A bearing fault diagnosis method based on physical heuristic

Abstract

The application discloses a bearing fault diagnosis method based on a physical heuristic, and relates to the field of bearing fault diagnosis. The method comprises the following steps: acquiring an original vibration signal of a bearing to be diagnosed and inputting a bearing fault diagnosis model trained in advance; filtering by using N Sinc band-pass filters with physical constraints to obtain N frequency band signals; after first convolution expansion, dividing into a first feature, a second feature and a third feature according to a preset proportion; calculating the kurtosis values of the frequency band signals and taking the maximum value, calculating the spatial average kurtosis of the three features respectively, calculating the weaving weight according to the two, performing channel-level resampling based on the weight, performing channel replacement after splicing to obtain a re-aggregated feature; inputting a classification network and outputting a bearing fault diagnosis result. The application significantly improves the cross-condition accuracy and realizes lightweight diagnosis through physical constraints and dynamic re-aggregation.

Description

Technical Field

[0001] This application relates to the field of bearing fault diagnosis, and in particular to a physical heuristic bearing fault diagnosis method. Background Technology

[0002] Electric motors are the core power source of modern industrial production, and their operational stability directly affects the precision and lifespan of the entire system. Rolling bearings, as key supporting components of motor transmission systems, operate under high speed, heavy load, and variable conditions for extended periods, making them highly susceptible to wear, fatigue spalling, or plastic deformation. Statistics show that approximately 30% of rotating machinery failures are caused by bearing failure. The early symptoms of such failures are subtle and difficult to detect in time. Without effective early warning systems, localized defects can rapidly expand, leading to unplanned downtime, production interruptions, and significant economic losses. Therefore, developing efficient and accurate fault diagnosis technologies is of great importance for achieving predictive maintenance of motor equipment and ensuring the safety of industrial systems.

[0003] With the development of deep learning technology, bearing fault diagnosis methods based on convolutional neural networks have been widely used. These methods typically use the original vibration signal as input and automatically extract fault features using convolutional layers. However, in cross-condition diagnosis scenarios, due to the differences in data distribution between training and testing conditions, and the fact that testing conditions often lack fault labels, existing models exhibit significantly reduced generalization robustness and lower diagnostic accuracy when faced with complex industrial field signals.

[0004] Previous studies have proposed a network architecture based on multi-scale feature decoupling and reconvergence. This architecture utilizes a one-dimensional convolutional neural network to extract transient impact and periodic characteristics from the original vibration signal. It constructs parallel feature extraction paths with different receptive fields through multi-level channel segmentation: shallow branches preserve low-level temporal details, while deep branches extract higher-order fault semantics, thus alleviating to some extent the limitations of a single receptive field in representing non-stationary vibration signals. However, this type of architecture still has the following shortcomings: First, the convolutional layers used in the front-end decoupling process lack physical constraints and are easily affected by frequency drift under specific working conditions, resulting in a lack of physical consistency in the extracted features. Second, the back-end re-aggregation process uses a static splicing method, which lacks information interaction between the features of each branch, making it difficult for features of different scales to coordinate effectively and resulting in insufficient consistency in judgment. Third, existing models, in pursuit of diagnostic accuracy, have large parameter scales and computational overhead, making it difficult to meet the real-time monitoring needs under the condition of limited industrial edge computing resources.

[0005] Therefore, there is an urgent need for a bearing fault diagnosis method that can improve the generalization performance across operating conditions by introducing physical constraints and enhancing cross-scale information interaction while maintaining lightweight design, so as to solve the limitations of existing technologies in complex data distribution and cross-operating condition scenarios. Summary of the Invention

[0006] The purpose of this application is to provide a physics-inspired bearing fault diagnosis method that can solve the problems of poor generalization ability across operating conditions and limited edge computing power in the existing technology. While maintaining extremely high diagnostic accuracy, it can significantly reduce parameter overhead and meet the needs of real-time monitoring at the industrial edge.

[0007] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a physics-inspired bearing fault diagnosis method, including: Obtain the original vibration signal of the bearing to be diagnosed; The original vibration signal is input into a pre-trained bearing fault diagnosis model. The processing of the original vibration signal by the bearing fault diagnosis model includes: Adaptive physical heuristic spectral decoupling of the original vibration signal includes: filtering the original vibration signal using N Sinc bandpass filters to obtain N frequency band signals; N is an integer greater than 1; the low cutoff frequency and high cutoff frequency of each Sinc bandpass filter are learnable parameters, and the high cutoff frequency is greater than the low cutoff frequency and does not exceed half of the sampling rate of the original vibration signal; Multi-scale asymmetric feature extraction is performed on the N-band signals, including: expanding the N-band signals into an m-channel feature map through a first convolution operation, where m is an integer greater than N; dividing the m-channel feature map into a first feature and a first remaining channel group along the channel dimension according to a preset ratio; performing a second convolution operation on the first remaining channel group to obtain a second intermediate feature; dividing the second intermediate feature into a second feature and a second remaining channel group along the channel dimension; and performing a third convolution operation on the second remaining channel group to obtain a third feature. The process of interleaving feature re-aggregation for the first feature, the second feature, and the third feature includes: calculating the kurtosis value of each frequency band signal in the N frequency band signals and taking the maximum value among all kurtosis values; calculating the spatial average kurtosis of each of the first feature, the second feature, and the third feature; calculating the weaving weights of each of the first feature, the second feature, and the third feature based on the maximum value and the spatial average kurtosis; performing channel-level resampling on the first feature, the second feature, and the third feature based on the weaving weights; concatenating the resampled first feature, the resampled second feature, and the resampled third feature; and performing channel permutation on the concatenated feature to obtain the reaggregated feature. The reconvergence features are input into the classification network, and the bearing fault diagnosis results are output.

[0008] Optionally, the training process of the bearing fault diagnosis model includes: Construct a vibration signal sample set containing labels for various bearing fault types; The bearing fault diagnosis model is trained using the sample set to optimize the low and high cutoff frequencies of the Sinc bandpass filter, the parameters of the first convolution operation, the second convolution operation, and the third convolution operation, as well as the parameters of the classification network.

[0009] Optionally, the loss function of the bearing fault diagnosis model during training is: ; in, For the total loss, For classification cross-entropy loss, For physical consistency loss, This is the preset balance coefficient; The physical consistency loss for: ; in, To preset the kurtosis anchor point threshold, For the bearing fault diagnosis model, the first training sample used in a single parameter update process is... The average kurtosis value is obtained by averaging the kurtosis values ​​of the road frequency band signal. For the index of the frequency band signal, This represents the total number of channels in the frequency band.

[0010] Optionally, the convolution kernel for each Sinc bandpass filter is generated according to the following steps: Based on the low cutoff frequency and high cutoff frequency of the Sinc bandpass filter, a first low-pass filter response and a second low-pass filter response are constructed respectively, and both the first low-pass filter response and the second low-pass filter response are in the form of a sinc function. Subtracting the response of the second low-pass filter from the response of the first low-pass filter yields the ideal band-pass filter response. The element-wise multiplication of the ideal bandpass filter response with the Hamming window yields the convolution kernel of the Sinc bandpass filter.

[0011] Optionally, the low cutoff frequency and the high cutoff frequency are determined according to the following formula during each forward propagation: The low cutoff frequency for: ; in, The preset minimum low cutoff frequency, For learnable low-frequency parameters; The high cutoff frequency for: ; in, For learnable bandwidth parameters, This is the preset minimum bandwidth offset. The sampling rate of the original vibration signal. This is a clamping operation.

[0012] Optionally, the following formula is used to calculate the first... Kurtosis value of the road band signal: ; in, For the first Kurtosis value of the road band signal. For the first The data sequence of the frequency band signal, for The mean, for standard deviation It represents the mathematical expectation.

