjust the network parameters such as the convolutional layer, kernel size, and batch, and obtain the trained CNN-LSTM model.

[0086] In step (3), when adjusting the parameters of the CNN-LSTM model, the calculation of the convolutional layer can be calculated using the following formula:

[0087]

[0088] In the formula, represents the input of the jth neuron of the l+1th layer, f is the activation function, M is the number of feature maps, is the output of the jth neuron of the 1st layer, represents the convolution operation, represents the convolution kernel of the 1st neuron in the lth layer and the neuron in the l+1th layer, and b represents the bias.

[0089] The pooling layer is located after the convolutional layer, and the mathematical model is expressed as follows:

[0090]

[0091] wherein, is the input of k layer, Pool(k) is the output of pooling, m*n is the size of the pooling region.

[0092] In order to better extract features, three layers of convolution are designed. The constructed CNN-LSTM model has 21 layers, including input layer, convolution layer, normalization layer, ReLU layer, pooling layer, LSTM layer, full connection layer, Softmax layer, output layer, etc., as shown in Figure 5 .

[0093] Each state randomly selects 70% as the training set and 30% as the test set, and selects the Softmax classifier. The number of convolution kernels in each layer is determined on the premise that the convolution layer is set to three layers. The experimental results under different configuration schemes are shown in Table 2, wherein the configuration schemes include 1(16, 32, 16), 2(16, 32, 64), 3(16, 64, 16), 4(16, 64, 64), 5(32, 32, 16), 6(32, 64, 16), 7(32, 64, 64), 8(32, 32, 64), 9(64, 32, 16), 10(64, 64, 16), 11(64, 64, 32), 12(64, 32, 64), Epoch is set to 100, batch is set to 64, and learning rate is 0.01. Test.

[0094] Table 2 Running results of different convolution kernel numbers

[0095]

[0096]

[0097] It can be seen from Table 2 that as the number of convolution kernels in each layer increases, the training time and test time of the model also increase, and the accuracy does not keep growing. Through comparative analysis, the number of convolution kernels used in the convolution layer is in the form of (16, 32, 64).

[0098] The above scheme is used for the following test, the batch is set to 32, 64, 128 in turn, Epoch is set to 100, and learning rate is set to 0.01, as shown in Table 3. When the batch is set to 128, the running time is the shortest and the accuracy is the highest. Therefore, 128 is set as the batch size of the model.

[0099] Table 3 Running results of different batches

[0100]

[0101] Epoch is set to 20, 40, 60, 80, 100, and the learning rate is set to 0.01. Referring to Table 4, although the accuracy is highest when Epoch is 100, the Epoch is set to 60 considering the time cost.

[0102] Table 4 running results of different Epochs

[0103]

[0104] The learning rate is set to 0.001, 0.005, and 0.01. Referring to Table 5, when the learning rate is 0.001, the running time and accuracy are optimal, so the learning rate is set to 0.001.

[0105] Table 5 running results of different learning rates

[0106]

[0107] The final result of the setting of the hyperparameters is as follows: the convolutional layer is set to 3 layers, the number of kernels is (16, 32, 64), the batch size is 128, the Epoch is 60, and the learning rate is 0.001 for the model structure.

[0108] In order to better improve the efficiency of diagnosis, the parameters of the LSTM layer will be adjusted as follows. The number of layers is set to 1, 2, and 3. As can be seen from Table 6, with the increase of the number of layers, the accuracy does not achieve the expected effect, so the number of layers is set to 1.

[0109] Table 6 running results of different numbers of LSTM layers

[0110]

[0111] The number of hidden units of LSTM is usually determined according to the complexity of the task and the size of the data set. Generally, the more the number of hidden units, the stronger the representation ability of the model, but it will also increase the complexity of the model and the training time. On the other hand, too few hidden units may lead to underfitting of the model, which cannot capture the complex relationship of the data well. Therefore, the number of hidden units is set to 100.

[0112] (4) Replace the Softmax layer in the trained CNN-LSTM model with the least square support vector machine (LSSVM).

[0113] In step (4), the classifier of the CNN-LSTM model is not the original Softmax function, but is replaced by LSSVM for classification. When the fully connected layer is input to the next layer, Softmax is not selected as the classifier, and the training result is input to LSSVM.

