A method for estimating the health state of a proton exchange membrane fuel cell based on EIS prediction

Abstract

The present application belongs to the technical field of fuel cell health state estimation, and in particular to a proton exchange membrane fuel cell health state estimation method based on EIS prediction. The method comprises the following steps: S1: collecting proton exchange membrane fuel cell operation data and impedance spectrum data; S2: preprocessing the operation data; S3: establishing an EIS prediction model based on a time series neural network; S4: verifying the effectiveness of the impedance spectrum; S5: decomposing the effective impedance spectrum by using a DRT method; S6: extracting the polarization resistance characteristics corresponding to different polarization processes according to the relaxation time distribution function; S7: establishing a mapping model between the polarization resistance characteristics and the health state; and S8: online health state estimation. The present application solves the problems of great difficulty in obtaining and high cost in testing of electrochemical impedance spectroscopy in practical application, and improves the engineering application feasibility of the method in online or quasi-online health state monitoring of proton exchange membrane fuel cells.

Description

Technical Field

[0001] This invention relates to the field of fuel cell health status estimation technology, specifically a method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) possess advantages such as high energy conversion efficiency, low operating temperature, fast start-up speed, and environmental friendliness, making them promising candidates for applications in fuel cell vehicles, distributed power generation, and other clean energy systems. The core components of a PEMFC mainly include the membrane electrode assembly (MEA), gas diffusion layer, catalyst layer, and bipolar plates. Among these, the MEA has a significant impact on the fuel cell's output performance, operational stability, and lifespan.

[0003] However, proton exchange membrane fuel cells (PEMFCs) are typically not in ideal steady-state operation during actual operation. Instead, they are subject to the combined effects of various factors, including dynamic load changes, start-stop cycles, temperature and humidity fluctuations, and uneven gas transport. With increasing operating time, degradation phenomena such as membrane aging, catalyst activity decline, increased ohmic impedance, and decreased mass transfer performance easily occur within the fuel cell, leading to a decrease in stack output capacity, reduced efficiency, and a continuous decline in health. Therefore, accurately assessing the health status of PEMFCs has become an important research topic in the fields of fuel cell condition monitoring, lifespan prediction, and operation control.

[0004] In existing technologies, most fuel cell health status estimation methods are based on modeling and analysis of external operating parameters such as output voltage, current, and temperature. While these methods are relatively simple to implement, the external operating parameters mainly reflect the external response characteristics of the fuel cell and are difficult to comprehensively characterize internal electrochemical degradation processes such as membrane electrode aging, catalyst deactivation, and limited mass transfer. Therefore, under complex operating conditions, they often suffer from insufficient health status characterization and limited estimation accuracy.

[0005] Electrochemical impedance spectroscopy (EIS) can reflect various electrochemical processes within a fuel cell, such as ohmic polarization, charge transfer polarization, and mass transfer polarization, from a frequency domain perspective. It is highly sensitive to changes in material properties, interface states, and reaction kinetics. Compared to state estimation methods that rely solely on external operating parameters, EIS-based analysis can more effectively characterize the internal degradation features of fuel cells, thus possessing significant application value in the field of fuel cell health assessment.

[0006] However, existing EIS-based analysis methods still have certain limitations. On the one hand, traditional EIS testing typically relies on dedicated impedance testing equipment, which is complex, costly, and lacks real-time performance, making it difficult to directly meet the application requirements of online health status monitoring for fuel cells. On the other hand, the impedance spectrum of a fuel cell contains the superposition response of multiple polarization processes. These polarization processes at different time constants are coupled in the frequency domain. When using conventional feature extraction or equivalent circuit fitting methods, it is difficult to accurately distinguish the specific impact of each polarization process on fuel cell performance degradation, thus limiting the accuracy of health status estimation results and the ability to interpret mechanisms.

[0007] The relaxation time distribution method can decompose the mutually coupled polarization processes in the impedance spectrum within the time constant domain, which helps to identify the polarization resistance characteristics corresponding to different polarization processes. This provides a more refined characterization method for analyzing the internal degradation mechanism and assessing the health status of fuel cells. If the impedance spectrum information can be obtained by combining it with the EIS prediction method, and the polarization processes in the impedance spectrum can be further separated and characterized using the DRT method, it is expected to establish an effective mapping relationship between the health status of fuel cells and polarization resistance characteristics, thereby improving the accuracy and interpretability of health status estimation.

