Method for evaluating inter-stack interaction during fuel cell stack decay process

Abstract

The present application relates to a kind of fuel cell stack attenuation process inter-leaf interaction evaluation method, method includes the following steps: S1, actual voltage data and actual parameter data are obtained;S2, voltage data are input into first space-time graph neural network model, obtain first voltage prediction value;S3, parameter data are input into second space-time graph neural network model, obtain second voltage prediction value;S4, using SHAP analysis method, based on the first voltage prediction value and second voltage prediction value obtain the local Shapley value of multiple samples, based on the local Shapley value of multiple samples calculate global Shapley value, obtain the space-time association between single cell voltage and each parameter respectively and each single cell output voltage.Compared with prior art, the present application has the advantages of comprehensively analyzing the inter-leaf interaction of fuel cell stack attenuation process while reducing the damage to the battery.

Description

Technical Field

[0001] This invention relates to the technical features of fuel cell stacks, and in particular to a method for evaluating the inter-cell interactions during the degradation process of a fuel cell stack. Background Technology

[0002] In hydrogen energy conversion devices, proton exchange membrane fuel cells (PEMFCs) are widely considered a promising power technology due to their high energy efficiency, low pollution, and low noise, making them suitable for mobile, stationary, and portable power applications. Although fuel cell technology has largely met the needs of commercial applications, its limited lifespan remains one of the major challenges.

[0003] In practical applications, commercial fuel cell stacks typically consist of multiple individual cells connected in series to increase the total output power. However, interactions between individual cells can lead to uneven output voltage, affecting the overall performance and lifespan of the stack. Currently, research on inter-cell interactions in fuel cell stacks mainly involves artificially introducing faults into individual cells of a model or actual stack and observing changes in the output and internal parameters of adjacent cells. While these studies provide insights into inter-cell interactions, the analytical methods fail to fully capture the impact of internal parameters between individual cells and are prone to damaging the cells. Summary of the Invention

[0004] The purpose of this invention is to provide an evaluation method for the inter-cell interactions during the degradation process of a fuel cell stack, in order to comprehensively analyze the inter-cell interactions during the degradation process while reducing damage to the cells.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for assessing the inter-cell interactions during the degradation process of a fuel cell stack, the method comprising the following steps:

[0007] S1. Obtain actual voltage data and actual parameter data, wherein the voltage data is the single cell voltage of multiple single cells at multiple times, and the parameter data is the parameter values ​​at the same time.

[0008] S2. Input the voltage data into the first spatiotemporal neural network model to obtain the first voltage prediction value;

[0009] S3. Input the parameter data into the second spatiotemporal neural network model to obtain the second voltage prediction value;

[0010] S4. Using the SHAP analysis method, based on the first voltage prediction value and the second voltage prediction value, the local Shapley values ​​of multiple samples corresponding to the two voltage prediction values ​​are obtained. Based on the local Shapley values ​​of multiple samples, the global Shapley values ​​corresponding to the two voltage prediction values ​​are calculated to obtain the spatiotemporal correlation between the single cell voltage and each parameter and the output voltage of each single cell.

[0011] Furthermore, the first spatiotemporal graph neural network model and the second spatiotemporal graph neural network model are T-GCN networks.

[0012] Furthermore, the T-GCN network consists of two parts: a graph convolutional network and a gated recurrent unit.

[0013] Furthermore, the training process of the first spatiotemporal graph neural network model is as follows:

[0014] The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are obtained for training. The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are input into the first spatiotemporal graph neural network. The first spatiotemporal graph neural network outputs the predicted single-cell voltages. The loss function is calculated to train the first spatiotemporal graph neural network, and the first spatiotemporal graph neural network model is obtained.

