Aging modeling and lifetime prediction of a proton exchange membrane fuel cell using an extended Kalman filter

Bartlechner J., Vrlić M., Hametner C., Jakubek S.

Determining the State-of-Health (SoH) of fuel cell systems during operation is vital for implementing model-based control strategies that aim to minimize degradation and extend the fuel cell lifetime. This paper introduces a novel observer architecture designed to estimate the internal states as well as the SoH of fuel cell systems in real time. The proposed observer offers three key advantages: (1) it decouples the dynamics of internal states from SoH, thus enhancing numerical stability, (2) by incorporating multiple measurement points, assessing the SoH for various components within the fuel cell (e.g. membrane, catalyst layer) becomes possible, and (3) in combination with the used physical real-time capable model, the observer architecture facilitates real-time evaluation of the SoH during dynamic operation. The observer's benefits are demonstrated through simulations and measurement data.

Zhang Y., Tang X., Xu S., Sun C.

Proton-exchange membrane fuel cells (PEMFCs) play a crucial role in the transition to sustainable energy systems. Accurately estimating the state of health (SOH) of PEMFCs under dynamic operating conditions is essential for ensuring their reliability and longevity. This study designed dynamic operating conditions for fuel cells and conducted durability tests using both crack-free fuel cells and fuel cells with uniform cracks. Utilizing deep learning methods, we estimated the SOH of PEMFCs under dynamic operating conditions and investigated the performance of long short-term memory networks (LSTM), gated recurrent units (GRU), temporal convolutional networks (TCN), and transformer models for SOH estimation tasks. We also explored the impact of different sampling intervals and training set proportions on the predictive performance of these models. The results indicated that shorter sampling intervals and higher training set proportions significantly improve prediction accuracy. The study also highlighted the challenges posed by the presence of cracks. Cracks cause more frequent and intense voltage fluctuations, making it more difficult for the models to accurately capture the dynamic behavior of PEMFCs, thereby increasing prediction errors. However, under crack-free conditions, due to more stable voltage output, all models showed improved predictive performance. Finally, this study underscores the effectiveness of deep learning models in estimating the SOH of PEMFCs and provides insights into optimizing sampling and training strategies to enhance prediction accuracy. The findings make a significant contribution to the development of more reliable and efficient PEMFC systems for sustainable energy applications.

Jia C., He H., Zhou J., Li K., Li J., Wei Z.

Proton exchange membrane fuel cell (PEMFC) is a highly promising renewable energy conversion technology. However, durability issues have hindered their large-scale commercialization process. Performance degradation prediction is an essential component of PEMFC prognostics and health management and is critical for extending the service life of fuel cell. Given that, this paper proposes a novel data-driven prediction model that fuses multi-head self-attention (MHSA) mechanism and bi-directional long short-term memory (BiLSTM). This model can effectively capture different types of dependencies from large-scale high-dimensional data and achieve global information modeling. Specifically, the preprocessed historical voltage data and PEMFC system operating parameters are fed into the proposed prediction model. Where BiLSTM understands the contextual information and temporal dependencies in sequence data by calculating the hidden states in both forward and backward directions. MHSA captures the complex relationships and extracts key information in the input sequence by simultaneously learning multiple sets of attention weights between different locations. Finally, the proposed model is validated based on the health monitoring data under stationary and quasi-dynamic conditions. The validation results indicate that the proposed model can ensure absolute errors of less than 0.6 × 10−3 V for at least 71.9% of the prediction results under stationary and quasi-dynamic conditions (less than 1.2 × 10−3 V for at least 97.6% of prediction results).

Xia Z., Wang Y., Ma L., Zhu Y., Li Y., Tao J., Tian G.

Durability and reliability are the major bottlenecks of the proton-exchange-membrane fuel cell (PEMFC) for large-scale commercial deployment. With the help of prognostic approaches, we can reduce its maintenance cost and maximize its lifetime. This paper proposes a hybrid prognostic method for PEMFCs based on a decomposition forecasting framework. Firstly, the original voltage data is decomposed into the calendar aging part and the reversible aging part based on locally weighted regression (LOESS). Then, we apply an adaptive extended Kalman filter (AEKF) and long short-term memory (LSTM) neural network to predict those two components, respectively. Three-dimensional aging factors are introduced in the physical aging model to capture the overall aging trend better. We utilize the automatic machine-learning method based on the genetic algorithm to train the LSTM model more efficiently and improve prediction accuracy. The aging voltage is derived from the sum of the two predicted voltage components, and we can further realize the remaining useful life estimation. Experimental results show that the proposed hybrid prognostic method can realize an accurate long-term voltage-degradation prediction and outperform the single model-based method or data-based method.

