A physically priori parameter guided explainable fault diagnosis method

Abstract

This invention provides a physically-guided, interpretable fault diagnosis method, belonging to the field of mechanical fault diagnosis. The method simultaneously inputs monitoring data and the geometric and operating parameters of mechanical components: First, a physical parameter encoder performs a lightweight mapping of the geometric and operating parameters, generating a physically meaningful adaptive dilation rate vector; second, a physically adaptive dilated convolutional layer is constructed, using the aforementioned adaptive dilation rate vector as the variable sampling stride between sampling points within the convolutional kernel to extract features from the input monitoring data; finally, this convolutional layer is embedded into a standard convolutional neural network architecture, and fault classification is achieved through end-to-end training. This invention, by introducing a physically-guided adaptive dilation rate into the convolutional structure, enables the network to adapt to different structures and operating conditions during the feature extraction stage, significantly improving the accuracy of fault diagnosis and the interpretability of the model.

Description

Technical Field

[0001] This invention belongs to the field of mechanical fault diagnosis, specifically relating to an interpretable fault diagnosis method guided by physical prior parameters. Background Technology

[0002] Rolling bearings, gears, and other core components of rotating machinery are directly related to the operational safety of the entire machine due to their health status. Convolutional neural networks (CNNs) are widely used in intelligent fault diagnosis methods based on monitoring data due to their powerful feature extraction capabilities. However, traditional CNNs use convolutional kernels with fixed structures, meaning their receptive fields and sampling positions are fixed and cannot be adaptively adjusted based on the component's geometric parameters and real-time rotational speed. Because the sampling structure of the convolutional kernel is not linked to the physical mechanism of the fault, its feature extraction process lacks clear physical interpretability, limiting the model's reliability in engineering applications. In recent years, variants such as dilated convolution and deformable convolution have improved the flexibility of feature extraction to some extent by introducing dilation rates or learning offsets. However, the dilation rates or offsets in these methods are usually directly given or learned by the network directly from the feature space of the monitoring signal. Their learning process does not establish an explicit correlation with the component's geometric parameters, rotational speed, or other physical quantities, resulting in a lack of physical guidance for adjusting the sampling structure. This makes it difficult to guarantee that the learned deformation corresponds to the actual physical process of the fault, and the model's interpretability problem remains. Therefore, how to introduce explicit guidance of geometric and operating parameters into the sampling structure design of convolution kernels, so that the control of sampling interval comes from the physical parameter space rather than the pure signal feature space, thereby giving the feature extraction process clear physical interpretability while maintaining the advantages of data-driven end-to-end training, has become a technical problem that urgently needs to be solved in the field of mechanical fault diagnosis. Summary of the Invention

[0003] To address the aforementioned issues, this invention proposes a physically-guided, interpretable fault diagnosis method. This method uniformly divides the sampling points of a one-dimensional convolutional kernel into multiple intervals along the sequence dimension. A lightweight physical parameter encoder maps the geometric and operational parameters of the rotating machinery component to a set of adaptive dilatation rate vectors, which serve as the sampling interval configuration parameters between adjacent intervals. Since the values ​​of this dilatation rate vector directly originate from the physical parameter space rather than the monitoring signal feature space, its changes reflect the differences between the component's physical properties and operating state, thus establishing an explicit correlation between the sampling grid distribution of the convolutional kernel and the physical priors of fault generation. Through this physically-guided sampling structure adjustment, the network can obtain a receptive field configuration that matches the component's physical characteristics in the initial stage of feature extraction. This provides a more physically consistent feature foundation for subsequent high-dimensional discriminative feature extraction and fault classification, effectively improving the model's interpretability and diagnostic accuracy.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A physically prior parameter-guided interpretable fault diagnosis method includes the following steps:

[0006] S1: Construct a physical parameter encoder. Taking rolling bearings as an example, based on the fault characteristic frequency theory formula, determine the geometric and operating parameters, including bearing pitch diameter D, number of balls Z, ball diameter d, contact angle α, and rotational frequency f. r The above parameters are input into the neural network for nonlinear mapping, and the output is an adaptive dilation rate vector used to adjust the sampling point interval inside the convolution kernel; for other mechanical parts such as gears, their physical parameters can be adjusted accordingly.

