Mechanical equipment lightweight intelligent fault diagnosis method based on Kolmogorov-Arnold network

Abstract

The invention discloses a mechanical equipment lightweight intelligent fault diagnosis method based on a Kolmogorov-Arnold network, and the method comprises the steps: firstly obtaining original vibration monitoring data of mechanical equipment under different fault types, and constructing an equipment vibration monitoring fault data set; a KAN-based fault diagnosis model is constructed, and a learnable nonlinear function is adopted to replace a fixed linear weight in convolution; then, the output is converted into a one-dimensional feature vector through KAN convolution operation; inputting the one-dimensional feature vector into a KANLinear layer so as to realize the mapping of the high-dimensional feature to different fault types; then calculating training loss, taking the total loss as an optimization target of a training stage, and updating model parameters by using a gradient descent method; iteratively optimizing the fault diagnosis model; and finally, testing the fault diagnosis model by using the test set. According to the method, high diagnosis precision can be maintained, meanwhile, the model parameter quantity is remarkably reduced, the calculation cost is reduced, and therefore the overall calculation efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical equipment fault diagnosis, and in particular to a lightweight intelligent fault diagnosis method for mechanical equipment based on a Kolmogorov-Arnold network. Background Art

[0002] Mechanical fault diagnosis is a key technology in industrial equipment maintenance. It can effectively prevent equipment failures, reduce maintenance costs and improve equipment reliability. At present, the methods of mechanical fault diagnosis mainly include model-based methods, signal processing-based methods and data-driven machine learning methods. Traditional model-based diagnosis methods rely on the physical model of the equipment, but the actual mechanical system is complex and changeable, and it is very difficult to establish an accurate model; while signal processing-based methods, such as time domain and frequency domain analysis, although they can effectively extract some fault features, are difficult to handle complex nonlinear faults and require a lot of experience and prior knowledge ([1] Li Han, Xiao Deyun. A review of data-driven fault diagnosis methods [J]. Control and Decision, 2011, 26(01): 1-9+16.).

[0003] In this context, data-driven machine learning methods have gradually attracted widespread attention. Due to its outstanding performance in the field of image processing, convolutional neural networks (CNNs) have been introduced into the field of fault diagnosis in recent years. They are used to automatically extract features from vibration signals and reduce the dependence on prior knowledge ([2] Wu Dinghai, Ren Guoquan, Wang Huaiguang, et al. A review of mechanical fault diagnosis methods based on convolutional neural networks [J]. Journal of Mechanical Strength, 2020, 42(05): 1024-1032.). CNN effectively captures local features in the data through convolution operations and is suitable for processing high-dimensional data. However, CNN models often contain a large number of parameters, resulting in high computational costs, and still have certain limitations when processing complex nonlinear signals.

[0004] To solve this problem, the Kolmogorov-Arnold network (KAN) provides a new architecture ([3] Ziming Liu. Kan: Kolmogorov–arnold networks. arXiv preprint arXiv: 2404.19756, 2024.). According to the Kolmogorov-Arnold theorem, any multivariable continuous function can be represented by the superposition of a finite number of univariate functions. Based on this theorem, KAN introduces learnable B-spline functions between network layers to replace linear activation functions, thereby realizing the design of adjustable nonlinear activation functions. This design reduces the number of model parameters while enhancing the nonlinear expression ability of the model, effectively improving the generalization ability of the fault diagnosis model.

[0005] In summary, the current fault diagnosis technology has the disadvantages of insufficient extraction of complex nonlinear features, large number of model parameters, and high computational cost. Combining the advantages of convolutional neural networks and KAN, a hybrid network architecture is constructed to reduce the number of model parameters while ensuring high diagnostic accuracy, which has become one of the effective ways to solve the complex signal processing problem in mechanical fault diagnosis. Summary of the invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a lightweight intelligent fault diagnosis method for mechanical equipment based on the Kolmogorov-Arnold network. By combining the spatial feature extraction capability of convolutional neural networks (CNN) and the nonlinear representation advantage of KAN, an efficient and lightweight hybrid neural network model is constructed. It can not only maintain high diagnostic accuracy while significantly reducing the amount of model parameters and reducing computational costs, thereby improving the overall computing efficiency.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A lightweight intelligent fault diagnosis method for mechanical equipment based on Kolmogorov-Arnold network includes the following steps:

[0009] Step 1: Obtain the original vibration monitoring data of mechanical equipment under different fault types;

[0010] Step 2: Construct equipment vibration monitoring fault data set O = {O 1 ,O 2 ,…O m ,…O n}, indicating that there are n different types of faults, among which O m =(T m ,E m ), that is, each fault type contains training set data T m And the test set data E m ,in Indicates that the training set contains N T Samples; Indicates that the training set contains N E The length of each sample is L.

