MSRC-KAN-PAM-based interpretable rotating machine fault diagnosis method

Abstract

The invention discloses an interpretable rotating machine fault diagnosis method based on MSRC-KAN-PAM. The method comprises the following steps: 1) data acquisition: acquiring vibration signals of key transmission parts (such as a bearing and a gear) of a rotating machine in various health states; 2) data preprocessing: segmenting the vibration signals into sample sets through sliding window sampling, and dividing the sample sets into a training set, a verification set and a test set; 3) model construction: constructing an MSRC-KAN-PAM model based on a multi-scale residual error convolution (MSRC), a KAN and a power spectral density activation graph (PAM), wherein the MSRC-KAN-PAM model is constructed on the basis of the MSRC, the KAN and the PAM; 4) model training, verification and evaluation: training the model on the training set and the verification set, and evaluating the model performance on the test set; and 5) interpretable fault diagnosis: performing fault diagnosis on the rotating machine by using the trained model, and visualizing the diagnosis standard of the health status in the frequency domain. The method realizes extraction and integration of multi-scale features from different channel dimensions of the vibration signal in the time domain, performs fault diagnosis by using the KAN, and explains the diagnosis standard of the health status in the frequency domain.

Description

Technical Field

[0001] The present invention belongs to the technical field of rotating machinery fault diagnosis, and particularly relates to an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM. Background Technique

[0002] With the rapid development of modern mechanical systems, rotating machinery has become indispensable in intelligent equipment, and the academic and industrial communities have paid great attention to its safety. Under high-intensity working conditions, key transmission components of rotating machinery (such as bearings and gears) will inevitably have faults such as wear, corrosion, deformation, and fracture. Faulty transmission components directly affect the operation reliability of rotating machinery, and may lead to serious accidents, economic losses, and even casualties. Therefore, carrying out fault diagnosis and predictive maintenance of rotating machinery has important research value.

[0003] Traditional data-driven fault diagnosis methods can be divided into three steps: signal acquisition, feature extraction, and state recognition. The collected signals can be vibration signals, current signals, acoustic signals, and temperature signals. Signal processing methods are widely used for feature extraction, such as empirical mode decomposition, Hilbert vibration decomposition, atomic decomposition, empirical wavelet transform, variational mode decomposition, and synchrosqueezing transform. The extracted features are used for state recognition through machine learning algorithms, such as logistic regression, K-nearest neighbor, naive Bayes, decision tree, support vector machine, and artificial neural network. However, machine learning algorithms are only suitable for small-scale data, and feature extraction through signal processing highly depends on expert prior knowledge and manual feature selection, which limits the generalization ability of these methods.

[0004] In recent years, deep learning technology has received extensive attention in the field of fault diagnosis due to its powerful fault feature extraction ability and end-to-end diagnosis characteristics. Deep learning models such as deep belief network DBN, multi-layer perceptron MLP, autoencoder AE, convolutional neural network CNN, and recurrent neural network RNN have been widely studied and applied to rotating machinery fault diagnosis. In particular, CNN-based methods have performed well in various rotating machinery fault diagnosis tasks. However, due to its complex hierarchical structure and a large number of parameters that are difficult to analyze, CNN faces challenges in interpretability analysis, and its decision-making mechanism is often regarded as a black box system.

[0005] The vibration signals monitored during the operation of key transmission components of rotating machinery contain rich time-frequency domain feature information. Traditional signal analysis methods based on Fourier transform, wavelet analysis, etc. have a solid theoretical foundation and clear physical meaning, and it is a very feasible solution to use them to improve the interpretability of CNN.

[0006] The differences compared with the prior art are as follows:

[0007] Technical Comparison with Patent CN109299705B "Rotating Machinery Fault Diagnosis Method Based on One-Dimensional Deep Residual Convolutional Neural Network"

[0008] Patent CN109299705B proposes a rotating machinery fault diagnosis method based on one-dimensional deep residual convolutional neural network, aiming to complete the rotating machinery fault diagnosis task; this patent proposes an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM, aiming to complete the interpretable rotating machinery fault diagnosis task. There are essential differences in their technical objectives.