[0007] S2: Construct a physically adaptive dilated convolutional layer. Introduce the adaptive dilation rate vector generated in step S1, guided by geometric and operational parameters, into the standard one-dimensional convolutional kernel. Remap the coordinate offsets of each sampling point within the convolutional kernel based on the adaptive dilation rate vector to perform an adaptive dilated convolution operation that expands the receptive field. In this layer, the dilation rate element value corresponding to the adaptive dilation rate vector is inserted only between specified sparse sampling point intervals, unlike conventional dilated convolution which inserts a fixed dilation rate between every two adjacent sampling points. This increases the receptive field to capture long-range fault features while maintaining sensitivity to adjacent local signal details, thereby enhancing the physical consistency of feature extraction.

[0008] S3: Construct a convolutional neural network including a feature extractor and a fault classifier with the physical adaptive dilated convolutional layer, perform end-to-end training using labeled monitoring data, and output fault category diagnosis results.

[0009] Furthermore, in step S1, the physical parameter encoder is specifically implemented as follows:

[0010] Taking rolling bearings as an example, the input physical parameter vector P=[D, Z, d, α, f] r The input is fed into a multilayer perceptron network containing L hidden layers;

[0011] Let the output of the l-th hidden layer be h. l =σ(W l h l−1 +b l ), where h0=P, σ(∙) is a nonlinear activation function (such as ReLU), W l and b l These are the weight matrix and bias vector of the l-th layer, respectively; the output of the last hidden layer is mapped to an adaptive inflation rate vector r=[r1, r2, …, r] through a linear output layer. N-1 ]∈R N-1 ,Right now:

[0012] ;

[0013] Where N is the number of intervals divided by the sampling points, r i This represents the adaptive inflation rate between the i-th and (i+1)-th intervals of the convolution kernel;

[0014] To dynamically model the relationships between different physical parameters and thus better learn the adaptive dilation rate, a self-attention module is introduced before the output layer to recalibrate the hidden representations.

[0015] Let h be the hidden representation input to the self-attention module. l , will h l Expanded to sequence form H∈R D×d (where D is the sequence length and d is the feature dimension), and then, a self-attention mechanism is applied to H:

[0016] ;

[0017] ;

[0018] Among them, W Q W K W V ∈R d×d Z is the learnable weight matrix; Z is the attention output.

[0019] Then, residual connections and layer normalization are performed:

[0020] ;

[0021] Obtain enhanced feature h e .

[0022] Furthermore, the implementation method of the physically adaptive dilated convolutional layer in step S2 is as follows:

[0023] Let the original standard one-dimensional convolution kernel W∈R S The corresponding S sampling points are uniformly divided into N intervals along the sequence dimension, and each interval contains n=S / N consecutive sampling points.

[0024] Assign a set of adaptive inflation rate vectors r generated in step S1 to the N intervals;

[0025] Taking the reference position p0 of the first sampling point of the convolution kernel as a reference, and accumulating the dilation rates of each interval, the actual sampling coordinate p of any sampling point within the convolution kernel can be expressed as p = p0 + p n + r sum , where p nr represents the relative position of the sampling points within each interval. sum This indicates the accumulation of the expansion rate. That is, the starting position of the sampling point in the next interval needs to be recursively calculated based on the sum of all sampling step sizes in the previous interval to ensure the continuity of the sampling points in each interval on the input signal coordinate axis.

[0026] For sampling positions whose coordinates are non-integer after the above calculation, linear interpolation is used to obtain the corresponding signal values ​​from adjacent integer points. The specific calculation formula is as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] Where w is the convolution kernel weight; x(q) is the element value of the input signal x at sampling point q;

[0032] Therefore, by assigning different dilation rates to different intervals, a physically adaptive dilated convolutional layer with structure and working condition awareness is constructed.

[0033] Furthermore, in step S3, the feature extractor is composed of stacked physical adaptive dilated convolutional layers, standard convolutional layers, activation function layers, and pooling layers;

[0034] The physically adaptive dilated convolutional layer is placed in the first layer of the feature extractor and is used to adaptively expand and sparsify the coordinate interval of the sampling points in the convolution kernel according to the input geometric parameters and operating parameters, so that the first layer convolution operation can adaptively adjust the coverage of the receptive field and the density distribution of its internal sampling points according to the physical properties and operating status of the current component.