[0008] Therefore, in view of the problems existing in the fuel cell technology, such as insufficient characterization of internal degradation features, difficulty in obtaining EIS online, severe coupling of impedance spectrum polarization process, and limited accuracy and generalization ability of health status estimation, it is urgent to propose a proton exchange membrane fuel cell health status estimation method based on EIS prediction and DRT polarization resistance, so as to achieve accurate estimation of the health status of proton exchange membrane fuel cells. Summary of the Invention

[0009] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0010] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0011] A method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction includes the following steps:

[0012] S1: Collect operational data and impedance spectrum data of proton exchange membrane fuel cells at different operating stages to construct a sample dataset;

[0013] S2: Preprocess the runtime data and construct time-series input features;

[0014] S3: Establish an EIS prediction model based on a time-series neural network to predict the impedance spectrum of the fuel cell. The prediction model includes any one of the following: a recurrent neural network model, a gated recurrent unit (GRU) model, a long short-term memory (LSTM) network model, or a time-series deep learning model with an attention mechanism.

[0015] S4: The validity of the impedance spectrum is verified using the Kramers-Kronig relationship and residual threshold; when the maximum relative residual does not exceed the preset threshold, the impedance data is considered to meet the requirements of subsequent DRT analysis.

[0016] S5: The effective impedance spectrum is decomposed using the DRT method to obtain the relaxation time distribution function. The DRT method treats the electrochemical system as an ohmic resistor connected in series with an infinite number of ideal R / / C units, and obtains the relaxation time distribution function by deconvolution, thereby realizing the decoupled characterization of each polarization process.

[0017] S6: Extract the polarization resistance characteristics corresponding to different polarization processes based on the relaxation time distribution function;

[0018] S7: Establish a mapping model between polarization resistance characteristics and health status;

[0019] S8: Online health status estimation: First, the current operating parameters of the fuel cell are collected in real time; then, the operating parameters are input into the EIS prediction model to obtain the predicted impedance spectrum under the current state; then, the validity of the predicted impedance spectrum is checked, and the polarization resistance characteristics are extracted using the DRT method; finally, the polarization resistance characteristics are input into the health status estimation model to output the current fuel cell health status estimate.

[0020] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the operating data in S1 includes output voltage, output current, output power, temperature, pressure, flow rate, operating time, and load change information; the above operating data is aligned with the electrochemical impedance spectroscopy data at the corresponding time points, and combined with pre-set health status labels to construct a sample database; the fuel cell health status SOH is expressed in a normalized form, i.e.:

[0021]

[0022] in, These are the characterization parameters of the fuel cell at the current moment. These are the characterization performance parameters corresponding to the initial state of the fuel cell.

[0023] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the preprocessing step S2 includes outlier removal, missing value completion, smoothing and denoising, normalization, and time-series window reconstruction. The input sequence is constructed using a time window approach, specifically as follows: Let the input feature vector at a certain time t be:

[0024]

[0025] in, These represent the operating parameters of voltage, current, temperature, pressure, and flow rate at time t, respectively.

[0026] Construct an input sequence of length L:

[0027]

[0028] This is used to characterize the dynamic operating characteristics of fuel cells over a period of time and to serve as input for the EIS prediction model.

[0029] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the basic update process of the gated recirculation unit (GRU) model in S3 is expressed as follows:

[0030]

[0031]

[0032]

[0033]

[0034] in, To update the door, To reset the door, It is in a hidden state. The sigmoid activation function is used, and ⊙ represents the Hadamard product;

[0035] Based on the hidden state, the real and imaginary parts of the impedance corresponding to each frequency point within the target frequency range are output, that is:

[0036]

[0037] in,

[0038]

[0039] The angular frequency corresponding to the k-th frequency point. and These are the real and imaginary parts of the predicted impedance, respectively.

[0040] During model training, mean squared error is used as the loss function:

[0041]

[0042] in, and These are the real and imaginary parts of the measured impedance, respectively.

[0043] In a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the relative residual of the predicted impedance spectrum in S4 is expressed as follows:

[0044]

[0045] in, The impedance spectrum to be tested. The reference impedance value is obtained by fitting the model; if

[0046]

[0047] Then the impedance spectrum is determined to meet the validity requirements, where This is a preset threshold.

[0048] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health state estimation method described in this invention, the relationship between the fuel cell impedance and the relaxation time distribution function in step S5 is expressed as follows:

[0049]

[0050] in, For ohm resistance, Let τ be the relaxation time distribution function, τ be the relaxation time constant, and ω be the angular frequency.

[0051] Discretizing the continuous distribution, we can write it as:

[0052]

[0053] in, The distribution coefficient to be determined is... For discrete-time constant nodes, n is the number of relaxor elements;

[0054] Introducing an L2 regularization term into the cost function, we get:

[0055] Where x is the distribution coefficient vector to be determined, A is the coefficient matrix, λ is the regularization parameter, and L is the smoothing constraint matrix.

[0056] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the specific method of S6 is as follows: Charge transfer-related polarization resistance, mass transport-related polarization resistance, proton conduction resistance, and polymer membrane interface contact resistance are used as important characteristic parameters for the quantitative analysis of fuel cell health status; for the i-th polarization process, its corresponding polarization resistance is obtained by integrating the relaxation time distribution function within the corresponding time constant interval.

