Bearing life prediction method of graph wavelet attention network fusing hidden physical information
By combining adaptive graph construction and graph wavelet attention network with GRU model, the problem of ignoring the time dimension and physical correlation of bearing degradation features in existing methods is solved, achieving accurate prediction of bearing remaining service life and improving model interpretability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGXI UNIV
- Filing Date
- 2026-05-06
- Publication Date
- 2026-07-21
Smart Images
Figure CN122433005A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bearing remaining service life prediction technology, and in particular to a bearing life prediction method based on graph wavelet attention networks that integrate implicit physical information. Background Technology
[0002] Rotating machinery plays a crucial role in the conversion of motion and the transfer of energy within mechanical equipment. Rolling bearings, as core components of rotating machinery, profoundly affect the reliability and safety of the mechanical system through their operating condition. Remaining service prediction technology, a key technological support for predictive maintenance of mechanical equipment, can utilize known historical data to assess the health status of equipment before failure occurs, thus helping to prevent catastrophic failures and reduce maintenance costs.
[0003] In modern industry, with the massive accumulation of industrial monitoring data and the increasing complexity of non-stationary operating conditions of equipment, artificial intelligence-based methods are emerging as a new paradigm for bearing RUL (Remaining Lifetime) prediction. These methods extract degradation information from monitoring data throughout the bearing's entire lifecycle to accurately infer the remaining time from the current moment until bearing failure. Traditional machine learning methods obtain the final prediction value by constructing a mapping relationship between bearing degradation features and remaining bearing life. Yan et al. defined two new dimensionless degradation features and used SVM to evaluate the degradation stage of bearings. Shi et al. designed an Extreme Learning Machine (ELM) using geometric structure information from the raw data to improve prediction accuracy. However, these traditional machine learning-based methods require manual design of degradation features. Given the large amount of data generated in industrial processes, relying on manual design of degradation features is time-consuming, labor-intensive, and lacks adaptability.
[0004] With the rapid development of deep learning methods, new ideas have been provided to address the difficulties and challenges faced in current research. Xu et al. proposed a parallel convolutional neural network to extract and fuse features from multiple signals, making the prediction results more robust. Xiao et al. achieved adaptive extraction of hidden features from multiple signal inputs by integrating convolution and involution operations. Suh et al. used convolutional neural networks to reconstruct features for RUL prediction, effectively reducing prediction errors. Although CNNs can effectively extract degradation information in the bearing degradation process, their design of convolutional kernels makes it difficult to fully utilize the temporal features in the degradation process. Recurrent neural network-based models have more advantages in extracting temporal features. Sun et al. designed a lightweight Bi-LSTM model with automatic pruning to mitigate the negative impact of model redundancy. Li et al. proposed a parallel memory network composed of LSTM and GRU, utilizing the complementary advantages of the two models to effectively extract temporal feature information in the bearing degradation process. Lu et al. embedded physical information into LSTM to achieve more accurate predictions while conforming to physical laws. Transformers, with their unique attention mechanism, are also widely used for feature extraction in the bearing degradation process. Wang et al. effectively extracted degradation features from vibration signals and quantified the uncertainty of prediction results by constructing a Bayesian large-kernel attention network. Zhang et al. combined attention mechanisms with temporal convolutional networks to dynamically weight the contributions of features at different time steps, improving the efficiency of feature extraction. Zhang et al. proposed a novel local enhancement channel self-attention mechanism that can adaptively extract long-term dependencies and local contextual relationships, thereby improving the model's prediction performance. Ren et al. improved the Transformer to adaptively learn time series of different lengths, realizing dynamic representation of multi-sensor signals and greatly enriching the representation of bearing degradation features. Although the above deep learning methods can effectively capture local and temporal dependent features in the bearing degradation process, they neglect the correlation between different samples, resulting in a failure to utilize the interdependence between different nodes to improve prediction accuracy.
[0005] To investigate the correlation dependencies between different samples, researchers modeled complex topological structures to further reveal the correlations in the bearing degradation process. Wu et al. decoupled bearing monitoring data using multi-resolution methods and constructed a multi-resolution hypergraph to characterize the potential structure between bearing samples. Cui et al. converted time series into node features and used a distance matrix to measure the dynamic similarity between different time series. He et al. constructed a dual correlation graph considering both spatial and temporal similarities between different samples, obtaining more comprehensive node correlation features. Xiao et al. designed a heterogeneous graph that enabled the model to further capture the multi-relationship representation of nodes caused by heterogeneity, thus providing a more comprehensive assessment of the bearing's health status. Jin et al. effectively extracted topological and dynamic features from bearing vibration signals by coordinating GCN and CNN, improving the sensitivity to subtle degradation patterns in bearing vibration signals. Song et al. extracted features from different data formats by constructing a spatiotemporal correlation graph of multidimensional features, enhancing the model's generalization ability and spatial perception of high-dimensional features. To capture the spatiotemporal dependencies between multi-sensor signals, Wang et al. developed a gated graph convolutional network to fuse multi-sensor signals, effectively extracting degradation features. However, aggregating relevant features through a predefined graph topology may reduce the model's prediction accuracy and robustness. Therefore, some researchers have proposed adaptive graphs to address this issue. Wei et al. introduced an attention mechanism to automatically construct the graph during training, thus more accurately reflecting the correlations between different nodes. Zhang et al. constructed a dynamic graph structure that effectively fused pairwise graphs and hypergraphs, enhancing the contribution of important nodes to the prediction of bearing remaining service life. Zhong et al. combined the advantages of hypergraph neural networks and self-attention mechanisms, enabling the model to autonomously learn higher-order correlations between nodes and acquire features from different channels and multiple regions, thereby improving the model's prediction accuracy. Therefore, utilizing the correlations between bearing degradation features can further enhance the ability to express bearing degradation trends.
[0006] Meanwhile, while deepening the network architecture can yield richer feature representations, the highly nonlinear and complex structure of deep learning networks inevitably exacerbates the 'black box' nature of the model, further reducing its interpretability. Against this backdrop, Physical Information Networks (PINs) improve the physical consistency and interpretability of prediction results by embedding prior physical knowledge into the model's training phase and constraining the optimization space through physical rules. For example, Zhao et al. introduced a dual-constraint PIN loss function, using physical information to guide the learning of dynamic wavelets, achieving multi-scale dynamic analysis of bearing vibration signals. Yin et al. embedded the complex dynamics of bearing degradation into the prediction of remaining service life by converting the prediction of bearing degradation amplitude into a transformation of phase space trajectories. Herwig et al. integrated signal processing methods into a neural network framework to achieve adaptive optimization of bearing monitoring signals, providing a reliable solution for fusing physical information. Kumar et al. improved the Huber loss function, making the model more focused on the accuracy of RUL prediction at near-fault conditions. Yang et al. integrated physical information into a dynamic adaptive inverse discrete Fourier transform frequency domain module, achieving compatibility between physical information and data-driven models, improving prediction performance while enhancing interpretability. While the aforementioned models improve interpretability by incorporating prior physical knowledge into the training process, they still have certain limitations in complex industrial scenarios. Traditional physical information models require explicit integration of specific physical constraints into the training process, but in real industrial environments, it is difficult to obtain accurate physical relationships between monitoring data and the actual real-world bounded limits (RUL). Furthermore, introducing excessively rigid physical boundaries into the training process will further reduce the model's generalization performance.