[0035] The subsequent stacked standard convolutional layers further extract high-dimensional discriminative features oriented towards specific fault categories based on the physical prior matching features output by the physically adaptive dilated convolutional layers.

[0036] In step S3, the training process of the fault diagnosis network is as follows:

[0037] Labeled training and monitoring data are input into the network. After the feature extractor extracts features, the data is input into the fault classifier to calculate the cross-entropy classification loss. During training, the goal is to minimize the cross-entropy classification loss. All learnable weights in the feature extractor, fault classifier, and physical parameter encoder are updated synchronously through the error backpropagation mechanism.

[0038] Under the supervision of classification loss, the encoder learns to map the input geometric and operating parameters into an adaptive inflation rate vector that is beneficial to fault category discrimination, thereby gradually reducing the classification error during the training process.

[0039] The cross-entropy classification loss function is defined as follows:

[0040] ;

[0041] Where B is the batch size, M is the number of fault categories, and y m_i Let y be the true label of the i-th sample. mt_i This represents the predicted probability of the m-th class output by the fault classifier.

[0042] The beneficial effects of this invention are as follows:

[0043] This invention proposes a physically-guided, interpretable fault diagnosis method. Addressing the issues of fixed sampling structures in traditional convolutional kernels and the lack of correlation between feature extraction and component physical properties, this method introduces an adaptive dilatation vector generated by physical prior parameters of rotating machinery components into a standard one-dimensional convolutional kernel. This constructs a physically adaptive dilated convolutional layer (for rolling bearings, this includes pitch diameter, number of balls, ball diameter, contact angle, and rotational frequency; for other components such as gears, geometric and operating parameters such as module, number of teeth, pressure angle, and rotational speed are adjusted accordingly). This adaptive dilatation vector is generated by a physical parameter encoder mapping from the component's physical properties. Its values ​​are directly derived from the physical parameter space rather than the monitoring signal feature space, establishing an explicit correlation between the interval distribution of sampling points within the convolutional kernel and the physical priors of fault generation. Through this physically-guided sampling structure adjustment, the network obtains a receptive field configuration consistent with the component's physical characteristics in the initial feature extraction stage, providing a more physically interpretable feature input foundation for subsequent network layers, thereby effectively improving the diagnostic accuracy and interpretability of the fault diagnosis model. Attached Figure Description

[0044] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0045] Figure 1 This is a schematic diagram of the structure of the physically adaptive dilated convolutional layer in this invention.

[0046] Figure 2 This is an overall flowchart of the method of the present invention.

[0047] Figure 3 Visualization of the first-layer convolutional features of each method using GRAD-CAM. Detailed Implementation

[0048] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0049] In one embodiment of the present invention, a physically prior parameter-guided interpretable fault diagnosis method includes the following steps:

[0050] S1: Construct a physical parameter encoder. Taking rolling bearings as an example, based on the fault characteristic frequency theory formula, determine the geometric and operating parameters, including bearing pitch diameter D, number of balls Z, ball diameter d, contact angle α, and rotational frequency f. r The above parameters are input into the neural network for nonlinear mapping, and the output is an adaptive dilation rate vector used to adjust the sampling point interval inside the convolution kernel; for other mechanical parts such as gears, their physical parameters can be adjusted accordingly.

[0051] In step S1, the physical parameter encoder is specifically implemented as follows: taking a rolling bearing as an example, the input physical parameter vector P=[D, Z, d, α, f] is... r The input is fed into a multilayer perceptron network containing L hidden layers; let the output of the l-th hidden layer be h. l =σ(W l h l−1 +b l ), where h0=P, σ(∙) is a nonlinear activation function (such as ReLU), W l and b l These are the weight matrix and bias vector of the l-th layer, respectively; the output of the last hidden layer is mapped to an adaptive inflation rate vector r=[r1, r2, …, r] through a linear output layer. N-1 ]∈R N-1 ,Right now:

[0052] ;

[0053] Where N is the number of intervals divided by the sampling points, r i Let h represent the adaptive dilation rate between the i-th and (i+1)-th intervals of the convolutional kernel. To dynamically model the relationships between different physical parameters and thus better learn the adaptive dilation rate, a self-attention module is introduced before the output layer to recalibrate the hidden representation: Let h be the hidden representation input to the self-attention module. l , will h l Expanded to sequence form H∈R D×d(where D is the sequence length and d is the feature dimension), and then, a self-attention mechanism is applied to H:

[0054] ;

[0055] ;

[0056] Among them, W Q W K W V ∈R d×d Z is the learnable weight matrix; Z is the attention output.