[0015] Furthermore, the training process of the second spatiotemporal graph neural network model is as follows:

[0016] Obtain the parameter values ​​and corresponding graphs at the same time for training. Input the parameter values ​​and corresponding graphs at the same time into the second spatiotemporal graph neural network. The second spatiotemporal graph neural network outputs the predicted single-cell voltage. Calculate the loss function to train the second spatiotemporal graph neural network and obtain the second spatiotemporal graph neural network model.

[0017] Furthermore, the corresponding graph is a graph composed of individual cells as nodes and the connection relationships between individual cells as edges, with the nodes connected sequentially from beginning to end.

[0018] Furthermore, the local Shapley value of the sample is:

[0019]

[0020] Where f represents the spatiotemporal graph neural network model, F is the set of all input features, and |F| is the magnitude of F; {x ′ 1,…,x ′ n} are variables that need to be explained; S refers to the input of the spatiotemporal graph neural network model, indicating that F does not contain a subset of features i; f(S) refers to the voltage prediction value of the model when input S;

[0021] Where S is the voltage data of a single cell removed, the local Shapley value corresponding to that voltage data is obtained; at this time, f(SU{x′) i}) represents the first predicted voltage value;

[0022] When S is parameter data with one parameter removed, the local Shapley value corresponding to that parameter data is obtained; at this time, f(S∪{x′) i}) represents the second voltage prediction value.

[0023] Furthermore, the global Shapley value is:

[0024]

[0025] in, is the local Shapley value of feature i in sample j, and N is the total number of samples.

[0026] Furthermore, the actual parameter data is obtained by estimating parameters based on the actual polarization curve measurement results of each single cell during the durability test and the single cell voltage model.

[0027] Furthermore, the parameter data includes current density, open-circuit voltage, ohmic resistance, constants related to electron transport coefficient, exchange current density, and limiting current density.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] This invention establishes the relationship between inter-cell output performance and inter-cell internal parameters and output performance during the decay process using a spatiotemporal graph neural network. Combined with interpretable artificial intelligence to interpret the relationships established by machine learning, it comprehensively analyzes the inter-cell mutual influence during the fuel cell stack decay process. This allows for the identification of individual cells and internal parameters that significantly affect the output performance of a single cell, which helps improve the structural design and control strategies of fuel cells, enabling them to operate better within a suitable operating range. This, in turn, enhances the performance and durability of fuel cells. Furthermore, the parameters used in this invention are from a decay dataset and do not affect the normal operation of the fuel cell stack. Attached Figure Description

[0030] Figure 1 This is a flowchart of the present invention;

[0031] Figure 2 This is a schematic diagram of the variable load conditions of the present invention;

[0032] Figure 3 Output the dynamic SHAP graph affected by the No. 8 battery, where Figure 3 (a) shows the impact of the historical voltage of battery No. 8 on the current voltage. Figure 3 (b) shows the impact of the historical voltage of batteries 6 and 7 on the current situation; Figure 3 (c) represents the impact of the historical voltage of batteries 9 and 10 on the current voltage. Figure 3 (d) is a graph showing the voltage of battery No. 8 changing over time. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0034] This invention, without compromising the normal operation of the fuel cell stack, proposes an evaluation method for the inter-cell interaction during the fuel cell stack degradation process. This method combines Spatiotemporal Graph Neural Network (ST-GNN) and Explainable Artificial Intelligence (XAI) techniques to capture the impact of adjacent cell output performance and their internal parameters on the individual cell's output performance. By analyzing fuel cell stack durability test data, the main factors affecting the output performance of individual cells and their corresponding internal parameters can be identified. This provides a reliable basis for optimizing fuel cell stack control strategies, improving structural design, and selecting optimal operating conditions. This invention establishes the relationship between inter-cell output performance and inter-cell internal parameters and output performance during the degradation process using a spatiotemporal graph neural network. It then combines this with Explainable Artificial Intelligence to interpret the relationships established by machine learning, identifying the individual cells and internal parameters that significantly influence the output performance of a single cell. The flowchart of the proposed method is shown below. Figure 1 As shown. The method of the present invention includes the following steps:

[0035] S1. Obtain actual voltage data and actual parameter data, wherein the voltage data is the single cell voltage of multiple single cells at multiple times, and the parameter data is the parameter values ​​at the same time.

