A classification method for bearing fault diagnosis

Abstract

The application belongs to the technical field of bearing fault diagnosis, and relates to a bearing fault diagnosis classification method.The method comprises the following steps: firstly, obtaining a bearing fault original signal, and converting the signal into a time-frequency graph by using continuous wavelet transform; secondly, optimizing the size of a convolution kernel, the number of the convolution kernel, the size of a batch size and a learning rate of a convolutional neural network classification model in an improved red fox optimization algorithm, and constructing a bearing fault diagnosis classification model; and finally, using the time-frequency graph obtained by the continuous wavelet transform as a training set to train the classification model, and outputting a classification result.The application adds reflection learning and an elite reverse strategy to the red fox optimization algorithm, so that the improved algorithm has improved convergence speed and accuracy; the red fox optimization algorithm is used to optimize the parameters of the convolutional neural network, so that the influence of the randomization of the parameters of the traditional convolutional neural network on the classification result and the long learning time is reduced, and the application can provide accurate classification services for the classification of bearing fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of bearing fault diagnosis technology, and specifically relates to a classification method for bearing fault diagnosis. Background Technology

[0002] Bearings are among the most critical mechanical components in modern industrial systems, and also among the most prone to failure. If a bearing fails, not only will its own operation be affected, but various related parts and equipment will also experience problems, ranging from minor production losses to serious safety accidents. Therefore, improving the accuracy and stability of bearing fault diagnosis has significant theoretical and engineering implications.

[0003] The classification of bearing fault diagnosis is based on vibration signals obtained from sensors, and various analytical methods are used to diagnose and classify bearing faults. There are three commonly used classification methods: 1. Vibration-based diagnostic techniques; 2. Analysis model-based diagnostic techniques; 3. Data-driven diagnostic techniques.

[0004] Because the signals generated by rolling bearing faults are affected by environmental noise, they are often non-stationary and non-linear. Some studies rely solely on human experience and signal analysis methods for diagnosis, resulting in inaccurate classifications and hindering the scientific and effective classification of bearing faults. Therefore, an effective classification method is urgently needed for bearing fault diagnosis. Summary of the Invention

[0005] The purpose of this invention is to provide a classification method for bearing fault diagnosis, so as to solve the problems of low classification accuracy and poor model capability in the prior art mentioned in the background.

[0006] The present invention achieves the above objectives through the following technical solutions:

[0007] A method for classifying bearing faults includes the following steps:

[0008] S1: Acquire the vibration signal of the bearing to be diagnosed and perform continuous wavelet transformation to generate a time-frequency diagram;

[0009] S2: Construct a bearing diagnosis and classification model based on a convolutional neural network, and use the time-frequency graph as a training set to train the convolutional neural network to initialize the network topology of the convolutional neural network;

[0010] S3: The convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, and an optimized bearing diagnosis classification model is constructed based on the optimal parameters;

[0011] The optimal parameters include the convolution kernel, the number of convolution kernels, the batch size, and the learning rate.

[0012] S4: Acquire the vibration signal of the bearing to be diagnosed again and perform continuous wavelet transformation to generate a time-frequency diagram. Use this time-frequency diagram as the training set of the optimized bearing diagnosis classification model. After training and testing, output the classification result.

[0013] As a further optimization of the present invention, step S2 includes:

[0014] S2.1: Determine the number of network layers: Use one input layer, two convolutional layers, two max pooling layers, one fully connected layer, and one output layer;

[0015] S2.2: Selection of transfer function and training method: The ReLU function is used for the transfer function between layers, the softmax function is used as the classification function for the output layer, and the gradient descent method is selected for the training method;

[0016] S2.3: Determine the number of network training iterations and training objectives;

[0017] S2.4: Using the time-frequency graph as a training set, train the convolutional neural network to initialize the network topology of the convolutional neural network;

[0018] S2.5: Initialize the weight matrix and threshold matrix of the convolutional neural network using random functions.