Hua Z., Zheng Z., Pahon E., Péra M., Gao F.

The proton exchange membrane fuel cells (PEMFC) system is a promising eco-friendly power converter device in a wide range of applications, especially in the transportation area. Insufficient service life is one of the key issues that hinder its large-scale commercial application. Degradations of the materials, suboptimal operating procedures, and disturbances from the external environment and load all would have a terrible impact on the durability performance of PEMFC. Prognostic and health management (PHM) can estimate the remaining useful life (RUL) in advance and make the proper decisions at the right time to extend the service life of the system by condition-based maintenance. At the very least, the PHM can provide degradation information and reserve enough maintenance time for the operators to avoid some fatal damages. Analyzing the working principles and the degradation phenomena of the PEMFC system are the foundations of degradation prediction. Developing accurate and dynamic models to describe the degradation mechanisms, exploring accurate, efficient, and robust methods to realize the RUL prediction are some critical challenges of PHM nowadays, especially under dynamic operating conditions. This paper focuses on comparing different models for degradation mechanisms, discussing some key issues of PHM, and reviewing the degradation prediction methods. • Lifetime prediction challenges of the PEMFC system are presented. • Degradation mechanisms and models of the PEMFC system are discussed. • Existing lifetime prediction methods of the PEMFC system are compared.

Long B., Wu K., Li P., Li M.

The remaining useful life (RUL) prediction for hydrogen fuel cells is an important part of its prognostics and health management (PHM). Artificial neural networks (ANNs) are proven to be very effective in RUL prediction, as they do not need to understand the failure mechanisms behind hydrogen fuel cells. A novel RUL prediction method for hydrogen fuel cells based on the gated recurrent unit ANN is proposed in this paper. Firstly, the data were preprocessed to remove outliers and noises. Secondly, the performance of different neural networks is compared, including the back propagation neural network (BPNN), the long short-term memory (LSTM) network and the gated recurrent unit (GRU) network. According to our proposed method based on GRU, the root mean square error was 0.0026, the mean absolute percentage error was 0.0038 and the coefficient of determination was 0.9891 for the data from the challenge datasets provided by FCLAB Research Federation, when the prediction starting point was 650 h. Compared with the other RUL prediction methods based on the BPNN and the LSTM, our prediction method is better in both prediction accuracy and convergence rate.

Zhao J., Li X., Shum C., McPhee J.

• Reviewed control-oriented PEMFC models with high computing speed and accuracy. • Compared 1D physical models by incorporating transport & electrochemical phenomena. • Examined 0D analytical & empirical models with low computing resource requirements. • Scrutinized data-driven models with AI algorithms for real-time control. The real-time model-based control of polymer electrolyte membrane (PEM) fuel cells requires a computationally efficient and sufficiently accurate model to predict the transient and long-term performance under various operational conditions, involving the pressure, temperature, humidity, and stoichiometry ratio. In this article, recent progress on the development of PEM fuel cell models that can be used for real-time control is reviewed. The major operational principles of PEM fuel cells and the associated mathematical description of the transport and electrochemical phenomena are described. The reduced-dimensional physics-based models (pseudo-two-dimensional, one-dimensional numerical and zero dimensional analytical models) and the non-physics-based models (zero-dimensional empirical and data-driven models) have been systematically examined, and the comparison of these models has been performed. It is found that the current trends for the real-time control models are (i) to couple the single cell model with balance of plants to investigate the system performance, (ii) to incorporate aging effects to enable long-term performance prediction, (iii) to increase the computational speed (especially for one-dimensional numerical models), and (iv) to develop data-driven models with artificial intelligence/machine learning algorithms. This review will be beneficial for the development of physics or non-physics based models with sufficient accuracy and computational speed to ensure the real-time control of PEM fuel cells.

Ma R., Xie R., Xu L., Huangfu Y., Li Y.