[0114] LSSVM is an improved support vector machine based on statistical theory, which can convert the solution of a quadratic optimization problem into the solution of a linear equation system, and the expression of the linear equation system is:

[0115]

[0116] wherein γ is a regularization parameter used to determine the trade-off between the model complexity and accuracy, b represents a bias term, E is a column vector with elements of 1, α represents a Lagrange multiplier vector, y represents output data, and Ω is a kernel function symmetric matrix of input data, and the elements in the kernel function matrix adopt a radial basis function, and the expression of the radial basis function is:

[0117]

[0118] wherein σ represents the bandwidth of the kernel function, and σ>0.

[0119] (5) using the electric eel foraging optimization algorithm (EEFO) to optimize the parameters of LSSVM.

[0120] The parameter optimization of LSSVM using EEFO in step (5) is to optimize two parameters γ and σ in LSSVM, and the specific optimization process of EEFO is as follows:

[0121] Set the number of individuals in the population n and the maximum number of iterations T, and randomly initialize the eel population x i (i = 1, …, n), evaluate the fitness of the candidate position of the eel individual fit(x i ), and obtain the position vector x prey of the optimal individual at this stage. Determine whether x prey satisfies the convergence condition, if it satisfies the convergence condition, output x prey , that is, the optimized γ and σ.

[0122] If the convergence condition is not met, calculate the energy factor E(t) = 4sin(1-t / T)×ln(1 / r7), wherein r7 is a random number in (0,1). When E>1, implement the interaction behavior on the population, and the expression of the interaction behavior is

[0123]

[0124] wherein p1 and p2 are random numbers in (0,1), x i is the position of the electric eel randomly selected in the current population, x r (t) = Low + r × (Up-Low), Up and Low represent the upper limit and the lower limit respectively, and r is a random vector in (0,1).

[0125] When E≤1 and r7<1 / 3, the population implements rest behavior, and the rest behavior expression is

[0126] v i (t+1) = R i (t+1) + n2(R i (t+1) round(rand) x i (t)

[0127] where n2:N(0,1), R i (t+1) = Z(t) + a|Z(t)-x prey (t)| represents the rest area, and a is the rest area ratio.

[0128] When E≤1 and r7>2 / 3, the population implements migration behavior, and the migration behavior expression is

[0129] v i (t+1) = -r5R i (t+1) + r6H r (t+1) - L(H r (t+1) - x i (t))

[0130] where r5 and r6 are random numbers in (0,1), L is a Levy flight function, represents any position in the hunting area, and β is the hunting area ratio.

[0131] In the remaining cases, the population implements hunting behavior, and the hunting behavior expression is

[0132] v i (t+1) = H prey (t+1) + η(H prey (t+1) - round(rand) x i (t))

[0133] where η is a curling factor, represents the hunting area.

[0134] After the population performs interaction, rest, migration and hunting calculations as required, the fitness of the population individuals fit(x i ) is evaluated, and the position vector x prey of the optimal individual is obtained again. It is judged whether x prey satisfies the convergence condition. If the convergence condition is still not satisfied, the population position is updated, and the population position update expression is

[0135]

[0136] After the population position is updated, the iterative calculation of interaction, rest, migration and hunting behavior is carried out according to the energy factor and the random number condition, then the fitness of the population individual is evaluated, the optimal individual position vector is formed, and it is judged whether the convergence condition is met, if not, the population position is updated and the iterative calculation is continued. prey and output the optimized parameters gamma and sigma.

[0137] When the parameters of LSSVM are optimized using EEFO, EEFO converges at the 13th iteration, at which time the fitness value is minimum, EEFO finds the optimal solution of the parameters, and the optimization convergence curve is as shown in Figure 6 .

[0138] (6) input the test sample set into the improved CNN-LSTM model to obtain the fault diagnosis result.

[0139] In step (6), the test sample is input into the improved model, and the confusion matrix obtained is as shown in Figure 7 , only 4 fault 8 and 1 fault 9 are misjudged as other fault types, and the remaining fault numbers are identified, and the classification effect is good.

[0140] The EEFO optimization algorithm in the method of the application is tested and compared with three kinds of optimization methods of grey wolf (GWO), slime mold (SMA) and sparrow (SSA), and the classification accuracy of four methods on experimental data is given in Table 7.