[0019] As a further optimization of the present invention, in step S3, the convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, specifically including:

[0020] S3.1: Initialize the red fox population, and use the accuracy of the cross-entropy function between the classification results of the convolutional neural network model and the actual results as the fitness function of the red fox algorithm;

[0021] S3.2: Select the position of the red fox individual with the best fitness value, simulate the red fox's life habits of foraging, hunting, and escaping hunters according to the improved red fox optimization algorithm, and iteratively update the position of the red fox individual through its five stages of finding prey, reflecting and learning, surrounding prey, elite reverse strategy, evading hunters and developing the population. Select the best individual after iteration until the maximum number of iterations is reached or the fitness meets the preset termination condition.

[0022] S3.3: If the termination condition is not met, eliminate the worst individual in the red fox population and use the best individual to reproduce offspring. Repeat step S3.2 until the iteration ends, and obtain the best individual position as the optimal convolution kernel size, number of convolution kernels, batch size and learning rate for the convolutional neural network classification model.

[0023] As a further optimization of the present invention, in step S3.2, the improved red fox optimization algorithm specifically includes the following:

[0024] S3.21: Algorithm Premise: The individual positions of the red fox population are initialized as X = (X1, X2, ..., X...). n ), where n is the number of individuals in the population, X1=(x1, x2, ..., x m ), x i ∈(a, b), a, b ∈ R, m is the dimension of the individual's position; Let represent the position of the i-th red fox during the t-th iteration; a fitness function is pre-defined, assuming the red foxes are active within a specific spatial range, and the red fox with the best fitness is denoted as the optimal individual, called α fox;

[0025] S3.22: Calculate the fitness value and select the red fox individual with the lowest fitness; select the cross-entropy function between the training set and the actual values ​​of the convolutional neural network as the fitness function for the red fox individual:

[0026]

[0027] Where y i For the accurate value of classification, s i For the actual classification output, the smaller the fitness value of the red fox individual, the higher the classification accuracy of the algorithm;

[0028] S3.23: Hunting Prey – Global Search Phase; In this phase, individual red foxes venture out to hunt prey. The fox pack communicates with each other, sharing the locations where prey is most easily caught, causing the pack to move towards the optimal individual's location. If the fitness value after the move is better than the original location, the location is updated; otherwise, it returns to the original location. In one iteration, the individual and the optimal individual... The distance is expressed as:

[0029] The formula for updating individual location is:

[0030]

[0031] in It is a random number within that interval;

[0032] S3.24: Introduce reflective learning to update individual positions; compare and contrast the red fox's positions before and after the update, and select the optimal position to update. The formula for reflective learning is as follows:

[0033]

[0034] in, This is the updated position after the red fox moves with the alpha fox. This is the Red Fox's starting position, X f It represents the new position generated after reflective learning; ω = [-1, 1] represents the learning factor;

[0035] S3.25: Surrounding the Prey – Local Search Phase; After discovering suspicious prey, the red fox hunts by observing its surroundings, camouflaging and hiding, and waiting for an opportunity to strike. The mathematical model is as follows:

[0036]

[0037] Where μ∈[0,1] is a random number within this interval, to balance the approximation and camouflage stages; the expression for the red fox's activity radius r when surrounding its prey is as follows:

[0038]

[0039] Where a∈(0, 0.2) is defined as the approximation parameter; φ0 is a random number between 0 and 2π, representing the red fox's observation angle; θ∈(0, 1) is the initially set random number, simulating the influence of weather factors during the red fox's hunt; when the time is right, the red fox begins to surround and approach its prey, and its position is updated as follows:

[0040]

[0041] Where φ1, φ2, ..., φ n-1 It is a random number between 0 and 2π; This indicates the new location for the red fox;

[0042] S3.26: Adopt an elite reverse learning strategy; let the position of the elite individual in the current group be...