[0057]

[0058] in, This represents the time constant interval corresponding to the i-th polarization process;

[0059] Therefore, the polarization resistance eigenvector is constructed as follows:

[0060]

[0061] in, For ohm resistance, These are the polarization resistances corresponding to different polarization processes.

[0062] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the health status estimation model in S7 is expressed as follows:

[0063]

[0064] in, The health status mapping function can be implemented using a linear regression model, support vector regression model, random forest model, neural network model, or deep learning model.

[0065] By using polarization resistance characteristics and partial impedance spectrum characteristics as inputs, an enhanced health state estimation model is constructed, namely:

[0066]

[0067] in, These are the selected impedance spectrum characteristic parameters;

[0068] The following loss function is used during model training:

[0069]

[0070] in, This represents the true health status of the i-th sample. To estimate health status.

[0071] As a preferred embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method described in this invention, the online estimation process in S8 is expressed as follows:

[0072]

[0073] in, These are the current running parameters. To predict the impedance spectrum, This represents the current polarization resistance characteristics. This is an estimate of the health status at the current moment.

[0074] Compared with the prior art, the beneficial effects of this invention are: 1. By constructing an EIS prediction model based on operating parameters, this invention realizes the prediction and acquisition of electrochemical impedance spectroscopy of fuel cells, reduces the dependence of traditional EIS testing on special equipment and offline testing conditions, and solves the problems of high difficulty in obtaining electrochemical impedance spectroscopy and high testing cost in practical applications, thereby improving the feasibility of this method in the engineering application of online or quasi-online health status monitoring of proton exchange membrane fuel cells.

[0075] 2. By combining the predicted EIS with the DRT method, this invention can decouple and analyze the polarization processes coupled under different time constants in the impedance spectrum of a fuel cell, extract key characteristic parameters such as polarization resistance, thereby enhancing the characterization ability of the internal degradation mechanism of the fuel cell and improving the accuracy and mechanism interpretation of the health status estimation results.

[0076] 3. This invention organically combines EIS prediction, DRT polarization resistance extraction, and health status estimation to form a complete technical solution that takes into account linearity, accuracy, and interpretability. It can more comprehensively reflect the health status changes of fuel cells during dynamic degradation, and provide more reliable technical support for subsequent life assessment, condition monitoring, and operation control. Attached Figure Description

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0078] Figure 1 This is a technical framework diagram of a proton exchange membrane fuel cell health status estimation method based on EIS prediction according to the present invention.

[0079] Figure 2This is a schematic diagram of the EIS-GRU model structure of a proton exchange membrane fuel cell health status estimation method based on EIS prediction according to the present invention.

[0080] Figure 3 In this embodiment of the proton exchange membrane fuel cell health status estimation method based on EIS prediction of the present invention, the current density is 0.3 A∙cm⁻¹. -2 Plots of EIS forecast results ((a) Nyquist plot of EIS at hour 1392; (b) Nyquist plot of EIS at hour 1440).

[0081] Figure 4 The figure shows the impedance spectrum characteristics and Lin–KK consistency test results in an embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method of the present invention (a) 0.3 A·cm. 2 (a) Nyquist plot at the operating point; (b) corresponding Lin-KK verification result plot).

[0082] Figure 5 The graph shows the variation of polarization impedance of a fuel cell with endurance time at different current densities in an embodiment of the EIS-based proton exchange membrane fuel cell health status estimation method of the present invention (a) corresponding to 0.3 A·cm. -2 Current density; (b) corresponds to 0.9 A·cm -2 Current density; (c) corresponds to 1.6 A·cm -2 Current density). Detailed Implementation

[0083] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0084] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0085] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0086] This invention provides a method for estimating the health status of proton exchange membrane fuel cells based on EIS prediction. By modeling fuel cell operating data, the method achieves the prediction and acquisition of electrochemical impedance spectroscopy (EIS). Combined with the DRT method, the method decomposes and characterizes different polarization processes in the impedance spectrum, extracts polarization resistance characteristic parameters with clear physical meaning, and thus establishes an effective mapping relationship between the fuel cell health status and impedance characteristics, thereby improving the accuracy and interpretability of health status estimation.

[0087] This invention overcomes the difficulties of online acquisition in traditional EIS methods and the insufficient characterization of internal degradation in existing health status estimation methods. By combining EIS prediction results with DRT polarization resistance analysis, it reduces the dependence on measured impedance testing while effectively extracting and analyzing the internal degradation characteristics of fuel cells, thereby improving the adaptability and practicality of the method in complex operating conditions and engineering application scenarios.