[0057] Then, residual connections and layer normalization are performed:

[0058] ;

[0059] Obtain enhanced feature h e .

[0060] S2: Construct a physically adaptive dilated convolutional layer. Introduce the adaptive dilation rate vector generated in step S1, guided by geometric and operational parameters, into the standard one-dimensional convolutional kernel. Remap the coordinate offsets of each sampling point within the convolutional kernel based on the adaptive dilation rate vector to perform an adaptive dilated convolution operation that expands the receptive field. In this layer, the dilation rate element value corresponding to the adaptive dilation rate vector is inserted only between specified sparse sampling point intervals, unlike conventional dilated convolution which inserts a fixed dilation rate between every two adjacent sampling points. This increases the receptive field to capture long-range fault features while maintaining sensitivity to adjacent local signal details, thereby enhancing the physical consistency of feature extraction.

[0061] The implementation of the physically adaptive dilated convolutional layer in step S2 is as follows: Let the original standard one-dimensional convolutional kernel W∈R S The corresponding S sampling points are uniformly divided into N intervals along the sequence dimension, and each interval contains n = S / N consecutive sampling points; an adaptive dilation rate vector r generated in step S1 is assigned to the N intervals; taking the reference position p0 of the first sampling point of the convolution kernel as a reference, the actual sampling coordinate p of any sampling point in the convolution kernel is expressed as p = p0 + p0 after accumulating the dilation rates of each interval. n + r sum , where p n r represents the relative position of the sampling points within each interval. sumThe summation of the expansion rate means that the starting position of the sampling point in the next interval needs to be calculated based on the sum of all sampling step sizes in the previous interval to ensure the continuity of the sampling points in each interval on the input signal coordinate axis. For sampling positions whose coordinates are not integers after the above calculation, linear interpolation is used to obtain the corresponding signal value from the adjacent integer points. The specific calculation formulas are shown in equations (5) to (8).

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] Where w is the kernel weight; x(q) is the element value of the input signal x at the sampling point q; thus, by assigning different dilation rates in different intervals, a physically adaptive dilated convolutional layer with structure and working condition awareness is constructed.

[0067] S3: Construct a convolutional neural network including a feature extractor and a fault classifier with the physical adaptive dilated convolutional layer, perform end-to-end training using labeled monitoring data, and output fault category diagnosis results.

[0068] In step S3, the feature extractor is composed of a stacked physical adaptive dilated convolutional layer, a standard convolutional layer, an activation function layer, and a pooling layer. The physical adaptive dilated convolutional layer is placed at the beginning of the feature extractor and is used to adaptively expand and sparsify the coordinate interval of the sampling points within the convolutional kernel according to the input geometric parameters and operating parameters. This allows the first-layer convolutional operation to adaptively adjust the coverage of the receptive field and the density distribution of its internal sampling points according to the physical properties and operating state of the current component. The subsequently stacked standard convolutional layer further extracts high-dimensional discriminative features for specific fault categories based on the physical prior matching features output by the physical adaptive dilated convolutional layer.

[0069] In step S3, the training process of the fault diagnosis network is as follows: labeled training monitoring data is input into the network, features are extracted by the feature extractor, and then input into the fault classifier to calculate the cross-entropy classification loss. During training, minimizing the cross-entropy classification loss is the optimization objective. All learnable weights in the feature extractor, fault classifier, and physical parameter encoder are synchronously updated through an error backpropagation mechanism. Under the supervision of the classification loss, the encoder learns to map the input geometric and operating parameters into an adaptive inflation rate vector that is beneficial for fault category discrimination, thereby gradually reducing the classification error during the training process. The cross-entropy classification loss function is defined as:

[0070] ;

[0071] Where B is the batch size, M is the number of fault categories, and y m_i Let y be the true label of the i-th sample. mt_i This represents the predicted probability of the m-th class output by the fault classifier.