[0043] X best = (x1, x2, ..., x n )

[0044] Then the reverse solution Defined as:

[0045]

[0046] Where, k∈[0,1], a j b j It is x i Boundary values;

[0047] S3.27: Evade hunters and develop the population; the bottom 5% of individuals with the worst fitness values ​​in the population are hunted and eliminated by hunters, and the α red fox couple with the best fitness values ​​(X) are selected. best1 X best2 Establish a habitat model; the formula for calculating the habitat center is:

[0048]

[0049] in, This represents the best-fitting red fox individual; the habitat fox pack activity diameter is defined as:

[0050]

[0051] S3.28: Determine if the termination condition is met; if the termination condition is met, obtain the optimal individual position, i.e., the optimal kernel size (first and second layers), number of kernels (first and second layers), batch size, and learning rate of the convolutional neural network, and then construct a new convolutional neural network.

[0052] S3.29: If the termination condition is not met, eliminate the worst individual, select the best individuals to breed new individuals, and repeat step S3.22.

[0053] As a further optimization of the present invention, in S3.24, to prevent excessive randomness during reflective learning, the following constraints are imposed on the learning factor:

[0054]

[0055] Where: r∈[0,π] is a random number, t is the current number of iterations, and T is the maximum number of iterations; individuals have strong reflective behavior in the early stage, which can improve hunting ability and achieve self-improvement; in the later stage, as individuals get closer and closer to prey, reflective behavior gradually decreases, and the learning factor ω also gradually decreases.

[0056] As a further optimization of the present invention, in step S3.26, the elite reverse learning strategy is adopted, in which the top 20% of individuals in fitness are selected to form an elite fox group F. best And the elite fox population was obtained using the inverse solution. In mixed fox populations Then select the top 50% of red foxes in terms of fitness as the next generation.

[0057] As a further optimization of the present invention, in step S3.27, during the process of avoiding hunters and developing the population, the parameter k∈(0,1) is set when developing the population, as shown below:

[0058]

[0059] When k < 0.45, the α red fox couple reproduces, producing new individuals, which can be denoted as:

[0060]

[0061] The beneficial effects of this invention are as follows:

[0062] (1) In this invention, a classification model for bearing fault diagnosis is established based on a convolutional neural network to classify bearing faults. First, the vibration signal obtained by the sensor is converted into a time-frequency diagram through continuous wavelet transform. Then, the time-frequency diagram is used as the input of the classification model. Finally, the parameters of the convolutional neural network are optimized by combining the improved Red Fox optimization algorithm to determine the optimal parameters, thereby completing the model construction. New vibration signals are added to the model for training and learning to improve the classification accuracy of fault diagnosis.

[0063] (2) In this invention, the performance of the Red Fox Optimization Algorithm is improved by modifying it. First, reflective learning is introduced into the Red Fox Optimization Algorithm to compare the positions of the Red Foxes before and after the update, thereby improving the hunting ability of individuals and preventing the algorithm from getting stuck in local optima. Second, an elite reverse learning strategy is adopted to select high-quality individuals as the next generation of the population, thereby increasing population diversity, preventing the algorithm from converging too early, and improving the efficiency of the algorithm. Compared with other traditional optimization algorithms, the improved algorithm has improved convergence speed and accuracy. At the same time, the Red Fox Optimization Algorithm is used to optimize parameters, reducing the situation where the classification results are not ideal due to the setting of parameters by personal subjective factors, and providing a more accurate classification rate for bearing fault diagnosis classification. Attached Figure Description

[0064] Figure 1 This is a flowchart of the bearing fault diagnosis and classification method in a specific embodiment of the present invention;

[0065] Figure 2 This is a flowchart illustrating the improved Red Fox optimization algorithm in a specific embodiment of the present invention. Detailed Implementation

[0066] The present invention will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present invention and should not be construed as limiting the scope of protection of the present invention. Those skilled in the art can make some non-essential improvements and adjustments to the present invention based on the above-described contents.

