PEMFC degradation prediction method and system based on dynamic and static image fusion

Abstract

The application provides a PEMFC degradation prediction method and system based on dynamic and static graph fusion, and belongs to the technical field of battery degradation prediction; the method comprises the following steps: defining a PEMFC degradation prediction problem and extracting degradation features of different time resolutions through multi-scale patch representation; for patch representation under different scales, static prior graphs and sample adaptive dynamic graphs are respectively constructed, and structural correlation features between variables are jointly extracted through a graph neural network and a gating fusion mechanism; graph time sequence features are obtained through cross-scale aggregation; the graph time sequence features are cooperatively predicted through an original time sequence enhancement branch and a target variable baseline branch, and a PEMFC stack voltage prediction result of a future preset time period is generated through an incremental output strategy. The application can simultaneously consider structural relationships, dynamic correlations and multi-scale time feature modeling in multivariate monitoring data, and comprehensively depict complex evolution rules in the degradation process.

Description

Technical Field

[0001] This invention belongs to the field of battery degradation prediction technology, and particularly relates to a PEMFC degradation prediction method and system based on dynamic and static graph fusion. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Proton exchange membrane fuel cells (PEMFCs), with their advantages of high energy conversion efficiency, low operating temperature, and rapid start-stop, have become a core technology for the efficient utilization of hydrogen energy, showing broad application prospects in fuel cell vehicles, distributed energy supply, and backup power. However, PEMFCs inevitably face problems such as catalyst degradation, membrane aging, carbon support corrosion, and hydrothermal management imbalance during long-term service, which can lead to output voltage decline, efficiency reduction, and reliability degradation. Therefore, accurate modeling and trend prediction of the PEMFC degradation process are of great significance for improving system life management, reducing operation and maintenance costs, and promoting its engineering application.

[0004] However, existing methods for predicting decline in PEMFCs generally suffer from the following technical problems: (1) Existing methods lack a unified model for the static structural prior relationship and the sample-level dynamic coupling relationship driven by the operating condition in the multivariate monitoring signal of PEMFC. Methods that rely solely on time dimension modeling are difficult to fully explore the structural coupling relationship between variables, while methods that only emphasize variable correlation modeling are prone to ignoring the continuous time evolution law in the degradation process. Therefore, it is difficult to simultaneously characterize the stable variable dependence under the stack topology constraint and the time-varying interaction characteristics during operation.

[0005] (2) The degradation process of PEMFC simultaneously includes local transient disturbances, short-term non-stationary fluctuations and long-term slow decay, and the non-stationarity and dynamic coupling changes that are widespread under complex conditions further increase the difficulty of degradation prediction. Existing single time resolution modeling methods are difficult to fully characterize the cross-scale degradation evolution law and short- and medium-term time series dependence. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a PEMFC degradation prediction method and system based on dynamic and static graph fusion, which can simultaneously take into account the structural relationships, dynamic correlations and multi-scale time feature modeling in multivariate monitoring data, thereby comprehensively depicting the complex evolutionary laws in the degradation process.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a PEMFC decay prediction method based on dynamic and static graph fusion.

[0008] PEMFC degradation prediction methods based on dynamic and static graph fusion include: Define the PEMFC degradation prediction problem and obtain multivariate historical observation sequences. Extract degradation features at different time resolutions through multi-scale patch representation. For patch representations at different scales, static prior graphs and sample adaptive dynamic graphs are constructed respectively, and structural correlation features between variables are jointly extracted by graph neural networks and gating fusion mechanisms. Based on shared time-series units and scale gating, the structural correlation features are aggregated across scales to obtain graph time-series features. At the same time, the original time-series enhancement branch and the target variable baseline branch are introduced to jointly predict the graph time-series features. The incremental output strategy is used to generate PEMFC stack voltage prediction results for a future preset period to achieve PEMFC degradation prediction.

[0009] Furthermore, the PEMFC degradation prediction problem is defined as follows: taking the value of the total PEMFC stack voltage at multiple future time steps as the prediction target, and defining the prediction task of the degradation prediction problem as learning the nonlinear mapping relationship from the input sequence to the future target variable under the condition that the multivariate monitoring sequence of multiple past time steps is known.

[0010] Furthermore, degradation features at different temporal resolutions are extracted through multi-scale patch representation, including: reconstructing the acquired multivariate historical observation sequence using a multi-scale patch mechanism, and mapping the same historical observation sequence to local segment representation spaces at different temporal resolutions.

[0011] Furthermore, the construction of the static prior graph includes: when the input features contain multiple individual voltages, firstly, locating the node index corresponding to each individual voltage, and establishing connections between individual voltage nodes within the same patch position; if the input features also contain the total pile voltage, then the node where the total pile voltage is located is used as a voltage convergence node, and connections are established with each individual voltage node; all spatial connections adopt a bidirectional edge form to support bidirectional information propagation; at the same time, temporal adjacency edges are established between adjacent patch positions of the same variable to preserve the continuous evolution relationship of the same monitored variable along local time segments.

[0012] Furthermore, the construction of the sample adaptive dynamic graph includes: first, performing linear mapping and layer normalization on the patch features of each node to obtain the node embedding representation; then, performing L2 normalization on the node embedding and using dot product similarity to calculate the correlation between nodes; finally, performing softmax normalization on the similarity score of the target node to the edge of the dynamic graph, which is used as the edge weight in the message propagation of the sample adaptive dynamic graph.

[0013] Furthermore, the processing of the original temporal enhancement branch includes: projecting the normalized multivariate historical observation sequence onto a latent space of a preset dimension; extracting local continuous temporal features through at least two layers of one-dimensional convolution; performing temporal pooling and linear mapping on the local continuous temporal features to obtain the original temporal features; using the first gating network to perform weighted fusion of the original temporal features and the graph temporal features, and generating the main branch incremental prediction vector corresponding to multiple future time steps through the main prediction head.

[0014] Furthermore, the processing of the target variable baseline branch includes: extracting the historical sequence of the target variable from the multivariate historical observation sequence; extracting the time dependence features of the target variable historical sequence using a gated recurrent unit for the target variable; mapping the time dependence features to the baseline incremental prediction vector corresponding to multiple future time steps through the baseline prediction head; and using a second gated network to perform weighted fusion of the baseline incremental prediction vector and the main branch incremental prediction vector to obtain the final incremental prediction vector.

[0015] The second aspect of the present invention provides a PEMFC decay prediction system based on dynamic and static graph fusion.

[0016] The PEMFC decay prediction system based on dynamic and static graph fusion includes: The problem definition module is configured to: define the PEMFC degradation prediction problem; The multi-scale static and dynamic graph feature extraction module is configured to: acquire multivariate historical observation sequences, extract degradation features at different time resolutions through multi-scale patch representations; construct static prior graphs and sample adaptive dynamic graphs for patch representations at different scales, and jointly extract structural correlation features between variables through graph neural networks and gating fusion mechanisms. The cross-scale temporal aggregation module is configured to: perform cross-scale aggregation of the structural association features based on shared temporal units and scale gating to obtain graph temporal features; The multi-branch collaborative strategy module is configured to: introduce the original time-series enhancement branch and the target variable baseline branch to collaboratively predict the graph time-series features, and generate PEMFC stack voltage prediction results for a future preset period through an incremental output strategy, so as to achieve PEMFC degradation prediction.