[0011] Step 3: Construct a fault diagnosis model based on KAN, establish a KAN convolutional layer, and train the training set data T obtained in step 2. m Perform feature extraction and use learnable nonlinear functions to replace fixed linear weights in convolution;

[0012] The convolution process is to convolve the window in the sample S LSlide up, the input data in the window first undergoes nonlinear transformation of the B-spline function, and then extracts features through weighted combination of spline basis functions, and finally obtains the output result of KAN convolution; where the convolution kernel K M =[φ 1 φ 2 … φ M ] T Indicates that the convolution kernel size is M, S L =[a 1 a 2 … a L ] T Indicates that the length of a single sample is L; the convolution result at a certain position i of the sample is Each sample S L After one layer of KAN convolution, the output is O conv =[b 1 b 2 … b k … b N ] T , where b k =[c 1 c 2 … c l ], there are N convolution kernels in total, and the output length after convolution is l = L-N+1;

[0013] Step 4: The output feature O obtained by the KAN convolution operation in step 3 conv Flatten it and convert it into a one-dimensional feature vector O in =[d 1 d 2 …d FL ], where d FL =N×l;

[0014] Step 5: Create a KANLinear layer and transform the one-dimensional feature vector O obtained in step 4 in Input into the KANLinear layer to realize the mapping of high-dimensional features to different fault types; the output part is composed of the base linear layer output (BaseOutput) and the B-spline output (SplineOutput);

[0015] Step 6: Calculate the training loss, which includes cross entropy loss and regularization loss;

[0016] Step 7: Substitute the total loss L obtained in step 6 reg As the optimization target in the training phase, the model parameter η is updated using the gradient descent method:

[0017]

[0018] In the formula, α represents the learning rate;

[0019] Step 8: Repeat steps 3 to 7 to continuously iterate and optimize the fault diagnosis model until the maximum number of iterations is reached;

[0020] Step 9: Use the test set E divided in step 2 m ,The fault diagnosis model is tested by accuracy, precision, recall and F1-score indicators.

[0021] In step 3, each element φ in the KAN convolution kernel is defined as:

[0022] φ=w 1 spline(x)+w 2 ·silu(x) (1)

[0023] Where x is the input data, spline(x) is the B-spline function, silu(x) is the SiLU activation function, and w 1 and w 2 are the weights of the B-spline function and the SiLU activation function respectively; the calculation of the B-spline function depends on the input data x and the predefined grid grid, which is defined as follows:

[0024]

[0025] Among them, R represents the order of the B-spline function, grid k Represents the kth grid point in the grid; the definition of the grid is as follows:

[0026] grid=[{k·h+GLIM 0 |k∈{-R,...,D+R}}] (3)

[0027] Where GLIM is the specified grid range, GLIM 1 As the upper limit, GLIM 0 is the lower limit; D is the grid size, h is the step size, and is defined as:

[0028]

[0029] The output part in step 5 is composed of the base linear layer output (BaseOutput) and the B-spline output (SplineOutput), and the specific calculation method is as follows:

[0030] BaseOutput = W base ·SiLU(O in ) (5)

[0031] SplineOutput = W spline ·spline(O in ) (6) In the formula, The weight matrix corresponding to the base linear layer, The weight matrix corresponding to the B-spline; the final output is Output = BaseOutput + SplineOutput.

[0032] The specific calculation formula of the loss in step 6 is as follows:

[0033]

[0034] Where, L ce is the cross entropy loss, B is the number of data samples in the batch, y i,j represents the true label value of sample i under category c, p i,j represents the predicted probability that sample i belongs to category j; L reg is the total loss including the cross entropy loss and the regularization term, where λ is the regularization coefficient and μ 1 , μ 2 They are μ 2 The weight of the regularization direction and entropy regularization term, M represents the number of network layers, Φ m is the weight matrix of the mth layer.

[0035] The specific calculation formulas for the accuracy, precision, recall, and F1-score indicators in step 9 are as follows:

[0036]

[0037]

[0038] In the formula, TP represents true positive examples, FP represents false positive examples, and FN represents false negative examples.