[0072] Fault diagnosis was performed on a bearing dataset publicly available from Shandong University of Science and Technology under different operating speeds. The fault diagnosis accuracy of the method presented in this invention was compared with that of deformable convolution, dilated convolution, and standard CNN. The diagnostic results are shown in Table 1. This dataset includes normal, inner ring fault, outer ring fault, and ball fault. Inner ring fault, outer ring fault, and ball fault have three fault severity levels: 0.2mm, 0.4mm, and 0.6mm, respectively, totaling 10 categories. Six operating conditions were tested under a constant load of 20N: 1000rpm, 1500rpm, 1800rpm, 2000rpm, 2500rpm, and 3000rpm, with a sampling frequency of 25.6k. The bearing used was a 6205 bearing, and its basic parameters are shown in Table 2. When constructing the dataset, the sliding window length was set to 2048 to include information on multiple bearing rotations and to match the model input size. Each fault category under each operating condition had 700 samples, including 600 single-class training samples and 100 test samples. The experiment was repeated 5 times, and the average classification accuracy was taken as the final classification performance index of the algorithm. In the experiment, the optimizer used was SGD, the number of epochs was set to 100, the initial learning rate was 0.01, the learning rate was halved after every 20 training epochs, the batch size was set to 100, and the training iterations were continued until the training set loss tended to stabilize. After training, the model was applied to test samples to evaluate its fault diagnosis performance.

[0073] Table 1. Accuracy of different methods on the Shandong University of Science and Technology bearing dataset

[0074]

[0075] Table 2. Basic parameters of 6205 bearing

[0076]

[0077] The results show that the method of this invention achieved the highest diagnostic accuracy under the current experimental settings. Compared with control schemes such as fixed expansion rate and learning offset driven by monitoring data, the adaptive expansion rate configuration guided by physical prior parameters in this invention significantly improves the model's fault identification capability, verifying that the physical guidance mechanism that integrates bearing geometric parameters and rotational frequency information can effectively enhance the feature extraction performance of convolutional neural networks. It should be noted that this embodiment uses rolling bearings as an example for verification, but the method of this invention is also applicable to other rotating mechanical components such as gears; only the corresponding physical parameters need to be adjusted.

[0078] To further verify the interpretability of this method, gradient-weighted class activation mapping was used to visualize the features extracted by the first convolutional layer at 1000 rpm, as shown below. Figure 3 As shown in the figure, the physical adaptive dilated convolutional layer proposed in this invention exhibits a highly concentrated high-activation response region near the impact component of the input vibration signal when extracting features, while the activation distribution of the control method is relatively dispersed. This phenomenon indicates that the adaptive dilation rate vector generated by the physical prior parameters establishes a closer correspondence between the sampling grid distribution of the convolutional kernel and the location pattern of the fault impact, thus demonstrating stronger physical interpretability in the initial stage of feature extraction.

Claims

1. A physically-prior-parameter-guided interpretable fault diagnosis method, characterized in that, Includes the following steps: S1: Construct a physical parameter encoder. Taking rolling bearings as an example, based on the fault characteristic frequency theory formula, determine the geometric and operating parameters, including bearing pitch diameter D, number of balls Z, ball diameter d, contact angle α, and rotational frequency f. r The above parameters are input into the neural network for nonlinear mapping, and the output is an adaptive dilation rate vector used to adjust the sampling point interval inside the convolution kernel; for other mechanical parts such as gears, their physical parameters can be adjusted accordingly. S2: Construct a physically adaptive dilated convolutional layer. Introduce the adaptive dilation rate vector generated in step S1, guided by geometric and operational parameters, into the standard one-dimensional convolutional kernel. Remap the coordinate offsets of each sampling point within the convolutional kernel based on the adaptive dilation rate vector to perform an adaptive dilated convolution operation that expands the receptive field. In this layer, the dilation rate element value corresponding to the adaptive dilation rate vector is inserted only between specified sparse sampling point intervals, unlike conventional dilated convolution which inserts a fixed dilation rate between every two adjacent sampling points. This increases the receptive field to capture long-range fault features while maintaining sensitivity to adjacent local signal details, thereby enhancing the physical consistency of feature extraction. S3: Construct a convolutional neural network including a feature extractor and a fault classifier with the physical adaptive dilated convolutional layer, perform end-to-end training using labeled monitoring data, and output fault category diagnosis results.