[0009] Patent CN109299705B enables the network to learn deeper and more abstract fault features of training samples through stacked one-dimensional residual modules. Then, the Adam optimization algorithm is used to optimize all hyperparameters to complete the extraction of deep features and fault classification; this patent extracts and integrates multi-scale features from different channel dimensions of vibration signals in the time domain, uses KAN for fault diagnosis, and interprets the diagnostic criteria for healthy states in the frequency domain. There are essential differences in their technical ideas.

[0010] Patent CN109299705B constructs a one-dimensional deep residual convolutional neural network model, which is an improvement of the network structure based on the convolutional neural network CNN architecture; this patent constructs an MSRC-KAN-PAM model, which belongs to the design and development of the network structure. There are essential differences at the algorithm level.

[0011] Technical Comparison with Patent CN117932431A "An Unsupervised Rotating Machinery Fault Diagnosis Method Based on Multi-Scale Feature Residual Neural Network"

[0012] Patent CN117932431A proposes an unsupervised rotating machinery fault diagnosis method based on multi-scale feature residual neural network, aiming to complete the unsupervised rotating machinery fault diagnosis task; this patent proposes an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM, aiming to complete the interpretable rotating machinery fault diagnosis task. There are essential differences in their technical objectives.

[0013] Patent CN117932431A uses a multi-scale feature residual neural network to extract the features of rotating machinery vibration signals and uses the maximum mean discrepancy and minimum entropy boundary method for fault diagnosis; this patent extracts and integrates multi-scale features from different channel dimensions of vibration signals in the time domain, uses KAN for fault diagnosis, and interprets the diagnostic criteria for healthy states in the frequency domain. There are essential differences in their technical ideas.

[0014] Patent CN117932431A constructs a multi-scale extended residual neural network model, which is based on the convolutional neural network (CNN) architecture and belongs to the improvement of the network structure; this patent constructs the MSRC-KAN-PAM model, which belongs to the design and development of the network structure. There are essential differences between the two at the algorithm level. Summary of the Invention

[0015] In view of the above problems, the present invention proposes an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM. The proposed method has three main objectives: (1) Extract and integrate multi-scale features from different channel dimensions of vibration signals in the time domain; (2) Use the responsiveness and flexibility of KAN for fault diagnosis; (3) Explain the diagnostic criteria for the healthy state in the frequency domain.

[0016] To achieve the above objectives, the technical solution adopted by the present invention is:

[0017] An interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM, characterized in that it includes the following steps:

[0018] Step 1, data acquisition:

[0019] Collect vibration signals of key transmission components of rotating machinery, including bearings and gears, in various healthy states;

[0020] Step 2, data preprocessing:

[0021] Segment the vibration signals into a sample set by sliding window sampling, and divide it into a training set, a validation set, and a test set;

[0022] Step 3, model construction:

[0023] Based on the multi-scale residual convolution (MSRC), Kolmogorov-Arnold network (KAN), and power spectral density activation map (PAM), construct the MSRC-KAN-PAM model;

[0024] Step 4, model training, validation, and evaluation:

[0025] Train the model on the training set and the validation set, and evaluate the model performance on the test set;

[0026] Step 5, interpretable fault diagnosis:

[0027] Use the trained model to perform fault diagnosis on the rotating machinery, and visualize the diagnostic criteria for the healthy state in the frequency domain.

[0028] As a further improvement of the present invention, the specific steps of the first step are as follows:

[0029] One or more sensors are installed at different positions or in different directions near the rotating mechanical transmission components to be diagnosed, including bearings and gears, and a data acquisition device is used to collect vibration signals in various healthy states.

[0030] As a further improvement of the present invention, the specific steps of step two are as follows:

[0031] During sliding window sampling, there is no overlap between adjacent windows, and a certain interval is maintained; each sample contains 1024 signal points; all samples are subjected to mean-standard deviation (mean-std) normalization processing.