[0141] Table 7 Comparison of fault diagnosis rates of different methods

[0142]

[0143] Table 7 shows that under the same population size and iteration number conditions, the fault diagnosis accuracy of the method is generally higher than that of other methods. Although GWO can quickly converge to a better solution in the iteration process, it sometimes falls into a local optimal solution and is difficult to escape. In contrast, SMA can solve complex optimization problems, but is sensitive to parameter settings. On the other hand, SSA can realize diversified search strategies, but may lead to unstable convergence. The method proposed in this paper uses EEFO with efficient information transmission function and excellent perception ability, and its accuracy can reach 98.57%, which is better than other methods.

[0144] The method of the present application obtains each modal component through geometric modal decomposition, selects appropriate SGC by calculating correlation coefficient, respectively calculates the fuzzy scatter entropy of each component, and constructs a feature sample set by using the fuzzy scatter entropy. The rationality and reliability of the network are ensured by optimizing the structure of the network and adjusting the hyperparameters. The present method replaces the SoftMax layer in the model with LSSVM, effectively solving the problem that the model does not work well in processing complex boundaries, and further improves the accuracy by optimizing the regularization parameter and kernel function parameter of LSSVM through EEFO.

[0145] The above only represents the preferred embodiments of the present application and should not be regarded as limiting the present application. Obviously, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present application. Therefore, if these modifications and variations belong to the scope of the claims of the present application and equivalent technologies thereof, the present application also intends to include these modifications and variations.

Claims

1. A bearing fault diagnosis method based on SGMD and an optimized CNN model, characterized in that, Includes the following steps: (1) Collect bearing fault diagnosis signals under different working conditions and preprocess them; (2) Perform symplectic geometric mode decomposition (SGMD) on vibration signals under different working conditions to obtain a series of symplectic geometric mode components (SGC). Select appropriate SGCs based on the Pearson correlation coefficient index and calculate the fuzzy spread entropy (FDE) of each SGC. Use the FDE as a feature vector to construct a feature sample set of vibration signals. (3) Integrate the Convolutional Neural Network (CNN) and the Long Short-Term Memory Network (LSTM) model to construct a CNN-LSTM model. Use the training sample set to train the CNN-LSTM model and adjust the number of convolutional layers, kernel size, epoch, learning rate, number of LSTM layers and hidden units to obtain the trained CNN-LSTM model. (4) Replace the normalized exponential function layer Softmax in the trained CNN-LSTM model with a least squares support vector machine (LSSVM); (5) The electric eel foraging optimization algorithm EEFO was used to optimize the parameters of LSSVM; (6) Input the test sample set into the improved CNN-LSTM model to obtain the fault diagnosis results.

2. The fault diagnosis method based on SGMD and an optimized CNN model according to claim 1, characterized in that: The symplectic geometric mode decomposition steps of the vibration signal in step (2) are as follows: Assume a one-dimensional vibration signal x = (x1, x2, ..., x...) n According to Takens' embedding theorem, the time-series delay topological equivalence method is used to map x into a multidimensional signal, obtaining the trajectory matrix X: Where d is the embedding dimension, τ is the delay time, and m = n - (d-1)τ. Construct a covariance matrix A using the trajectory matrix X, where A = X T X; The trajectory matrix X is reconstructed, and the reconstructed trajectory matrix Z is obtained by passing through a series of initial single-component matrices Z. i Construct Z = Z1 + Z2 + ... + Zd (i = 1, 2, ..., d) d； Among them, Z i =Q i S i Q i Let S be the eigenvector of matrix A. i This is the transformation coefficient matrix. Define the initial single-component matrix Z i The middle element is z ij , 1≤i≤d, 1≤j≤m; the initial single-component matrix Z is transformed using diagonal averaging. i Transforming it into a one-dimensional time series signal of length n, the diagonal averaging expression is as follows: where d * = min(m, d), m * = max(m, d), when m < d, otherwise The single-component matrix Z is calculated using the above formula. i The corresponding one-dimensional single-component signal Y i =(y1,y2,…,y n By successively performing diagonal averaging on each single-component matrix, d single-component signals can be obtained, i.e., Y = Y1 + Y2 + L + Y. d ; Based on the periodic similarity evaluation index, component recombination is performed on d single-component signals. First, Y1 is compared with the remaining components in terms of periodic similarity. Highly similar single-component signals are superimposed to obtain SGC1. Then, SGC1 is separated from Y. The first single-component signal after Y separation is compared with the remaining components in terms of periodic similarity to obtain SGC1. 2； SGC can be obtained after h iterations. h Finally, the remaining components are summed to obtain the residual term g of the signal. h The normalized mean square error (NMSE) between the residual signal and the original signal after h iterations is constructed as follows: When NMSE h If the value is less than the threshold, the entire decomposition process ends; otherwise, iterative decomposition continues until the termination condition is met. The final decomposition result is expressed as follows: In the formula, N represents the number of SGCs.