[0067] Example 1

[0068] like Figure 1 As shown, the present invention provides a classification method for bearing fault diagnosis, comprising the following steps:

[0069] S1: Acquire the vibration signal of the bearing to be diagnosed and perform continuous wavelet transformation to generate a time-frequency diagram;

[0070] S2: Construct a bearing diagnosis and classification model based on a convolutional neural network, and use the time-frequency graph as a training set to train the convolutional neural network to initialize the network topology of the convolutional neural network;

[0071] S3: The convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, and an optimized bearing diagnosis classification model is constructed based on the optimal parameters;

[0072] The optimal parameters include the convolution kernel, the number of convolution kernels, the batch size, and the learning rate.

[0073] S4: Acquire the vibration signal of the bearing to be diagnosed again and perform continuous wavelet transformation to generate a time-frequency diagram. Use this time-frequency diagram as the training set of the optimized bearing diagnosis classification model. After training and testing, output the classification result.

[0074] Furthermore, in step S2, constructing a classification model for bearing fault diagnosis based on a convolutional neural network includes the following steps:

[0075] S2.1: Determine the number of network layers: Use one input layer, two convolutional layers, two max pooling layers, one fully connected layer, and one output layer;

[0076] S2.2: Selection of transfer function and training method: The ReLU function is used for the transfer function between layers, the softmax function is used as the classification function for the output layer, and the gradient descent method is selected for the training method;

[0077] S2.3: Determine the number of network training iterations and training objectives;

[0078] S2.4: Using the time-frequency graph as a training set, train the convolutional neural network to initialize the network topology of the convolutional neural network;

[0079] S2.5: Initialize the weight matrix and threshold matrix of the convolutional neural network using random functions.

[0080] Furthermore, in step S3, the optimal convolutional kernel size (first layer and second layer), the number of convolutional kernels (first layer and second layer), the batch size, and the learning rate of the convolutional neural network are obtained based on the improved Red Fox optimization algorithm.

[0081] The convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, specifically including:

[0082] S3.1: Initialize the red fox population, and use the accuracy of the cross-entropy function between the classification results of the convolutional neural network model and the actual results as the fitness function of the red fox algorithm;

[0083] S3.2: Select the position of the red fox individual with the best fitness value, simulate the red fox's life habits of foraging, hunting, and escaping hunters according to the improved red fox optimization algorithm, and iteratively update the position of the red fox individual through its five stages of finding prey, reflecting and learning, surrounding prey, elite reverse strategy, evading hunters and developing the population. Select the best individual after iteration until the maximum number of iterations is reached or the fitness meets the preset termination condition.

[0084] S3.3: If the termination condition is not met, eliminate the worst individual in the red fox population and use the best individual to reproduce offspring. Repeat step S3.2 until the iteration ends, and obtain the best individual position as the optimal convolution kernel size, number of convolution kernels, batch size and learning rate for the convolutional neural network classification model.

[0085] Furthermore, in step S3.2, the improved Red Fox optimization algorithm specifically includes the following:

[0086] S3.21: Algorithm Premise: The individual positions of the red fox population are initialized as X = (X1, X2, ..., X...). n ), where n is the number of individuals in the population, X1=(x1, x2, ..., x m ), x i ∈(a, b), a, b ∈ R, m is the dimension of the individual's position; Let represent the position of the i-th red fox during the t-th iteration; a fitness function is pre-defined, assuming the red foxes are active within a specific spatial range, and the red fox with the best fitness is denoted as the optimal individual, called α fox;

[0087] S3.22: Calculate the fitness value and select the red fox individual with the lowest fitness; select the cross-entropy function between the training set and the actual values ​​of the convolutional neural network as the fitness function for the red fox individual:

[0088]

[0089] Where y i For the accurate value of classification, s i For the actual classification output, the smaller the fitness value of the red fox individual, the higher the classification accuracy of the algorithm;

[0090] S3.23: Hunting Prey – Global Search Phase; In this phase, individual red foxes venture out to hunt prey. The fox pack communicates with each other, sharing the locations where prey is most easily caught, causing the pack to move towards the optimal individual's location. If the fitness value after the move is better than the original location, the location is updated; otherwise, it returns to the original location. In one iteration, the individual and the optimal individual... The distance is expressed as:

[0091]

[0092] The formula for updating individual location is:

[0093]

[0094] in It is a random number within that interval;

[0095] S3.24: Introduce reflective learning to update individual positions; compare and contrast the red fox's positions before and after the update, and select the optimal position to update. The formula for reflective learning is as follows:

[0096]

[0097] in, This is the updated position after the red fox moves with the alpha fox. This is the Red Fox's starting position, X f It represents the new position generated after reflective learning; ω∈[-1, 1] represents the learning factor;

[0098] Furthermore, to prevent excessive randomness in the reflective learning process, the following constraints are imposed on the learning factors:

[0099]

[0100] Where: r∈[0,π] is a random number, t is the current number of iterations, and T is the maximum number of iterations; individuals have strong reflective behavior in the early stage, which can improve hunting ability and achieve self-improvement; in the later stage, as individuals get closer and closer to prey, reflective behavior gradually decreases, and the learning factor ω also gradually decreases.

[0101] S3.25: Surrounding the Prey – Local Search Phase; After discovering suspicious prey, the red fox hunts by observing its surroundings, camouflaging and hiding, and waiting for an opportunity to strike. The mathematical model is as follows:

[0102]

[0103] Where μ∈[0,1] is a random number within this interval, to balance the approximation and camouflage stages; the expression for the red fox's activity radius r when surrounding its prey is as follows:

[0104]

[0105] Where a∈(0, 0.2) is defined as the approximation parameter; φ0 is a random number between 0 and 2π, representing the red fox's observation angle; θ∈(0, 1) is the initially set random number, simulating the influence of weather factors during the red fox's hunt; when the time is right, the red fox begins to surround and approach its prey, and its position is updated as follows:

[0106]

[0107] Where φ1, φ2, ..., φ n-1 It is a random number between 0 and 2π; This indicates the new location for the red fox;

[0108] S3.26: Adopt an elite reverse learning strategy; let the position of the elite individual in the current group be...

[0109] X best = (x1, x2, ..., x n )

[0110] Then the reverse solution Defined as:

[0111]

[0112] Where, k∈[0,1], a j b j It is x i Boundary values;

[0113] Furthermore, in step S3.26, the elite reverse learning strategy is adopted, selecting the top 20% of individuals in terms of fitness to form an elite fox group F. best And the elite fox population was obtained using the inverse solution. In mixed fox populations Then select the top 50% of red foxes in terms of fitness as the next generation.

[0114] S3.27: Evade hunters and develop the population; the bottom 5% of individuals with the worst fitness values ​​in the population are hunted and eliminated by hunters, and the α red fox couple with the best fitness values ​​(X) are selected. best1 X best2 Establish a habitat model; the formula for calculating the habitat center is:

[0115]

[0116] in, This represents the best-fitting red fox individual; the habitat fox pack activity diameter is defined as:

[0117]

[0118] Furthermore, in the process of evading hunters and developing the population, the parameter k∈(0,1) is set when developing the population, as shown below:

[0119]

[0120] When k < 0.45, the α red fox couple reproduces, producing new individuals, which can be denoted as:

[0121]

[0122] By adopting the above technical solution and setting parameter k, the migration or breeding stages of fox groups can be distinguished.

[0123] S3.28: Determine if the termination condition is met; if the termination condition is met, obtain the optimal individual position, i.e., the optimal kernel size (first and second layers), number of kernels (first and second layers), batch size, and learning rate of the convolutional neural network, and then construct a new convolutional neural network.

[0124] S3.29: If the termination condition is not met, eliminate the worst individual in the red fox population and use the best individual to reproduce offspring. Repeat step S42 until the iteration ends, and obtain the best individual position as the optimal convolutional kernel size (first and second layers), number of convolutional kernels (first and second layers), batch size, and learning rate for the convolutional neural network classification model.