[0017] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the PEMFC decay prediction method based on dynamic and static graph fusion as described in the first aspect of the present invention.

[0018] A fourth aspect of the present invention provides an electronic device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the PEMFC decay prediction method based on dynamic and static graph fusion as described in the first aspect of the present invention.

[0019] The above one or more technical solutions have the following beneficial effects: After defining the PEMFC degradation prediction problem, this invention constructs static prior graphs and sample adaptive dynamic graphs for patch representations at different scales. Structural correlation features between variables are jointly extracted using graph neural networks and a gating fusion mechanism. These structural correlation features are then aggregated across scales based on shared temporal units and scale gating to obtain graph temporal features. By constructing this unified graph temporal modeling framework, the stable coupling characteristics determined by the PEMFC stack topology and voltage series relationships can be simultaneously characterized, as well as the dynamic variable interactions caused by changes in operating conditions such as load variations and hydrothermal state fluctuations. This enhances the ability to model the multivariate correlation evolution laws in complex degradation processes.

[0020] This invention introduces an original time-series enhancement branch and a target variable baseline branch to collaboratively predict graph time-series features, and generates PEMFC stack voltage prediction results for a preset future time period through an incremental output strategy, thereby achieving PEMFC degradation prediction. Thus, this invention can simultaneously capture local transient disturbances, short-term non-stationary fluctuations, and long-term slow decay trends, thereby improving the model's ability to characterize complex degradation modes and short-to-medium-term time-series dependencies.

[0021] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1 This is a flowchart of the PEMFC decay prediction method based on dynamic and static graph fusion in Embodiment 1 of the present invention.

[0024] Figure 2 This is a schematic diagram of the multi-scale static and dynamic image feature extraction module in Embodiment 1 of the present invention.

[0025] Figure 3 This is a structural flowchart of the multi-branch collaborative strategy in Embodiment 1 of the present invention.

[0026] Figure 4 This is a schematic diagram of the total voltage degradation curves of FC1 and FC2 stacks in Embodiment 1 of the present invention; wherein, Figure 4 (a) in the figure represents a schematic diagram of the total voltage degradation curve of the FC1 stack. Figure 4 (b) in the figure represents a schematic diagram of the total voltage degradation curve of the FC2 stack.

[0027] Figure 5 This is a comparison chart of the prediction results for FC1-Step1 under the default partitioning in Embodiment 1 of the present invention; wherein, Figure 5 (a) in the diagram represents the prediction error of FC1-Step1 under the default partitioning. Figure 5 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step1 under the default partitioning.

[0028] Figure 6 This is a comparison chart of the prediction results for FC1-Step3 under the default division in Embodiment 1 of the present invention; wherein, Figure 6 (a) in the diagram represents the prediction error of FC1-Step3 under the default partitioning. Figure 6 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step3 under the default partitioning.

[0029] Figure 7 This is a comparison chart of the prediction results for FC1-Step5 under the default division in Embodiment 1 of the present invention; wherein, Figure 7 (a) in the diagram represents the prediction error of FC1-Step5 under the default partitioning. Figure 7 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step5 under the default partitioning.

[0030] Figure 8 This is a comparison chart of the prediction results for FC2-Step1 under the default partitioning in Embodiment 1 of the present invention; wherein, Figure 8 (a) in the diagram represents the prediction error of FC2-Step1 under the default partitioning. Figure 8 (b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step1 under the default partitioning.

[0031] Figure 9 This is a comparison chart of the prediction results for FC2-Step3 under the default partitioning in Embodiment 1 of the present invention; wherein, Figure 9 (a) in the diagram represents the prediction error of FC2-Step3 under the default partitioning. Figure 9(b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step3 under the default partitioning.

[0032] Figure 10 This is a comparison chart of the prediction results for FC2-Step5 under the default division in Embodiment 1 of the present invention; wherein, Figure 10 (a) in the diagram represents the prediction error of FC2-Step5 under the default partitioning. Figure 10 (b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step5 under the default partitioning.

[0033] Figure 11 This is a comparison chart of the robustness of FC1-Step1 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 11 (a) in the diagram represents the prediction error of FC1-Step1 under different data partitioning ratios. Figure 11 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step1 under different data division ratios.

[0034] Figure 12 This is a comparison chart of the robustness of FC1-Step3 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 12 (a) in the diagram represents the prediction error of FC1-Step3 under different data partitioning ratios. Figure 12 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step3 under different data division ratios.

[0035] Figure 13 This is a comparison chart of the robustness of FC1-Step5 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 13 (a) in the figure represents the prediction error of FC1-Step5 under different data partitioning ratios. Figure 13 (b) in the figure represents a comparison between the predicted and actual values ​​of FC1-Step5 under different data division ratios.

[0036] Figure 14 This is a comparison chart of the robustness of FC2-Step1 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 14 (a) in the diagram represents the prediction error of FC2-Step1 under different data partitioning ratios. Figure 14 (b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step1 under different data partitioning ratios.

[0037] Figure 15 This is a comparison chart of the robustness of FC2-Step3 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 15(a) in the diagram represents the prediction error of FC2-Step3 under different data partitioning ratios. Figure 15 (b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step3 under different data division ratios.

[0038] Figure 16 This is a comparison chart of the robustness of FC2-Step5 under different data partitioning ratios in Embodiment 1 of the present invention; wherein, Figure 16 (a) in the figure represents the prediction error of FC2-Step5 under different data partitioning ratios. Figure 16 (b) in the figure represents a comparison between the predicted and actual values ​​of FC2-Step5 under different data division ratios. Detailed Implementation

[0039] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0040] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0041] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0042] Example 1 This embodiment discloses a PEMFC decay prediction method based on dynamic and static graph fusion.

[0043] like Figure 1 As shown, the PEMFC degradation prediction method based on dynamic and static graph fusion includes: Step S1: Define the PEMFC degradation prediction problem and obtain multivariate historical observation sequences. Extract degradation features at different time resolutions through multi-scale patch representation. Step S2: For patch representations at different scales, construct static prior graphs and sample adaptive dynamic graphs respectively, and extract structural correlation features between variables by jointly using graph neural networks and gating fusion mechanisms; Step S3: Based on shared time-series units and scale gating, the structural correlation features are aggregated across scales to obtain graph time-series features; at the same time, the original time-series enhancement branch and the target variable baseline branch are introduced to jointly predict the graph time-series features, and the PEMFC stack voltage prediction results for the future preset period are generated through an incremental output strategy to achieve PEMFC degradation prediction.

[0044] Based on the above process, this invention can simultaneously take into account the structural relationships, dynamic correlations and multi-scale time feature modeling in multivariate monitoring data, thereby comprehensively depicting the complex evolutionary laws in the degradation process.