[0007] Literature reviews indicate that graph convolutional neural networks can effectively improve model prediction performance by utilizing the correlation between bearing degradation features. Furthermore, introducing physical information can further enhance model interpretability and improve the reliability of prediction results. However, existing models still have some problems that urgently need to be addressed: (1) Existing prediction methods based on graph convolutional neural networks often use two methods to construct correlation graphs. One is to construct the topology structure through predefined correlation relationships. This graph construction method ignores the dynamic changes of bearing degradation features in the time dimension, which greatly reduces the generalization performance of the model. The other is to adaptively construct the topology structure based on the bearing degradation features. This construction method relies entirely on the nonlinear changes between features to construct the graph structure, ignoring the physical correlation between features.
[0008] (2) Traditional graph convolution methods are poor at focusing local features during information transmission. When faced with non-stationary data in the bearing degradation process, it is often difficult to achieve more refined feature aggregation, which further limits the accuracy of the model in extracting bearing degradation features.
[0009] (3) Existing physical information models often require explicit definition of partial differential equations in the bearing degradation process as constraints. However, considering the complexity of the degradation process, it is difficult to express the physical relationship between the sensing data and the remaining service life using analytical expressions. Summary of the Invention
[0010] The purpose of this invention is to propose a bearing life prediction method based on a graph wavelet attention network that integrates implicit physical information, thereby improving the accuracy of bearing remaining service life prediction while enhancing the interpretability of the model. First, an initial adjacency matrix is constructed based on node similarity, and a gating mechanism is introduced to dynamically adjust this initial adjacency matrix. Furthermore, this embodiment proposes a novel graph wavelet attention network that leverages the advantages of wavelet transform in processing non-stationary data and focusing on local features to achieve multi-scale decoupling of bearing degradation features. Finally, the physical correlation between the hidden features extracted by the PINN network implicit learning model and the bearing remaining service life (RUL) is utilized to dynamically adapt to the differences in bearing degradation modes under different conditions. The main contributions of this invention are summarized as follows: (1) A novel adaptive graph construction method is proposed, which uses a predefined adjacency matrix and gating mechanism to realize dynamic adjustment of graph topology and achieve more accurate spatial dynamic relationship modeling.
[0011] (2) A graph wavelet attention network was designed to solve the problem that traditional graph convolutional networks are difficult to handle non-stationary data and focus on local features, and to achieve more accurate extraction of bearing degradation features.
[0012] (3) By using the neural network to implicitly learn the physical correlation between sensor data and remaining lifespan, and by using implicit physical bias to guide network learning, the data-driven mechanism and physical mechanism are integrated, so that the model can fit the data distribution while satisfying the physical prior knowledge, thus improving the reliability of model prediction.
[0013] To achieve the above objectives, the present invention provides the following solution: A bearing lifetime prediction method based on graph wavelet attention networks that integrate latent physical information includes: A method for constructing a pre-defined adaptive adjacency matrix is used to obtain the dynamic adaptive graph adjacency matrix of bearing monitoring signal samples; Based on the dynamic adaptive graph adjacency matrix, a preset graph wavelet attention network is used to decouple the bearing degradation features at multiple scales, and attention-weighted fusion of the convolution results at different scales is performed to obtain the fused degradation features. The fused degradation features are input into the GRU model to extract the temporal evolution dependency of the bearing degradation features; Based on the aforementioned temporal evolution dependency, a partial differential equation is constructed to describe the implicit physical relationship between the remaining service life of the bearing and the hidden states extracted by the network. Based on the aforementioned implicit physical relationship, a time-dimensional partial differential operator is introduced to form implicit physical information that characterizes the degradation law. The implicit physical bias of the implicit physical information network is used to guide the network learning and output the final predicted value of the bearing's remaining service life.
[0014] Optionally, the dynamic adaptive graph adjacency matrix of the bearing monitoring signal samples is obtained by using a pre-defined adaptive graph construction method, including: The initial adjacency matrix is constructed by calculating the similarity between the features of each bearing monitoring signal sample node; The connection strength between different nodes in the initial adjacency matrix is calculated using a gating mechanism. Based on the connection strength, the initial adjacency matrix is dynamically and adaptively adjusted to obtain the dynamic adaptive graph adjacency matrix.
[0015] Optionally, the dynamic adaptive graph adjacency matrix is: ; in, It is a dynamic adaptive graph adjacency matrix. The initial adjacency matrix, This indicates element-wise multiplication. Represents a node With nodes The connection strength score between them N The number of nodes.
[0016] Optionally, based on the dynamic adaptive graph adjacency matrix, multi-scale decoupling of bearing degradation features using a preset graph wavelet attention network includes: Based on the dynamic adaptive graph adjacency matrix, a graph wavelet transform matrix is constructed and a multi-scale graph wavelet operator is generated; The multi-scale graph wavelet operator is used as the convolution kernel to perform graph convolution operations. By stacking multiple graph wavelet convolution operations, the decoupling of multi-scale degradation features is achieved.
[0017] Optionally, using the multi-scale graph wavelet operator as a convolution kernel to perform graph convolution operations includes: ; in, For a given Graph wavelet operators at different scales It is a learnable diagonal matrix. The learnable matrix parameters of the feature transformation, The wavelet convolution results are shown below at different scales. For graph wavelet operators at different scales, For bias.
[0018] Optionally, attention-weighted fusion of convolution results at different scales includes: ; in, express The results of graph wavelet operator convolution at different scales. Represents a learnable matrix. For attention-weighted results, T This is a transpose operation.
[0019] Optionally, the implicit physical relationship is: ; in, This represents the predicted remaining service life of the bearing and the hidden states learned by the network. The implicit physical relationship between them p This indicates the predicted remaining service life of the bearing. express about The first-order partial derivative reflects the remaining service life of the bearing as a function of its hidden state. The instantaneous rate of change, express about The first-order partial derivative reflects the rate of change of the degradation rate. and Indicates hidden state Modulation effect on degradation rate and rate of change, It is a set of learnable parameters.