[0125] This invention classifies bearing faults by establishing a classification model for bearing fault diagnosis based on a convolutional neural network. First, the vibration signals obtained from sensors are converted into time-frequency maps using continuous wavelet transform. These time-frequency maps are then used as input to the classification model. Finally, an improved Red Fox optimization algorithm is used to optimize the parameters of the convolutional neural network, determining the optimal parameters to complete the model construction. New vibration signals are added to the model for training and learning, thereby improving the classification accuracy of fault diagnosis.

[0126] This invention improves the performance of the Red Fox Optimization Algorithm by modifying it. First, reflective learning is introduced into the Red Fox Optimization Algorithm to compare the positions of red foxes before and after updates, thereby enhancing the hunting ability of individuals and preventing the algorithm from getting trapped in local optima. Second, an elite back-learning strategy is employed to select high-quality individuals as the next generation of the population, increasing population diversity, preventing premature convergence, and improving algorithm efficiency. Compared to other traditional optimization algorithms, the improved algorithm shows improvements in convergence speed and accuracy. Furthermore, by utilizing the Red Fox Optimization Algorithm for parameter optimization, it reduces the possibility of unsatisfactory classification results caused by subjective parameter settings, providing a more accurate classification rate for bearing fault diagnosis.

[0127] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A classification method for bearing fault diagnosis, characterized in that: Includes the following steps: S1: Acquire the vibration signal of the bearing to be diagnosed and perform continuous wavelet transformation to generate a time-frequency diagram; S2: Construct a bearing diagnosis and classification model based on a convolutional neural network, and use the time-frequency graph as a training set to train the convolutional neural network to initialize the network topology of the convolutional neural network; S3: The convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, and an optimized bearing diagnosis classification model is constructed based on the optimal parameters; The optimal parameters include the convolution kernel, the number of convolution kernels, the batch size, and the learning rate. S4: Acquire the vibration signal of the bearing to be diagnosed again and perform continuous wavelet transformation to generate a time-frequency diagram. Use this time-frequency diagram as the training set for the optimized bearing diagnosis classification model. After training and testing, output the classification result. In step S3, the convolutional neural network is optimized based on the improved Red Fox optimization algorithm to obtain the optimal parameters of the convolutional neural network, specifically including: S3.1: Initialize the red fox population, and use the accuracy of the cross-entropy function between the classification results of the convolutional neural network model and the actual results as the fitness function of the red fox algorithm; S3.2: Select the position of the red fox individual with the best fitness value, simulate the red fox's life habits of foraging, hunting, and escaping hunters according to the improved red fox optimization algorithm, and iteratively update the position of the red fox individual through its five stages of finding prey, reflecting and learning, surrounding prey, elite reverse strategy, evading hunters and developing the population. Select the best individual after iteration until the maximum number of iterations is reached or the fitness meets the preset termination condition. S3.3: If the termination condition is not met, eliminate the worst individual in the red fox population and use the best individual to reproduce offspring. Repeat step S3.2 until the iteration ends, and obtain the best individual position as the optimal convolution kernel size, number of convolution kernels, batch size and learning rate for the convolutional neural network classification model.

2. The classification method for bearing fault diagnosis according to claim 1, characterized in that, Step S2 includes: S2.1: Determine the number of network layers: Use one input layer, two convolutional layers, two max pooling layers, one fully connected layer, and one output layer; S2.2: Selection of transfer function and training method: The ReLU function is used for the transfer function between layers, the softmax function is used as the classification function for the output layer, and the gradient descent method is selected for the training method; S2.3: Determine the number of network training iterations and training objectives; S2.4: Using the time-frequency graph as a training set, train the convolutional neural network to initialize the network topology of the convolutional neural network; S2.5: Initialize the weight matrix and threshold matrix of the convolutional neural network using random functions.