[0032] As a further improvement of the present invention, the specific steps of step three are as follows:

[0033] The MSRC-KAN-PAM model consists of a feature extraction module, a classification module, and a visualization module;

[0034] The feature extraction module is composed of multiple multi-scale residual convolutions (MSRC) connected in sequence, and the number of multi-scale residual convolutions (MSRC) is adjusted according to different task requirements;

[0035] For the multi-scale residual convolution (MSRC), first, parallel multi-scale convolutions Conv1d with different kernel sizes are used to extract multi-local receptive field features of the vibration signal;

[0036] Secondly, for the features extracted at each scale, layer normalization (LN) is used to stabilize the feature distribution, and the risk of overfitting is reduced through residual connection (Add);

[0037] Then, the multi-scale features are concatenated (Concat) along the channel dimension;

[0038] Finally, a hyperbolic tangent function (Tanh) is used to perform non-linear mapping, as shown in the following formula:

[0039]

[0040] Where, represents the input signal, C 1 and L 1 respectively represent the channel dimension and time dimension of the input signal, k l represents the size of the convolution kernel, represents the weight of the convolution kernel k l , represents the feature extracted by the convolution kernel k l , represents the output feature, n represents the number of different convolution kernel sizes, and L 2 represents the time dimension of the output feature;

[0041] The layer normalization LN is as shown in the following formula:

[0042]

[0043] where represents the j-th feature of the l-th layer, and L represents the time dimension of the feature, represents the normalized value of, respectively represent the mean and variance of, and ε represents a very small constant used to prevent invalid calculations when the variance is 0, respectively represent the scale and translation parameters to be learned;

[0044] The hyperbolic tangent function Tanh is as shown in the following formula:

[0045]

[0046] In the classification module, first, global power average pooling GPAP is used to reduce the dimensionality of features in the time dimension;

[0047] Then, the Kolmogorov - Arnold network KAN maps the high - dimensional features to the classification dimension of the health state, as shown in the following formula:

[0048]

[0049] where represents the features extracted by the last multi - scale residual convolution MSRC of the feature extraction module, M and L respectively represent the channel dimension and time dimension of the feature, F m represents the feature of the m - th channel, G m represents the global power average pooling GPAP value of F m , y c represents the feature value of the c - th category output by the Kolmogorov - Arnold network KAN, w c m represents connecting y c and G m the weight of;

[0050] The Kolmogorov - Arnold network KAN is implemented by stacking layers. The mapping transformation of each layer acts on the output of the previous layer to produce the input of the next layer. Each layer is structured as a learnable activation function matrix and is parameterized and optimized during the training process, as shown in the following formula:

[0051] Φ = {φ q,p}, p = 1,…, n in , q = 1,..., n out (11)

[0052] φ l,j,i , l = 0, …, L - 1, j = 1, …, n l+1 , i = 1, …, n l (12)

[0053]

[0054] Among them, n in and n out respectively represent the input feature dimension and the output feature dimension, φ l,j,i represents the learnable activation function connecting the i-th neuron in the l-th layer and the j-th neuron in the (l + 1)-th layer, x l+1,j represents the activation value of the j-th neuron in the (l + 1)-th layer, Φ l represents the function matrix of the l-th layer, containing n l ×n l+1 learnable activation functions;

[0055] The learnable activation function is the weighted sum of a spline function and a bias function, as shown in the following formula:

[0056] φ(x) = w s spline(x) + w b b(x) (16)

[0057]

[0058] Among them, spline(·) represents the linear combination of B-spline functions, c i represents the learnable combination coefficient, b(·) represents the bias function, that is, the Sigmoid linear unit function SiLU, w s and w b represent the learnable weight factors;

[0059] In the visualization module, first, calculate the power spectral density PSD of the input signal and the power spectral density PSD of each channel feature extracted by the last multi-scale residual convolution MSRC of the feature extraction module respectively;

[0060] Then, use the connection weights between the global power average pooling GPAP and the Kolmogorov - Arnold network KAN to perform weighted summation on the power spectral density PSD of each channel feature to obtain the power spectral density activation map PAM;

[0061] Finally, visualize the power spectral density PSD of the input signal and the power spectral density activation map PAM, and interpret the classification criteria of the health state in the frequency domain, as shown in the following formula:

[0062] P m = PSD(F m) (19)

[0063]

[0064] Among them, F m represents the feature of the m-th channel extracted by the last multi-scale residual convolution MSRC of the feature extraction module, and P m represents the power spectral density PSD of F m , and P AM c represents the power spectral density activation map PAM of the c-th category. ReLU(·) represents the rectified linear unit function, that is, ReLU(x) = max(0, x).