[0088] This invention improves the estimation accuracy, stability, and generalization ability of the proton exchange membrane fuel cell health status estimation model under different operating conditions, different aging stages, and different degrees of degradation, providing reliable technical support for fuel cell condition monitoring, fault diagnosis, life assessment, and subsequent operation control.

[0089] Specifically, this invention provides a method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction. This method takes measurable operating parameters during the operation of the proton exchange membrane fuel cell as input. First, it establishes a mapping relationship between operating parameters and electrochemical impedance spectroscopy (EIS) to predict the impedance spectrum of the fuel cell under its current operating state. Then, it verifies the validity of the predicted impedance spectrum and uses the relaxation time distribution (DRT) method to decompose the mutually coupled polarization processes in the impedance spectrum, extracting polarization resistance characteristics under different time constants. Finally, it establishes a mapping relationship between the polarization resistance characteristics and the state of health (SOH) of the fuel cell, achieving a quantitative estimate of the health status of the proton exchange membrane fuel cell. This technical route is consistent with the process of "establishing the coupling relationship between EIS and health status—constructing an EIS-GRU model—combining DRT polarization process analysis—completing quantitative analysis of health status."

[0090] The technical framework of this invention can be summarized as follows: Data acquisition module → Data preprocessing module → EIS prediction module → Impedance spectrum validity verification module → DRT decomposition module → Polarization resistance extraction module → Health status estimation module. (See technical framework diagram below.) Figure 1 As shown.

[0091] Specifically, the steps include the following:

[0092] S1: Operational Data Acquisition and Sample Construction: First, operational data and corresponding impedance spectroscopy data of the proton exchange membrane fuel cell (PEMFC) at different operational stages are collected. Operational data includes, but is not limited to, output voltage, output current, output power, temperature, pressure, flow rate, operating time, and load variation information. The above operational data is aligned with the corresponding electrochemical impedance spectroscopy data and combined with pre-defined health status labels to construct a sample database for subsequent training and validation of the EIS prediction model and health status estimation model.

[0093] In this invention, the fuel cell health state (SOH) can be represented in a normalized form, namely:

[0094]

[0095] in, These are the characterization parameters of the fuel cell at the current moment. These are the performance parameters characterizing the fuel cell in its initial state. These parameters can be the maximum output power, rated operating voltage, characteristic impedance, or other performance quantities that reflect the degree of fuel cell degradation. This definition method is suitable for uniformly mapping the healthy state to the 0-1 range, facilitating subsequent modeling and comparison.

[0096] S2: Data Preprocessing and Feature Construction: Since the collected operational data and impedance spectral data may contain noise, outliers, and dimensional inconsistencies, preprocessing is necessary before model construction. The preprocessing process includes outlier removal, missing value completion, smoothing and denoising, normalization, and temporal window reconstruction to improve sample consistency and model input quality.

[0097] To enhance the model's ability to express the decay evolution pattern, this invention preferably uses a time window approach to construct the input sequence. Let the input feature vector at a certain time t be:

[0098]

[0099] in, Let represent the operating parameters such as voltage, current, temperature, pressure, and flow rate at time t, respectively. Further, an input sequence of length L can be constructed:

[0100]

[0101] This is used to characterize the dynamic operating characteristics of fuel cells over a period of time and to serve as input for the EIS prediction model.

[0102] S3: Construction of EIS Prediction Model Based on Time-Sequence Neural Network: To overcome the problems of high testing cost, poor real-time performance, and difficulty in online application of traditional EIS testing, this invention establishes an EIS prediction model based on time-series neural network, which directly predicts the corresponding impedance spectrum based on fuel cell operating data. The EIS-GRU model is used to predict the real and imaginary parts of the impedance during the fuel cell degradation process, and the model's good generalization ability and prediction accuracy are verified. Specific results are as follows: Figure 2 As shown.

[0103] The EIS prediction model uses a gated recurrent unit (GRU) network, and its basic update process can be expressed as follows:

[0104]

[0105]

[0106]

[0107]

[0108] in, To update the door, To reset the door, It is in a hidden state. is the Sigmoid activation function, and ⊙ represents the Hadamard product.

[0109] Based on the hidden state, the real and imaginary parts of the impedance at each frequency point within the target frequency range can be output, that is:

[0110]

[0111] in,

[0112]

[0113] The angular frequency corresponding to the k-th frequency point. and These are the real and imaginary parts of the predicted impedance, respectively.

[0114] During model training, mean squared error can be used as the loss function:

[0115]

[0116] in, and These represent the real and imaginary parts of the measured impedance, respectively. By minimizing this loss function, the mapping from the running data to the impedance spectrum is learned.