[0039] Compared with the prior art, the effective effects of the present invention are:

[0040] The present invention proposes a lightweight intelligent fault diagnosis method for mechanical equipment based on a Kolmogorov-Arnold network. During the convolution process, a learnable B-spline function is used to replace the fixed linear activation function in the traditional convolution for nonlinear activation, and the grid parameters are adaptively adjusted according to the distribution of input data. The fault features in the vibration signal are extracted more efficiently, and the ability to capture complex nonlinear features is improved. In addition, the KANLinear layer uses a B-spline basis function and a spline weight matrix to replace the linear weights in the traditional fully connected layer, so that the input features and the output space are mapped more flexibly and nonlinearly, which not only enhances the flexibility of feature extraction, but also effectively reduces the number of parameters required to maintain high diagnostic accuracy, thereby achieving faster convergence and better generalization. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the present invention.

[0042] Figure 2 Schematic diagram of the model structure used in the embodiment of the present invention and the comparative method. Specific implementation methods

[0044] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0045] Reference Figure 1 , a lightweight intelligent fault diagnosis method for mechanical equipment based on Kolmogorov-Arnold network, comprising the following steps:

[0046] Step 1: Obtain original vibration monitoring data of mechanical equipment (such as rotating bearings) under different fault types;

[0047] Step 2: Construct equipment vibration monitoring fault data set O = {O 1 ,O 2 ,…O m ,…O n}, indicating that there are n different types of faults, among which O m =(T m ,E m ), that is, each fault type contains training set data T m And the test set data E m ,in Indicates that the training set contains N T Samples; Indicates that the training set contains N E The length of each sample is L.

[0048] Step 3: Construct a fault diagnosis model based on KAN, establish a KAN convolutional layer, and train the training set data T obtained in step 2. mFor feature extraction, a learnable nonlinear function is used to replace the fixed linear weights in ordinary convolution. Each element φ in the KAN convolution kernel is defined as:

[0049] φ=w 1 spline(x)+w 2 ·silu(x) (1)

[0050] Where x is the input data, spline(x) is the B-spline function, silu(x) is the SiLU activation function, and w 1 and w 2 are the weights of the B-spline function and the SiLU activation function respectively; the calculation of the B-spline function depends on the input data x and the predefined grid grid, which is defined as follows:

[0051]

[0052] Among them, R represents the order of the B-spline function, grid k Represents the kth grid point in the grid; the definition of the grid is as follows:

[0053] grid=[{k·h+GLIM 0 |k∈{-R,…,D+R}}] (3)

[0054] Where GLIM is the specified grid range, GLIM 1 As the upper limit, GLIM 0 is the lower limit; D is the grid size, h is the step size, and is defined as:

[0055]

[0056] The convolution process is to convolve the window in the sample S L Slide up, the input data in the window first undergoes nonlinear transformation of the B-spline function, and then extracts features through weighted combination of spline basis functions, and finally obtains the output result of KAN convolution; where the convolution kernel K M =[φ 1 φ 2 … φ M ] T Indicates that the convolution kernel size is M, S L =[a 1 a 2 … a L ] T Indicates that the length of a single sample is L; the convolution result at a certain position i of the sample is Each sample S L After one layer of KAN convolution, the output is O conv =[b1 b 2 … b k … b N ] T , where b k =[c 1 c 2 … c l ], there are N convolution kernels in total, and the output length after convolution is l = L-N+1;

[0057] The KAN convolution kernel replaces fixed weights with B-spline functions defined on a preset grid, and builds a feature capture mechanism based on a multi-scale grid. Compared with traditional fixed-step convolution, this mechanism is extremely flexible and can adaptively adjust the convolution operation according to the different ranges and scales of the input data, thereby more accurately capturing local feature changes and improving the generalization ability and expressiveness of the model when processing complex data distributions.