3. The fault diagnosis method based on SGMD and an optimized CNN model according to claim 1, characterized in that: In step (2), when constructing the feature sample set, three SGCs with larger correlation coefficients are selected from each preprocessed signal segment, and the FDE corresponding to the SGC is calculated to obtain the three-dimensional feature vector [e1,e2,e3], which is used as the feature sample set.

4. The fault diagnosis method based on SGMD and an optimized CNN model according to claim 1, characterized in that: The feature sample set in step (2) is divided into a training feature sample set and a test feature sample set.

5. The fault diagnosis method based on SGMD and an optimized CNN model according to claim 1, characterized in that: The LSSVM in step (4) is an improved support vector machine based on statistical theory, which can transform the solution of a quadratic optimization problem into the solution of a system of linear equations. The expression of the system of linear equations is... Where γ is the regularization parameter used to determine the trade-off between model complexity and accuracy, b represents the bias term, E is a column vector with elements of 1, α represents the Lagrange multiplier vector, y represents the output data, and Ω is the kernel function symmetric matrix of the input data. The elements in the kernel function matrix use radial basis functions, and its expression is: In the formula, σ represents the bandwidth of the kernel function, and σ > 0.

6. The fault diagnosis method based on SGMD and an optimized CNN model according to claim 1, characterized in that: The parameter optimization of LSSVM using EEFO in step (5) optimizes the two parameters γ and σ in LSSVM. The specific optimization process of EEFO is as follows: Set the number of individuals n and the maximum number of iterations T in the population, and randomly initialize the eel population x. i (i = 1, ..., n), evaluate the fitness fit(x) of candidate positions for individual eels. i ), to obtain the position vector x of the optimal individual in this stage. prey Determine x prey Check if the convergence condition is met. If the convergence condition is met, output x. prey That is, the optimized γ and σ. If the convergence condition is not met, calculate the energy factor E(t) = 4sin(1-t / T) × ln(1 / r7), where r7 is a random number in (0,1). When E>1, implement interactive behavior on the population. The expression for the interactive behavior is... In the formula, p1 and p2 are random numbers within (0,1), and x i The location of the electric eel is randomly selected within the current population. x r (t) = Low + r × (Up - Low), where Up and Low represent the upper and lower bounds, respectively, and r is a random vector within (0,1). When E≤1 and r7<1 / 3, the population engages in resting behavior. The expression for resting behavior is as follows: v i (t+1)=R i (t+1)+n2(R i (t+1)round(rand)x i (t)) Where n2:N(0,1), R i (t+1)=Z(t)+α|Z(t-x) prey (t)| represents the rest area, and α is the ratio of the rest area; When E≤1 and r7>2 / 3, the population exhibits migration behavior. The expression for this migration behavior is: v i (t+1)=-r5R i (t+1)+r6H r (t+1)-L(H r (t+1)-x i (t)) In the formula, r5 and r6 are random numbers in (0,1), and L is the Lévy flight function. This represents any location within the hunting area, where β is the hunting area ratio. In other cases, the population engages in hunting behavior, expressed as follows: v i (t+1)=H prey (t+1)+η(H prey (t+1)-round(rand)x i (t)) Where η is the curl factor, Indicates the hunting area. After the population has performed interactions, rest, migration, and hunting as required, the fitness (fit(x)) of individual population members is assessed. i ), and re-obtain the optimal individual's position vector x prey Determine x prey Check if the convergence condition is met. If the convergence condition is still not met, update the population position. The population position update expression is: After updating the population location, iterative calculations of interaction, rest, migration, and hunting behaviors are performed based on energy factors and random number conditions. Then, the fitness of individual individuals in the population is evaluated to form the optimal individual location vector. It is then determined whether the convergence condition is met. If not, the population location is updated and iterative calculations continue. This process is repeated until the converged optimal individual location vector x is obtained. prey It also outputs the optimization parameters γ and σ.

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