[0013] Optionally, the spatial mean kurtosis of the first feature, the second feature, and the third feature can be calculated using the following formula: ; in, The feature index takes values ​​of 1, 2, and 3, corresponding to the first feature, the second feature, and the third feature, respectively. For the first Spatial average kurtosis of each feature For the first The total number of channels for each feature For channel indexing, For the first The first feature The data sequence consisting of all spatial location elements of the feature map of each channel. is the kurtosis value of the data sequence.

[0014] Optionally, the following formula is used to calculate the first... The weaving weights corresponding to each feature: ; ; in, The maximum value among all kurtosis values. For the first Spatial average kurtosis of each feature For the first The score corresponding to each feature For the first The weaving weights corresponding to each feature The preset temperature coefficient, The feature index is used to traverse the first feature, the second feature, and the third feature.

[0015] Optionally, channel-level resampling is performed on the first feature, the second feature, and the third feature based on the weaving weights, specifically including: Determine the number of channels contained in each of the first feature, the second feature, and the third feature, and use the sum of the number of channels of the three features as the total number of channels; For each of the first, second, and third features, the weaving weight corresponding to the feature is multiplied by the total number of channels, rounded to the nearest integer to obtain the target number of channels corresponding to the feature, and the following operations are performed: If the target number of channels is greater than the number of channels contained in the feature itself, then all channels of the feature are retained, and the number of channels to be supplemented is calculated. The number of channels to be supplemented is equal to the target number of channels minus the number of channels contained in the feature itself. The quotient obtained by dividing the number of channels contained in the feature itself by the number of channels to be supplemented is used as the first step length. Step sampling is performed from the existing channels of the feature according to the first step length to obtain a number of supplementary channels equal to the number of channels to be supplemented. The supplementary channels are merged with all retained channels to obtain the resampled feature. Wherein, the step sampling is sampling at equal intervals according to the corresponding step length in the channel dimension. If the number of target channels is less than the number of channels contained in the feature itself, then the quotient obtained by dividing the number of channels contained in the feature itself by the number of target channels is used as the second step size. The feature's existing channels are sampled step by step according to the second step size to obtain a number of channels equal to the number of target channels, which are used as the resampled feature. If the number of target channels is equal to the number of channels contained in the feature itself, then the feature remains unchanged and is used as the resampled feature.

[0016] Optionally, the resampled first feature, resampled second feature, and resampled third feature are concatenated, and channel permutation is performed on the concatenated features to obtain re-aggregated features, specifically including: The resampled first feature, the resampled second feature, and the resampled third feature are concatenated sequentially along the channel dimension to obtain the concatenated feature. The number of groups is determined based on the proportional relationship between the number of target channels corresponding to the resampled first feature, the resampled second feature, and the resampled third feature; wherein, the proportional relationship is a simplified integer ratio, and the number of groups is equal to the sum of the values ​​in the simplified integer ratio; Based on the total number of channels in the spliced ​​features and the number of groups, the number of channels in each channel group is determined; according to the number of channels in each channel group, the spliced ​​features are divided into the number of channel groups along the channel dimension, and each channel group contains the same number of channels. The selection process proceeds cyclically from the first channel group to the last channel group. Each time, one channel is selected from each channel group, and the selected channels are arranged into a new channel sequence. This selection process is repeated until all channels in all channel groups have been selected, resulting in an alternating channel sequence. The staggered channel sequence is used as a re-aggregation feature.

[0017] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a physically-inspired bearing fault diagnosis method. It utilizes N Sinc bandpass filters with learnable parameters and sampling rate constraints to adaptively decouple the original vibration signal using physical heuristics, thereby capturing physically consistent, condition-invariant features and reducing interference from frequency drift. The signal is then expanded into an m-channel feature map through a first convolution operation and divided into first, second, and third features according to a preset ratio, achieving multi-scale asymmetric feature extraction. By calculating the maximum value of the band signal kurtosis and the spatial average kurtosis of each of the three features, weaving weights are obtained. Based on these weights, the three features are resampled at the channel level, and after concatenation, channel permutation is performed, enabling features of different scales to interweave and fuse along the channel dimension, thus enhancing the consistency of the discrimination information. Furthermore, since the Sinc filters only rely on two parameters—low cutoff frequency and high cutoff frequency—and channel permutation does not introduce new parameters, the computational cost is reduced while simultaneously achieving the aforementioned spectral decoupling, multi-scale feature extraction, and interweaving re-convergence, making it suitable for real-time monitoring at industrial edge environments. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1This is a schematic diagram of the framework of a physics-inspired bearing fault diagnosis method proposed in this application; Figure 2 This is a schematic diagram comparing the adaptive physics-inspired spectral decoupling mechanism of this application with the standard one-dimensional convolutional neural network extraction mechanism; Figure 3 A schematic diagram illustrating the execution logic of the adaptive physics-inspired spectrum decoupling algorithm provided in this application; Figure 4 A schematic diagram of the topological transformation logic for the interleaved feature re-aggregation mechanism provided in this application; Figure 5 A bubble chart comparing the efficiency of this application with other lightweight networks; Figure 6 This is a schematic diagram of the APSD filter response of sample 1 under roller fault in the CWRU dataset; Figure 7 This is a schematic diagram of the APSD filter response of sample 2 under roller fault in the CWRU dataset; Figure 8 This is a schematic diagram of the APSD filter response of sample 3 under roller failure in the CWRU dataset; Figure 9 This is a schematic diagram of the APSD filter response of sample 1 under inner ring fault in the CWRU dataset; Figure 10 This is a schematic diagram of the APSD filter response of sample 2 under inner circle fault in the CWRU dataset; Figure 11 This is a schematic diagram of the APSD filter response of sample 3 under inner circle fault in the CWRU dataset; Figure 12 This is a schematic diagram of the APSD filter response of sample 1 under outer ring fault in the CWRU dataset; Figure 13 This is a schematic diagram of the APSD filter response of sample 2 under outer ring fault in the CWRU dataset; Figure 14 This is a schematic diagram of the APSD filter response of sample 3 under outer ring fault in the CWRU dataset; Figure 15 This is a schematic diagram of the APSD filter response of sample 1 in the normal state of the CWRU dataset. Figure 16 This is a schematic diagram of the APSD filter response of sample 2 in the normal state of the CWRU dataset. Figure 17 This is a schematic diagram of the APSD filter response of sample 3 in the normal state of the CWRU dataset. Figure 18 This is a schematic diagram of the APSD filter response of sample 1 under inner ring fault in the PU dataset; Figure 19This is a schematic diagram of the APSD filter response of sample 2 under inner ring fault in the PU dataset; Figure 20 This is a schematic diagram of the APSD filter response of sample 3 under inner ring fault conditions in the PU dataset. Figure 21 This is a schematic diagram of the APSD filter response of sample 1 under outer ring fault in the PU dataset; Figure 22 This is a schematic diagram of the APSD filter response of sample 2 under outer ring fault in the PU dataset; Figure 23 This is a schematic diagram of the APSD filtering response of sample 3 under outer ring fault in the PU dataset; Figure 24 This is a schematic diagram of the APSD filter response of sample 1 in the normal state of the PU dataset; Figure 25 This is a schematic diagram of the APSD filter response of sample 2 in the normal state of the PU dataset. Figure 26 This is a schematic diagram of the APSD filter response of sample 3 in the normal state of the PU dataset. Figure 27 The diagram shows a comparison of the t-SNE feature distributions of DAFNet and APFD-IFR on the CWRU dataset. (a) is a schematic diagram of DAFNet, and (b) is a schematic diagram of APFD-IFR. Figure 28 The diagrams show the comparison of t-SNE feature distributions of DAFNet and APFD-IFR on the PU dataset. (a) is a schematic diagram of DAFNet, and (b) is a schematic diagram of APFD-IFR. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] To make the objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] This application provides a physically-inspired bearing fault diagnosis method, the overall framework of which is an Adaptive Physics-inspired Feature Decoupling and Interleaved Feature Reaggregation (APFD-IFR) framework. The APFD-IFR framework includes Adaptive Physics-inspired Feature Decoupling (APFD) and Interleaved Feature Reaggregation (IFR); wherein, APFD decouples complex fault features in the frequency and spatial domains respectively through the synergy of Adaptive Physics-inspired Spectral Decoupling (APSD) and Multi-scale Asymmetric Spatial Decoupling (MASD). The method specifically includes steps 1 and 2. Wherein: Step 1: Obtain the original vibration signal of the bearing to be diagnosed.