[0117] S4: Validation of Predicted Impedance Spectrum: Since DRT analysis is essentially based on linear, causal, and time-invariant systems, it is necessary to determine whether the predicted impedance spectrum meets the corresponding conditions before performing DRT decomposition. The Kramers-Kronig relationship and residual threshold can be used to verify the validity of the impedance spectrum; when the maximum relative residual does not exceed the preset threshold, the impedance data can be considered to meet the requirements of subsequent DRT analysis.

[0118] In this invention, the relative residual of the predicted impedance spectrum can be expressed as:

[0119]

[0120] in, The impedance spectrum to be tested. This is the reference impedance value obtained through fitting the model. If...

[0121]

[0122] Then the impedance spectrum is determined to meet the validity requirements, where This is a preset threshold.

[0123] S5: Impedance Spectrum Decomposition Based on DRT Method: After obtaining the effective impedance spectrum, the DRT method is used to decompose the polarization processes at different time constants in the impedance spectrum. The DRT method treats the electrochemical system as an ohmic resistor connected in series with an infinite number of ideal R / / C units, and obtains the relaxation time distribution function by deconvolution, thereby achieving decoupled characterization of each polarization process.

[0124] The relationship between fuel cell impedance and relaxation time distribution function can be expressed as:

[0125]

[0126] in, For ohm resistance, Let τ be the relaxation time distribution function, τ be the relaxation time constant, and ω be the angular frequency.

[0127] To facilitate numerical solutions, the continuous distribution is discretized and can be written as follows:

[0128]

[0129] in, The distribution coefficient to be determined is... is the discrete-time constant node, and n is the number of relaxor elements.

[0130] Furthermore, to improve inversion stability, an L2 regularization term is introduced into the cost function, resulting in:

[0131] Where x is the distribution coefficient vector to be determined, A is the coefficient matrix, λ is the regularization parameter, and L is the smoothing constraint matrix. By solving the above optimization problem, the relaxation time distribution curve can be obtained, and then the polarization process corresponding to different time constant intervals can be identified.

[0132] S6: Polarization Resistance Feature Extraction: Based on the DRT distribution results, peak values ​​within different time constant ranges can be identified, and corresponding polarization resistance features can be extracted. Charge transfer-related polarization resistance, mass transport-related polarization resistance, proton conduction resistance, and polymer membrane interface contact resistance are used as important feature parameters for the quantitative analysis of fuel cell health status.

[0133] For the i-th polarization process, the corresponding polarization resistance can be obtained by integrating the relaxation time distribution function over the corresponding time constant interval:

[0134]

[0135] in, Let be the time constant interval corresponding to the i-th polarization process.

[0136] Therefore, the polarization resistance eigenvector can be constructed:

[0137]

[0138] in, For ohm resistance, This represents the polarization resistance corresponding to different polarization processes. This eigenvector can characterize the changes in the internal electrochemical processes of a fuel cell under different decay stages.

[0139] S7: Construction of a Health State Estimation Model Based on Polarization Resistance Characteristics: After obtaining the polarization resistance characteristics, a mapping model between the polarization resistance characteristics and the health state of the fuel cell is established. The EIS and DRT distributions show significant differences under different degradation states. Utilizing the variation law of polarization resistance, the electrochemical reaction processes and degradation behavior at various frequency bands during the dynamic degradation process of the fuel cell can be quantitatively characterized.

[0140] The health status estimation model can be expressed as:

[0141]

[0142] in, The health status mapping function can be implemented using a linear regression model, support vector regression model, random forest model, neural network model, or deep learning model.

[0143] Furthermore, polarization resistance characteristics and partial impedance spectrum characteristics can be used together as input to construct an enhanced health state estimation model, namely:

[0144]

[0145] in, These are the selected impedance spectrum characteristic parameters.

[0146] The following loss function can be used during model training:

[0147]

[0148] in, This represents the true health status of the i-th sample. To estimate health status.

[0149] S8: Online health status estimation process: After the model training is completed, in the actual application process, the current operating parameters of the fuel cell are first collected in real time; then the operating parameters are input into the EIS prediction model to obtain the predicted impedance spectrum under the current state; then the effectiveness of the predicted impedance spectrum is checked, and the polarization resistance features are extracted using the DRT method; finally, the polarization resistance features are input into the health status estimation model to output the current fuel cell health status estimate.

[0150] The online estimation process can be represented as:

[0151]

[0152] in, These are the current running parameters. To predict the impedance spectrum, This represents the current polarization resistance characteristics. This is an estimate of the health status at the current moment.

[0153] Example 1

[0154] This embodiment provides a method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction and DRT polarization resistance. The method first establishes the coupling relationship between electrochemical impedance spectroscopy and the fuel cell health status; then, it combines fuel cell EIS data with a deep learning neural network to construct an EIS-GRU health status estimation model; next, it verifies the effectiveness of the model's prediction results; finally, it uses the DRT method to decouple and analyze the polarization process at different decay stages, thereby achieving a quantitative assessment of the fuel cell health status.