[0045] As operating time increases, the total voltage of a PEMFC stack gradually decreases, and its degradation process typically exhibits a complex dynamic evolution characterized by both long-term decay trends and short-term fluctuations. Many studies have predicted the remaining lifespan or degradation trend of fuel cells based on time-series data; however, these methods often primarily model along the time dimension, failing to adequately utilize the structural coupling relationships between variables monitored by multiple sensors. Furthermore, emphasizing variable connectivity while neglecting the original continuous time-series patterns and the evolutionary inertia of the target variable itself makes it difficult to comprehensively characterize the PEMFC degradation process. To address these issues, this invention proposes a PEMFC degradation prediction method based on dynamic and static graph fusion. The dynamic-static fusion graph network model can jointly model multi-scale time features, stable structural relationships, sample-level dynamic correlations, and autoregressive priors of the target variable within a unified framework, achieving high-precision multi-step prediction of the total voltage of the PEMFC stack. The core process of this invention can be summarized in the following three steps: 1) Multi-scale degradation feature extraction. The input 24-dimensional multivariate historical observation sequence is first normalized using RevIN, and then segmented into multi-scale local segments with different patch lengths and step sizes to simultaneously preserve short-term perturbation information and long-term degradation trends; 2) Static and dynamic graph co-modeling. For each scale's patch representation, a static prior graph is constructed. Adaptive dynamic graph of samples Furthermore, stable relationships and dynamic correlation features between variables are extracted through a combination of graph neural networks and gating mechanisms; 3) Multi-branch collaborative prediction. The fused graph features are aggregated across scales through shared temporal units and scale gating, and then combined with the original temporal enhancement branch and the target variable baseline branch for collaborative prediction. Finally, the future reactor voltage prediction result is generated through incremental output.

[0046] Furthermore, in the specific implementation process, the multi-scale static and dynamic graph feature extraction module is the core component of the method of this invention. Its goal is to simultaneously characterize the local fluctuations, long-term trends, and complex coupling relationships between variables during the PEMFC degradation process, based on 24-dimensional multivariate monitoring features. Unlike traditional methods that only model along the time dimension or only utilize the single-variable historical sequence of the total PEMFC stack voltage, the multi-scale static and dynamic graph feature extraction module uses 24 input channels as the basic objects for structural modeling and constructs "variable-patch" node representations at different time resolutions. That is, each sensor variable not only retains its own temporal evolution characteristics but also interacts with other variables through static prior maps and sample adaptive dynamic maps. Specifically, firstly, the normalized 24-dimensional historical observation sequence is divided into multi-scale patch representations. Then, static prior maps and dynamic similarity maps are constructed at each scale. Cross-variable structural association features are extracted through graph attention message passing. Finally, cross-scale aggregation is achieved using shared temporal units and scale gating. Figure 2 The multi-scale static and dynamic graph feature extraction module is demonstrated: the input 24-dimensional sequence is first divided into patch representations at different scales, then static and dynamic graphs are constructed at each scale, and the final graph temporal features are obtained through graph attention propagation and cross-scale temporal aggregation.

[0047] To facilitate understanding of the technical solution of the present invention, the specific implementation methods of the technical solution of the present invention will be further explained and described below.

[0048] In step S1, the PEMFC degradation prediction problem is defined and multivariate historical observation sequences are obtained. Degradation features at different temporal resolutions are extracted using multi-scale patch representation. This can be achieved through the following steps: Step S1-1: Define the PEMFC degradation prediction problem.

[0049] Suppose PEMFC at time... Multivariate monitoring vector Represented as: ; in, In this embodiment, the number of input variables is specified. ; Indicates time No. The observed values ​​of each monitoring variable.

[0050] by Characterizing the length of the historical observation window, in this embodiment ;by Indicates time At that time The input sequence is composed of multivariate observations arranged in chronological order. In conjunction with the code implementation, the model input adopts a multivariate model, containing 24 channel features. Therefore, Represented as: ; The prediction target of this invention is the total voltage of the PEMFC stack. In the future The values ​​at each time step are denoted as: ; Wherein, P represents the prediction step size, which in this embodiment takes the value of 1, 3 or 5; Indicates from time At that time The true total pile voltage target vector; Indicates time The true value of the total stack voltage, and Therefore, the objective of this invention can be stated as: in the known past... Under the condition of multivariate monitoring sequences at several time steps, learn the nonlinear mapping relationship from the input sequence to the future target variable, that is: ; in, Represents the future output of the model The predicted vector of total pile voltage at each time step This represents a nonlinear prediction function.

[0051] Unlike univariate autoregressive predictions that rely solely on the historical trajectory of the target variable, the model in this invention aims to fully utilize the time dependence, variable coupling relationships, and degradation patterns at different time scales in the PEMFC multi-sensor monitoring data to improve the prediction accuracy of total reactor voltage degradation trends under complex operating conditions. Specifically, the model considers not only the target variable... By combining its own historical evolution with auxiliary information provided by other operating state variables and voltage characteristics, the PEMFC degradation prediction is modeled as a multivariate, multi-scale, and structurally related time series prediction problem.

[0052] Considering that PEMFC runtime data typically exhibits significant non-stationarity and complex coupling relationships between different variables, further improvements can be made to the prediction function. The paper introduces multi-scale patch representation, static prior graph and dynamic similarity graph modeling, cross-scale time series aggregation, and baseline branching of target variable to simultaneously characterize short-term fluctuations, long-term decay trends and dynamic interaction relationships between variables.

[0053] Step S1-2, multi-scale patch mechanism.

[0054] The degradation process of PEMFC typically involves multiple dynamic modes, including short-term perturbations, local recovery, and long-term decay. Modeling at only a single time scale often fails to capture both fine-grained fluctuations and the global degradation trend. To address this, this invention employs a multi-scale patch mechanism to reconstruct the input sequence, mapping the same historical observations to local segment representation spaces at different time resolutions.

[0055] Let the input sequence after RevIN normalization be: ; For the m-th scale, its patch length is... and sliding step size Represented as Then the patch representation at this scale It can be written as: ; in, , This indicates the number of patches at this scale, and it is calculated as follows: ; In this invention, two patch configurations are used by default: (4,2) and (12,6). The shorter-scale patch focuses more on local perturbations, instantaneous fluctuations, and short-range dependencies, while the longer-scale patch is more conducive to extracting slow degradation patterns and trend features over long time spans. Through this multi-scale segmentation, the model can observe PEMFC degradation signals at different time resolutions, providing a hierarchical input representation for subsequent graph structure modeling.

[0056] In step S2, static prior maps and sample adaptive dynamic maps are constructed for patch representations at different scales, and structural correlation features between variables are jointly extracted using graph neural networks and gating fusion mechanisms. This can be achieved through the following steps: Step S2-1: Construct a static prior graph and a sample adaptive dynamic graph.