[0023] Step 2: Input the original vibration signal into the pre-trained bearing fault diagnosis model. The processing of the original vibration signal by the bearing fault diagnosis model includes: Step 21, performing adaptive physical heuristic spectral decoupling on the original vibration signal, including: filtering the original vibration signal using N Sinc bandpass filters to obtain N frequency band signals; N is an integer greater than 1; the low cutoff frequency and high cutoff frequency of each Sinc bandpass filter are learnable parameters, and the high cutoff frequency is greater than the low cutoff frequency and does not exceed half of the sampling rate of the original vibration signal.

[0024] Step 22 involves performing multi-scale asymmetric feature extraction on the N-band signals, including: expanding the N-band signals into an m-channel feature map through a first convolution operation, where m is an integer greater than N; dividing the m-channel feature map into a first feature and a first remaining channel group along the channel dimension according to a preset ratio; performing a second convolution operation on the first remaining channel group to obtain a second intermediate feature; dividing the second intermediate feature into a second feature and a second remaining channel group along the channel dimension; and performing a third convolution operation on the second remaining channel group to obtain a third feature.

[0025] Step 23 involves performing interleaved feature re-aggregation on the first feature, the second feature, and the third feature, including: calculating the kurtosis value of each frequency band signal in the N frequency band signals and taking the maximum value among all kurtosis values; calculating the spatial average kurtosis of each of the first feature, the second feature, and the third feature; calculating the weaving weights of each of the first feature, the second feature, and the third feature based on the maximum value and the spatial average kurtosis; performing channel-level resampling on the first feature, the second feature, and the third feature based on the weaving weights; concatenating the resampled first feature, the resampled second feature, and the resampled third feature; and performing channel permutation on the concatenated feature to obtain the reaggregated feature.

[0026] Step 24: Input the re-aggregation features into the classification network and output the bearing fault diagnosis results.

[0027] like Figure 1 As shown, the convolution module provided in this embodiment includes a first CBR 1×1 unit cascaded in sequence. The system consists of a CBR 1×3 unit and a second CBR 1×1 unit; wherein the first CBR 1×1 unit has a stride s=1 and padding p=0; the CBR 1×3 unit has a stride s=1 and padding p=1; and the second CBR 1×1 unit has a stride s=1 and padding p=0. The CBR 1×1 unit is composed of a sequentially connected Conv 1×1 convolutional layer, a batch normalization layer (BN), and a ReLU activation function; the CBR 1×3 unit is composed of a sequentially connected Conv 1×3 convolutional layer, a batch normalization layer (BN), and a ReLU activation function. This represents the total number of channels in the frequency band. For the frequency band signal index, FC stands for Fully Connected (FC), FC×3 represents three consecutive fully connected layers, s represents stride, and p represents padding.

[0028] By implementing steps 1 and 2 above, this application introduces a physically constrained Sinc bandpass filter at the feature extraction front end. This allows for adaptive locking of the fault-sensitive frequency band using only a few learnable parameters, thereby shielding frequency drift interference under specific operating conditions and achieving adaptive physical heuristic spectral decoupling. This extracts physically consistent, condition-invariant features. Furthermore, by constructing a multi-scale asymmetric feature extraction path, it balances the collaborative representation of low-level temporal details and high-level semantic information, alleviating the limitations of a single receptive field in representing complex non-stationary signals. Through adaptive dynamic guidance based on measured physical statistical indices, it selectively enhances and structurally interweaves features at each scale at the channel level, achieving interleaved feature re-aggregation. This breaks down the logical isolation between different branches and enhances the discriminative consistency of complex representations. In summary, this application significantly improves the generalization diagnostic accuracy and robustness under cross-operating conditions while maintaining model lightweightness, meeting the real-time diagnostic needs of industrial edge computing.

[0029] In this embodiment, the bearing fault diagnosis model includes: an Adaptive Physics-inspired Spectral Decoupling (APSD) module, a Multi-scale Asymmetric Spatial Decoupling (MASD) module, an Interleaved Feature Reaggregation (IFR) module, and a classification network. Specifically, the APSD module performs the Adaptive Physics-inspired Spectral Decoupling operation described in step 21; the MASD module performs the Multi-scale Asymmetric Feature Reaggregation operation described in step 22; the IFR module performs the Interleaved Feature Reaggregation operation described in step 23; and the classification network performs the classification operation described in step 24.

[0030] In an exemplary embodiment of this application, step 21, where the adaptive physical heuristic spectral decoupling constitutes the initial feature extraction stage of the adaptive physical heuristic feature decoupling mechanism, is characterized by establishing spectral decoupling boundaries and introducing a physically heuristic SincNet convolutional layer. Unlike standard one-dimensional convolutional neural networks (1D CNNs) that rely on random initialization of unconstrained weights, APSD explicitly defines bandpass filters through parameterized mathematical functions, thereby achieving spectral-level decoupling of fault features and operating noise at the underlying level.

[0031] Within the APSD framework, the convolution kernel of each Sinc bandpass filter consists of a low cutoff frequency. and high cutoff frequency Two learnable parameters determine this. To ensure physical validity, this application mandates... > Constraints greater than 0.

[0032] Specifically, in order to separate fault impulse characteristics from background noise at the signal source and to make the frequency edges of the filter smoother and avoid frequency leakage, the convolution kernel of each Sinc bandpass filter is generated according to the following steps: First, based on the low cutoff frequency of the Sinc bandpass filter... and high cutoff frequency The responses of the first low-pass filter are constructed respectively. Second low-pass filter response The response of the first low-pass filter and the response of the second low-pass filter All are in sinc function form: ; ; in, For discrete-time indexing; It is a discrete-time index sequence that is centrosymmetric about the center, and its values ​​are determined by the kernel length. Sure, It is an odd number, specifically: A = ( +1, ... -2, -1, 0, 1, 2... ); Secondly, the response of the second low-pass filter The response of the first low-pass filter Subtracting them yields the response of the ideal bandpass filter. : ; ; Then, since the time-domain truncation of an ideal rectangular filter can lead to spectral leakage and the Gibbs phenomenon, the APSD mechanism introduces a smoothing process: The response of the ideal bandpass filter With Hanming Window Element-wise multiplication is performed to obtain the convolution kernel of the Sinc bandpass filter. : ; Among them, the Hanming window Defined as: ; ; The final generated weight matrix constitutes the adaptive filter bank, such as Figure 2As shown, the Adaptive Physics-inspired Spectral Decoupling (APSD) injects a physical inductive bias, focusing the feature extraction process on the fault-sensitive frequency band, thereby achieving spectral-level decoupling of features and noise at the signal processing source. This deterministic physical constraint helps the bearing fault diagnosis model capture consistent feature signatures under different operating environments, providing a robust representational foundation for Single Domain Generalization (SDG). In contrast, the kernel weights of standard one-dimensional convolutional neural networks (1D CNNs) lack explicit physical constraints, exhibit a wide frequency response, and the extracted features are prone to containing redundant information, posing a risk of feature shift when operating conditions change.