[0020] Optionally, the hidden physical information is: ; Among them, among them, This indicates how the predicted remaining service life of the bearing changes over time t. This represents the predicted remaining service life of the bearing and the hidden states learned by the network. The implicit physical relationship between them.
[0021] The beneficial effects of this invention are as follows: This invention can effectively learn the physical relationship between perceived data and bearing RUL. The implicit physical information bias can effectively guide the model learning, achieving accurate prediction of bearing RUL.
[0022] Compared to the construction method of traditional correlation graphs, the dynamic adaptive graph proposed in this invention is fine-tuned on the basis of satisfying physical correlation, effectively characterizing the potential structure of bearing degradation data.
[0023] The GWAN network proposed in this invention can decouple the degradation features of bearings at multiple scales, and the attention mechanism can effectively focus on key features at different scales, thereby effectively improving the prediction accuracy and adaptability of the model.
[0024] Experimental results on two publicly available bearing lifecycle datasets demonstrate that HPI-GWAN exhibits good performance, and the effectiveness of the proposed model has been thoroughly verified through experiments. Attached Figure Description
[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 This invention relates to the construction of a dynamic adaptive graph adjacency matrix in an embodiment of the invention. Figure 2 This is a schematic diagram of wavelet convolution in an embodiment of the present invention; Figure 3 This is a schematic diagram of spatiotemporal feature extraction during bearing degradation according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the implicit physical information calculation process according to an embodiment of the present invention; Figure 5 This is an overall architecture diagram of HPI-GWAN for predicting the remaining service life of bearings according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the PRONOSTIA experimental platform setup according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the XJTU-SY bearing testing platform according to an embodiment of the present invention; Figure 8 This is a partial bearing RUL prediction result from the PHM2012 bearing dataset of this invention. Figure 9 This is a comparison chart of the prediction performance of various models for the PHM2012 bearing dataset in this embodiment of the invention. Figure 10 This is a partial bearing RUL prediction result from the XJTU-SY bearing dataset of this invention. Figure 11 This is a comparison chart of the prediction performance of various models on the XJTU-SY bearing dataset, as an embodiment of the present invention. Figure 12 This is a visualization of the features extracted by the implicit physical constraint model in an embodiment of the present invention; wherein, ( a (This is a visualization of Bearing 1-6;) b (This is a visualization of Bearing 1-6;) c (This is a visualization of Bearing 1-6;) d (This is a visualization of Bearing 1-6) Figure 13 This is a quantitative comparison chart of each ablation model in the embodiments of the present invention; Figure 14 The model prediction error under different physical constraint levels in the embodiments of the present invention; wherein, ( a (This is a comparison chart of RMSE values;) b (This is a comparison chart of MAE data.) Figure 15 Here are model fitting goodness-of-fit diagrams for different numbers of wavelet kernels in embodiments of the present invention; where, ( a () is a goodness-of-fit graph on the PHM2012 dataset; b () is a goodness-of-excellence plot on the XJTU-SY dataset; Figure 16 This is a schematic diagram of the parameter sensitivity analysis results of an embodiment of the present invention; wherein, ( a This is a schematic diagram of the results on the PHM2012 dataset; b () is a schematic diagram of the results on the XJTU-SY dataset. Detailed Implementation
[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0029] This embodiment proposes a bearing lifetime prediction method based on a graph wavelet attention network that integrates implicit physical information, mainly including: A pre-defined adaptive graph construction method is used to obtain the dynamic adaptive graph adjacency matrix of bearing monitoring signal samples; Based on the dynamic adaptive graph adjacency matrix, a preset graph wavelet attention network is used to decouple the bearing degradation features at multiple scales, and attention-weighted fusion of the convolution results at different scales is performed to obtain the fused degradation features. The fused degradation features are input into the GRU model to extract the temporal evolution dependency of the bearing degradation features; Based on the aforementioned temporal evolution dependency, a partial differential equation is constructed to describe the implicit physical relationship between the remaining service life of the bearing and the hidden states extracted by the network. Based on the aforementioned implicit physical relationship, a time-dimensional partial differential operator is introduced to form implicit physical information that characterizes the degradation law. The implicit physical bias of the implicit physical information network is used to guide the network learning and output the final predicted value of the bearing's remaining service life.
[0030] The process involves constructing a latent physical relationship between the remaining bearing life and the hidden states extracted by the network using partial differential equations. Based on this relationship, time-dimensional partial differential operators are introduced to form latent physical information characterizing the degradation pattern. The latent physical bias of the latent physical information network guides model learning, ultimately outputting the predicted remaining bearing life. The latent physical information network relies on this latent physical information for computation, and it checks whether the computational results conform to the latent physical information. If they do, the latent physical bias is small; otherwise, it is large.
[0031] This embodiment proposes a graph wavelet attention network incorporating implicit physical information, which mainly includes the construction of a dynamic adaptive graph, the extraction of spatial features through the graph wavelet attention network and the extraction of temporal features using GRU, and finally the implicit physical information model implicitly guiding the model's learning process.
[0032] Furthermore, using a pre-defined adaptive graph construction method, the dynamic adaptive graph adjacency matrix of the bearing monitoring signal samples is obtained, including: The initial adjacency matrix is constructed by calculating the similarity between the features of each bearing monitoring signal sample node; The connection strength between different nodes in the initial adjacency matrix is calculated using a gating mechanism. Based on the connection strength, the initial adjacency matrix is dynamically and adaptively adjusted to obtain the dynamic adaptive graph adjacency matrix.
[0033] Specifically, the dynamic adaptive graph construction in this embodiment is as follows: Graph convolutional networks can aggregate the features of nodes and their neighbors using adjacency matrices, thereby leveraging topological structures to process non-Euclidean space data during feature extraction. Typically, a graph is represented as... ,in Represents a set of nodes. Representative edge set, This represents the weight of the edge. Alternatively, it can be represented by the adjacency matrix. To represent the structure of a graph, nodes and nodes The connection between them can be determined by To indicate, among which The calculation formula can be expressed as formula (1): (1); This embodiment proposes a dynamic adaptive graph construction method to compensate for the prediction errors caused by the inaccuracy of information in traditional manually defined adjacency matrices. Specifically, as follows... Figure 1 As shown. The bearing monitoring signal can be represented as ,in Represents the total number of samples. Represents the number of sample nodes. Represents the feature dimension of the sample node. This represents the length of the time window. First, calculate the length for each sample. The initial adjacency matrix is constructed using the similarity between node features, and the calculation formula is defined as follows: (2); in, The norm of the computed node features is represented. and Representing nodes respectively and nodes eigenvectors.
