A fuel cell stack fault locating method based on magnetic field data

Abstract

The present application relates to the technical field of fuel cell fault diagnosis, in particular to a fuel cell stack fault positioning method based on magnetic field data, comprising the following steps: data preprocessing; Bootstrap enhanced random forest feature selection; mutual information feature selection; parameter optimized random forest training; OOB error guided integration; beneficial effects are: through the double feature selection mechanism, the global and local features are fused, and the magnetic field features with high positioning ability are effectively identified.More importantly, the selected features are highly consistent with the electrochemical mechanism, and have clear physical interpretability, thereby improving the efficiency and reliability of the model.

Description

Technical Field

[0001] This invention relates to the field of fuel cell fault diagnosis, specifically a method for locating fuel cell stack faults based on magnetic field data. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs), as key components in hydrogen energy conversion, have shown great promise in applications such as vehicle propulsion, distributed power generation, and portable power supplies. However, in actual operation, PEMFC stacks are prone to failures such as membrane dryness, flooding, and gas starvation, which seriously affect their durability and reliability. Therefore, to ensure the safety and efficiency of PEMFC stack operation, it is crucial to conduct accurate fault diagnosis and locate faulty individual cells.

[0003] Fault diagnosis of PEMFC stacks can be classified based on various physical signals, such as voltage, electrochemical impedance spectroscopy (EIS), temperature, current density, and magnetic field. Among these, voltage, as the parameter most directly reflecting the electrical performance of the fuel cell, has become a hot research topic in online fault diagnosis. Compared to voltage, EIS and temperature better reflect the internal operating state of the PEMFC stack and are therefore widely used as key parameters in fault diagnosis. Furthermore, according to the Butler-Volmer equation, the current density within the PEMFC directly determines its electrochemical performance; therefore, current density is also an important signal for fault detection. According to the Biot-Savart law, changes in current density caused by faults within the PEMFC will result in measurable anomalies in its external magnetic field. Current research has verified the feasibility of fault detection based on magnetic field signals. In {Li Z, Cadet C and Outbib R. Diagnosis for PEMFC Based on Magnetic Measurements and Data-Driven Approach. IEEE Transactions on Energy Conversion, 2019, 34, 964-972}, Li et al. developed an array of 30 magnetic sensors surrounding the stack, reconstructing the internal current density through an external magnetic field to identify in-stack faults; in {Akimoto Y and Okajima K. Experimental Study of Non-Destructive Approach on PEMFC Stack Using Tri-Axis Magnetic Sensor Probe. Journal of Power and Energy Engineering, 2015, 03, 1-8}, Akimoto et al. inserted triaxial magnetic sensors into the in-stack cooling channels to measure the magnetic field and identify the operating status.

[0004] In summary, although fault diagnosis has become a key focus of fuel cell research, there is still a lack of highly feasible and accurate fault location methods for engineering practice. While voltage signals are easy to acquire, large-scale PEMFC systems require wiring and electrical connections between multiple cells, resulting in complex system structures and potential reliability issues. EIS and temperature, while reflecting the overall operating status, are insufficient to reveal detailed information about individual cells within the stack. Current density measurement allows for monitoring and analysis of individual cell behavior, but often requires modifications to the stack structure, leading to high costs and limited practical applicability. Existing magnetic field diagnostic research struggles to achieve real-time acquisition of magnetic field information for all cells within the stack. For example, existing magnetic sensor arrays require movement around the outside of the stack to measure the magnetic field distribution around each cell; similarly, existing technologies require moving magnetic probes from the cathode side of one cell to another to obtain individual cell magnetic field data. These methods are complex and time-consuming in practical applications, making it difficult to simultaneously acquire magnetic field information for all cells within the stack, thus becoming a key equipment bottleneck restricting the construction of online fault location systems for PEMFCs. Furthermore, magnetic field-based fault location still faces significant challenges in data processing. Different fault types generate relatively similar magnetic field signals at the same location within the stack, making it difficult to simultaneously classify fault types and locate faults. Summary of the Invention

[0005] The purpose of this invention is to provide a method for locating fuel cell stack faults based on magnetic field data, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for fault location of a fuel cell stack based on magnetic field data, comprising the following steps:

[0007] Step 1: Data preprocessing;

[0008] Step 2: Bootstrap-enhanced random forest feature selection;

[0009] Step 3: Mutual information feature selection;

[0010] Step 4: Random forest training with parameter optimization;

[0011] Step 5: OOB error boot integration.