[0065] Beneficial effects:

[0066] Multi-scale residual features

[0067] The multi-scale convolution structure uses parallel convolution kernels with different kernel sizes (large kernels capture low-frequency features and small kernels focus on high-frequency features) to extract and integrate multi-local receptive field features from different channel dimensions of vibration signals. The residual connection retains the original feature information, which not only alleviates the vanishing gradient but also reduces the risk of overfitting.

[0068] Representation of complex fault modes

[0069] Introduce the Kolmogorov-Arnold network KAN to replace the traditional fully connected layer FC as the health state classification layer. Utilize the responsiveness and flexibility of its learnable activation function to enhance the model's representation ability for complex fault modes and improve the accuracy of health state classification.

[0070] Diagnostic criteria are interpretable

[0071] By visualizing the power spectral density PSD and the power spectral density activation map PAM of the input signal, establish an explicit mapping relationship of "frequency component - health state", accurately locate the specific frequency components of the input signal, reveal the theoretical basis for the model's decision-making, and interpret the diagnostic criteria of the health state in the frequency domain.

[0072] This technical solution can clearly trace the complete path from "original vibration signal → multi-scale residual features → representation of complex fault modes → interpretable diagnostic criteria", meeting the traceability requirements of the ISO13379 standard for rotating machinery fault diagnosis. While ensuring high diagnostic accuracy, it breaks through the "black box" limitation of deep learning and is especially suitable for high-end equipment such as wind turbines, planetary gearboxes, and aero-engines with strict requirements for diagnostic reliability. Description of the drawings

[0073] Figure 1 is the flowchart of the method of the present invention;

[0074] Figure 2 Structural schematic diagram of the MSRC-KAN-PAM model for the method of the present invention;

[0075] Figure 3 Structural schematic diagram of the multi-scale residual convolution MSRC for the method of the present invention;

[0076] Figure 4 Diagnostic criteria for visualizing various health states in the frequency domain. Specific embodiments

[0077] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0078] In this embodiment, as Figure 1 shown, an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM includes the following steps: Step 1, data acquisition: collect vibration signals of key transmission components (such as bearings, gears) of rotating machinery in various health states; Step 2, data preprocessing: divide the vibration signals into a sample set by sliding window sampling, and divide them into a training set, a validation set, and a test set; Step 3, model construction: based on the multi-scale residual convolution MSRC, Kolmogorov-Arnold network KAN, and power spectral density activation map PAM, construct the MSRC-KAN-PAM model; Step 4, model training, validation and evaluation: train the model on the training set and the validation set, and evaluate the model performance on the test set; Step 5, interpretable fault diagnosis: use the trained model to diagnose the faults of the rotating machinery, and visualize the diagnostic criteria of the health state in the frequency domain.

[0079] In Step 1, install one or more sensors at different positions or directions near the rotating machinery transmission components (such as bearings, gears) to be diagnosed, and use data acquisition equipment to collect vibration signals in various health states.

[0080] In Step 2, in order to avoid test leakage, when performing sliding window sampling, there is no overlap between adjacent windows, and a certain interval is maintained; each sample contains 1024 signal points; all samples are subjected to mean-standard deviation mean-std normalization processing.

[0081] In this embodiment, an acceleration sensor is installed on the bearing seat at the motor drive end to collect vibration signals of the rolling bearing. During the collection process, the motor speed is 1797 r / min, and the sampling frequency is 12 kHz. There are nine fault types for the motor rolling bearing, and vibration signals of ten health states including the normal state are collected, as shown in Table 1 below:

[0082]

[0083] In this embodiment, the vibration signals of each health state are segmented into 1,160 samples through sliding window sampling. Among them, 700 samples are used for training, 230 samples are used for validation, and 230 samples are used for testing.