[0155] The basic data used in this embodiment comes from the fuel cell dynamic operating condition durability test. To simulate the dynamic cyclic operating conditions in vehicles, the FC-DLC operating condition was improved, and a 1488-hour durability test was conducted on a single fuel cell using the improved FC-DLC operating condition. At the same time, an accelerated degradation durability test under vehicle operating conditions was also conducted using an 85kW vehicle fuel cell stack, providing basic data support for subsequent health status estimation and impedance analysis.

[0156] This embodiment includes the following steps.

[0157] I. Operational Data and EIS Sample Construction

[0158] During fuel cell durability testing, operating parameters and corresponding electrochemical impedance spectroscopy (EIS) data were collected at different durability stages. The operating parameters included output voltage, output current, operating time, and DC bias conditions during impedance testing; the impedance spectroscopy data included frequency, real part of impedance, and imaginary part of impedance. To establish the mapping relationship between fuel cell degradation stages and impedance characteristics, durability time, impedance test frequency, and DC bias were used as input features, and the real and imaginary parts of impedance were used as output targets to construct an EIS prediction sample set.

[0159] To facilitate the quantification of health status, this embodiment defines the health status of a fuel cell as follows:

[0160]

[0161] in, The characteristic quantity representing the performance of the fuel cell at the current moment is... These are the characteristic quantities corresponding to the initial state. These characteristic quantities can be the maximum output power, rated operating voltage, or other performance parameters that reflect the degree of degradation.

[0162] II. Construction of EIS-GRU Prediction Model

[0163] Considering the significant time-series variation characteristics of fuel cell EIS data during endurance testing, this embodiment employs a gated cyclic unit (GRU) network to construct an impedance spectrum prediction model. Using the endurance time series as the main thread and frequency and DC bias as input variables, a mapping relationship between frequency and the real and imaginary parts of impedance is established for different endurance times.

[0164] The update process for the GRU network is as follows:

[0165]

[0166]

[0167]

[0168]

[0169] in, To update the door, To reset the door, σ represents the hidden state, σ is the Sigmoid activation function, and ⊙ represents the Hadamard product.

[0170] The predicted impedance spectrum output by the model is expressed as follows:

[0171]

[0172] in, The angular frequency corresponding to the k-th frequency point. To predict the real part of the impedance, This is to predict the imaginary part of the impedance.

[0173] During model training, the mean squared error between predicted and measured values ​​is used as the loss function:

[0174]

[0175] in, and These are the real and imaginary parts of the measured impedance, respectively.

[0176] In this embodiment, the accuracy of the EIS-GRU model under different training set ratios is verified. The results show that when the training set ratio is 0.7, the RMSE is 0.0182, MAPE is 4.26%, R² is 0.8858, and the training time is 128s; when the training set ratio is 0.8, the RMSE is 0.0094, MAPE is 2.91%, R² is 0.9319, and the training time is 167s; when the training set ratio is 0.9, the RMSE is 0.0076, MAPE is 2.16%, R² is 0.9745, and the training time is 232s. Another set of results shows that when the training set proportions are 0.7, 0.8, and 0.9, the RMSEs are 0.0191, 0.0105, and 0.0089, respectively; the MAPEs are 5.56%, 3.35%, and 2.46%, respectively; and the R²s are 0.7866, 0.9243, and 0.9549, respectively. Therefore, the EIS-GRU model can accurately predict the real and imaginary parts of impedance during fuel cell degradation, providing reliable input for subsequent DRT analysis.

[0177] In addition, such as Figure 3As shown, under the condition of current density of 0.3 A·cm⁻², when predicting the EIS at the 1392nd and 1440th hours, the established model can reconstruct the corresponding Nyquist curve well. Specifically, when predicting at the 1392nd hour, the RMSE, MAPE, and R² of the real part of the impedance are 0.0176, 3.728%, and 0.901, respectively, and the RMSE, MAPE, and R² of the imaginary part of the impedance are 0.0182, 3.904%, and 0.865, respectively.

[0178] III. Verification of the effectiveness of predicted impedance spectrum

[0179] Since DRT is essentially a linear system analysis method, it is necessary to verify whether the impedance data satisfies the conditions of causality, linearity, and time invariance before performing DRT decomposition. Therefore, this embodiment uses the Kramers-Kronig relationship to verify the validity of the impedance spectrum.

[0180] In practical calculations, a model consisting of multiple RC components connected in series is used to fit the impedance data, and the consistency between the measured impedance spectrum and the fitting results is evaluated using the relative residual. The relative residual can be expressed as:

[0181]

[0182] When the maximum relative residual does not exceed 1%, the impedance data is considered to satisfy the KK relationship and can be used for subsequent DRT analysis.