[0057] After obtaining the patch representations at each scale, this invention further constructs a static prior graph and a sample adaptive dynamic graph at each scale to simultaneously characterize the stable structural relationships and time-varying dynamic correlations in the PEMFC multivariate monitoring signal. The static graph (i.e., the static prior graph) constructed in this invention is a structural prior graph based on the PEMFC stack structure and variable semantic relationships, used to provide stable edge connection constraints for the graph neural network.

[0058] For the m-th scale, the model uses both "variable-patch location" as graph nodes. That is, the representation of the same variable at different patch locations is considered a different node, and the representations of different variables at the same patch location are also considered different nodes. Based on this node definition, the model can simultaneously describe the relationships between variables and the connections between local time segments. The static prior graph is mainly used to encode relatively stable stack structure relationships. In the code implementation, when the input features include individual cell voltages U1~U5, the model first locates the node index corresponding to each individual cell voltage and establishes connections between individual cell voltage nodes within the same patch location; if the input features also include the total stack voltage... Then further As a voltage convergence node, it establishes connections with each individual voltage node; simultaneously, all spatial connections employ bidirectional edges to support bidirectional information propagation. Furthermore, the model establishes temporal adjacency edges between adjacent patch locations of the same variable, thereby preserving the continuous evolution of the same monitored variable along local time segments. The resulting static graph... It can be represented as: ; in, This represents the set of nodes at this scale. This represents the static edge set composed of the stack voltage structure relationship and the temporal adjacency relationship of the same variable. This static graph remains fixed during training and testing to provide a stable structural prior.

[0059] However, relying solely on a fixed static graph is insufficient to characterize the dynamic changes in variable relationships within PEMFC under different degradation stages and operating conditions. Therefore, this invention further constructs a sample-adaptive dynamic graph. Unlike the static graph, the edge set of the dynamic graph (i.e., the sample-adaptive dynamic graph) is adaptively generated by the patch features of the current sample. Specifically, the model first performs linear mapping and layer normalization on the patch features of each node to obtain a node embedding representation; then, L2 normalization is applied to the node embeddings, and dot product similarity is used to calculate the correlation between nodes. Finally, the similarity score of the dynamic graph edges is softmax normalized according to the target node and used as the edge weight in the dynamic graph message propagation.

[0060] For each sample, the model searches for similar neighbors in both the time and channel dimensions: in the time dimension, for the same variable, nodes with high similarity across different patch positions are selected; in the channel dimension, for the same patch position, nodes with high similarity across different variables are selected. This approach captures both the dynamic relationships between the same variable across different local time segments and the dynamic coupling relationships between different sensor variables at the same local time scale.

[0061] To avoid an overly dense dynamic graph and reduce the impact of noisy edges, the model further employs strategies such as top-k filtering, similarity quantile pruning, and maximum edge count constraints to retain high-confidence edges. The resulting candidate edges are then expanded into bidirectional edges, forming a weighted dynamic graph. Represented as: ; in, This represents the set of dynamic graph edges adaptively generated from the current sample. This represents the corresponding normalized edge weight.

[0062] Compared to static graphs, dynamic graphs can dynamically adjust the node connection relationships according to the local degradation state of different samples, and are therefore more suitable for characterizing the time-varying coupling characteristics between variables under complex working conditions.

[0063] Step S2-2: Graph attention message passing.

[0064] After obtaining the static and dynamic graphs, this invention performs graph attention message passing on the two types of graphs respectively. Let the node input features at the m-th scale be... Then the outputs of the static graph branch and the dynamic graph branch can be expressed as follows: ; ; Among them, the static graph branch mainly aggregates stable neighborhood information determined by the prior of the stack structure, while the dynamic graph branch aggregates dynamic association information based on sample-level similarity edge weights.

[0065] During graph attention propagation, different adjacent edges are assigned different importance based on node features. For dynamic graph branches, edge weights further adjust the attention coefficients, making the model pay more attention to nodes with higher similarity and stronger correlation in the current sample. Compared to existing uniform graph convolutions with fixed adjacency matrices, this invention uses a graph attention message passing layer instead of directly using the standard GAT. This layer further introduces node embedding and dynamic graph edge weights on top of node feature attention to enhance the ability to model structural relationships. Therefore, it is more suitable for the characteristics of uneven relationship strength and key interactions changing with operating conditions in PEMFC multivariate degradation scenarios.

[0066] After obtaining the representations of the static graph branch and the dynamic graph branch, the model further employs a gating fusion mechanism to adaptively integrate the two. Specifically, the model outputs the static graph branch... and dynamic graph branch output The concatenated graphs are input into a gated network and then processed through softmax to obtain the fusion weights of the two graph branches. ; in, This represents the gate temperature coefficient.

[0067] Finally, the fused graph features at the m-th scale Represented as: ; Through the aforementioned dual-graph collaborative modeling mechanism, the model can achieve an adaptive balance between stable structural priors and sample-level dynamic correlations: the static graph ensures the model's stable utilization of the stack voltage-structure relationship, while the dynamic graph enhances the model's adaptability to changes in operating conditions and differences in degradation stages. Together, they improve the structural representation capability in PEMFC multivariate degradation prediction.

[0068] In step S3, the structural correlation features are aggregated across scales based on shared temporal units and scale gating to obtain graph temporal features. Simultaneously, an original temporal enhancement branch and a target variable baseline branch are introduced to collaboratively predict the graph temporal features. An incremental output strategy is then used to generate PEMFC stack voltage prediction results for a future preset time period, thereby achieving PEMFC degradation prediction. This can be achieved through the following steps: Step S3-1: Cross-scale time aggregation.

[0069] Since the fused graph features at different scales reflect degradation patterns at different temporal resolutions, this invention further designs a cross-scale temporal aggregation module to uniformly integrate multi-scale information. Specifically, for the fused graph features at each scale... The model first organizes the data into a time series format, then inputs it into shared time series units for dependency extraction. This process is denoted as: ; in, This represents the temporal summary features extracted at the m-th scale. Indicates the first The node response vectors at each scale are rearranged according to their time segment location and the dimensions of the monitored variables. The time series matrix. Since this invention shares the GRU across different scales, it can reduce the number of parameters and help maintain consistency in multi-scale time series modeling.

[0070] Building upon this, the model further employs a scale-gating mechanism to weight and fuse features at different scales. Let the scale weights be... The cross-scale aggregation result can then be written as: ; ; in, This represents the proportion of contribution of features at different scales to the final graph branch representation. Represents the temporal summary features of the graph; The temperature coefficient representing scale-gated temperature. Indicates the number of scales; express The first of the scales The weights of each scale are determined. Since short scales are better at capturing local fluctuations and rapid changes, while long scales are better at representing slow decay and long-term trends, the model can learn the global contribution weights of different time scales to the temporal features of the final graph during training through learnable scale gating, thereby achieving adaptive weighted fusion of short-scale and long-scale information.