[0012] Preferably, the data preprocessing step specifically includes:

[0013] The characteristic vector of the magnetic field strength measured around the fuel cell stack is Z-score normalized to eliminate the dimensional differences of the magnetic field strength at different locations and directions, so that the mean of all characteristics is 0 and the standard deviation is 1.

[0014] Preferably, the Bootstrap-enhanced random forest feature selection step specifically includes:

[0015] A random subspace strategy is applied to randomly extract a subset of features from the feature space, and a multiple bootstrap sampling method is used to improve the stability of feature importance assessment. By calculating the permutation importance of OOB samples, key points of magnetic field distribution with strong distinguishing ability for different fault states of the fuel cell stack are identified.

[0016] Preferably, the mutual information feature selection step specifically includes:

[0017] The mutual information between magnetic field features and state labels that were not evaluated during the Bootstrap-enhanced random forest feature selection phase was calculated to discover magnetic field feature points that are highly correlated with different fault types such as flooding, membrane dryness, and gas starvation, while also identifying the specific battery location where the fault occurred.

[0018] Preferably, the parameter-optimized random forest training steps include:

[0019] An adaptive feature dimension control strategy is adopted to select the most important feature subset based on the number of samples, ensuring that the number of selected features matches the number of samples. The final feature set is formed by merging features selected by two methods: Bootstrap-enhanced random forest feature selection and mutual information feature selection.

[0020] Preferably, the OOB error booting integration steps specifically include:

[0021] After training a random forest model based on selected features, the out-of-bounds error rate is calculated. When the error rate exceeds a preset threshold, a second targeted random forest is trained, which assigns higher weights to misclassified samples. Finally, the output of the two models is predicted by weighted ensemble.

[0022] Preferably, the method further includes constructing simulation and experimental datasets to verify fault location performance:

[0023] The simulation dataset is designed to simulate various operating conditions and different faults occurring on single cells at different locations, and Gaussian white noise is added to simulate real-world interference; the experimental dataset is obtained through actual data collection and is used to verify the fault diagnosis capability and practicality of the method.

[0024] Preferably, in the step of constructing the simulation and experimental dataset:

[0025] The simulation dataset has multiple nodes configured on the side of the fuel cell stack to collect magnetic field data, and multiple samples are generated for each operating condition. The experimental dataset starts collecting data after the fuel cell stack stabilizes, and data is collected continuously multiple times for each state. The experiment is repeated multiple times to obtain sufficient samples.

[0026] Preferably, the method further includes a performance evaluation step:

[0027] The accuracy of the model is compared with that of other mainstream machine learning methods in terms of accuracy and training and prediction costs, thus verifying the superiority and robustness of the proposed method.

[0028] Preferably, the method is applicable to in-situ and online monitoring scenarios of proton exchange membrane fuel cell stacks:

[0029] By extracting physically interpretable features to reflect electrochemical behavior, accurate identification and location of internal faults in the fuel cell stack can be achieved, thereby improving the durability and reliability of the fuel cell stack.

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] The proposed method for fault localization of fuel cell stacks based on magnetic field data utilizes a dual-feature selection mechanism to fuse global and local features, effectively identifying magnetic field features with high localization capabilities. More importantly, the selected features are highly consistent with the electrochemical mechanism, possessing clear physical interpretability, thereby improving the model's efficiency and reliability.

[0032] Compared with traditional models (such as CNN, LSTM, RF, and KNN), EDFS-RF demonstrates superiority in both fault location accuracy and computational efficiency. This method not only reduces feature dimensionality and enhances model stability but also captures both global and local fault-related features simultaneously. While ensuring high location accuracy and low computational cost, EDFS-RF also exhibits strong robustness, making it suitable for real-time fault diagnosis and precise location at the single-cell level in fuel cell stacks. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method of the present invention;

[0034] Figure 2 This is a confusion matrix diagram of a typical experiment under different simulation training sample sizes of the present invention;

[0035] Figure 3 This is a confusion matrix diagram of a typical experiment under different experimental training sample sizes of the present invention.

[0036] Figure 4 This is a confusion matrix diagram of different models of the present invention for a typical experiment of simulation data;

[0037] Figure 5 This is a confusion matrix diagram of a typical experiment using different models of the present invention for experimental data. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the present invention clear and complete, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some, not all, embodiments of the present invention, and are merely illustrative of the embodiments of the present invention. They are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1: This invention provides a technical solution: a method for locating faults in a fuel cell stack based on magnetic field data, comprising the following steps:

[0040] First, the magnetic field data is Z-score normalized to eliminate dimensional differences in magnetic field strength at different locations and directions:

[0041] (1)

[0042] in and These are the mean and standard deviation vectors of the magnetic field features, respectively. Standardization makes all features have a mean of 0 and a standard deviation of 1, thus allowing magnetic field data from sensors at different locations to be compared on the same scale, providing a fair evaluation basis for subsequent feature selection.