[0034] Then, the connection strength between different nodes in the initial adjacency matrix is calculated using a gating mechanism. The specific calculation process is represented by the following formula: (3); in, Represents learnable parameters. For bias.
[0035] The predefined graph is dynamically and adaptively adjusted based on the score of the gating mechanism. The specific calculation process is defined by the following formula: (4); in, This indicates element-wise multiplication. Represents a node With nodes The connection strength score between them.
[0036] Furthermore, based on the aforementioned dynamic adaptive graph adjacency matrix, a preset graph wavelet attention network is used to perform multi-scale decoupling of bearing degradation features, including: Based on the dynamic adaptive graph adjacency matrix, a graph wavelet transform matrix is constructed and a multi-scale graph wavelet operator is generated; The multi-scale graph wavelet operator is used as the convolution kernel to perform graph convolution operations. By stacking multiple graph wavelet convolution operations, the decoupling of multi-scale degradation features is achieved.
[0037] Specifically, in this embodiment, the graph wavelet attention network is: Traditional graph convolutional networks aggregate features of related nodes using adjacency matrices, ensuring that each node's representation includes not only its own information but also information from its neighboring nodes. The basic information propagation calculation formula is as follows: (5); in, It adds a self-loop adjacency matrix to ensure that each node contains its own information. yes The degree matrix, Indicates the first Layer node characteristics, It is the weight matrix that needs to be learned. It is an activation function.
[0038] The graph wavelet attention network organically fuses wavelet transform and graph convolutional networks to achieve multi-scale decoupling of bearing degradation features, deeply extracting important local information in the bearing degradation process, such as... Figure 2 As shown, firstly, a graph wavelet transform matrix is constructed based on the dynamic adaptive adjacency matrix, and a multi-scale wavelet operator is generated. Based on the generated multi-scale graph wavelet operator, the degradation features of the bearing are decoupled at multiple scales, and an attention mechanism is used to dynamically focus on different local features.
[0039] Multi-scale graph wavelet operators: Wavelet transform is a classic time-frequency analysis tool, highly suitable for analyzing non-stationary data across multiple time scales. By scaling and translating the mother wavelet function, a series of wavelet basis functions are constructed, thereby achieving multi-scale decoupling of non-stationary data. Due to its powerful capabilities, wavelet transform has been integrated into various network architectures in recent years and is widely used in image classification, semantic segmentation, signal processing, and other fields. (Scale is...) Location is The mathematical expression for the wavelet coefficients is formula (6): (6); in Represents the mother wavelet function. Indicates complex conjugation. This represents the corresponding wavelet coefficient.
[0040] Wavelet operators are a crucial component for extracting spatial features, enabling multi-scale decoupling of bearing degradation features. At each time step of the bearing degradation features, the adjacency matrix generated by the dynamic adaptive graph generation module serves as the input to the multi-scale wavelet operator, where singular values... This matrix can represent the main information about the connectivity relationships in the adjacency matrix, and the calculation process is shown in the formula: (7); in and It is a real orthogonal matrix. Operators for constructing diagonal matrices convert the scalar sequence within parentheses into a diagonal matrix, with all off-diagonal elements set to 0. Operators for the rank of a matrix.
[0041] The graph wavelet transform matrix can transform the time-domain features of graph nodes to the frequency-domain features of the graph, obtaining frequency-domain features at different frequency resolutions. Given different wavelet scales... Controlling the frequency domain resolution of wavelets The smaller the value, the better it can capture high-frequency information of nodes and obtain local node associations. The larger the value, the better it is at capturing low-frequency information from nodes and obtaining the global graph structure. Given the singular values of the adjacency matrix... To construct the graph wavelet transform matrix And graph wavelet inverse transform matrix The specific calculation formula is defined as follows: (8); in, Describes an orthogonal singular vector matrix. This indicates the generation of an exponential wavelet kernel.
[0042] To generate wavelet operators that balance fixed-heat kernel characteristics and learnability, trainable wavelet kernels are incorporated into wavelet transform. This is achieved by integrating graph topological information... Wavelet scale information and learnable kernel information The mathematical expression of the integrated generative graph wavelet operator is defined as follows: (9); Through calculation Graph wavelet operators at different scales can be used to obtain multi-scale wavelet operators, each corresponding to a different scale. and trainable kernel The calculation formula for the multi-scale wavelet operator is as follows: (10); in, Represents a list of scales. Indicates the first A diagonal matrix with trainable kernels.
[0043] Graph wavelet attention convolution; This embodiment proposes a novel graph wavelet attention network that utilizes multi-scale graph wavelet operators to decouple the degradation information of bearings at multiple scales. This approach solves the problem of traditional graph convolution methods failing to focus on local features. Furthermore, by introducing an attention mechanism to dynamically focus on degradation features at different scales, information redundancy caused by multi-scale decoupling is avoided. This also allows the model to simultaneously focus on both global and local graph information, ultimately improving the model's accuracy. At a given time step... The following samples ,in Indicates the number of nodes. To represent the feature dimension, a multi-scale graph wavelet operator is used as the convolution kernel to perform graph convolution operations. The specific execution formula is defined as follows: (11); in It is given Graph wavelet operators at different scales It is a learnable diagonal matrix. These are the learnable matrix parameters of the feature transformation.
[0044] Decoupling of degenerate features at multiple scales can be achieved by stacking multiple graph wavelet convolution operations. Graph wavelet attention convolutions at different scales are defined as follows: An attention mechanism is used to dynamically focus the importance of different scales. The attention-weighted multi-scale fusion features are defined by the following formula: (12); in express The results of graph wavelet operator convolution at different scales. This represents a learnable matrix.
[0045] In this embodiment, the fused degradation features are input into the GRU model, and the temporal evolution dependencies of the bearing degradation features are extracted, including: Since the degradation process of a bearing can be viewed as a change in the bearing's state over time, effectively extracting the changes in spatial features over time is crucial for state assessment after the spatial information of the bearing degradation process has been extracted. Figure 3 This embodiment demonstrates how to use graph wavelet convolution and gated recurrent units to extract the spatiotemporal dependencies in the bearing degradation process for predicting the remaining service life of the bearing.
[0046] GRU, with its update and reset gates, can effectively learn contextual information from data, making it an effective method for analyzing time-dependent patterns of bearing degradation. The update gate determines the degree to which bearing degradation information from the previous time step is retained in the current time step, and its calculation formula is defined as follows: (13); in To update the gate output, For activation function, This is the input for the current time step. It is the hidden state of the previous time step. and These are learnable parameters.