[0071] In summary, this invention establishes a graph temporal feature extraction framework suitable for PEMFC multivariate degradation modeling through a processing flow that includes multi-scale patch representation, static and dynamic graph construction, graph attention propagation, gating fusion, and cross-scale temporal aggregation. This module utilizes multi-scale temporal information and jointly encodes stable relationships and dynamic associations between variables, providing a core feature foundation for subsequent multi-branch collaborative prediction.

[0072] Step S3-2: Multi-branch collaborative prediction and training strategy.

[0073] Graph time-series summarization features obtained after multi-scale static and dynamic graph aggregation Subsequently, if prediction relies solely on graph branches, although it can effectively characterize the structural dependencies and time-varying associations between variables, it still has two limitations in practical modeling: First, the patch graphing and graph feature propagation process will compress, to some extent, the fine-grained local continuous patterns in the original time series; second, Historical trajectories often contain strong autoregressive priors, but relying solely on implicit learning of multivariate graphical branches for this information may lead to unstable trend modeling. Therefore, this invention further constructs a multi-branch collaborative prediction framework consisting of graphical branches, original time-series enhancement branches, and target variable baseline branches, and performs end-to-end optimization under a unified training objective; the collaborative relationships of the three types of branches and the two-level gating are as follows: Figure 3 As shown.

[0074] 1) Original timing enhancement branch.

[0075] The advantage of graph branches lies in their explicit modeling of multivariate interactions. However, in scenarios aimed at PEMFC degradation prediction, local continuous changes, instantaneous perturbations, and short-range patterns in the original time series are equally important. To compensate for the local temporal information that may be lost during graph representation, this invention introduces an original temporal enhancement branch, which directly performs convolutional modeling on the input sequence.

[0076] Let the normalized input sequence be To more clearly describe the processing of the original temporal enhancement branch, this invention introduces three intermediate representations: low-dimensional projection representation. Local convolution features and pooling summary vector This branch first projects the 24-dimensional original input into a low-dimensional latent space, then extracts local continuous temporal patterns through two layers of one-dimensional convolution, and finally obtains the original temporal summary features through pooling and linear mapping. This process can be formally represented as: ; ; ; ; in, This represents the low-dimensional projection representation obtained from the 24-dimensional input feature map. This represents the local temporal features extracted through two layers of one-dimensional convolution. This represents the global summary vector after pooling the convolutional features. σ represents the final output of the original temporal enhancement branch; σ represents the nonlinear activation function. and This represents a one-dimensional convolution operation. This represents a time-dimensional pooling operation; and These represent the trainable weight matrix and bias of the input projection layer, respectively. and represents the trainable weight matrix and bias of the linear mapping layer after pooling, respectively. The formation process consists of four stages: input projection, local convolutional coding, global pooling summarization, and linear mapping, which enables the original temporal enhancement branch to more clearly reflect its compensation effect on local continuous patterns in 24-dimensional multivariable input.

[0077] In obtaining and Then, the model adaptively fuses the two through a first-layer gating mechanism. Specifically, the fusion weights are dynamically learned by the gating network, and can be expressed as follows: ; in, This is the temperature coefficient.

[0078] Accordingly, the main predictive feature representation can be written as ; ; in, and Let the weights be the fusion weights corresponding to the graph temporal features and the original temporal features, respectively. Both are non-negative scalars and satisfy the following conditions: ; This represents the fusion characteristics of the output of the first gating network; Indicates the main forecast head; This represents the incremental prediction vector for the next P steps output by the main branch.

[0079] This design enables the model to adaptively balance the contributions of structured graph features and original temporal features based on sample features, thereby improving its ability to express complex degradation patterns in PEMFC.

[0080] 2) Baseline branch of the target variable.

[0081] In addition to the multivariate graph branch and the original time series branch, this invention also introduces a target variable baseline branch to explicitly utilize... The motivation is that, for degradation prediction tasks, the target variable usually has a strong continuous evolution pattern. Introducing a target variable-specific modeling path in addition to complex multivariate modeling can help improve the smoothness and trend stability of the prediction results.

[0082] Specifically, let the target variable be a historical sequence. Recorded as: ; The baseline branch of the target variable first extracts its time-dependent features using a dedicated GRU, and then generates a baseline prediction representation through linear mapping. It can be written as: ; in, This represents a gated recurrent unit specifically designed for the historical sequence of the target variable, used to extract the time-dependent features of the target variable itself; This indicates the final hidden state output by the gated loop unit; Indicates the baseline prediction header, used to... Mapped to Dimensional baseline incremental prediction vector Unlike the graph branch, this branch does not explicitly model multivariate structural relationships, but focuses on learning the evolutionary inertia of the target variable itself, thus providing a stable trend benchmark for the final prediction.

[0083] Building upon this, the present invention further employs a second-layer gating mechanism to represent the main prediction features. and baseline prediction representation Perform fusion. Let the gating coefficient be... Then the future predicted increment It can be represented as: ; ; This design means that the model does not simply add the outputs of each branch, but rather adaptively adjusts the weight distribution between the "autoregressive prior of the target variable" and the "multivariate structured prediction" based on the current sample state. Thus, the model retains the expressive advantages of multivariate information modeling while also constraining the stability of the prediction results through the target variable branch.

[0084] Step S3-3: Incremental prediction strategy.

[0085] Unlike directly predicting future absolute values, this invention employs an incremental prediction strategy to generate the final output. Considering the continuous evolution of PEMFC stack voltage degradation, directly regressing future absolute values ​​often introduces local fluctuation errors, while predicting the increment of change relative to the current moment better reflects the actual evolution of the degradation signal.

[0086] Let the last observation value of the target variable at the current time be... The prediction results in the normalized space Defined as: ; in, This represents the cumulative summation operation along the predicted step direction.

[0087] When the prediction step size is single step, the above equation can be degenerated into: ; in, Indicates time The predicted total stack voltage; This represents the total pile voltage observation value at the last moment of the input history window; Indicates the model prediction from time [time]. At that time The increment of the total stack voltage change.

[0088] Through this residual output format, the model can progressively extrapolate future evolution trajectories based on the current state, thereby enhancing the smoothness and trend consistency of the prediction curve. Subsequently, the model utilizes the statistical information stored in RevIN to... Inverse normalization is performed to restore the data to the preprocessed normalized space. Then, the original physical dimensions are restored using the min-max statistics of the training set, finally yielding the prediction results under the physical dimensions. .

[0089] Furthermore, to better demonstrate the superiority of the present invention, the following experiments were conducted in this embodiment: 1) Data set and data preprocessing.

[0090] This embodiment uses the PEMFC degradation dataset released in the IEEE 2014 PHM Data Challenge for training and testing. This dataset includes two sub-datasets, FC1 and FC2, with the experimental subjects being PEMFC stacks composed of five individual cells. FC1 operates under steady-state conditions, while FC2 operates under quasi-dynamic conditions with an additional frequency of 5 kHz and an amplitude of 7 A to simulate the aging process under different operating conditions. The runtimes of FC1 and FC2 are approximately 1154 h and 1020 h, respectively. During the experiment, sensors continuously recorded key operating parameters of the stack, including voltage, current, temperature, gas flow rate, and pressure. Since FC1 is closer to steady-state conditions, while FC2 exhibits stronger dynamic fluctuations, they can be used to evaluate the model's predictive capabilities in stable and complex non-stationary scenarios, respectively.