[0043] The core of the EDFS-RF method is a dual feature selection strategy, which combines two complementary feature evaluation methods. The first is Bootstrap-enhanced Random Forest feature selection, which focuses on identifying magnetic field feature points that contribute the most to the overall classification. Considering the high-dimensionality of the electric pile magnetic field data, directly calculating the importance of all features would be computationally intensive. Therefore, a random subspace strategy is first applied to randomly extract a subset of features from the feature space:

[0044] (2)

[0045] in This is the minimum number of features to be randomly selected. To address the small sample size of the magnetic field data and improve the stability of feature importance assessment, a multiple bootstrap sampling method is employed.

[0046] (3)

[0047] in This refers to the number of Bootstrap samples, with each Bootstrap sample containing approximately 70% of the original training data.

[0048] (4)

[0049] in Indicates from A sample was randomly drawn with replacement from the sample. A set of indexes for each sample. It is a feature In the Random forest importance scores on each Bootstrap sample are calculated using the importance of the OOB samples permutation:

[0050] (5)

[0051] in It is the number of decision trees used. It is a feature In the A tree of Bootstrap samples The importance of the arrangement represents the increase in OOB error after the feature is randomly arranged. This process of selecting features through Bootstrap-enhanced random forest can identify key points of magnetic field distribution that have a strong ability to distinguish different fault states of the fuel cell stack.

[0052] The second approach is feature selection based on mutual information, which focuses on capturing the nonlinear relationship between magnetic field characteristics and stack states. For features not evaluated in the first stage, their mutual information with the state label is calculated:

[0053] (6)

[0054] Mutual information assessment can discover magnetic field feature points that are highly correlated with different fault types such as flooding, membrane dryness, and gas starvation, and it also has the ability to identify the specific battery location where the fault occurs.

[0055] Given the limited number of samples, EDFS-RF employs an adaptive feature dimension control strategy to ensure that the number of selected features matches the sample size.

[0056] (7)

[0057] in and These represent the minimum number of features selected from the feature sets after filtering using Bootstrap-enhanced Random Forest and mutual information-based feature selection, respectively. Selecting the subset of features with the highest importance:

[0058] (8)

[0059] The final feature set is formed by merging features selected by the two methods: This dual selection ensures that it includes both features that contribute significantly to the overall structure and local features that are highly relevant to specific fault types and locations, making it particularly suitable for the complex spatial characteristics of the stack's magnetic field distribution.

[0060] After training the random forest model based on selected features, EDFS-RF also introduces an ensemble optimization mechanism based on out-of-bounds (OOB) errors. This design addresses the problem of difficulty in distinguishing similar faults at different cell locations within the fuel cell stack. The OOB error rate is calculated as follows:

[0061] (9)

[0062] When the error rate exceeds a preset threshold, the system trains a second targeted random forest, assigning higher weights to misclassified samples to provide special attention to difficult-to-classify samples. The final prediction is obtained by weighted ensemble of the outputs of the two models.

[0063] (10)

[0064] (11)

[0065] in, These are the weights of the main model. and These are the predicted probability distributions of two random forest models. Predicted labels. It is the function that makes the final score function The category index that yields the maximum value This integration strategy significantly improves the ability to distinguish between similar fault states.

[0066] Compared to traditional random forests and other machine learning methods, EDFS-RF has significant advantages in processing electric stack magnetic field data. It mitigates the curse of dimensionality through feature selection, improves stability under small sample conditions through bootstrap enhancement, comprehensively captures the relationship between magnetic field distribution and fault states through complementary feature evaluation methods, and enhances the ability to identify difficult-to-distinguish samples through an OOB ensemble mechanism. More importantly, EDFS-RF significantly reduces computational resource requirements and training time while maintaining high recognition accuracy, making it more suitable for online monitoring applications of electric stacks.

[0067] Example 2, based on Example 1, proposes a method for fault location of fuel cell stacks based on magnetic field data, including the following steps:

[0068] 1. Dataset Construction

[0069] To validate the proposed method, two datasets were constructed based on a PEMFC stack simulation model and fault experiments. The simulation dataset included 12 operating conditions, simulating four types of faults occurring in single cells (cells #1, #2, and #3) at three different locations, along with one normal operating condition. Due to the model mesh setup, 409×34 nodes were configured on the side of the stack for collecting magnetic field data. Therefore, each sample consists of a 13906-dimensional feature vector, with 50 samples generated for each operating condition, resulting in a dataset of 650 samples (13×50). To eliminate environmental magnetic field interference, all data were corrected using a background magnetic field under zero current load. To better reflect real-world measurement scenarios, Gaussian white noise of varying intensities was added to the original simulation data, with signal-to-noise ratios (SNR) of 20, 30, and 40 dB. This noise-adding strategy simulates real-world environmental interference and sensor errors, thereby enhancing the robustness of the method.