[0047] The reset gate determines the degree to which bearing degradation information from the previous time step is forgotten in the current time step, and its calculation formula is as follows: (14); in To update the gate output, For activation function, This is the input for the current time step. It is the hidden state of the previous time step. and These are learnable parameters.
[0048] In this embodiment, based on the temporal evolution dependency, a partial differential equation is constructed to describe the hidden physical information between the remaining service life of the bearing and the hidden states extracted by the network, including: Physical information networks (PINs) incorporate prior physical knowledge into neural networks, making the network training process conform to physical laws and improving prediction accuracy. However, in industrial scenarios, bearings typically operate in complex environments, and their operating conditions are influenced by a combination of factors. It is difficult to construct corresponding physical constraint equations using bearing status signals monitored by sensors and their corresponding remaining service life. Therefore, this embodiment introduces implicit physical information to capture the implicit physical relationship between the features learned by the network model and the remaining service life value. The process is as follows: Figure 4 As shown, by obtaining the corresponding implicit physical relationships, the evolutionary rules of the model's feature extraction can be revealed, improving the model's interpretability while increasing prediction accuracy.
[0049] The input to the implicit physical information model is the time-domain and frequency-domain features (s) and corresponding time (t) of the bearing degradation process. A designed graph wavelet attention network and GRU are used to capture the spatiotemporal information of the bearing degradation process as a potential solution to the partial differential equation. This allows the establishment of a partial differential equation that can learn the implicit relationship between the bearing's remaining service life (RUL) and the potential solution. The mapping relationship between the state information extracted by the neural network and the bearing's RUL can be determined by a nonlinear operator. This is used to represent the implicit physical information. The final implicit physical information can be defined by the following formula: (15); This formula describes the bearing degradation process as a coupled effect of remaining service life changing with time and condition. Wherein, This indicates the variation of the RUL predicted value with time t. This represents the RUL prediction value and the hidden state learned by the network. The implicit physical relationship between them.
[0050] To further elaborate Having learned about the implicit physical relationship, this embodiment uses a second-order partial differential equation to represent the relationship between RUL and the hidden state. The physical relationship between them. It can be expressed as: (16); in, express about The first-order partial derivative reflects the RUL with respect to the hidden state. The instantaneous rate of change, express about The first-order partial derivative reflects the rate of change of the degradation rate. and Reflects the hidden state Modulation effect on degradation rate and rate of change, It characterizes the interaction between degradation rate and rate of change, and can capture the coupling features in complex nonlinear degradation processes. It is a set of learnable parameters.
[0051] To ensure that the latent physical information learned by the model can be used to guide model optimization, a physical information loss term is introduced to ensure that each degraded sample follows the corresponding physical degradation process. The physical information loss term is defined as follows: (17); in, Represents the total number of samples. Indicates the first RUL predicted value for each sample Indicates the first The time corresponding to each sample Indicates the first The hidden state extracted by the model for each sample.
[0052] By integrating dynamic adaptive graph construction, graph wavelet attention network, GRU, and acquisition of latent physical information, the overall architecture of HPI-GWAN proposed in this embodiment can be obtained, such as... Figure 5 As shown.
[0053] (1) An initial adjacency matrix was constructed by calculating the similarity of the node features of the bearing monitoring signal sample, and the node connection strength of the initial adjacency matrix was dynamically adjusted using a gating mechanism to obtain the dynamic adaptive graph adjacency matrix of the sample. .
[0054] (2) Graph wavelet attention network uses the adjacency matrix of the dynamically adaptive graph. Based on this, a multi-scale graph wavelet operator is generated. Through graph wavelet kernel transformation, the multi-scale decoupling of bearing degradation features is achieved. Attention-weighted fusion of convolution results at different scales is performed, effectively integrating global and local features.
[0055] (3) The spatial features of bearing degradation extracted by the graph wavelet attention network are input into the GRU to capture the dependence of these features over time.
[0056] (4) Using the spatiotemporal evolution features captured by the graph wavelet attention network and GRU, a partial differential equation describing the implicit physical relationship between the bearing RUL and the hidden state was constructed. This partial differential equation is characterized by a nonlinear operator containing multiple-order partial derivatives, and the model training is constrained by introducing a physical information loss term. The final loss function of the HPI-GWAN model can be defined as: (18); in Mean squared error loss is used to measure the deviation between the model's predictions and the actual values. This is a physical information loss term, ensuring that the features learned by the model follow the implicit physical laws of feature degradation. and These are weighting coefficients used to balance the importance of fitting accuracy and physical constraints.
[0057] The following embodiment demonstrates the effectiveness of the proposed HPI-GWAN model through extensive experiments on two bearing datasets.
[0058] Experimental setup: Evaluation indicators In this embodiment, the prediction accuracy of the proposed model is measured by calculating multiple evaluation metrics for the predicted values. These mainly include root mean square error (RMSE), mean absolute error (MAE), engineering application score (EAS), and absolute coefficient (...). RMSE better measures the volatility of prediction results, MAE is used to evaluate the prediction error of the model, and EAS uses an asymmetric weighting design, which results in a higher score for the metric when the predicted value is higher than the actual value, making it more in line with the actual needs of engineering applications. These are used to evaluate the goodness of fit of the model. The calculation formulas for each evaluation index are shown below: (19); (20); (twenty one); (twenty two); in, This is the actual lifespan of the bearing. These are the model's predicted values. This represents the total number of samples for different bearings. This represents the average value of the actual bearing life.
[0059] Data preprocessing: Preprocessing of bearing monitoring data is a crucial step in obtaining bearing degradation characteristics. In this embodiment, the choice of data preprocessing method not only affects the representation of bearing degradation characteristics but also further influences the construction of the adaptive correlation diagram. Therefore, this embodiment selects 14-dimensional time-domain and frequency-domain features as the data processing method. The specific calculation methods are shown in Table 1. These features have been sufficiently proven to effectively characterize the trend of bearing degradation. To enhance the generalization ability of the model, the calculated features and labels are normalized. Simultaneously, the calculated features are enhanced with a cumulative sum function using the same processing method. The mathematical expression of the cumulative sum function is: (twenty three); in, Indicates the bearing at time The calculation of the first time at time t One feature; Indicates the bearing at time The calculation of the first time at time t A cumulative feature.
[0060] Table 1 Data Processing Method Hyperparameter configuration To determine the optimal configuration of the model parameter settings proposed in this embodiment, a controlled variable approach is used. These hyperparameters mainly include the number of nodes, k The number of nearest neighbors, the number of layers in the graph wavelet attention network, the number of graph wavelet operators, the training batches, and the batch size are all selected. Table 2 lists the final parameter selection results for the model.
[0061] Table 2 shows the final parameter selection results for the model.