[0058] Step 4: The output feature O obtained by the KAN convolution operation in step 3 conv Flatten it and convert it into a one-dimensional feature vector O in =[d 1 d 2 …d FL ], where d FL =N×l;

[0059] Step 5: Create a KANLinear layer and transform the one-dimensional feature vector O obtained in step 4 in Input into the KANLinear layer to realize the mapping of high-dimensional features to different fault types; the output part is composed of the base linear layer output (BaseOutput) and the B-spline output (SplineOutput), and the specific calculation method is as follows:

[0060] BaseOutput = W base ·SiLU(O in ) (5)

[0061] SplineOutput = W spline ·spline(O in ) (6) In the formula, The weight matrix corresponding to the base linear layer, The weight matrix corresponding to the B-spline; the final output is Output = BaseOutput + SplineOutput;

[0062] The KANLinear layer achieves efficient feature mapping and extraction by combining the B-spline function with the basic linear layer. Compared with the traditional fully connected layer, the KANLinear layer uses the weight matrix defined by the B-spline function on the preset grid, making the model more flexible and adaptable when processing data of different scales and distributions. This layer decomposes the input data through an adjustable multi-scale grid and combines it with learnable spline weights to capture local feature changes while maintaining the integrity of global features. The combination of the basic linear layer and the spline function output further enhances the nonlinear expression ability of the model.

[0063] Step 6: Calculate the training loss. The loss includes cross entropy loss and regularization loss. The specific calculation formula is as follows:

[0064]

[0065] Where, L ce is the cross entropy loss, B is the number of data samples in the batch, y i,j represents the true label value of sample i under category c, p i,j represents the predicted probability that sample i belongs to category j; L reg is the total loss including the cross entropy loss and the regularization term, where λ is the regularization coefficient and μ 1 , μ 2 They are μ 2 The weight of the regularization direction and entropy regularization term, M represents the number of network layers, Φ m is the weight matrix of the mth layer;

[0066] Step 7: Substitute the total loss L obtained in step 6 reg As the optimization target in the training phase, the model parameter η is updated using the gradient descent method:

[0067]

[0068] In the formula, α represents the learning rate;

[0069] Step 8: Repeat steps 3 to 7 to continuously iterate and optimize the fault diagnosis model until the maximum number of iterations is reached;

[0070] Step 9: Use the test set E divided in step 2 m , the fault diagnosis model is tested by indicators such as accuracy, precision, recall, and F1-score. The specific calculation formula is as follows:

[0071]

[0072] In the formula, TP represents true positive examples, FP represents false positive examples, and FN represents false negative examples.

[0073] The effectiveness of the present invention is verified below by taking the fault diagnosis of Case Western Reserve's public bearing fault data set as an example.

[0074] From the Case Western Reserve public bearing fault data set, we selected the normal bearing data and nine fault type data under the working condition of motor load 0 and speed 1797. Each type of data was divided into training set and test set in a 1:1 ratio, including 50 training samples and test samples respectively; the training set data was input into the fault diagnosis model for model training; the fault diagnosis model contains two KAN convolutional layers and one KANLinear layer, and the dimensions of the KAN convolutional layers are 5 and 25 respectively. The model training parameters are shown in Table 1:

[0075] Table 1. Fault diagnosis model training parameters

[0076]

[0077] After the fault diagnosis model training is completed, the test set data is input into the fault diagnosis model to obtain the test results of the model. In order to fully verify the effectiveness of the method of the present invention, the test accuracy, precision, recall rate and F1 score are used to evaluate the performance of the model. At the same time, the method of the present invention is compared with the comparative method. Figure 2 , the network model used in comparison method 1 has the same number of parameters as the method of the present invention, but uses ordinary convolutional layers and fully connected layers; the network model used in comparison method 2 has the same number of parameters as the method of the present invention, but uses ordinary convolutional layers and KANLinear layers; the network model used in comparison method 3 has the same number of parameters as the method of the present invention, but uses KAN convolutional layers and ordinary fully connected layers; comparison method 4 uses ordinary convolutional layers and fully connected layers, but the number of parameters is much larger than that of the method of the present invention. It can be seen from Table 2 that under the condition of the same number of parameters, the fault diagnosis model combining the use of KAN convolutional layers and KANLinear layers is significantly better than the comparison method in multiple performance indicators such as precision, recall rate, F1 score and test accuracy, which fully verifies the effectiveness and superiority of the method of the present invention in complex nonlinear signal feature extraction and mapping. Compared with the model that only uses the traditional convolutional layer or the fully connected layer, the introduction of the KAN convolutional layer or the KANLinear layer alone can also improve the diagnostic precision and accuracy of the model to a certain extent; under the condition of ensuring high diagnostic accuracy, the number of parameters required for the traditional convolutional neural network is more than that of the method of the present invention, which proves that the method of the present invention can maintain a high performance level while optimizing the model structure and reducing parameter consumption.