[0070] In the experimental dataset, data was collected after the stack stabilized at a sampling frequency of 0.1 Hz. Data was collected continuously for 75 minutes under each condition, repeated five times, resulting in a total of 2250 samples. The raw data was first processed to remove environmental interference through magnetic field measurements under zero current load, followed by a moving average filter to reduce high-frequency noise. Each sample contains 16-dimensional magnetic field features, measured by a magnetic sensing array. Therefore, the simulation dataset is well-suited for evaluating the fault location performance of the EDFS-RF method. Due to limitations of actual experimental conditions, the experimental dataset cannot identify the location of specific faulty cells within the stack; therefore, it is used to verify the fault diagnosis capability of the proposed method. Furthermore, its sample distribution reflects actual operating conditions, which helps to evaluate the practicality and generalization ability of the proposed method. The simulation and experimental dataset results are as follows:

[0071] Table 1. Comparison of simulation and experimental datasets

[0072]

[0073] 2. Fault location accuracy verification

[0074] To evaluate the localization performance of EDFS-RF, different numbers of samples (200, 300, 400, and 500) were randomly selected from the simulated dataset as the training set, and the remaining samples were used as the test set. Each experiment was repeated 100 times to reduce the impact of randomness (the same method was used for the experimental dataset). Table 2 shows the localization accuracy of the proposed method on the simulated and experimental datasets. The results show that the accuracy continuously improves with the increase of the number of samples. Even using only 200 samples (approximately 27% of the simulated dataset), the method still achieves an accuracy of 87.7963%; when the training samples are expanded to 500, the accuracy increases to 96.6654%, indicating a significant enhancement in the stability and robustness of the model.

[0075] Table 2. Accuracy of the model with different sample sizes

[0076]

[0077] On the experimental dataset, even with only 400 training samples (approximately 3.5%), the method achieved an average accuracy of 94.4608%, demonstrating good adaptability under small sample learning conditions. When the number of training samples increased to 700, the localization accuracy further improved to 97.4475%. Figure 2 The results show that EDFS-RF can accurately identify various faults at different locations in the simulation data, with the accuracy of locating membrane dry faults approaching 100%. Although there are slight misjudgments between hydrogen and air depletion, the overall accuracy remains at a high level, further verifying the high efficiency of EDFS-RF in PEMFC reactor fault location.

[0078] from Figure 3 As can be seen, EDFS-RF also exhibits high fault identification accuracy in the experimental data, demonstrating its good generalization ability and strong adaptability. Sensor noise, environmental interference, and equipment fluctuations present in the real environment did not affect the performance of this method, further verifying its robustness in practical applications. Compared to the simulated data, the identification accuracy of the experimental data is slightly higher, which may be attributed to the more typical and clear fault modes in the experiment, thereby reducing model complexity and facilitating better generalization performance under small sample conditions.

[0079] 8.3 Performance Comparison

[0080] To further verify the superiority of the EDFS-RF method, it was compared with several mainstream machine learning methods, including Convolutional Neural Networks (CNN), Random Forests (RF), Long Short-Term Memory Networks (LSTM), and k-Nearest Neighbors (KNN). In each experiment, 300 samples were randomly selected from the simulation dataset as the training set, and the remaining samples were used for testing.

[0081] Table 3. Performance comparison results of different methods using simulation and experimental datasets.

[0082]

[0083] Table 3 summarizes the localization performance of different methods on simulation and experimental datasets. It can be seen that EDFS-RF significantly outperforms other methods in accuracy while maintaining low training and prediction costs. In the simulation dataset, although KNN has the shortest training time, its prediction time and accuracy are both unsatisfactory. CNN performs competitively, but its training time is more than five times that of EDFS-RF, and it requires more computational resources. While RF performs well in terms of computational efficiency, it lags behind EDFS-RF in localization accuracy, further highlighting the important role of the dual feature selection strategy.