[0183] In this embodiment, the validity of typical EIS data for a fuel cell in the frequency range of 0.1 Hz to 10 kHz was verified using the Lin-KK tool. The results are as follows: Figure 4 As shown, the maximum residual of the real part of the impedance is 0.58% and the maximum residual of the imaginary part of the impedance is 0.76% across the entire frequency range. All residuals are less than 1%, indicating that the obtained EIS data meets the quality requirements and can be used for DRT analysis.

[0184] IV. Decomposition of DRT Polarization Process

[0185] After obtaining valid EIS data, the relaxation time distribution (DRT) method was used to decompose the polarization process in the impedance spectrum. Proton exchange membrane fuel cells are complex electrochemical systems with multiple coupled physicochemical processes. The polarization processes at different time constants superimpose in the impedance spectrum, therefore, the DRT method is needed to convert them to the time constant domain for decoupling.

[0186] The impedance spectrum and the relaxation time distribution function satisfy the following relationship:

[0187]

[0188] in, For ohm resistance, Let τ be the relaxation time distribution function, τ be the relaxation time constant, and ω be the angular frequency.

[0189] To facilitate numerical solutions, the above relationship is discretized and can be written as:

[0190]

[0191] in, The distribution coefficient, is the discrete-time constant node, and M is the number of discrete relaxation units.

[0192] To suppress the influence of noise and outliers on the distribution results, an L2 regularization penalty term is added to the right side of the cost function, and the solution expression is:

[0193] min_x‖Z−Ax‖2²+λ‖Lx‖2²

[0194] Where x is the distribution coefficient vector, A is the coefficient matrix, λ is the regularization parameter, and L is the constraint matrix. This method enhances the stability and noise resistance of the DRT solution process.

[0195] V. Polarization Resistance Feature Extraction

[0196] Based on the DRT decomposition results, peak values ​​within different time constant intervals are identified, and the corresponding polarization resistance parameters are extracted. The polarization resistance corresponding to the i-th polarization process can be expressed as:

[0197]

[0198] in, Let be the time constant interval corresponding to the i-th polarization process.

[0199] The polarization resistance features extracted in this embodiment include, but are not limited to, charge transfer-related polarization resistance, oxygen mass transfer-related polarization resistance, membrane proton transport resistance, catalyst layer ionomer proton transport resistance, and polymer membrane interface contact resistance. A polarization resistance feature vector is constructed as follows:

[0200]

[0201] It can perform multidimensional characterization of the internal degradation state of fuel cells.

[0202] In this embodiment, the variation patterns of different polarization resistances during the durability process show significant differences, such as... Figure 5As shown, for example, the proton conduction resistance and polymer membrane interfacial contact resistance remained relatively stable from 0 to 672 hours. At a current density of 0.9 A·cm⁻², the proton conduction resistance remained at approximately 0.032 Ω·cm² for the first 672 hours, and the polymer membrane interfacial contact resistance remained at approximately 0.014 Ω·cm². From 672 hours onwards, they gradually decreased, reaching 0.0206 Ω·cm² and 0.008 Ω·cm² respectively by 1488 hours, representing decreases of 35.63% and 42.86%. These results indicate that different polarization resistances exhibit different sensitivities to the fuel cell degradation process and can serve as an important basis for quantitative analysis of health status.

[0203] VI. Health Status Assessment

[0204] After obtaining the polarization resistance characteristics, a mapping relationship between the polarization resistance characteristics and the health state of the fuel cell is established. The health state estimation model can be expressed as:

[0205]

[0206] in, This is a health status mapping function. It can be implemented using regression models, support vector regression models, random forest models, neural network models, or deep learning models.

[0207] In this embodiment, a complete technical chain is formed through EIS prediction, KK validity verification, DRT decomposition, and polarization resistance extraction, encompassing "operating parameters—predicted impedance spectrum—polarization resistance characteristics—health status output," thereby achieving a quantitative assessment of the health status of a proton exchange membrane fuel cell. The research results show that this method not only solves the problems of difficult and costly traditional EIS acquisition but also quantitatively characterizes the electrochemical reaction processes and degradation behavior at various frequency bands during the dynamic decay of the fuel cell, thus providing a more comprehensive reflection of the fuel cell's health status.