[0091] Considering the dimensional differences in the original multi-sensor data and the potential for noise, spikes, and local fluctuations in long-term operational data, direct use for model training could easily introduce invalid perturbations and affect prediction accuracy. Therefore, this embodiment first averages the original data at 1-hour intervals to reduce the interference of high-frequency noise on model building. Then, the LOESS method is used to smooth the sampled sequence. It is important to note that normalization is performed only using statistics from the training segment. LOESS smoothing is used only for visualization before time-series partitioning; future window information is not used in the model training data. The smoothing windows for FC1 and FC2 are set to 20 and 10, respectively. Smaller smoothing windows help retain more detailed changes under quasi-dynamic testing conditions; therefore, FC2 uses a smaller window to enhance the characterization of local dynamic features. The smoothed total stack voltage degradation curves for FC1 and FC2 are shown below. Figure 4 As shown; where, Figure 4 (a) in the figure represents a schematic diagram of the total voltage degradation curve of the FC1 stack. Figure 4 (b) in the figure represents the schematic diagram of the total voltage degradation curve of the FC2 stack. It can be seen that the overall degradation process of FC1 is relatively stable, while FC2 has more obvious local fluctuations and non-stationary changes. This provides a basis for evaluating the model's predictive ability from the perspectives of stable scenarios and complex dynamic scenarios.

[0092] In terms of feature construction, this embodiment adopts a multivariate input mode, with To predict the target, and to avoid any single variable dominating the training process due to differences in feature scales, max-min normalization is applied to all sensor data. Let the original variable be x, and its normalization result be defined as... ; in, and These represent the minimum and maximum values ​​of the variable within the training set, respectively. This process maps all input variables to a similar numerical range, improving the numerical stability and convergence efficiency of the model training. It's important to note that min-max normalization, as a data preprocessing step, unifies the numerical scale of variables from different sensors; RevIN, on the other hand, is an instance-level normalization module within the model, used to mitigate distribution drift between different samples. They operate at different levels: the former focuses on unifying the dataset scale, while the latter focuses on dynamic distribution correction at the sample level.

[0093] 2) Experiment setup.

[0094] To verify the effectiveness of the proposed model in the PEMFC multivariate degradation prediction task, this embodiment conducts model training and testing under a unified experimental configuration. In the current implementation, the model input adopts a multivariate mode, with... The target prediction is used as the objective variable, and the input sequence length is set to 48 (seq_len=48). The prediction step size is set to 1, 3, and 5 respectively to compare the changes in model performance under different prediction spans. The number of input channels is set to enc_in=24, consistent with the 24-dimensional input features constructed in the data processing stage.

[0095] In terms of model structure, the method of this invention adopts a multi-scale graph temporal fusion framework. Specifically, the multi-scale representation module uses two sets of patch configurations by default, namely patch_configs=[(4,2),(12,6)], corresponding to shorter and longer time scales respectively, to simultaneously model local perturbation information and long-term degradation trends. The graph structure modeling part adopts a dual-branch fusion mode of static graph and dynamic graph, namely edge_mode='both', thereby simultaneously utilizing stable structural relationships and sample-level dynamic associations. The hidden layer dimension of the graph temporal backbone is set to d_model=512, and the number of graph convolutional layers is set to num_gnn_layers=2. In addition, the model enables multi-scale modeling use_multiscale=1, reversible instance normalization use_revin=1, and retains the original temporal enhancement branch use_raw_temporal=1, where the original temporal branch dimension is set to raw_dim=32. These settings together constitute the core structural configuration of the model of this invention. Based on the current implementation, the main structural parameters of the model can be summarized as shown in Table 1.

[0096] Table 1 Summary of main structural parameters of the model

[0097] 3) Evaluation indicators.

[0098] This embodiment verifies the effectiveness of the proposed method through three key evaluation indicators, namely root mean square error. Coefficient of determination and mean absolute percentage error These metrics will measure model performance from different perspectives, among which, It reflects the absolute magnitude of the deviation between the predicted value and the actual value. To measure the goodness of fit between predicted and actual values, The mean absolute error (MAE) measures the relative magnitude of prediction error as a percentage, and is used to measure the average absolute deviation between the predicted and actual results. Its specific definition is as follows: ; ; ; ; in, Indicates the first The true value of each sample Indicates the first The predicted value for each sample, This represents the mean of all true values. This represents the total number of samples.

[0099] 4) Experimental analysis.

[0100] 4.1) Detailed analysis of the prediction results.

[0101] To more intuitively evaluate the degradation prediction performance of the proposed method, this embodiment first conducts prediction experiments with 1, 3, and 5 time steps on the FC1 and FC2 datasets under the default data partitioning conditions. The experimental results are shown in Table 2, and... Figures 5-10 The two subgraphs (a) and (b) of each figure are shown.

[0102] Table 2 Comparison of prediction performance between existing models and the model of this invention

[0103] As can be seen from Table 2, existing methods have gradually evolved from mechanistic modeling and statistical state estimation to deep learning and graph time series modeling, but there are still shortcomings in the unified modeling of stable structural relationships, dynamic variable associations and multi-scale time features.

[0104] Figures 5-10FC1 and FC2 in the model correspond to the prediction results under steady-state and quasi-dynamic conditions, respectively. Visualized curves are used to further observe the degree of fit between the predicted trajectory and the actual degradation trend. Both numerical indicators and visualizations verify the model performance. To ensure fair comparison between different models, this embodiment uses the same data preprocessing process, the same training / validation / testing split ratio, the same input sequence length seq_len=48, and the same prediction step size settings pred_len=1, 3, 5 for all baseline models and the proposed method. RMSE, MAPE, and R² are used as unified evaluation metrics. All comparison results are obtained through retraining and testing under this unified experimental protocol. Overall, the proposed method exhibits high prediction accuracy under both datasets and three prediction step sizes, and achieves good results in RMSE and... It performed best in key indicators such as [list of indicators].

[0105] Specifically, on the FC1 dataset, the RMSE of the method proposed in this invention at steps 1, 3, and 5 are 0.00022, 0.00076, and 0.00145, respectively. The RMSE values ​​are 0.99973, 0.99697, and 0.98902, respectively, indicating that the model can accurately track the stack voltage degradation trend under relatively stable operating conditions. On the FC2 dataset, the RMSE values ​​of the proposed method are 0.00087, 0.00219, and 0.00381, respectively. The values ​​are 0.99892, 0.99312, and 0.97910, respectively. Although FC2 exhibits stronger dynamic fluctuations and is more difficult to predict, the method of this invention still maintains high fitting accuracy, indicating that the model has a strong adaptability to non-stationary degradation under complex working conditions.