[0033] Furthermore, such as Figure 3 As shown, this application addresses learnable parameters. and Physical constraint mapping is performed. In the diagram, channel 1, channel 2, ..., channel N represent N parallel Sinc bandpass filter channels, each channel being independently configured with a set of learnable parameters. and Each low cutoff frequency is generated through physical constraint mapping. and high cutoff frequency To ensure that each filter automatically adjusts within the effective frequency range and that the high cutoff frequency does not exceed half the sampling rate, the low cutoff frequency... and the high cutoff frequency The low cutoff frequency is determined according to the following formula during each forward propagation: and high cutoff frequency for: ; ; in, The preset minimum low cutoff frequency, For learnable low-frequency parameters; For learnable bandwidth parameters, This is the preset minimum bandwidth offset. The sampling rate of the original vibration signal. This is a clamping operation. Through this clamping operation, not only is it guaranteed that... > It also follows the Nyquist-Shannon sampling theorem, restricting the decoupling process to the physically effective frequency domain space.

[0034] In some embodiments, this application follows the guiding principle of "background noise avoidance and core feature preservation" for setting frequency boundary parameters. It is recommended to set it as the base frequency. The frequency is 1.5 to 2 times higher, designed to filter out DC components while avoiding low-frequency mechanical noise. For the CWRU dataset with a sampling rate of 12kHz, it is set to 50Hz to filter out fundamental frequency interference; while for the PU dataset with a sampling rate of 64kHz and more complex background noise, it is increased to 70Hz to enhance the suppression of power harmonics and mechanical interference. Detailed parameters are shown in Table 1.

[0035] Table 1 Parameter initialization for different datasets

[0036] In some embodiments, the minimum bandwidth parameter The frequency was uniformly set to 50Hz. This constraint aims to ensure that the filter window covers the resonant energy band excited by the fault. According to diagnostic theory, the fault impulse manifests in the frequency domain as an energy spectral peak with a certain width, accompanied by frequency shift. Interval modulation sidebands. The rotational speeds of the dataset used in this application are between 1500 and 1797 rpm, corresponding to... Approximately 25–30 Hz. Therefore, a baseline of 50 Hz ensures that the filter can completely enclose the main resonant frequency and at least its first-order modulation sideband, i.e. ≥2 This configuration prevents feature truncation due to insufficient bandwidth and, as a mathematical safety baseline, effectively avoids dead channels during the adaptive optimization process.

[0037] In some embodiments, the kernel length is constantly set to a=65. Utilizing the difference in sampling frequency, this configuration constructs an observation window of approximately 5.4 ms on the CWRU dataset, focusing on capturing the envelope features of the vibration waveform; while on the high-frequency sampling PU dataset, this physical scale is reduced to approximately 1.0 ms, enhancing the localization accuracy of transient pulses of fatigue damage. To address the potential representational limitations of a single-scale window, the APFD mechanism achieves co-mapping of cross-scale features through its internal hierarchical compensation logic.

[0038] In some embodiments, the number of parallel channels N is 8. Considering the total number of fault categories, this value retains approximately 2 to 3 times the feature space redundancy while covering the dominant resonance bands of each category. This redundancy design aims to capture low-frequency modulation components in the signal, thereby enabling the bearing fault diagnosis model to maintain robust diagnostic performance when faced with frequency jumps caused by varying operating conditions.

[0039] In an exemplary embodiment of this application, in step 22, the MASD module immediately follows the spectral boundary established by the APSD module and extracts the spatial dimension of features through an asymmetric nested structure. The MASD module establishes hierarchical multi-scale constraints in the feature space by constructing parallel branches of heterogeneous depth. Shallow branches focus on preserving transient impact features localized in the time domain, while deep nested branches are responsible for extracting higher-order nonlinear semantics. This multi-dimensional spatial mapping strategy effectively overcomes the limitations of a single receptive field operator in representing complex waveforms and achieves spatial-level decoupling of heterogeneous discriminative information.

[0040] Specifically, such as Figure 1 As shown, this embodiment sets the branch depth i=3 based on the number of trunk channels m=36, and extracts shallow, middle and deep features using three sets of convolutional sequences with different numbers of layers. This two-level asymmetric segmentation topology enhances the adaptability of the bearing fault diagnosis model to multi-scale signals. For the high-frequency sampled PU dataset, the MASD module effectively captures long-range pulse features through the layer-by-layer expansion of the receptive field of deep branches; while for the low-frequency sampled CWRU dataset, the heterogeneous depth branch design helps to decouple the envelope information a second time, preserving discriminative details under complex interference. The MASD module overcomes the limitations of a fixed receptive field, and the information aggregation between branches will be described in detail in the IFR module in step 23.

[0041] Therefore, APFD integrates the frequency localization capability of the APSD module and the scale decomposition capability of the MASD module, constructing a frequency-space coupled feature processing system, which provides theoretical support at the characterization level for robust diagnosis under various operating conditions.

[0042] In an exemplary embodiment of this application, in step 23, the IFR module re-aggregates the three heterogeneous features stripped by APFD. The backbone channel number m=36 is divided into three groups of 12-channel feature streams, which then enter the resampling stage for feature re-aggregation. For ease of description, the first feature is denoted as branch P1, the second feature as branch P2, and the third feature as branch P3; in the following description, branch P1, branch P2, and branch P3 have the same meaning as the first feature, the second feature, and the third feature.

[0043] Specifically, after the front-end APSD module performs adaptive bandpass filtering, this application calculates the kurtosis value of each of the N frequency band signals, forming a kurtosis vector Kur=[Kur1,Kur2,…,Kur…]. N To ensure that this metric is not distorted by the nonlinear transformations (such as ReLU and Pooling) of the intermediate convolutional layers, the system defines these N kurtosis values ​​as physically perceptible shadow parameters and passes them through to the backend IFR module as the physical basis for intervening in the feature weaving logic.

[0044] The following formula is used to calculate the first... The kurtosis value of the road band signal is calculated using the fourth-order standard moment formula: ;in, For the first Kurtosis value of the road band signal. For the first The data sequence of the frequency band signal, for The mean, for standard deviation It represents the mathematical expectation.

[0045] Take the maximum value among all kurtosis values It represents the physical signature of the current signal that most resembles a fault.

[0046] The spatial mean kurtosis of the first feature, the second feature, and the third feature is calculated using the following formula: ; in, The feature index takes values ​​of 1, 2, and 3, corresponding to the first feature, the second feature, and the third feature, respectively. For the first Spatial average kurtosis of each feature For the first The total number of channels for each feature For channel indexing, For the first The first feature The data sequence consisting of all spatial location elements of the feature map of each channel. is the kurtosis value of the data sequence.

[0047] Calculate the first value based on the maximum value and the spatial average kurtosis. The scores corresponding to each feature: ; in, The maximum value among all kurtosis values. For the first Spatial average kurtosis of each feature For the first The score corresponding to each feature.

[0048] This score measures whether there was indeed a physical impact at the front end, i.e. Large, and that branch did indeed capture the impact, namely Large. If the front end The large size indicates a malfunction, but in a certain branch... If the value is very low, it means that the branch is full of noise and will be automatically suppressed; conversely, the branch that captures the strongest impact will get the highest weaving weight.

[0049] Use with temperature coefficient The Softmax function converts the physics score into branch reorganization weights, which are calculated using the following formula: The weaving weights corresponding to each feature: ; in, For the first The weaving weights corresponding to each feature The preset temperature coefficient, This refers to the feature index used to traverse the first feature, the second feature, and the third feature. This is used to adjust the intensity of intervention and prevent the weights from becoming too extreme, which could lead to a loss of feature diversity.