[0084] In this embodiment, as Figure 2 shown, in step three, the MSRC-KAN-PAM model consists of a feature extraction module, a classification module, and a visualization module;

[0085] In this embodiment, the feature extraction module is composed of three multi-scale residual convolutions MSRC connected in sequence;

[0086] In this embodiment, as Figure 3 shown, for the multi-scale residual convolution MSRC, first, parallel multi-scale convolutions Conv1d with different kernel sizes are used to extract the multi-local receptive field features of the vibration signal. Secondly, for each scale feature extracted, layer normalization LN is used to stabilize the feature distribution, and the risk of overfitting is reduced through residual connection Add. Then, the multi-scale features are concatenated Concat along the channel dimension. Finally, a hyperbolic tangent function Tanh is used to perform non-linear mapping, as shown in the following formula:

[0087]

[0088] Among them, represents the input signal, C 1 and L 1 respectively represent the channel dimension and time dimension of the input signal, k l represents the size of the convolution kernel, represents the weight of the convolution kernel k l , represents the feature extracted by the convolution kernel k l , represents the output feature, n represents the number of different convolution kernel sizes, and L 2 represents the time dimension of the output feature;

[0089] The layer normalization LN is as shown in the following formula:

[0090]

[0091] Among them, represents the j-th feature of the l-th layer, L represents the time dimension of the feature, represents the normalized value of, respectively represent the mean and variance of, and ε represents a very small constant used to prevent invalid calculations when the variance is 0. respectively represent the scale and translation parameters to be learned;

[0092] The hyperbolic tangent function Tanh is as shown in the following formula:

[0093]

[0094] In the classification module, first, global power average pooling GPAP is used to perform feature dimensionality reduction in the time dimension. Then, the Kolmogorov - Arnold network KAN maps the high - dimensional features to the classification dimension of the health state, as shown in the following formula:

[0095]

[0096] Among them, represents the features extracted by the last multi - scale residual convolution MSRC of the feature extraction module. M and L respectively represent the channel dimension and time dimension of the features, F m represents the features of the m - th channel, G m represents the global power average pooling GPAP value of F m , y c represents the feature value of the c - th category output by the Kolmogorov - Arnold network KAN, w c m represents the connection of y c and G m ;

[0097] The Kolmogorov - Arnold network KAN is implemented by stacking layers. The mapping transformation of each layer acts on the output of the previous layer to generate the input of the next layer. Each layer is structured as a learnable activation function matrix and is parameterized and optimized during the training process, as shown in the following formula:

[0098] Φ = {φ q,p}, p = 1, …, n in , q = 1,..., n out (11)

[0099] φ l,j,i , l = 0,..., L - 1, j = 1, …, n l+1 , i = 1,..., n l (12)

[0100]

[0101] Among them, n in and n out respectively represent the input feature dimension and output feature dimension, φ l,j,irepresents the learnable activation function connecting the $i$-th neuron in the $l$-th layer and the $j$-th neuron in the $(l + 1)$-th layer, $x$ l+1,j represents the activation value of the $j$-th neuron in the $(l + 1)$-th layer, $\Phi$ l represents the function matrix of the $l$-th layer, containing $n$ l ×$n$ l+1 learnable activation functions;

[0102] The learnable activation function is a weighted sum of a spline function and a bias function, as shown in the following formula:

[0103] $\varphi(x)=w$ s $_{spline}(x)+w$ b $_{b}(x)\ (16)$

[0104]

[0105]

[0106] where, $spline(\cdot)$ represents the linear combination of B-spline functions, $c$ i represents the learnable combination coefficient, $b(\cdot)$ represents the bias function, i.e., the Sigmoid linear unit function SiLU, $w$ s and $w$ b represent the learnable weight factors to better control the overall amplitude of the learnable activation function;

[0107] In the visualization module, first, the power spectral density PSD of the input signal and the power spectral density PSD of each channel feature extracted by the last multi-scale residual convolution MSRC of the feature extraction module are calculated respectively. Then, the power spectral density PSD of each channel feature is weighted and summed (activated) using the connection weights between the global power average pooling GPAP and the Kolmogorov - Arnold network KAN to obtain the power spectral density activation map PAM. Finally, the power spectral density PSD of the input signal and the power spectral density activation map PAM are visualized to interpret the classification criteria of the health state in the frequency domain, as shown in the following formula:

[0108] $P$ m $=PSD(F$ m ) $(19)$

[0109]

[0110] where, $F$ m represents the feature of the $m$-th channel extracted by the last multi-scale residual convolution MSRC of the feature extraction module, $P$ m represents the power spectral density PSD of $F$ m , $P$ AM cDenote the power spectral density activation map PAM of the c-th category, and ReLU(·) represents the rectified linear unit function, i.e., ReLU(x) = max(0, x);

[0111] In this embodiment, the Welch method is adopted to calculate the power spectral density PSD.

[0112] In this embodiment, the detailed parameter configuration of the MSRC-KAN-PAM model is shown in Table 2 below:

[0113]

[0114] Note: d represents the output channel dimension of MSRC, k l represents the convolutional kernel size of MSRC, s represents the convolutional stride, p represents the convolutional padding, d g represents the output time dimension of GPAP, d k represents the output classification dimension of KAN, and C represents the number of health states.

[0115] In this embodiment, C = 10.

[0116] In this embodiment, in step four, the training of the MSRC-KAN-PAM model uses the multi-class cross-entropy loss function to calculate the training loss, and the Adam optimization algorithm is used to update the model parameters. The hyperparameter configuration is as follows: the initial learning rate of the Adam optimization algorithm is 0.01, the batch size is 64, and the number of iterations is 100.

[0117] In this embodiment, the MSRC-KAN-PAM model achieves 100% accuracy on the test set. As Figure 4 shown, visualize the power spectral density PSD of the input signal and the power spectral density activation map PAM of the features extracted by the MSRC-KAN-PAM model to interpret the diagnostic criteria for the health state in the frequency domain. Compared with the frequency characteristics of the input signal, the diagnostic criteria of the MSRC-KAN-PAM model focus on specific frequency components of the input signal. In other words, the trained MSRC-KAN-PAM model will predict the health state of the input signal based on specific frequency components.

[0118] It can be seen from the above embodiments that the present invention is an interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM. Compared with the prior art, the advantages of the present invention are: (1) extracting and integrating multi-scale features from different channel dimensions of vibration signals in the time domain; (2) using the responsiveness and flexibility of KAN for fault diagnosis; (3) interpreting the diagnostic criteria for the health state in the frequency domain.

[0119] The above are only the preferred embodiments of the present invention, and are not any other form of limitation to the present invention. Any modification or equivalent change made according to the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. An interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM, characterized by: The following steps are involved: Step 1: Data collection: Collect vibration signals of key transmission components of rotating machinery, including bearings and gears, in various health states; Step 2: Data preprocessing: The vibration signal is divided into sample sets through sliding window sampling, and then divided into training set, validation set and test set; Step 3: Model building: Based on multi-scale residual convolution (MSRC), Kolmogorov-Arnold network (KAN) and power spectral density activation map (PAM), a MSRC-KAN-PAM model was constructed. Step 4: Model training, verification and evaluation: Train the model on the training set and validation set, and evaluate the model performance on the test set; Step 5: Explainable fault diagnosis: Use the trained model to diagnose faults in rotating machinery and visualize the diagnostic criteria of the health status in the frequency domain.

2. The interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM according to claim 1 is characterized in that: The step 1 specifically includes the following steps: One or more sensors are installed at different positions or directions near the rotating mechanical transmission parts that need to be diagnosed, including bearings and gears, and vibration signals under various health conditions are collected using data acquisition equipment.

3. The interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM according to claim 1 is characterized in that: The step 2 specifically includes the following steps: When sliding window sampling, there is no overlap between adjacent windows and a certain interval is maintained; each sample contains 1024 signal points; all samples are normalized by mean-standard deviation.