[0106] Based on the performance of the baseline models, iTransformer's overall performance on this task is weaker than most graphical models, especially in the multi-step prediction tasks of FC1 and FC2. Its RMSE increases significantly with the increase of prediction step size, indicating that relying solely on attention mechanisms for multivariate time-series modeling is still insufficient to fully characterize the complex variable coupling relationships and non-stationary fluctuations in the PEMFC degradation process. In contrast, graphical models such as FGN, GraphSAGE, and MTGNN achieve lower prediction errors in most settings, demonstrating that explicitly modeling the structural relationships between variables plays an important role in predicting PEMFC stack voltage degradation.

[0107] Further comparisons reveal that while existing graph models generally outperform most pure time-series modeling methods, significant differences remain between different graph models. FGN and MTGNN perform well across multiple prediction step sizes, indicating that adaptive relation modeling can effectively improve the performance of multivariate degradation prediction. However, the proposed method shows shortcomings in RMSE and... Further improvements were achieved in terms of metrics, indicating that simply constructing a graph structure is not enough to achieve optimal prediction results. The key is how to organically integrate multi-scale time representation, static prior relationships, dynamic graph associations, and the autoregressive prior of the target variable itself.

[0108] 4.2) Robustness analysis under different data partitioning ratios.

[0109] To further verify the stability of the proposed method under different data availability conditions, this embodiment sets three training / validation / test ratios of 3:1:6, 5:1:4, and 7:1:2 in addition to the default partitioning ratio, and selects representative models with good performance in the prior art, FGN, GraphSAGE, and MTGNN, as comparison objects. The comparison results are shown in Table 3, and... Figures 11-16 As shown.

[0110] Table 3 Comparison of prediction performance under different data partitioning ratios

[0111] From Table 3, and Figures 11-16 The comparison results shown in sub-figures (a) and (b) of each figure demonstrate that the method proposed in this invention exhibits a stable advantage under all three data partitioning conditions. On the FC1 dataset, whether it's a 3:1:6 partition with fewer training samples or a 7:1:2 partition with more training samples, the RMSE and [other performance characteristics] of the method proposed in this invention are [highly accurate / stable]. All of these are superior to other comparative models. For example, under the 3:1:6 condition, the RMSE of the method of this invention on FC1 is 0.00050. The RMSE reached 0.99870; under the default 5:1:4 partitioning, the RMSE further decreased to 0.00022. Increased to 0.99973.

[0112] On the FC2 dataset, the method proposed in this invention also maintains optimal results. Specifically, under the three partitions of 3:1:6, 5:1:4, and 7:1:2, the RMSE of the method in this invention are 0.00097, 0.00087, and 0.00082, respectively. The scores were 0.99864, 0.99892, and 0.99902, respectively, all outperforming the other baseline methods. This result demonstrates that the performance improvement of the proposed model does not depend on a specific data partition, but rather exhibits good stability and generalization ability under both relatively abundant and relatively scarce training data conditions.

[0113] Overall, as the proportion of the training set increases, the model typically achieves more stable prediction results; conversely, when the proportion of the training set decreases and the test interval expands, the task difficulty increases significantly. Nevertheless, the method of this invention consistently maintains its leading position under different partitioning conditions, demonstrating that the model can effectively extract key spatiotemporal features in PEMFC degradation even with limited samples. This result further validates the role of multi-scale modeling, static-dynamic graph fusion, and baseline branching of the target variable in improving model robustness.

[0114] 5) Ablation experiment.

[0115] To further verify the contribution of each key module in the proposed model to the prediction performance, this embodiment conducted ablation experiments on the FC2 dataset. Considering that FC2 has stronger dynamic fluctuations and more obvious non-stationarity, ablation analysis on this dataset can better reflect the effectiveness of the model structure design. Specifically, this embodiment set up six sets of experiments: the complete model of this invention, NoScale with multi-scale modeling removed, 1hop with weakened graph propagation range, NoStatic with static graph branches removed, NoDynamic with dynamic graph branches removed, and NoRevin with RevIN removed. The ablation results are shown in Table 4.

[0116] Table 4 Ablation experimental results on dataset (FC2)

[0117] As shown in Table 4, the overall comparison results indicate that the complete model of this invention achieves the best performance in prediction steps 1, 3, and 5. Specifically, the RMSE of the method of this invention on FC2 are 0.00087, 0.00219, and 0.00381, respectively, and the corresponding MAEs are 0.00045, 0.00117, and 0.00199, respectively. The performance scores were 0.99892, 0.99312, and 0.97910, respectively. In contrast, all ablation models showed varying degrees of performance degradation, indicating that the multi-scale static-dynamic graph fusion and multi-branch collaborative prediction mechanism proposed in this invention has significant effectiveness.

[0118] When the multi-scale mechanism is removed, the model's error increases significantly at each prediction step size. For example, the RMSE of NoScale predictions rises to 0.00104, 0.00255, and 0.00411 at 1, 3, and 5 steps, respectively, indicating that multi-scale patch representation plays an important role in simultaneously characterizing local fluctuations and long-term degradation trends. If modeling is only performed at a single scale, the model's ability to express complex degradation patterns will be significantly limited.

[0119] When only a weaker graph propagation range is retained, the overall performance of 1hop is also lower than that of the complete model, indicating that an appropriate graph feature propagation depth helps to enhance the modeling effect of dependencies between variables. Meanwhile, removing either the static or dynamic graph branch also decreases the model performance. Specifically, the RMSE of NoStatic increases to 0.00443 after 5 prediction steps, while NoDynamic further increases to 0.00466 after 5 prediction steps, indicating that static and dynamic graphs respectively perform the functions of modeling stable structural relationships and time-varying associations, and the two are clearly complementary in the model.

[0120] Furthermore, removing RevIN resulted in one of the most significant performance degradations. The RMSE of NoRevin increased to 0.00158 in 1-step prediction, and reached 0.00278 and 0.00441 in 3-step and 5-step prediction, respectively. This indicates that instance-level normalization plays a crucial role in mitigating input distribution variations, improving training stability, and enhancing prediction accuracy in PEMFC non-stationary degenerate sequence modeling.

[0121] Overall, the ablation experiments clearly demonstrate that the performance improvement of the model in this invention does not stem from a single module, but rather from the combined effect of multi-scale representation, dual-branch modeling of static and dynamic graphs, and RevIN normalization. The multi-scale mechanism enhances the model's ability to perceive degradation patterns at different temporal resolutions; the static and dynamic graphs strengthen the joint characterization of stable and dynamic coupling relationships; and RevIN improves the model's adaptability to complex non-stationary inputs. It is precisely the synergistic effect among these modules that enables the complete model to achieve optimal performance in the FC2 multi-step prediction task.

[0122] Based on the above experimental verification, it can be seen that this invention is aimed at the task of predicting PEMFC stack voltage degradation, focusing on... This study investigates multi-step point prediction and conducts systematic experiments on the FC1 and FC2 datasets of the IEEE 2014 PHM Data Challenge. Experimental results show that the proposed method achieves superior performance in 1-, 3-, and 5-step prediction tasks under the default data partitioning, with lower RMSE and lower accuracy. Overall, it outperforms the comparison model in terms of indicators, indicating that it can more accurately characterize the degradation trend of PEMFC stack voltage.