[0050] The first feature, the second feature, and the third feature each have m / 3 channels; therefore, the total number of output channels for the IFR module is m. Calculate the target number of channels for each feature. That is, the number of channels for this feature after resampling: ; Based on the braiding weights, channel-level resampling is performed on the first feature, the second feature, and the third feature, specifically including: Determine the first feature The second feature and the third feature The number of channels contained in each of the three is used as the total number of channels m. For each of the first, second, and third features, the weaving weight corresponding to the feature is multiplied by the total number of channels, and then rounded to the nearest integer to obtain the target number of channels corresponding to the feature. and perform the following operations: If the number of target channels is greater than the number of channels contained in the feature itself, that is Then all channels of the aforementioned feature are retained, i.e. The system identifies the target number of channels and calculates the number of channels that need to be added. The number of channels to be added is equal to the target number of channels minus the number of channels inherent in the feature itself. The first step length is obtained by dividing the number of channels contained in the feature itself by the number of channels that need to be supplemented. Then, sampling is performed across the existing channels of the feature according to this first step length to obtain supplementary channels equal to the number of channels that need to be supplemented. These supplementary channels are then merged with all remaining channels to obtain the resampled feature. The step sampling is performed at equal intervals along the channel dimension according to the corresponding step length. The first step length is: ; At this point, all the information of the feature is fully preserved, and some features are double-exposed, enhancing its presence at the logical level.

[0051] If the number of target channels is less than the number of channels contained in the feature itself, that is Then, the quotient obtained by dividing the number of channels contained in the feature itself by the target number of channels is used as the second step size. From the existing channels of the feature, step sampling is performed according to the second step size to obtain a number of channels equal to the target number of channels, which are then used as the resampled feature. The second step size is: ; At this point, the feature space of the feature is proportionally sparsified, and the feature is suppressed.

[0052] If the number of target channels is equal to the number of channels contained in the feature itself, that is... If the feature remains unchanged, it will be used as the resampled feature.

[0053] In one exemplary embodiment of this application, such as Figure 4 As shown, in step 23, the resampled first feature The second feature after resampling and the third feature after resampling The splicing process involves channel permutation of the spliced ​​features to obtain re-aggregated features, specifically including: For ease of description, the data of each channel is represented as a feature sequence of length L, that is, any feature can be represented as a two-dimensional tensor composed of the number of channels and the sequence length L.

[0054] The resampled first feature, resampled second feature, and resampled third feature are concatenated sequentially along the channel dimension to obtain the concatenated feature. At this point, the concatenated feature presents a structure of three sequentially arranged segments along the channel dimension: the first segment is the channel of the first feature, the middle segment is the channel of the second feature, and the last segment is the channel of the third feature. Since the feature sequence length of each channel is L, the concatenated feature can be represented as a tensor with m channels and a sequence length of L. The number of groups is determined based on the proportional relationship between the number of target channels corresponding to the resampled first feature, the resampled second feature, and the resampled third feature; wherein, the proportional relationship is a simplified integer ratio, and the number of groups is equal to the sum of the values ​​in the simplified integer ratio; Specifically, the number of target channels corresponding to the first feature, the second feature, and the third feature are respectively denoted as... Simplify it to its simplest integer ratio vector : ; in, The greatest common divisor, The values ​​are 1, 2, and 3; the sum of the values ​​in the simplest integer ratio is determined as the number of groups, and in this embodiment, this number of groups is denoted as the weaving factor. : .

[0055] in, This is a positive integer used to control the fineness of the weaving; in this scheme... At this time, the weaving factor It equals the sum of the values ​​in the simplest integer ratio.

[0056] Based on the total number of channels in the spliced ​​features and the number of groups, the number of channels in each channel group is determined; according to the number of channels in each channel group, the spliced ​​features are divided into the number of channel groups along the channel dimension, and each channel group contains the same number of channels.

[0057] Specifically, according to the said weaving factor The spliced ​​features are reshaped along the channel dimension as follows: There are 10 channel groups, and the number of channels in each channel group is equal to the total number of channels. With the weaving factor The merchant, that is Therefore, the reshaped features can be represented as Each channel group, The structure has 1 channel, and the feature sequence of each channel has a length of L; since the simplest integer ratio already reflects the proportional relationship between the number of target channels of the first feature, the second feature, and the third feature, the reshaped structure... Each channel group contains channels from the first feature, the second feature, and the third feature.

[0058] The selection process proceeds cyclically from the first channel group to the last channel group. One channel is selected from each channel group at a time, and the selected channels are arranged into a new channel sequence. This selection process is repeated until all channels in all channel groups have been selected, resulting in an alternating channel sequence.

[0059] Specifically, the process of cyclically selecting and arranging the channels from the first group to the last group is what is referred to as the process of selecting and arranging the channels. The transpose operation is performed on each channel group, which disperses the channels that were originally in the same channel group to different positions, and the channels that were originally in different channel groups are arranged alternately. The transposed features are then flattened, which involves sequentially reassembling the channels along the channel dimension into a single feature sequence, thus obtaining an interleaved channel sequence. Through this transpose and flattening operation, channels corresponding to different feature scales appear alternately in the final re-aggregated features, achieving deep interweaving of cross-scale features.

[0060] The staggered channel sequence is used as a re-aggregation feature.

[0061] In addition, this application also includes step 3: the training process of the bearing fault diagnosis model includes: Construct a vibration signal sample set containing labels for various bearing fault types; The bearing fault diagnosis model is trained using the sample set to optimize the low and high cutoff frequencies of the Sinc bandpass filter, the parameters of the first convolution operation, the second convolution operation, and the third convolution operation, as well as the parameters of the classification network.

[0062] Furthermore, the loss function of the bearing fault diagnosis model during the training process is: ; in, For the total loss, For classification cross-entropy loss, For physical consistency loss, This is the preset balance coefficient; The physical consistency loss for: ; in, To preset the kurtosis anchor point threshold, For the bearing fault diagnosis model, the first training sample used in a single parameter update process is... The average kurtosis value is obtained by averaging the kurtosis values ​​of the road frequency band signal. For the index of the frequency band signal, This represents the total number of channels in the frequency band.