2. The method of claim 1, wherein, In step S1, the physical parameter encoder is specifically implemented as follows: taking a rolling bearing as an example, the input physical parameter vector P=[D, Z, d, α, f] is... r The input is fed into a multilayer perceptron network containing L hidden layers; let the output of the l-th hidden layer be h. l =σ(W l h l−1 +b l ), where h0=P, σ(∙) is a nonlinear activation function (such as ReLU), W l and b l These are the weight matrix and bias vector of the l-th layer, respectively; the output of the last hidden layer is mapped to an adaptive inflation rate vector r=[r1, r2, …, r] through a linear output layer. N-1 ]∈R N-1 ,Right now: ； Where N is the number of intervals divided by the sampling points, r i Let h represent the adaptive dilation rate between the i-th and (i+1)-th intervals of the convolutional kernel. To dynamically model the relationships between different physical parameters and thus better learn the adaptive dilation rate, a self-attention module is introduced before the output layer to recalibrate the hidden representation: Let h be the hidden representation input to the self-attention module. l , will h l Expanded to sequence form H∈R D×d (where D is the sequence length and d is the feature dimension), and then, a self-attention mechanism is applied to H: ； ； Among them, W Q W K W V ∈R d×d Z is the learnable weight matrix; Z is the attention output. Then, residual connections and layer normalization are performed: ； Obtain enhanced feature h e .

3. The method of claim 1, wherein, The implementation of the physically adaptive dilated convolutional layer in step S2 is as follows: Let the original standard one-dimensional convolutional kernel W∈R S The corresponding S sampling points are uniformly divided into N intervals along the sequence dimension, and each interval contains n = S / N consecutive sampling points; an adaptive dilation rate vector r generated in step S1 is assigned to the N intervals; taking the reference position p0 of the first sampling point of the convolution kernel as a reference, the actual sampling coordinate p of any sampling point in the convolution kernel is expressed as p = p0 + p0 after accumulating the dilation rates of each interval. n + r sum , where p n r represents the relative position of the sampling points within each interval. sum The summation of the expansion rate means that the starting position of the sampling point in the next interval needs to be recursively calculated based on the sum of all sampling step sizes in the previous interval to ensure the continuity of the sampling points in each interval on the input signal coordinate axis. For sampling positions whose coordinates are not integers after the above calculation, linear interpolation is used to obtain the corresponding signal value from the adjacent integer points. The specific calculation formula is as follows: ； ； ； ； Where w is the kernel weight; x(q) is the element value of the input signal x at the sampling point q; thus, by assigning different dilation rates in different intervals, a physically adaptive dilated convolutional layer with structure and working condition awareness is constructed.

4. The method of claim 1, wherein, In step S3, the feature extractor is composed of a stacked physical adaptive dilated convolutional layer, a standard convolutional layer, an activation function layer, and a pooling layer. The physical adaptive dilated convolutional layer is placed at the beginning of the feature extractor and is used to adaptively expand and sparsify the coordinate interval of the sampling points within the convolutional kernel according to the input geometric parameters and operating parameters. This allows the first-layer convolutional operation to adaptively adjust the coverage of the receptive field and the density distribution of its internal sampling points according to the physical properties and operating state of the current component. The subsequently stacked standard convolutional layer further extracts high-dimensional discriminative features for specific fault categories based on the physical prior matching features output by the physical adaptive dilated convolutional layer.

5. The method of claim 1, wherein, In step S3, the training process of the fault diagnosis network is as follows: labeled training monitoring data is input into the network, features are extracted by the feature extractor, and then input into the fault classifier to calculate the cross-entropy classification loss. During training, minimizing the cross-entropy classification loss is the optimization objective. All learnable weights in the feature extractor, fault classifier, and physical parameter encoder are synchronously updated through an error backpropagation mechanism. Under the supervision of the classification loss, the encoder learns to map the input geometric and operating parameters into an adaptive inflation rate vector that is beneficial for fault category discrimination, thereby gradually reducing the classification error during the training process. The cross-entropy classification loss function is defined as: ； where B is batch size, M is the number of failure categories, y m_i is the true label of the i-th sample, y mt_i is the predicted probability of the m-th class output by the failure classifier.

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