[0123] Furthermore, under different data partitioning ratios, the method of this invention still maintains good prediction accuracy and stability, indicating that its performance advantage does not depend on a specific training / testing partition, but has a certain degree of robustness. Ablation experiments further verify the effectiveness of the key components of the model, demonstrating that the performance improvement of the complete model comes from the synergistic effect of multiple modules, rather than the accidental gain brought by a single factor.

[0124] Overall validation shows that, for multivariate PEMFC degradation prediction tasks, the rational use of structural relationships, dynamic correlations, and time-dependent information can help improve prediction accuracy and generalization ability under complex working conditions. Future research can focus on probabilistic prediction, RUL estimation, model interpretability, and cross-working-condition generalization ability to enhance the application value of the method in practical PEMFC health management scenarios.

[0125] Example 2 This embodiment discloses a PEMFC decay prediction system based on dynamic and static graph fusion.

[0126] The PEMFC decay prediction system based on dynamic and static graph fusion includes: The problem definition module is configured to: define the PEMFC degradation prediction problem; The multi-scale static and dynamic graph feature extraction module is configured to: acquire multivariate historical observation sequences, extract degradation features at different time resolutions through multi-scale patch representations; construct static prior graphs and sample adaptive dynamic graphs for patch representations at different scales, and jointly extract structural correlation features between variables through graph neural networks and gating fusion mechanisms. The cross-scale temporal aggregation module is configured to: perform cross-scale aggregation of the structural association features based on shared temporal units and scale gating to obtain graph temporal features; The multi-branch collaborative strategy module is configured to: introduce the original time-series enhancement branch and the target variable baseline branch to collaboratively predict the graph time-series features, and generate PEMFC stack voltage prediction results for a future preset period through an incremental output strategy, so as to achieve PEMFC degradation prediction.

[0127] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0128] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps in the PEMFC decay prediction method based on dynamic and static graph fusion as described in Embodiment 1 of this disclosure.

[0129] Example 4 The purpose of this embodiment is to provide an electronic device.

[0130] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the PEMFC decay prediction method based on dynamic and static graph fusion as described in Embodiment 1 of this disclosure.

[0131] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0132] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0133] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A PEMFC degradation prediction method based on dynamic and static graph fusion, characterized in that, include: Define the PEMFC degradation prediction problem and obtain multivariate historical observation sequences. Extract degradation features at different time resolutions through multi-scale patch representation. For patch representations at different scales, static prior graphs and sample adaptive dynamic graphs are constructed respectively, and structural correlation features between variables are jointly extracted through graph neural networks and gating fusion mechanisms. The construction of the static prior graph includes: when the input features contain multiple individual voltages, firstly, locating the node index corresponding to each individual voltage, and establishing connections between individual voltage nodes within the same patch position; if the input features also contain the total pile voltage, then the node where the total pile voltage is located is used as a voltage convergence node, and connections are established with each individual voltage node; all spatial connections adopt bidirectional edges to support bidirectional information propagation; simultaneously, temporal adjacency edges are established between adjacent patch positions of the same variable to preserve the continuous evolution relationship of the same monitored variable along local time segments. Based on shared time-series units and scale gating, the structural correlation features are aggregated across scales to obtain graph time-series features. At the same time, the original time-series enhancement branch and the target variable baseline branch are introduced to jointly predict the graph time-series features. The incremental output strategy is used to generate PEMFC stack voltage prediction results for a future preset period to achieve PEMFC degradation prediction. The processing of the original temporal enhancement branch includes: projecting the normalized multivariate historical observation sequence onto a latent space of a preset dimension; extracting local continuous temporal features through at least two layers of one-dimensional convolution; performing temporal pooling and linear mapping on the local continuous temporal features to obtain the original temporal features; using the first gating network to perform weighted fusion of the original temporal features and the graph temporal features, and generating incremental prediction vectors for the main branch corresponding to multiple future time steps through the main prediction head; The processing of the target variable baseline branch includes: extracting the historical sequence of the target variable from the multivariate historical observation sequence; extracting the time dependence features of the target variable historical sequence using a gated recurrent unit for the target variable; mapping the time dependence features to the baseline incremental prediction vector corresponding to multiple future time steps through the baseline prediction head; and using a second gated network to perform weighted fusion of the baseline incremental prediction vector and the main branch incremental prediction vector to obtain the final incremental prediction vector.

2. The PEMFC decay prediction method based on dynamic and static graph fusion as described in claim 1, characterized in that, The PEMFC degradation prediction problem is defined as follows: the total voltage of the PEMFC stack at multiple future time steps is used as the prediction target, and the prediction task of the degradation prediction problem is defined as learning the nonlinear mapping relationship from the input sequence to the future target variable under the condition that the multivariate monitoring sequence of multiple past time steps is known.

3. The PEMFC decay prediction method based on dynamic and static graph fusion as described in claim 1, characterized in that, Degradation features at different temporal resolutions are extracted through multi-scale patch representation, including: reconstructing the acquired multivariate historical observation sequence using a multi-scale patch mechanism, and mapping the same historical observation sequence to local segment representation spaces at different temporal resolutions.

4. The PEMFC decay prediction method based on dynamic and static graph fusion as described in claim 1, characterized in that, The construction of the sample adaptive dynamic graph includes: first, performing linear mapping and layer normalization on the patch features of each node to obtain the node embedding representation; then, performing L2 normalization on the node embedding and using dot product similarity to calculate the correlation between nodes; finally, performing softmax normalization on the similarity score of the target node to the edge of the dynamic graph, which is used as the edge weight in the message propagation of the sample adaptive dynamic graph.

5. A PEMFC decay prediction system based on dynamic and static graph fusion, employing the PEMFC decay prediction method as described in any one of claims 1-4, characterized in that, include: The problem definition module is configured to: define the PEMFC degradation prediction problem; The multi-scale static and dynamic graph feature extraction module is configured to: acquire multivariate historical observation sequences, extract degradation features at different time resolutions through multi-scale patch representations; construct static prior graphs and sample adaptive dynamic graphs for patch representations at different scales, and jointly extract structural correlation features between variables through graph neural networks and gating fusion mechanisms. The cross-scale temporal aggregation module is configured to: perform cross-scale aggregation of the structural association features based on shared temporal units and scale gating to obtain graph temporal features; The multi-branch collaborative strategy module is configured to: introduce the original time-series enhancement branch and the target variable baseline branch to collaboratively predict the graph time-series features, and generate PEMFC stack voltage prediction results for a future preset period through an incremental output strategy, so as to achieve PEMFC degradation prediction.

6. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the PEMFC decay prediction method based on dynamic and static graph fusion as described in any one of claims 1-4.

7. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the PEMFC decay prediction method based on dynamic and static graph fusion as described in any one of claims 1-4.

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