4. The interpretable rotating machinery fault diagnosis method based on MSRC-KAN-PAM according to claim 1 is characterized in that: The specific steps of step three are as follows: The MSRC-KAN-PAM model consists of a feature extraction module, a classification module and a visualization module; The feature extraction module is composed of a plurality of multi-scale residual convolutions MSRC connected in sequence, and the number of multi-scale residual convolutions MSRC is adjusted according to the needs of different tasks; The multi-scale residual convolution MSRC, firstly, utilizes parallel multi-scale convolution Conv1d with different kernel sizes to extract multi-local receptive field features of the vibration signal; Secondly, for each scale feature extracted, layer normalization LN is used to stabilize the feature distribution, and residual connection Add is used to reduce the risk of overfitting; Then, the multi-scale features are concatenated along the channel dimension; Finally, the hyperbolic tangent function Tanh is used to perform nonlinear mapping, as shown in the following formula: in, represents the input signal, C1 and L1 represent the channel dimension and time dimension of the input signal respectively, k l represents the size of the convolution kernel, represents the convolution kernel k l The weight of represents the convolution kernel k l The extracted features, represents the output feature, n represents the number of different convolution kernel sizes, and L2 represents the time dimension of the output feature; The layer normalization LN is shown in the following formula: in, represents the jth feature of the lth layer, L represents the time dimension of the feature, express The normalized value of Respectively The mean and variance of , ε represents a small constant used to prevent invalid calculations when the variance is 0, They represent the scale and translation parameters that need to be learned respectively; The hyperbolic tangent function Tanh is shown in the following formula: In the classification module, firstly, the feature dimension reduction is performed in the time dimension using global power average pooling (GPAP); Then, the high-dimensional features are mapped to the classification dimension of health status through the Kolmogorov-Arnold network KAN, as shown in the following formula: in, represents the features extracted by the last multi-scale residual convolution MSRC in the feature extraction module. M and L represent the channel dimension and time dimension of the features respectively. m represents the characteristics of the mth channel, G m Indicates F m The global power average pooling GPAP value, y c represents the eigenvalue of the cth category output by the Kolmogorov-Arnold network KAN, w c m Indicates connection y c With G m The weight of The Kolmogorov-Arnold network (KAN) is implemented by stacking layers. The mapping transformation of each layer acts on the output of the previous layer to generate the input of the next layer. Each layer is structured as a learnable activation function matrix, which is parameterized and optimized during the training process, as shown in the following formula: Φ={φ q,p },p=1,…,n in ,q=1,…,n out (11) φ l,j,i ,l=0,…,L-1,j=1,…,n l+1 ,i=1,…,n l (12) Among them, n in and n out Represent the input feature dimension and output feature dimension respectively, φ l,j,i represents the learnable activation function connecting the i-th neuron in layer l and the j-th neuron in layer l+1, x l+1,j represents the activation value of the jth neuron in the l+1th layer, Φ l Represents the function matrix of the lth layer, containing n l ×n l+1 A learnable activation function; The learnable activation function is a weighted sum of a spline function and a bias function, as shown in the following formula: φ(x)=w s spline(x)+w b b(x) (16) Where spline(·) represents the linear combination of B-spline functions, c i represents the learnable combination coefficient, b(·) represents the bias function, namely the Sigmoid linear unit function SiLU, w s and w b represents the learnable weight factor; In the visualization module, first, the power spectral density PSD of the input signal and the power spectral density PSD of each channel feature extracted by the last multi-scale residual convolution MSRC of the feature extraction module are calculated respectively; Then, the connection weights between the global power average pooling GPAP and the Kolmogorov-Arnold network KAN are used to perform weighted summation on the power spectral density PSD of each channel feature to obtain the power spectral density activation map PAM; Finally, visualize the power spectral density PSD and power spectral density activation map PAM of the input signal to explain the classification criteria of the health state in the frequency domain, as shown in the following formula: P m =PSD(F m ) (19) Among them, F m represents the feature of the mth channel extracted by the last multi-scale residual convolution MSRC of the feature extraction module, P m Indicates F m The power spectral density PSD, P AM c represents the power spectral density activation map PAM of the c-th category, and ReLU(·) represents the rectified linear unit function, that is, ReLU(x)=max(0,x).

Images