[0062] Selection of contrasting models: SAGCN-SA: This model calculates the cosine similarity of nodes in different windows and uses an attention mechanism to enable GCN to use different topologies in different layers.
[0063] T-GCN: This model combines GCN and GRU into a T-GCN module, which fully extracts the spatiotemporal information in the bearing degradation process.
[0064] DC-DGCN: This model utilizes dynamic spatial correlation maps to fuse the spatial degradation features of bearings and inputs them into a GRU to obtain spatiotemporal features.
[0065] ChebGCN-LSTM: Uses BiLSTM to capture the temporal degradation information of bearings and uses GCN to learn the spatial information in the node path.
[0066] ConvLSTM: This model extracts local features in the bearing degradation process through convolutional layers, and then combines them with a long short-term memory network to capture the bearing degradation process.
[0067] DA-LSTM: This model captures the deterioration trend of bearings through LSTM, and then uses an attention network to further mine useful information in the LSTM network.
[0068] Dataset introduction: PHM 2012 datasets: The PHM 2012 datasets were provided by the PRONOSTIA experimental platform. The overall structure of the bearing experimental platform for this dataset is as follows: Figure 6 As shown in Table 3, this dataset fully records the vibration data of 17 bearings under three operating conditions.
[0069] Table 3 Experimental Results XJTU-SY datasets: The XJTU-SY datasets were obtained through a self-developed bearing accelerated life testing platform. The overall structure of the testing platform is as follows: Figure 7 As shown in Table 4, this dataset consists of 15 sets of full-life vibration signals of bearings collected by accelerometers, including 6 training datasets and 9 test datasets under three operating conditions. The parameter settings for different operating conditions are shown in Table 4.
[0070] Table 4 Parameters under different working conditions Prediction results for the PHM 2012 dataset: To fully demonstrate the effectiveness of the proposed model, Figure 8 The results show the predictions for the remaining service life of bearings tested in the PHM 2012 dataset; among them, Figure 8 The diagrams include: Bearing 1-3 predicted values and prediction errors; Bearing 1-6 predicted values and prediction errors; Bearing 1-7 predicted values and prediction errors; Bearing 2-4 predicted values and prediction errors; Bearing 2-5 predicted values and prediction errors; and Bearing 3-3 predicted values and prediction errors. The red curve represents the prediction results of the proposed HPI-GWAN, the black curve represents the actual life value of the tested bearing, the blue shading represents the model's delayed prediction error, and the red shading represents the premature prediction error. As can be seen from the figures, the RUL predicted by the proposed model under different operating conditions is in high agreement with the actual RUL curves. In all tested bearings, the prediction error at a single point was generally controlled within 0.2. Particularly for Bearing1-6, Bearing1-7, Bearing2-4, and Bearing3-3, the degradation model in the later stages became more complex due to the differences in bearing failure modes under different operating conditions. As shown in the figure, the proposed model can effectively handle the influence of various interference factors, demonstrating its strong feature extraction capability and generalization performance. Furthermore, the model's delayed prediction error is smaller in Bearing1-6, Bearing2-4, and Bearing2-5, making it more suitable for practical engineering applications.
[0071] Furthermore, this embodiment compares the proposed HPI-GWAN model with other existing models to further illustrate the rationality of the designed model. The EAS evaluation values of the HPI-GWAN model and six other models under three operating conditions are as follows: Figure 9As shown in the figure, HPI-GWAN outperforms the six comparative models in most cases, achieving an average EAS score of 0.0073, the best performance among all compared models. Specifically, compared to the traditional spatiotemporal prediction models ConvLSTM and DA-LSTM, the graph neural network-based methods SAGCN-SA and T-GCN showed better prediction performance, with engineering application scores further reduced to 0.0077 and 0.0083, respectively. This data comparison fully demonstrates the superior performance of graph neural networks in using topological structures to characterize bearing degradation features. However, HPI-GWAN still outperforms the second-best performing SAGCN-SA model in prediction performance, with an engineering application score reduction of 5.1%. Furthermore, HPI-GWAN achieved the best prediction performance on test sets that are more difficult to predict, such as Bearing2-4, Bearing2-5, and Bearing3-3. This fully demonstrates that the graph wavelet attention network effectively captures the multi-scale topological features of bearing degradation. At the same time, HPI-GWAN, by constraining the model's optimization space with physical information, makes the model more robust and reduces the fluctuation of model prediction performance under different operating conditions.
[0072] Prediction results for the XJTU-SY dataset: To further verify the generalization and robustness of the designed model, Figure 10 The prediction results and error distribution of HPI-GWAN on the XJTU-SY dataset are shown; among them, Figure 10 The diagrams include illustrations of the predicted values and errors for Bearing1-3, Bearing1-4, Bearing1-5, Bearing2-3, Bearing2-5, and Bearing3-4. Experimental results show that the model's predicted trajectory has a high degree of consistency with the actual degradation trend of the bearings. Particularly noteworthy is that in the late stage of bearing degradation, the model's prediction error shows a trend of convergence or remaining within a very small range, indicating that the graph wavelet attention network is highly sensitive to the non-stationary degradation characteristics in the bearing degradation process. Furthermore, the predicted trajectory of the model shows that HPI-GWAN has strong generalization ability and robustness under different operating conditions. For example, Bearing1-5 exhibits rapid failure, while Bearing3-4 shows a relatively slow, progressive degradation, and HPI-GWAN can effectively control the prediction error within a small range.
[0073] Similarly, to compare the differences in prediction performance of different models on different datasets Figure 11The engineering application scores of each model on the XJTU-SY dataset are further demonstrated. The results show that HPI-GWAN achieves an engineering application score of 0.0070, the best result among all comparison methods. The baseline model T-GCN, which performed second best, had an average EAS of 0.0091, and HPI-GWAN improved the overall prediction accuracy by 24.3%. Through in-depth comparison of the prediction performance of various models on different bearings, this embodiment found that on the test bearings Bearing1-5 and Bearing3-5, due to differences in degradation modes, the prediction errors of conventional models such as Cheb-GCN-LSTM, ConvLSTM, and DA-LSTM increased significantly. However, HPI-GWAN maintained a lower prediction error on these challenging datasets, indicating that implicit physical information, as an optimization constraint, effectively solved the gradient shift caused by data distribution and minimized error fluctuations under different operating conditions.