[0063] Furthermore, a kurtosis activation adaptive gating unit is introduced at the connection between the APSD module and the MASD module to obtain the aforementioned physical consistency loss. Average difficulty value in The specific implementation steps are as follows: (1) During the forward propagation phase of training, the N-channel frequency band signals output by the APSD module are statistically evaluated in real time. Specifically, for each sample in the current training batch, the kurtosis values ​​of its N channels are calculated. Since the N-channel frequency band signals correspond to the outputs of N Sinc bandpass filters, the kurtosis value of each channel reflects the impact characteristic intensity of the frequency band currently locked by the filter. For Batch_Size samples in the current training batch, each sample generates N kurtosis values, thus obtaining a matrix with dimension [Batch_Size, N]. Each row in this matrix corresponds to the N-channel kurtosis values ​​of a sample, and each column corresponds to the kurtosis value of a filter channel on Batch_Size samples; (2) Calculate the mean of the matrix along the Batch dimension, that is, calculate the arithmetic mean of each column, and finally generate a one-dimensional feature vector of length N, that is, the mean kurtosis vector. The first kurtosis in the average kurtosis vector element Indicates the first The average kurtosis value of a Sinc bandpass filter across all samples in the current training batch is used to measure the overall impact characteristics of the frequency band locked by the filter in the current batch. (3) Preset physical salience threshold The selection of this threshold has a clear physical meaning: in probability theory, the kurtosis value of standard Gaussian white noise (pure noise without impulse characteristics) is 3.0. When the kurtosis value is less than 3.0, the signal exhibits a stationary process and is judged as invalid background noise; when the kurtosis value is greater than 3.0, the signal exhibits impulse characteristics and is judged as a significant frequency band containing potential fault impulse characteristics. (4) Gradient-forced guidance: If the average kurtosis of a channel is greater than or equal to If the system considers the channel to have captured valid physical features, no penalty will be triggered; if the average kurtosis of a channel is less than... The physical regularization module generates a penalty gradient, forcing the channel filter to change its frequency parameters. The specific process is as follows: By constructing an asymmetric physical penalty operator This paper introduces kurtosis into the loss function framework of neural networks. Based on this objective function, this application follows the following asymmetric gradient triggering criterion during parameter updates: when hour, Its partial derivatives (gradients) with respect to the parameters are zero: ; when hour, The physics constraint module generates a forced correction gradient. : ; In the total gradient Under collaborative optimization, filter parameters The evolution (including low and high cutoff frequencies) executes the following logic: When the frequency band captured by the filter is in a physical dead zone ( When <3), the generated correction gradient It plays a dominant role in parameter updates. Under the action of the optimizer, the gradient-driven filter is shifted on the spectral axis, forcing it out of the current low-kurtosis plateau noise region. Once the filter captures a physically significant frequency band, such that the average kurtosis of the channel satisfies... When ≥3.0, physical loss item Reduced to zero, corresponding corrected gradient Then it disappears. At this point, the total gradient degenerates to one driven only by the classification loss. The filter parameters tend to stabilize at this high kurtosis frequency domain, thus achieving autonomous locking of the fault characteristic frequency band. It should be noted that the above gradient guidance process only applies to the physical consistency loss. The filter frequency parameters and classification network parameters involved are still determined by the classification cross-entropy loss. Driver updates, both are balanced by a coefficient Collaborative optimization; (5) Iterative Evolution: As training progresses, all Sinc filters, under the monitoring of physical parameters, eventually lock onto the physical frequency band with the strongest impact characteristics. Specifically, in the early stage of training, the low and high cutoff frequencies of each Sinc filter are randomly initialized values, and their corresponding frequency bands may fall in the noise region. At this time, the average kurtosis of each channel is generally lower than 3.0, and the physical consistency loss is large. The correction gradient continuously drives the filter to move towards the high kurtosis frequency band. As the training rounds increase, each filter gradually converges towards the frequency band where the fault impact energy is concentrated. The average kurtosis gradually increases and stabilizes above 3.0. The physical consistency loss tends to zero, and the filter frequency parameters no longer change significantly, completing the autonomous locking. After training is completed, the low and high cutoff frequencies of each Sinc filter are the finally determined frequency band boundaries, which are used for adaptive bandpass filtering of the original vibration signal in the inference stage.

[0064] After the above training process is completed, to further illustrate the lightweight effect of this application, the parameter distribution of each functional component of the APFD-IFR framework is analyzed. As shown in Table 2, at the front end of feature extraction, the APSD module establishes physical constraints through the Sinc function, fixing the initial layer parameters to 2N=16; in the middle layer, the MASD module integrates a grouped convolution strategy in nested branches, where the P2 branch and P3 branch adopt a decoupled configuration of groups=8 and groups=4 respectively, with corresponding theoretical parameter scales of 576 and 192; at the back end, the IFR module achieves cross-scale information interaction through tensor permutation without generating additional parameter increments. Statistically, the total number of trainable parameters for the entire framework is 45,799.

[0065] Table 2 Parameter Scale of Each Functional Module in the APFD-IFR Framework

[0066] As shown in Table 2, this application controls the number of parameters to 45,799 through APSD physical constraints, MASD grouped convolution, and IFR zero-parameter permutation. In summary, this application uses Sinc filtering to achieve physical spectrum decoupling, multi-scale asymmetric extraction to obtain multi-scale discrimination information, and kurtosis-guided resampling and channel permutation to achieve interleaving and re-convergence, thus ensuring diagnostic accuracy while meeting the real-time monitoring requirements at the edge.

[0067] To verify the effectiveness of the method proposed in the above embodiments of this application, this application conducted validation on two representative public datasets: the Case Western Reserve University (CWRU) dataset and the Paderborn University (PU) dataset. These two datasets exhibit significant heterogeneity in terms of sampling frequency, impairment mechanism, and environmental noise, posing a rigorous test to the model's generalization ability.

[0068] (1) CWRU Dataset: This dataset serves as a standard benchmark in the field of bearing diagnostics, used to verify the basic representation capabilities of the model. The experiment uses vibration signals of the drive-end bearing at a sampling frequency of 12kHz. It covers three damage levels: 7mil, 14mil, and 21mil. Based on the diagnostic task requirements of this application, four labels were selected: normal state, inner ring fault, outer ring fault, and roller fault. In terms of operating conditions, this application selected four operating environments with corresponding loads of 0, 1, 2, and 3HP, denoted as W0, W1, W2, and W3, respectively. Since the rotational speed of this dataset only fluctuates slightly with the load in the range of 1730~1797RPM, its physical characteristics can be regarded as torque changes at near constant speed. This setting aims to evaluate the generalization resilience of the APFD-IFR framework in the context of a single rotational speed to cope with the feature shift induced by torque fluctuations.

[0069] (2) PU Dataset: Compared with the CWRU dataset, the PU dataset includes not only artificial damage signals but also real fatigue damage signals, and its characteristics are closer to the actual situation in industrial settings. The experiment uses a 64kHz high-frequency sampling signal, including three states: normal, inner race fault, and outer race fault. In terms of the operating conditions selected for this dataset, this application selected three typical operating environments with a constant speed of 1500RPM for single-source domain generalization research, denoted as M0, M1, and M2, respectively.

[0070] For data preprocessing, the original long sequences were segmented into sample intervals of length 1024. Standard deviation normalization was performed on each sample to eliminate differences in amplitude dimensions between different operating conditions. The processed samples were stored independently in NumPy binary format, with each file containing a sample of shape (1, 1024). For the CWRU dataset, approximately 1000 samples were generated for each operating condition; for the PU dataset, approximately 6500 samples were generated for each operating condition. The data was divided in a 7:3 ratio, with 70% of the data used as the training set to train the model and 30% used as the test set to validate the model's performance.

[0071] Regarding implementation details, the APFD-IFR framework proposed in this application is implemented in the PyTorch deep learning library and accelerated by CUDA on a computing platform equipped with an NVIDIA GeForce RTX graphics card. The core training configuration is shown in Table 3 below.

[0072] Table 3 APFD-IFR Framework Training Hyperparameter Configuration

[0073] To comprehensively measure the classification ability of the model, this application uses accuracy, recall, and F1-score as core metrics, defined as follows: accuracy : ; Accuracy : ; Recall rate : ; F1 score: ; Among them, TP, TN, FP, and FN represent true positive, true negative, false positive, and false negative, respectively.

[0074] This application employs a more stringent single-source domain generalization evaluation protocol than traditional domain-adaptive methods. The model is trained using only labeled data under a single operating condition, such as the W0 condition of a CWRU or the M0 condition of a PU. After training, "W0→W1" indicates that the model trained under the W0 condition is used to test the data under the W1 condition. Throughout the entire training process, the model has absolutely no access to any information from the target domain.

[0075] (1) First, the performance of the model was validated on the CWRU dataset. Table 4 summarizes the cross-condition diagnostic accuracy under different fault sizes.

[0076] Table 4 Ablation experiment results (accuracy %) on the CWRU dataset

[0077] As shown in Table 4, in the 36 cross-condition diagnostic experiments on the CWRU dataset, the accuracy of DAFNet fluctuated significantly, with a minimum of 71.34% and an average of approximately 92.03%; APFD-IFR consistently achieved accuracy no lower than 97.97%, with an average of approximately 99.75%, representing an improvement of approximately 7.72 percentage points compared to DAFNet. These results demonstrate that the proposed method effectively suppresses condition shifts under different fault severity levels, exhibiting higher cross-condition diagnostic accuracy and robustness.