[0208] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction, characterized in that, Includes the following steps: S1: Collect operational data and impedance spectrum data of proton exchange membrane fuel cells at different operating stages to construct a sample dataset; S2: Preprocess the runtime data and construct time-series input features; S3: Establish an EIS prediction model based on a time-series neural network to predict the impedance spectrum of the fuel cell. The prediction model includes any one of the following: a recurrent neural network model, a gated recurrent unit (GRU) model, a long short-term memory (LSTM) network model, or a time-series deep learning model with an attention mechanism. S4: The validity of the impedance spectrum is verified using the Kramers-Kronig relationship and residual threshold; when the maximum relative residual does not exceed the preset threshold, the impedance data is considered to meet the requirements of subsequent DRT analysis. S5: The effective impedance spectrum is decomposed using the DRT method to obtain the relaxation time distribution function. The DRT method treats the electrochemical system as an ohmic resistor connected in series with an infinite number of ideal R / / C units, and obtains the relaxation time distribution function by deconvolution, thereby realizing the decoupled characterization of each polarization process. S6: Extract polarization resistance characteristics corresponding to different polarization processes based on the relaxation time distribution function. Specifically, the method is as follows: use charge transfer-related polarization resistance, mass transport-related polarization resistance, proton conduction resistance, and polymer membrane interface contact resistance as important characteristic parameters for the quantitative analysis of fuel cell health status; for the i-th polarization process, its corresponding polarization resistance is obtained by integrating the relaxation time distribution function within the corresponding time constant interval. in, This represents the time constant interval corresponding to the i-th polarization process; Therefore, the polarization resistance eigenvector is constructed as follows: in, For ohmic resistance, The polarization resistances are those corresponding to different polarization processes; S7: Establish a mapping model between polarization resistance characteristics and health status. The health status estimation model is expressed as follows: in, The health status mapping function can be implemented using a linear regression model, support vector regression model, random forest model, neural network model, or deep learning model. By using polarization resistance characteristics and partial impedance spectrum characteristics as inputs, an enhanced health state estimation model is constructed, namely: in, These are the selected impedance spectrum characteristic parameters; The following loss function is used during model training: in, This represents the true health status of the i-th sample. To estimate health status; S8: Online health status estimation: First, the current operating parameters of the fuel cell are collected in real time; then, the operating parameters are input into the EIS prediction model to obtain the predicted impedance spectrum under the current state; then, the validity of the predicted impedance spectrum is checked, and the polarization resistance characteristics are extracted using the DRT method; finally, the polarization resistance characteristics are input into the health status estimation model to output the current fuel cell health status estimate.

2. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The operating data in S1 includes output voltage, output current, output power, temperature, pressure, flow rate, operating time, and load change information. This operating data is aligned with the electrochemical impedance spectroscopy data at the corresponding times, and combined with pre-defined health status labels to construct a sample database. The fuel cell health status (SOH) is represented in a normalized form, i.e.: in, These are the characterization parameters of the fuel cell at the current moment. These are the characterization performance parameters corresponding to the initial state of the fuel cell.

3. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The preprocessing in S2 includes outlier removal, missing value completion, smoothing and denoising, normalization, and temporal window reconstruction. The input sequence is constructed using a time window approach, specifically as follows: Let the input feature vector at a certain time t be: in, These represent the operating parameters of voltage, current, temperature, pressure, and flow rate at time t, respectively. Construct an input sequence of length L: This is used to characterize the dynamic operating characteristics of fuel cells over a period of time and to serve as input for the EIS prediction model.

4. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The basic update process of the gated recurrent unit (GRU) model in S3 is expressed as follows: in, To update the door, To reset the door, It is in a hidden state. The sigmoid activation function is used, and ⊙ represents the Hadamard product; Based on the hidden state, the real and imaginary parts of the impedance corresponding to each frequency point within the target frequency range are output, that is: in, The angular frequency corresponding to the k-th frequency point. and These are the real and imaginary parts of the predicted impedance, respectively. During model training, mean squared error is used as the loss function: in, and These are the real and imaginary parts of the measured impedance, respectively.

5. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The relative residual of the predicted impedance spectrum in S4 is expressed as: in, The impedance spectrum to be tested. The reference impedance value is obtained by fitting the model; if Then the impedance spectrum is determined to meet the validity requirements, where This is a preset threshold.

6. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The relationship between the fuel cell impedance and the relaxation time distribution function in S5 is expressed as follows: in, For ohmic resistance, Let τ be the relaxation time distribution function, τ be the relaxation time constant, and ω be the angular frequency. Discretizing the continuous distribution, we can write it as: in, The distribution coefficient to be determined is... For discrete-time constant nodes, n is the number of relaxor elements; Introducing an L2 regularization term into the cost function, we get: Where x is the distribution coefficient vector to be determined, A is the coefficient matrix, λ is the regularization parameter, and L is the smoothing constraint matrix.

7. The method for estimating the health status of a proton exchange membrane fuel cell based on EIS prediction according to claim 1, characterized in that, The online estimation process in S8 is represented as follows: in, These are the current running parameters. To predict the impedance spectrum, This represents the current polarization resistance characteristics. This is an estimate of the health status at the current moment.

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