[0078] Table 2 Comparison of fault diagnosis index performance of different methods

[0079]

Claims

1. A lightweight intelligent fault diagnosis method for mechanical equipment based on Kolmogorov-Arnold network, characterized in that: The following steps are involved: Step 1: Obtain the original vibration monitoring data of mechanical equipment under different fault types; Step 2: Construct equipment vibration monitoring fault data set O = {O1, O2, …O m ,…O n }, indicating that there are n different types of faults, among which O m =(T m ,E m ), that is, each fault type contains training set data T m And the test set data E m ,in Indicates that the training set contains N T Samples; Indicates that the training set contains N E The length of each sample is L. Step 3: Construct a fault diagnosis model based on KAN, establish a KAN convolutional layer, and train the training set data T obtained in step 2. m Perform feature extraction and use learnable nonlinear functions to replace fixed linear weights in convolution; The convolution process is to convolve the window in the sample S L Slide up, the input data in the window first undergoes nonlinear transformation of the B-spline function, and then extracts features through weighted combination of spline basis functions, and finally obtains the output result of KAN convolution; where the convolution kernel K M =[φ1 φ2 … φ M ] T Indicates that the convolution kernel size is M, S L =[a1 a2 … a L ] T Indicates that the length of a single sample is L; the convolution result at a certain position i of the sample is Each sample S L After one layer of KAN convolution, the output is O conv =[b1 b2…b k …b N ] T , where b k =[c1 c2…c l ], there are N convolution kernels in total, and the output length after convolution is l = L-N+1; Step 4: The output feature O obtained by the KAN convolution operation in step 3 conv Flatten it and convert it into a one-dimensional feature vector O in =[d1 d2…d FL ], where d FL =N×l; Step 5: Create a KANLinear layer and transform the one-dimensional feature vector O obtained in step 4 in Input into the KANLinear layer to realize the mapping of high-dimensional features to different fault types; the output part is composed of the base linear layer output (BaseOutput) and the B-spline output (SplineOutput); Step 6: Calculate the training loss, which includes cross entropy loss and regularization loss; Step 7: Substitute the total loss L obtained in step 6 reg As the optimization target in the training phase, the model parameter η is updated using the gradient descent method: In the formula, α represents the learning rate; Step 8: Repeat steps 3 to 7 to continuously iterate and optimize the fault diagnosis model until the maximum number of iterations is reached; Step 9: Use the test set E divided in step 2 m ,The fault diagnosis model is tested by accuracy, precision, recall and F1-score indicators.

2. The method according to claim 1, characterized in that In step 3, each element φ in the KAN convolution kernel is defined as: φ=w1·spline(x)+w2·silu(x) (1) Where x is the input data, spline(x) is the B-spline function, silu(x) is the SiLU activation function, w1 and w2 are the weights of the B-spline function and the SiLU activation function respectively; the calculation of the B-spline function depends on the input data x and the predefined grid grid, which is defined as follows: Among them, R represents the order of the B-spline function, grid k Represents the kth grid point in the grid; the definition of the grid is as follows: grid=[{k·h+GLIM0|k∈{-R,...,D+R}}] (3) Where GLIM is the specified grid range, GLIM1 is the upper limit, and GLIM0 is the lower limit; D is the grid size, and h is the step size, which is defined as:

3. The method according to claim 1, characterized in that The output part in step 5 is composed of the base linear layer output (BaseOutput) and the B-spline output (SplineOutput), and the specific calculation method is as follows: BaseOutput = W base ·SiLU(O in (5)SplineOutput = W spline ·spline(O in )(6)In the formula, The weight matrix corresponding to the base linear layer, The weight matrix corresponding to the B-spline; the final output is Output = BaseOutput + SplineOutput.

4. The method according to claim 1, characterized in that: The specific calculation formula of the loss in step 6 is as follows: Where, L ce is the cross entropy loss, B is the number of data samples in the batch, y i,j represents the true label value of sample i under category c, p i,j represents the predicted probability that sample i belongs to category j; L reg is the total loss including the cross entropy loss and the regularization term, where λ is the regularization coefficient, μ1 and μ2 are the weights of the μ2 regularization direction and the entropy regularization term, M represents the number of network layers, and Φ m is the weight matrix of the mth layer.

5. The method according to claim 1, characterized in that The specific calculation formulas for the accuracy, precision, recall, and F1-score indicators in step 9 are as follows: In the formula, TP represents true positive examples, FP represents false positive examples, and FN represents false negative examples.

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