[0036] S2. Input the voltage data into the first spatiotemporal neural network model to obtain the first voltage prediction value;

[0037] S3. Input the parameter data into the second spatiotemporal neural network model to obtain the second voltage prediction value;

[0038] S4. Using the SHAP analysis method, based on the first voltage prediction value and the second voltage prediction value, the local Shapley values ​​of multiple samples corresponding to the two voltage prediction values ​​are obtained. Based on the local Shapley values ​​of multiple samples, the global Shapley values ​​corresponding to the two voltage prediction values ​​are calculated to obtain the spatiotemporal correlation between the single cell voltage and each parameter and the output voltage of each single cell.

[0039] The parameter data of this invention include current density, open-circuit voltage, ohmic resistance, constants related to electron transport coefficient, exchange current density, and limiting current density.

[0040] The actual parameter data are obtained by estimating parameters based on the actual polarization curve measurements of each single cell during the durability test and the single cell voltage model. The specific steps for parameter estimation are as follows:

[0041] A model for the variation of single-cell output voltage with current density i is derived theoretically:

[0042]

[0043] Among them, V cell It is the single-cell voltage (V); i is the current density (A / cm2); E OCV R0 is the open-circuit voltage (V); a and b are constants related to the electron transport coefficient; T is the temperature (K); i0 is the exchange current density (A / cm2); i L It is the limiting current density (A / cm2).

[0044] Based on the measurement results of the polarization curves of each cell in the fuel cell stack during the durability test, and based on the single cell voltage model, the time-varying parameters in the model are identified, and the internal parameters of each cell as the fuel cell stack decays are estimated.

[0045] In S2 and S3 of this invention, the spatiotemporal graph neural network T-GCN acquires and retains temporal information by utilizing a gated recurrent unit (GRU) structure on a graph convolutional network. It can fully leverage the historical information and spatiotemporal dependencies of the input variables. Each T-GCN unit consists of a graph convolutional network and a gated recurrent unit. First, using spatially correlated data from multiple past time points as input, the graph convolutional network extracts the spatial relationships between nodes at each time point. Second, the obtained time series with spatial features is input into the gated recurrent unit, and the dynamic changes of the time series are obtained through information transfer between units, capturing temporal features.

[0046] In this invention, the training process of the first spatiotemporal graph neural network model is as follows:

[0047] The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are obtained for training. The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are input into the first spatiotemporal graph neural network. The first spatiotemporal graph neural network outputs the predicted single-cell voltages. The loss function is calculated to train the first spatiotemporal graph neural network, and the first spatiotemporal graph neural network model is obtained.

[0048] The training process of the second spatiotemporal graph neural network model is as follows:

[0049] Obtain the parameter values ​​and corresponding graphs at the same time for training. Input the parameter values ​​and corresponding graphs at the same time into the second spatiotemporal graph neural network. The second spatiotemporal graph neural network outputs the predicted single-cell voltage. Calculate the loss function to train the second spatiotemporal graph neural network and obtain the second spatiotemporal graph neural network model.

[0050] Based on the experimental results of the fuel cell stack under durability testing, the current density of the stack, the output voltage of each cell, and the internal parameters of each cell are estimated. Based on the spatiotemporal graph neural network, the spatiotemporal correlation between the output voltage and current density of each cell, the internal parameters of each cell, and the output voltage of each cell is established.

[0051] This invention utilizes the interpretable artificial intelligence method SHAP analysis to measure the marginal contribution of each feature in different combinations by calculating the average contribution (i.e., Shapley value) of each feature to the prediction. For a model f and a set of features S, the local Shapley value of feature i... Its focus is on the impact and importance of variables on individual observed samples, and the specific calculation formula is as follows:

[0052]

[0053] Where F is the set of all input features; |F| is the size of F; {x ′ 1,…,x ′ n} represents the variables that need to be explained, i.e., the input features; S refers to the subset of F that does not contain feature i; f(S) refers to the model's predicted value when input S.