[0074] Visualization of Hidden Physical Information Features: To further explore the impact of latent physical information on the model's ability to extract hidden features. Figure 12 We use t-SNE to perform dimensionality reduction visualization of the hidden features extracted by the model with or without physical constraints. Figure 12 The four columns (ad) represent four different test bearings, among which, Figure 12 (in) a (This is a visualization of Bearing 1-6) Figure 12 (in) b (This is a visualization of Bearing 1-6) Figure 12 (in) c (This is a visualization of Bearing 1-6) Figure 12 (in) dThe first row of the chart visualizes Bearing1-6, where the color of the data points changes from blue to red to represent the bearing degradation process from 1.0 to 0.0 years of remaining service life. The first row shows the application of implicit physical information constraints to the test bearings. It can be seen that the high-dimensional features extracted by the model project a relatively continuous, smooth manifold curve in two-dimensional space, with clear boundaries between nodes at different degradation stages. As the remaining service life of the bearing decreases, the feature points exhibit a strict color gradient evolution, without obvious reversals or abrupt changes, further demonstrating that the implicit physical information effectively treats the bearing degradation process as a monotonous and irreversible physical process. The second row shows the distribution of the hidden states of the test bearings after removing the implicit physical information. It can be seen that the nodes at different degradation stages still maintain clear boundaries, which fully demonstrates that the combination of the graph wavelet attention network and the GRU module effectively extracts key information in the degradation process. However, after removing the implicit physical information constraints, the bearing's feature trajectory exhibits distortion and breakage. This phenomenon indicates that the purely data-driven graph wavelet attention network tends to statistically fit the extracted features when facing nonlinear bearing degradation characteristics, ignoring the physical evolution path in the bearing degradation process.
[0075] Ablation analysis: To analyze the effectiveness of the various components of the model, ablation experiments were designed for different modules in this embodiment. Detailed information on the various model components in the ablation experiments is shown in Table 5. Model I removed the GRU, Model II removed the implicit physical information constraint, Model III removed the attention mechanism of the graph wavelet kernel, and Model IV removed the adaptive adjustment of the adjacency matrix. Quantitative comparisons of each ablation model are as follows: Figure 13 As shown.
[0076] Table 5. Detailed information on the composition of various models. The quantitative analysis results of the ablation experiments were tested on two bearing datasets: PHM 2012 and XJTU-SY. As shown in the figure, the HPI-GWAN model achieved the best performance in both RMSE and MAE, with the lowest mean and median errors. This indicates that the complete model not only has the highest prediction accuracy but also exhibits the most concentrated prediction errors under different degradation conditions, demonstrating strong robustness and stability. Specifically, after removing the GRU module, due to the lack of modeling for the temporal patterns of bearing degradation characteristics, the overall prediction performance of Model I decreased, with an average RMSE of 0.131 and a more dispersed prediction error distribution. Secondly, Model II, due to the loss of implicit physical constraints, could not utilize implicit physical biases to guide model learning, weakening the model's robustness and generalization performance. This led to significant fluctuations in the model's prediction accuracy, with the average RMSE and MAE improving by 0.038 and 0.029 respectively compared to the proposed model. Furthermore, Model III removed the attention mechanism of the graph wavelet kernel, causing the model to fail to focus on key information at different graph wavelet kernel scales, resulting in reduced prediction accuracy and an average RMSE of 0.115. Finally, Model IV removed the adaptive adjustment mechanism of the adjacency matrix, lacking adaptive adjustment for degenerate features, and its average RMSE dropped to 0.126.
[0077] Physical constraint strength analysis: The strength of implicit physical information constraints determines the degree to which a neural network adheres to learned prior physical knowledge during training. When the constraint coefficient is small, the physical loss term is insufficient to constrain the model's optimization space. In this case, the network prioritizes data-driven graph wavelet neural network models, lacking effective guidance from implicit physical information biases. Conversely, when the constraint coefficient is large, excessively strong physical impairment terms dominate the overall optimization of the model, severely limiting the graph wavelet attention network's ability to flexibly represent the nonlinear degradation features of bearings. This causes the model to sacrifice fitting accuracy to meet physical constraints. Figure 14 The fluctuations in RMSE and MAE of the HPI-GWAN model under different physical constraint strengths are shown; among them, Figure 14 (in) a ( ) is a comparison chart of RMSE; where Figure 14 (in) bThe figure shows a comparison of MAE (Mean Average Root Meaning) values. It is noteworthy that the model achieves optimal prediction performance on both test datasets when the physical constraint strength is 0.01. At this point, the average RMSE and MAE for PHM 2012 are 0.096 and 0.080, respectively, while the average RMSE and MAE for XJTU-SY are 0.085 and 0.072, respectively. Therefore, choosing an appropriate implicit physical information constraint strength is effective, as it can effectively constrain the model's optimization space and avoid overfitting, while also preventing the neglect of physical information during bearing degradation caused by a purely data-driven approach.
[0078] Analysis of the number of wavelet kernels in the graph: The number of graph wavelet kernels determines the fineness and receptive field range of the model in capturing multi-scale topological features in the frequency domain. To determine the optimal number of graph wavelet kernels for the model, this embodiment uses radar charts for quantitative statistics, such as... Figure 15 As shown; where Figure 15 (in) a ) is a goodness-of-fit graph on the PHM2012 dataset; where Figure 15 (in) b ( ) is the goodness-of-performance graph on the XJTU-SY dataset. The model's performance is compared by considering different numbers of wavelet kernels in the graph. This embodiment found that model performance does not improve with the increase of the number of graph wavelet kernels, but rather exhibits a fluctuating trend. Specifically, in the PHM 2012 dataset, the HPI-GWAN model shows a high goodness of fit when the number of graph wavelet kernels is 14, with goodness of fits of 0.867, 0.873, and 0.968 for operating conditions 1, 2, and 3, respectively. This indicates that the degradation features of PHM 2012 are widely and complexly distributed in the frequency domain, requiring a large number of graph wavelet kernels for fine-grained decomposition to effectively capture the degradation trend of bearings. Furthermore, in the XJTU-SY dataset, when... The model exhibited optimal performance with an average goodness of fit of 0.839. Furthermore, the average goodness of fit decreased with increasing wavelet kernel count. This indicates that the effective frequency band of the degradation features of the XJTU-SY tested bearings is relatively concentrated, and key degradation trends can be extracted using fewer wavelet kernels. In summary, the number of wavelet kernels needs to be matched with the inherent complexity of the bearing degradation features. When the number of wavelet kernels is insufficient, the model's frequency domain resolution is too low to effectively decouple the complex degradation features in the frequency band, resulting in an inability to fully characterize more refined degradation features. Conversely, if the number of wavelet kernels is too high, the model's frequency domain resolution will be too high, introducing high-frequency background noise and leading to overfitting.