[0078] The model's performance was further validated on the PU dataset. Table 5 summarizes the cross-condition diagnostic accuracy under different damage modes.

[0079] Table 5. Diagnostic performance ablation experiment results (accuracy %) under the PU dataset.

[0080] As shown in Table 5, under the natural damage mode, the lowest accuracy of DAFNet drops to 91.18%, while APFD-IFR maintains above 97% in all cross-condition tasks, further verifying the generalization robustness of the proposed method in complex real fatigue damage scenarios.

[0081] Furthermore, comparative experiments were conducted between this application and mainstream lightweight networks SqueezeNet and ShuffleNet to evaluate network performance based on metrics such as parameter count, FPS, and computational complexity (MFlops), as shown in Table 6 below. Figure 5 As shown.

[0082] Table 6 Model Efficiency Comparison

[0083] Table 6 and Figure 5This paper summarizes the efficiency comparison between APFD-IFR and mainstream lightweight architectures. Experimental results show that this framework achieves an extremely small parameter count of 45,799 and a computational load of only 0.31 MFlops while maintaining a high throughput of 595 FPS. Compared with the second-best performing MicroNet, the computational overhead of this model is reduced by approximately 27 times, consistently ranking in the optimal region in the bubble graph. This order-of-magnitude compression of parameter size and computational intensity proves that the APFD and IFR mechanisms achieve extreme savings in hardware resources without sacrificing real-time performance, fully meeting the stringent requirements of edge devices for fault monitoring.

[0084] To further verify the cross-condition generalization capability of this application under lightweight conditions, the cross-condition transfer capability of this application and the aforementioned lightweight networks was compared on the CWRU and PU datasets. Table 7 summarizes the cross-condition diagnostic accuracy for different fault sizes on the CWRU dataset, and Table 8 summarizes the cross-condition diagnostic accuracy on the PU dataset.

[0085] Table 7. Comparison of lightweight model transfer capabilities across operating conditions on the CWRU dataset (accuracy %)

[0086] Table 8. Comparison of lightweight model transfer capabilities across operating conditions on the PU dataset (accuracy %)

[0087] As shown in Tables 7 and 8, in challenging cross-condition tasks such as 14mil and PU natural damage, lightweight networks like ShuffleNet and SqueezeNet achieved an accuracy as low as 58.60%, while APFD-IFR maintained an accuracy of at least 97.65% across all tasks. This demonstrates that, with only 45,799 parameters and a computational cost of only 0.31 MFlops, this application still exhibits significantly superior cross-condition generalization capabilities compared to other lightweight networks, validating the effectiveness of APSD physical constraints and IFR dynamic re-aggregation.

[0088] To further explore the underlying mechanism by which the APFD-IFR framework proposed in this application achieves the aforementioned cross-condition generalization advantages, a visualization analysis is conducted from two levels: physical interpretability and feature distribution. Specifically, the filtering response of the APSD module is first visualized in the time domain to verify its physical perception capability; then, t-SNE is used to perform dimensionality reduction mapping on the feature space to reveal the model's discrimination mechanism under extreme domain biases.

[0089] (1) Physical interpretability analysis To further explore the intrinsic decision-making logic of the APFD-IFR framework proposed in this application and verify its physical sensing capability, the time-domain response of the feature extraction process of the APSD module is visualized. Since the APSD module contains 8 parallel channels, to ensure the integrity of frequency domain coverage while simplifying the presentation, representative CH1 (low frequency band), CH5 (mid frequency band), and CH8 (high frequency band) are selected as observation windows to demonstrate the model's effect on stripping heterogeneous signal components from a multi-resolution perspective.

[0090] like Figures 6 to 17 As shown, the results present the response of the original signal after filtering by the APSD module under the CWRU dataset under roller fault, inner race fault, outer race fault, and normal conditions. Three samples were randomly selected for each fault type to verify stability. The results show that the high-frequency resonance channels (CH5 approximately 3.4kHz and CH8 approximately 6.0kHz) extract clear and regular periodic pulses in all fault samples, while normal samples only show stable random fluctuations. Within a 5.4ms physical window constructed with a convolution kernel length of a=65, the APSD module successfully captures the complete impact decay envelope, significantly enhancing the discriminative significance between healthy states. The high consistency of representation among different random samples confirms the robustness of this mechanism in eliminating operating condition interference, revealing the physical mechanism by which the model achieves extreme classification accuracy in the CWRU task.

[0091] like Figures 18 to 26 As shown in the figure, the response results of the original signal after filtering by the APSD module are presented in the PU dataset under inner ring fault, outer ring fault, and normal conditions. As can be seen from the figure, the APSD module achieves physical decomposition of the signal components: the low-frequency channel (CH1 approximately 100–200Hz) locks in the smooth periodic fundamental wave, while the high-frequency resonant channels (CH5 approximately 18.3kHz and CH8 approximately 32.0kHz) extract weak transient impulse signatures from strong background noise. It can be observed that the dark envelope of the fault samples in the high-frequency range above 18.3kHz exhibits significant impulse characteristics. Although its normalized amplitude is at a low order of 0.05, the discriminative significance of the feature is significantly improved compared to the original signal. The high consistency among different random samples verifies the stability of this physical signature. This purification effect of the underlying representation provides a representational basis for the robustness of the APFD-IFR framework in single-source domain generalization tasks.

[0092] The visualization results above demonstrate that the APSD module achieves a mapping from the original noisy waveform to a physically consistent representation through selective activation of heterogeneous channels. This underlying physical constraint effectively suppresses overfitting of the model to non-discriminatory artifacts, giving the reconstructed feature flow a clear discriminative boundary. By establishing representation stability across different operating conditions, this mechanism logically supports the robust performance of the APFD-IFR framework in single-source domain generalization tasks.

[0093] (2) Visual analysis To reveal the model's discrimination mechanism under extreme domain biases from the perspective of feature distribution, t-SNE was used to reduce the dimensionality of the feature space of the penultimate layer of the model. Experiments were conducted on the two most challenging tasks in the CWRU and PU datasets: the W0→W3 task with a size of 14mil, and the M1→M2 task under natural fatigue damage.

[0094] like Figure 13 As shown, the observation results indicate that Figure 27 The baseline model in (a) exhibits severe aliasing and distribution collapse in its feature space when facing large-span load offsets, leading to blurred fault category boundaries; in contrast, the features processed by APFD-IFR, i.e. Figure 27 In (b), the class exhibits extremely high intra-class cohesion and inter-class separability, and the originally intertwined feature points are reshaped into compact clusters that are independent of each other.

[0095] like Figure 14 As shown, the observation results indicate that Figure 28 The baseline model in (a) exhibits severe aliasing and distribution collapse in its feature space when facing natural fatigue damage; in contrast, the features processed by APFD-IFR, i.e. Figure 28 (b) in the example exhibits extremely high intra-class cohesion and inter-class separability.

[0096] The above visual comparison confirms that even in extreme domain offset scenarios, the architecture proposed in this application can still establish a clear decision boundary through the locking of underlying physical features and the weaving of backend topological information, thus verifying the generalization advantage of the proposed mechanism from the perspective of representation learning.

[0097] In summary, the above experiments verified the effectiveness of the APFD-IFR framework proposed in this application from four dimensions: diagnostic accuracy, lightweight design, physical interpretability, and feature separability. This demonstrates that the framework can significantly improve the generalized diagnostic accuracy and robustness under cross-conditions while maintaining extremely low parameter overhead, thus meeting the real-time monitoring needs of industrial edge computing.