[0054] The local Shapley values ​​calculated above are based on the first voltage prediction value and the second voltage prediction value, respectively. For the first voltage prediction value (f(S∪{x′)... i The model's input S is the voltage data after removing a single cell; the feature i is the voltage data of the removed single cell, and F is the voltage data of all single cells. The calculated local Shapley value is then the impact of removing that single cell.

[0055] For the second voltage prediction value (f(S∪{x′) i The model's input S is the parameter data after removing one parameter, specifically the parameters after removing current density, open-circuit voltage, ohmic resistance, constants related to electron transport coefficient, exchange current density, and limiting current density. Among these parameter data, current density is directly measured and not estimated. The feature i at this point is the parameter data after removing that parameter, and F represents all parameter data at the same time. The calculated local Shapley value is then the effect of the removed parameter.

[0056] The global Shapley score focuses on revealing the relationship between input features and output using the entire dataset. In this case, it is necessary to consider the model's input and output for each observation sample.

[0057]

[0058] in, is the Shapley value of feature i in sample j; N is the total number of samples. A sample represents data from different time periods. For single-cell voltages of multiple cells at multiple time points (t1~tn), the time period t1~tn is one sample, and t2~tn+1 is another sample. For each parameter value at the same time point, each time point corresponds to one sample.

[0059] The spatiotemporal correlation between the output voltage and current density of each individual cell, and the internal parameters of each individual cell and their output voltage, is established based on a spatiotemporal graph neural network. Based on interpretable artificial intelligence, the global contribution and the dynamic local contribution over time during the entire lifetime testing process are obtained. Then, taking the applied influencing parameters and the affected outputs as objects, the inter-cell influence is analyzed using Shapley contribution values.

[0060] Currently, most studies introduce artificial faults into normally operating fuel cell stacks and use direct comparison methods to observe the affected parameters, thereby analyzing the inter-cell impact. This invention, without affecting the normal operation of the fuel cell stack, utilizes spatiotemporal graph neural networks and interpretable artificial intelligence to analyze how the output performance of a single cell is affected by the output of adjacent cells and internal parameters during fuel cell stack degradation. By analyzing fuel cell stack durability test data, we can identify the cells that have a significant impact on the output performance of individual cells and their corresponding internal parameters. This method helps improve the structural design and control strategies of fuel cells, enabling them to operate better within a suitable operating range, thereby improving fuel cell performance and durability. Therefore, this invention is of great significance to the development of fuel cell technology.

[0061] The following detailed description of the inter-cell impact analysis method for the degradation process of a fuel cell stack proposed in this invention will be provided through a specific embodiment. This method evaluates the inter-cell output interaction during the degradation process of a fuel cell stack under variable load conditions, as well as the impact of internal parameters of adjacent cells on the output of a single cell.

[0062] First, durability testing is conducted to obtain the raw degradation dataset. This dataset should at least include the voltage of each cell in the fuel cell stack and the steady-state polarization curve data. The variable load conditions for the durability test are as follows: Figure 2As shown, the time for a single cycle is approximately 90 minutes. Subsequently, before model training, the data is resampled, smoothed, and normalized. Furthermore, based on different evaluation requirements, node features are set for the spatiotemporal graph model using battery voltage, current density, and internal parameter estimates. In addition, the static graph structure should be set according to the actual connection configuration of each individual cell in the battery stack.

[0063] After setting the number of hidden layer neurons, loss function, and optimizer, the hyperparameters of the model are tuned using the training and test sets to ensure that the model can accurately reflect the relationship between input and output.