[0084] Compared to the simulation dataset, the accuracy gap between the methods on the experimental dataset has narrowed, likely due to the lower dimensionality of the experimental data, which reduces processing complexity. However, EDFS-RF still demonstrates a significant advantage, particularly in achieving a better balance between prediction cost and recognition performance. Despite having the shortest training time, KNN's accuracy remains unsatisfactory. CNN performs reasonably well, but its training time is significantly longer than EDFS-RF, and it consumes more computational resources. While RF offers some advantages in computational efficiency, its lower accuracy further highlights the importance of a dual feature selection strategy. LSTM performs the worst among all methods.

[0085] Figure 4 The confusion matrices of various methods on the simulation dataset are compared. It can be seen that EDFS-RF performs more consistently across different fault localization scenarios, particularly excelling at distinguishing faults occurring in different locations but with similar characteristics. In contrast, other models show lower accuracy in identifying certain fault types, exhibiting a clear imbalance. Furthermore, from... Figure 5 As can be seen, all methods improved accuracy on the experimental dataset, with EDFS-RF showing the best overall performance and the strongest fault identification capability. CNN and LSTM performed reasonably well, but they risked overfitting with a limited number of samples, leading to unstable accuracy in some fault identification types; RF and KNN, on the other hand, had lower accuracy in identifying certain fault types.

[0086] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for fault location of fuel cell stacks based on magnetic field data, characterized in that: Includes the following steps: Step 1: Data preprocessing; Step 2: Bootstrap-enhanced random forest feature selection; Step 3: Mutual information feature selection; Step 4: Random forest training with parameter optimization; Step 5: OOB error boot integration; The data preprocessing steps specifically include: The characteristic vector of the magnetic field strength measured around the fuel cell stack is Z-score normalized to eliminate the dimensional differences of the magnetic field strength at different locations and directions, so that the mean of all characteristics is 0 and the standard deviation is 1. The Bootstrap-enhanced random forest feature selection step specifically includes: A random subspace strategy is applied to randomly extract a subset of features from the feature space, and a multiple bootstrap sampling method is used to improve the stability of feature importance assessment. The key points of magnetic field distribution with strong distinguishing ability for different fault states of the fuel cell are identified by calculating the permutation importance of OOB samples. The mutual information feature selection step specifically includes: The mutual information between magnetic field features and state labels that were not evaluated in the Bootstrap-enhanced random forest feature selection phase was calculated to discover magnetic field feature points that are highly correlated with different fault types such as flooding, membrane dryness and gas starvation, while identifying the specific battery location where the fault occurred. The random forest training steps for parameter optimization include: An adaptive feature dimension control strategy is adopted to select the most important feature subset based on the number of samples, ensuring that the number of selected features matches the number of samples. The final feature set is formed by merging features selected by two methods: Bootstrap-enhanced random forest feature selection and mutual information feature selection. The specific steps for integrating OOB error booting include: After training a random forest model based on selected features, the out-of-bounds error rate is calculated. When the error rate exceeds a preset threshold, a second targeted random forest is trained, which assigns higher weights to misclassified samples. Finally, the output of the two models is predicted by weighted ensemble.

2. The method for fault location of a fuel cell stack based on magnetic field data according to claim 1, characterized in that: The method also includes constructing simulation and experimental datasets to verify fault location performance: The simulation dataset is designed to simulate various operating conditions and different faults occurring on single cells at different locations, and Gaussian white noise is added to simulate real-world interference; the experimental dataset is obtained through actual data collection and is used to verify the fault diagnosis capability and practicality of the method.

3. The method for fault location of a fuel cell stack based on magnetic field data according to claim 2, characterized in that: In the step of constructing the simulation and experimental datasets: The simulation dataset has multiple nodes configured on the side of the fuel cell stack to collect magnetic field data, and multiple samples are generated for each operating condition; the experimental dataset starts collecting data after the fuel cell stack stabilizes, and data is collected continuously multiple times for each state, and the experiment is repeated multiple times.

4. The method for fault location of a fuel cell stack based on magnetic field data according to claim 3, characterized in that: The method also includes a performance evaluation step: The accuracy of the model is compared with that of other mainstream machine learning methods in terms of accuracy and training and prediction costs, to verify the superiority and robustness of the proposed method. Other mainstream machine learning methods include convolutional neural networks (CNN), random forests (RF), long short-term memory networks (LSTM), or k-nearest neighbors (KNN).

5. The method for fault location of a fuel cell stack based on magnetic field data according to claim 4, characterized in that: The method is applicable to both in-situ and online monitoring scenarios for proton exchange membrane fuel cell stacks. By extracting physically interpretable features to reflect electrochemical behavior, accurate identification and location of internal faults in the fuel cell stack can be achieved, thereby improving the durability and reliability of the fuel cell stack.

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