[0079] In the proposed HPI-GWAN model, the number of spatial nodes and the time step determine the breadth and time span of historical information that the model can capture. The average RMSE values for different numbers of spatial nodes and time steps are as follows: Figure 16 As shown; where, Figure 16 (in) a This is a schematic diagram of the results on the PHM2012 dataset; where Figure 16 (in) b The image shows the results on the XJTU-SY dataset. It can be seen that for the PHM 2012 and XJTU-SY datasets, the optimal combinations are 14 nodes and 2 time steps, and 15 nodes and 5 time steps, respectively. Under these configurations, the model achieves optimal prediction performance by balancing the spatiotemporal receptive field. Experimental results show that when the number of nodes and the time step are set too small, the model's receptive field is limited, resulting in an inability to fully capture the topological associations and temporal dependencies of bearing degradation. Conversely, if the number of nodes and the time step are set too large, the model will introduce a large amount of early redundant information and accumulated noise unrelated to the current degraded nodes. An appropriate node size effectively avoids information redundancy and noise interference in the construction of the spatial topology graph, and improves the model's spatial representation ability of the complex degradation features of bearings by adaptively adjusting the co-correlation of the multidimensional state variable space. A reasonable time step span ensures that the model fully captures the temporal evolution law in the bearing degradation process, effectively avoiding early irrelevant redundant information and accumulated errors.
[0080] Predicting the remaining service life (RUL) of bearings is crucial for the safety and reliability of rotating machinery. Accurate RUL predictions can better help people understand the health status of mechanical equipment, effectively avoiding accidents and increased downtime. Addressing the challenge that physical information models struggle to characterize the physical relationship between condition monitoring data and bearing RUL, this embodiment proposes a novel bearing RUL prediction method, HPI-GWAN. First, an adjacency matrix is constructed using the correlation between bearing degradation nodes. A gating mechanism is used to dynamically and adaptively adjust the adjacency matrix, ensuring both physical correlation and flexibility. Then, GWAN is designed as a learning module for multi-scale decoupling and dynamic feature aggregation of bearing degradation features. Simultaneously, a multi-layer GRU is used to capture the temporal correlation of GWAN aggregated features. Finally, an implicit physical information model is used to learn the physical correlation between hidden states and bearing RUL, and the optimization space is constrained by the implicit physical information bias, ultimately yielding the bearing RUL prediction result. Extensive experiments on the PHM 2012 and XJTU-SY datasets demonstrate the effectiveness of the HPI-GWAN model. The main conclusions are as follows: (1) The proposed HPI-GWAN can effectively learn the physical relationship between the perceived data and the bearing RUL. The implicit physical information bias can guide the model learning well and realize the accurate prediction of bearing RUL.
[0081] (2) Compared with the traditional correlation graph construction method, the proposed dynamic adaptive graph is fine-tuned on the basis of satisfying physical correlation, effectively characterizing the potential structure of bearing degradation data.
[0082] (3) The proposed GWAN network can decouple the degradation features of bearings at multiple scales. The attention mechanism can effectively focus on key features at different scales, effectively improving the prediction accuracy and adaptability of the model.
[0083] (4) Experimental results on two publicly available bearing lifecycle datasets show that HPI-GWAN has good performance, and the effectiveness of the proposed model has been fully verified by experiments.
[0084] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A bearing life prediction method using a graph wavelet attention network that integrates implicit physical information, characterized in that, include: A pre-defined adaptive graph construction method is used to obtain the dynamic adaptive graph adjacency matrix of bearing monitoring signal samples; Based on the dynamic adaptive graph adjacency matrix, a preset graph wavelet attention network is used to decouple the bearing degradation features at multiple scales, and attention-weighted fusion of the convolution results at different scales is performed to obtain the fused degradation features. The fused degradation features are input into the GRU model to extract the temporal evolution dependency of the bearing degradation features; Based on the aforementioned temporal evolution dependency, a partial differential equation is constructed to describe the implicit physical relationship between the remaining service life of the bearing and the hidden states extracted by the network. Based on the aforementioned implicit physical relationship, a time-dimensional partial differential operator is introduced to form implicit physical information that characterizes the degradation law. The implicit physical bias of the implicit physical information network is used to guide the network learning and output the final predicted value of the bearing's remaining service life.
2. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, The dynamic adaptive graph adjacency matrix of bearing monitoring signal samples is obtained using a pre-defined adaptive graph construction method, including: The initial adjacency matrix is constructed by calculating the similarity between the features of each bearing monitoring signal sample node; The connection strength between different nodes in the initial adjacency matrix is calculated using a gating mechanism. Based on the connection strength, the initial adjacency matrix is dynamically and adaptively adjusted to obtain the dynamic adaptive graph adjacency matrix.
3. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, The adjacency matrix of the dynamic adaptive graph is: ； in, It is a dynamic adaptive graph adjacency matrix. The initial adjacency matrix, This indicates element-wise multiplication. Represents a node With nodes The connection strength score between them N The number of nodes.
4. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, Based on the aforementioned dynamic adaptive graph adjacency matrix, a pre-defined graph wavelet attention network is used to perform multi-scale decoupling of bearing degradation features, including: Based on the dynamic adaptive graph adjacency matrix, a graph wavelet transform matrix is constructed and a multi-scale graph wavelet operator is generated; The multi-scale graph wavelet operator is used as the convolution kernel to perform graph convolution operations. By stacking multiple graph wavelet convolution operations, the decoupling of multi-scale degradation features is achieved.
5. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 4, characterized in that, Graph convolution operations using the multi-scale graph wavelet operator as the convolution kernel include: ； in, For a given Graph wavelet operators at different scales It is a learnable diagonal matrix. The learnable matrix parameters of the feature transformation, The wavelet convolution results are shown below at different scales. For graph wavelet operators at different scales, For bias.
6. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, Attention-weighted fusion of convolution results at different scales includes: ； in, express The results of graph wavelet operator convolution at different scales. Represents a learnable matrix. The result is the attention-weighted result, and T is the transpose operation.
7. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, The implicit physical relationship is expressed as follows: ； in, This represents the predicted remaining service life of the bearing and the hidden states learned by the network. The implicit physical relationship between them p This indicates the predicted remaining service life of the bearing. express about The first-order partial derivative reflects the remaining service life of the bearing as a function of its hidden state. The instantaneous rate of change, express about The first-order partial derivative reflects the rate of change of the degradation rate. and Indicates hidden state Modulation effect on degradation rate and rate of change, It is a set of learnable parameters.
8. The bearing life prediction method using a graph wavelet attention network that integrates implicit physical information according to claim 1, characterized in that, The implicit physical information is represented as follows: ； in, This indicates how the predicted remaining service life of the bearing changes over time t. This represents the predicted remaining service life of the bearing and the hidden states learned by the network. The implicit physical relationship between them.