3. The classification method for bearing fault diagnosis according to claim 1, characterized in that, In step S3.2, the improved Red Fox optimization algorithm specifically includes the following: S3.21: Algorithm Premise: The individual positions of the red fox population are initialized as follows: ,in The number of individuals in the population. Let be the dimension of the individual's position; Indicates the first During the nth iteration The location of only the red fox; A fitness function is predefined. Assuming the red foxes move within a specific spatial range, the red fox with the best fitness is denoted as the optimal individual, and is called the best individual. fox; S3.22: Calculate the fitness value and select the red fox individual with the lowest fitness; select the cross-entropy function between the training set and the actual values ​​of the convolutional neural network as the fitness function for the red fox individual: ； in For the accurate value of the classification, For the actual classification output, the smaller the fitness value of the red fox individual, the higher the classification accuracy of the algorithm; S3.23: Hunting Prey – Global Search Phase; In this phase, individual red foxes venture out to hunt prey. The fox pack communicates with each other, sharing the locations where prey is most easily caught, causing the pack to move towards the optimal individual's location. If the fitness value after the move is better than the original location, the location is updated; otherwise, it returns to the original location. In one iteration, the individual and the optimal individual... The distance is expressed as: ； The formula for updating individual location is: ； in It is a random number within that interval; S3.24: Introduce reflective learning to update individual positions; compare and contrast the red fox's positions before and after the update, and select the optimal position to update. The formula for reflective learning is as follows: ； in, It was the red fox that followed. Fox moved to its updated location. This is the red fox's starting position. It is a new position that arises from reflection and learning; Indicates the learning factor; S3.25: Surrounding the Prey – Local Search Phase; After discovering suspicious prey, the red fox hunts by observing its surroundings, camouflaging and hiding, and waiting for an opportunity to strike. The mathematical model is as follows: ； in, The random number within this interval is used to balance the approximation and camouflage phases; the red fox's activity radius when surrounding its prey. The expression is as follows: ； in, , is defined as the approximation parameter; It is between The random number between these values ​​represents the red fox's observation angle; The initial random number represents the influence of weather factors during a red fox's hunt; once the time is right, the red fox begins to surround and approach its prey, and its position is updated as follows: ； in, It is between Random numbers between; This indicates the new location for the red fox; S3.26: Adopt an elite-reverse learning strategy; let the position of the elite individual in the current group be: ； Then the reverse solution Defined as: ； in, yes Boundary values; S3.27: Evade hunters and develop the population; the bottom 5% of individuals with the worst fitness values ​​in the population are hunted and eliminated by hunters, and the individuals with the best fitness values ​​are selected. Red Fox Couple Establish a habitat model; the formula for calculating the habitat center is: ； in, This represents the best-fitting red fox individual; the habitat fox pack activity diameter is defined as: ； S3.28: Determine if the termination condition is met; if the termination condition is met, obtain the optimal individual position, i.e., the optimal kernel size, number of kernels, batch size, and learning rate of the convolutional neural network, and then construct a new convolutional neural network. S3.29: If the termination condition is not met, eliminate the worst individual, select the best individuals to breed new individuals, and repeat step S3.

22.

4. The bearing fault diagnosis classification method according to claim 3, characterized in that: In S3.24, to prevent excessive randomness during reflective learning, the following constraints are imposed on the learning factor: ； in: Random numbers on the screen For the current number of times, This represents the maximum number of iterations; individuals exhibit strong reflective behavior in the early stages, enhancing their hunting abilities and achieving self-improvement; however, as individuals get closer to their prey, reflective behavior gradually decreases, and the learning factor... It also gradually became smaller.

5. The classification method for bearing fault diagnosis according to claim 3, characterized in that: In step S3.26, the elite reverse learning strategy is adopted, selecting the top 20% of individuals in terms of fitness to form an elite fox group. And the elite fox population was obtained using the inverse solution. In mixed fox populations Then select the top 50% of red foxes in terms of fitness as the next generation.

6. The classification method for bearing fault diagnosis according to claim 3, characterized in that: In step S3.27, while evading hunters and developing the population, parameters are set during population development. The details are as follows: ； when hour, When a pair of red foxes reproduce, they produce offspring, which can be denoted as: 。

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