[0098] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A physics-inspired bearing fault diagnosis method, characterized in that, include: Obtain the original vibration signal of the bearing to be diagnosed; The original vibration signal is input into a pre-trained bearing fault diagnosis model. The processing of the original vibration signal by the bearing fault diagnosis model includes: Adaptive physical heuristic spectral decoupling of the original vibration signal includes: filtering the original vibration signal using N Sinc bandpass filters to obtain N frequency band signals; N is an integer greater than 1; the low cutoff frequency and high cutoff frequency of each Sinc bandpass filter are learnable parameters, and the high cutoff frequency is greater than the low cutoff frequency and does not exceed half of the sampling rate of the original vibration signal; Multi-scale asymmetric feature extraction is performed on the N-band signals, including: expanding the N-band signals into an m-channel feature map through a first convolution operation, where m is an integer greater than N; dividing the m-channel feature map into a first feature and a first remaining channel group along the channel dimension according to a preset ratio; performing a second convolution operation on the first remaining channel group to obtain a second intermediate feature; dividing the second intermediate feature into a second feature and a second remaining channel group along the channel dimension; and performing a third convolution operation on the second remaining channel group to obtain a third feature. The process of interleaving feature re-aggregation for the first feature, the second feature, and the third feature includes: calculating the kurtosis value of each frequency band signal in the N frequency band signals and taking the maximum value among all kurtosis values; calculating the spatial average kurtosis of each of the first feature, the second feature, and the third feature; calculating the weaving weights of each of the first feature, the second feature, and the third feature based on the maximum value and the spatial average kurtosis; performing channel-level resampling on the first feature, the second feature, and the third feature based on the weaving weights; concatenating the resampled first feature, the resampled second feature, and the resampled third feature; and performing channel permutation on the concatenated feature to obtain the reaggregated feature. The reconvergence features are input into the classification network, and the bearing fault diagnosis results are output.

2. The bearing fault diagnosis method based on physical heuristics according to claim 1, characterized in that, The training process of the bearing fault diagnosis model includes: Construct a vibration signal sample set containing labels for various bearing fault types; The bearing fault diagnosis model is trained using the sample set to optimize the low and high cutoff frequencies of the Sinc bandpass filter, the parameters of the first convolution operation, the second convolution operation, and the third convolution operation, as well as the parameters of the classification network.

3. The bearing fault diagnosis method based on physical heuristics according to claim 2, characterized in that, The loss function of the bearing fault diagnosis model during training is: ； in, For the total loss, For classification cross-entropy loss, For physical consistency loss, This is the preset balance coefficient; The physical consistency loss for: ； in, To preset the kurtosis anchor point threshold, For the bearing fault diagnosis model, the first training sample used in a single parameter update process is... The average kurtosis value is obtained by averaging the kurtosis values ​​of the road frequency band signal. For the index of the frequency band signal, This represents the total number of channels in the frequency band.

4. The bearing fault diagnosis method based on physical heuristics according to claim 1, characterized in that, The convolution kernel for each Sinc bandpass filter is generated according to the following steps: Based on the low cutoff frequency and high cutoff frequency of the Sinc bandpass filter, a first low-pass filter response and a second low-pass filter response are constructed respectively, and both the first low-pass filter response and the second low-pass filter response are in the form of a sinc function. Subtracting the response of the second low-pass filter from the response of the first low-pass filter yields the ideal band-pass filter response. The element-wise multiplication of the ideal bandpass filter response with the Hamming window yields the convolution kernel of the Sinc bandpass filter.

5. The bearing fault diagnosis method based on physical heuristics according to claim 1, characterized in that, The low cutoff frequency and the high cutoff frequency are determined according to the following formula during each forward propagation: The low cutoff frequency for: ； in, The preset minimum low cutoff frequency, For learnable low-frequency parameters; The high cutoff frequency for: ； in, For learnable bandwidth parameters, This is the preset minimum bandwidth offset. The sampling rate of the original vibration signal. This is a clamping operation.

6. The bearing fault diagnosis method based on physical heuristics according to claim 1, characterized in that, The following formula is used to calculate the first... Kurtosis value of the road band signal: ； in, For the first Kurtosis value of the road band signal. For the first The data sequence of the frequency band signal, for The mean, for standard deviation It represents the mathematical expectation.

7. The bearing fault diagnosis method based on physical heuristics according to claim 6, characterized in that, The spatial mean kurtosis of the first feature, the second feature, and the third feature is calculated using the following formula: ； in, The feature index takes values ​​of 1, 2, and 3, corresponding to the first feature, the second feature, and the third feature, respectively. For the first Spatial average kurtosis of each feature For the first The total number of channels for each feature For channel indexing, For the first The first feature The data sequence consisting of all spatial location elements of the feature map of each channel. is the kurtosis value of the data sequence.

8. The bearing fault diagnosis method based on physical heuristics according to claim 7, characterized in that, The following formula is used to calculate the first... The weaving weights corresponding to each feature: ； ； in, The maximum value among all kurtosis values. For the first Spatial average kurtosis of each feature For the first The score corresponding to each feature For the first The weaving weights corresponding to each feature The preset temperature coefficient, The feature index is used to traverse the first feature, the second feature, and the third feature.

9. The bearing fault diagnosis method based on physical heuristics according to claim 1, characterized in that, Based on the braiding weights, channel-level resampling is performed on the first feature, the second feature, and the third feature, specifically including: Determine the number of channels contained in each of the first feature, the second feature, and the third feature, and use the sum of the number of channels of the three features as the total number of channels; For each of the first, second, and third features, the weaving weight corresponding to the feature is multiplied by the total number of channels, rounded to the nearest integer to obtain the target number of channels corresponding to the feature, and the following operations are performed: If the target number of channels is greater than the number of channels contained in the feature itself, then all channels of the feature are retained, and the number of channels to be supplemented is calculated. The number of channels to be supplemented is equal to the target number of channels minus the number of channels contained in the feature itself. The quotient obtained by dividing the number of channels contained in the feature itself by the number of channels to be supplemented is used as the first step length. Step sampling is performed from the existing channels of the feature according to the first step length to obtain a number of supplementary channels equal to the number of channels to be supplemented. The supplementary channels are merged with all retained channels to obtain the resampled feature. Wherein, the step sampling is sampling at equal intervals according to the corresponding step length in the channel dimension. If the number of target channels is less than the number of channels contained in the feature itself, then the quotient obtained by dividing the number of channels contained in the feature itself by the number of target channels is used as the second step size. The feature's existing channels are sampled step by step according to the second step size to obtain a number of channels equal to the number of target channels, which are used as the resampled feature. If the number of target channels is equal to the number of channels contained in the feature itself, then the feature remains unchanged and is used as the resampled feature.

10. The physics-based bearing fault diagnosis method according to claim 9, characterized in that, The resampled first feature, resampled second feature, and resampled third feature are concatenated, and channel permutation is performed on the concatenated feature to obtain the re-aggregated feature, specifically including: The resampled first feature, the resampled second feature, and the resampled third feature are concatenated sequentially along the channel dimension to obtain the concatenated feature. The number of groups is determined based on the proportional relationship between the number of target channels corresponding to the resampled first feature, the resampled second feature, and the resampled third feature; wherein, the proportional relationship is a simplified integer ratio, and the number of groups is equal to the sum of the values ​​in the simplified integer ratio; Based on the total number of channels in the spliced ​​features and the number of groups, the number of channels in each channel group is determined; according to the number of channels in each channel group, the spliced ​​features are divided into the number of channel groups along the channel dimension, and each channel group contains the same number of channels. The selection process proceeds cyclically from the first channel group to the last channel group. Each time, one channel is selected from each channel group, and the selected channels are arranged into a new channel sequence. This selection process is repeated until all channels in all channel groups have been selected, resulting in an alternating channel sequence. The staggered channel sequence is used as a re-aggregation feature.

Images