[0064] After model training, the SHAP method is further used to interpret the contribution of input features to the relationships established by the model. Based on the entire lifetime test data, the calculated SHAP contribution values ​​are used to evaluate the impact of each input feature on the output of a single cell from both global and dynamic perspectives. For example... Figure 3 As shown, a boost converter at around 0.75V significantly alters the impact of adjacent cells on the output of the observed cell. The contribution of the earlier-numbered cells to the SHAP value initially increases and then decreases, while the opposite is true for later-numbered cells. By summing the SHAP values ​​over time, a global contribution assessment can be obtained for the entire durability test.

[0065] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for evaluating the inter-cell interactions during the degradation process of a fuel cell stack, characterized in that, The method includes the following steps: S1. Obtain actual voltage data and actual parameter data, wherein the voltage data is the single cell voltage of multiple single cells at multiple times, and the parameter data is the parameter values ​​at the same time. S2. Input the voltage data into the first spatiotemporal neural network model to obtain the first voltage prediction value; S3. Input the parameter data into the second spatiotemporal neural network model to obtain the second voltage prediction value; S4. Using the SHAP analysis method, based on the first voltage prediction value and the second voltage prediction value, the local Shapley values ​​of multiple samples corresponding to the two voltage prediction values ​​are obtained. Based on the local Shapley values ​​of multiple samples, the global Shapley values ​​corresponding to the two voltage prediction values ​​are calculated to obtain the spatiotemporal correlation between the single cell voltage and each parameter and the output voltage of each single cell.

2. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 1, characterized in that, The first and second spatiotemporal graph neural network models are T-GCN networks.

3. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 2, characterized in that, The T-GCN network consists of two parts: a graph convolutional network and a gated recurrent unit.

4. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 3, characterized in that, The training process of the first spatiotemporal graph neural network model is as follows: The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are obtained for training. The single-cell voltages and corresponding graphs of multiple single cells at multiple time points are input into the first spatiotemporal graph neural network. The first spatiotemporal graph neural network outputs the predicted single-cell voltages. The loss function is calculated to train the first spatiotemporal graph neural network, and the first spatiotemporal graph neural network model is obtained.

5. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 3, characterized in that, The training process of the second spatiotemporal graph neural network model is as follows: Obtain the parameter values ​​and corresponding graphs at the same time for training. Input the parameter values ​​and corresponding graphs at the same time into the second spatiotemporal graph neural network. The second spatiotemporal graph neural network outputs the predicted single-cell voltage. Calculate the loss function to train the second spatiotemporal graph neural network and obtain the second spatiotemporal graph neural network model.

6. A method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 4 or 5, characterized in that, The corresponding graph is a graph in which each individual battery is a node and the connection relationship between individual batteries is an edge, and the nodes are connected end to end in sequence.

7. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 1, characterized in that, The local Shapley value of the sample is: in, Let F represent the spatiotemporal graph neural network model, where F is the set of all input features, and |F| is the magnitude of F. These are the variables that need to be explained; S refers to the input of the spatiotemporal graph neural network model, indicating that F does not contain features. A subset of; This refers to the voltage prediction value of the model when input S is applied; Where S is the voltage data of a single cell removed, the local Shapley value corresponding to that voltage data is obtained; at this time... This is the first predicted voltage value; When S is parameter data with one parameter removed, the local Shapley value corresponding to that parameter data is obtained; at this time... This is the second predicted voltage value.

8. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 7, characterized in that, The global Shapley value is: in, It is a sample j Chinese characteristics i The local Shapley value, where N is the total number of samples.

9. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 1, characterized in that, The actual parameter data are obtained by estimating parameters based on the actual polarization curve measurement results of each single cell during the durability test and the single cell voltage model.

10. The method for evaluating the inter-cell interaction during the degradation process of a fuel cell stack according to claim 9, characterized in that, The parameter data includes current density, open-circuit voltage, ohmic resistance, constants related to electron transport coefficient, exchange current density, and limiting current density.

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