Prognostic of the proton-exchange membrane fuel cell can effectively extend the fuel cell lifespan, which can contribute to its large-scale commercialization. In this article, a hybrid prognostic approach is proposed to predict the fuel cell output voltage and other aging parameters that can reflect the stack’s internal degradation. During the training stage, the prognostic parameters are obtained by using the extended Kalman filter (EKF). Besides, the fuel cell output voltage is used to train the long short-term memory (LSTM) recurrent neural network. During the prediction stage, the hybrid EKF and LSTM method will predict the output voltage and aging parameters, and the degradation can be predicted under dynamic conditions. The proposed method is validated by experimental tests under static, quasi-dynamic, and dynamic conditions. Results indicate that the hybrid method can accurately predict the degradation trend of fuel cell voltage and aging parameters. The RMSE of the method is less than 0.0110, 0.0262, and 0.0317 under static, quasi-dynamic, and dynamic conditions, respectively, which are smaller than the conventional model-based methods or data-driven methods. Furthermore, the hybrid method can provide more detailed information for prognostic decision-making and better prolong the fuel cell lifespan.

Vichard L., Steiner N.Y., Zerhouni N., Hissel D.

Last years, the fuel cell has become well-known as an efficient and clean energy converter being a potential alternative to internal combustion engines. However, despite being very promising, the durability of those systems is still a bottleneck. Most of the time, a fuel cell is integrated in a hybrid system which considers the fuel cell stack, the battery, and the balance of plant. To keep improving the durability of such a system, diagnostic and prognostic tools are of particular importance and to implement such tools, modeling the system is a mandatory step. The purpose of this paper is to propose a critical review of the existing methods to model all elements of a hybrid fuel cell system according to operating conditions and degradation. In this review, interactions and major degradation mechanisms occurring at all components will be presented and the physics-based models, data-driven and hybrid models of these components reviewed. Finally, methods will be discussed, and advantages and drawbacks will be summarized. • Complete hybrid fuel cell system modeling methods. • Hybrid fuel cell system degradation modeling. • Hybrid fuel cell system degradation mechanisms. • Hybrid fuel cell system balance of plant degradation.

Mardle P., Cerri I., Suzuki T., El-kharouf A.

The dependency of the Nernst potential in an operating proton exchange membrane fuel cell (PEMFC) on the temperature, inlet pressure and relative humidity (RH) is examined, highlighting the synergistic dependence of measured open circuit potential (OCP) on all three parameters. An alternative model of the Nernst equation is derived to more appropriately represent the PEMFC system where reactant concentration is instead considered as the activity. Ex situ gas diffusion electrode (GDE) measurements are used to examine the dependency of temperature, electrolyte concentration, catalyst surface area and composition on the measured OCP in the absence of H2 crossover. This is supported by single-cell OCP measurements, wherein RH was also investigated. This contribution provides clarity on the parameters that affect the practically measured OCP as well as highlighting further studies into the effects of catalyst particle surrounding environment on OCP as a promising way of improving PEMFC performance in the low current density regime.

Zuo J., Lv H., Zhou D., Xue Q., Jin L., Zhou W., Yang D., Zhang C.

Xie R., Ma R., Pu S., Xu L., Zhao D., Huangfu Y.

Fuel cells are considered as one of the most promising candidates for future power source due to its high energy density and environmentally friendly properties, whereas the short lifespan blocks its large-scale commercialization. In order to enhance the reliability and durability of proton exchange membrane fuel cell, a fusion prognostic approach based on particle filter (model-based) and long-short term memory recurrent neural network (data-driven) is proposed in this paper. Both the remaining useful life estimation and the short-term degradation prediction can be achieved based on the prognostic method. For remaining useful life estimation, the particle filter method is used to identify the model parameters in the training phase and the long-short term memory recurrent neural network is used to update the parameters in the prediction phase. As for short-term degradation prediction, the particle filter and long-short term memory recurrent neural network are firstly trained individually in the training phase and then be fused to make predictions in the prediction phase. The proposed fusion structure is validated by the fuel cell experimental tests data, and results indicate that better prognostic performance can be obtained compared with the individual model-based or data-driven method.

Wang F., Mamo T., Cheng X.

Proton exchange membrane fuel cells (PEMFCs) have zero-emissions and provide power to a variety of devices, such as automobiles and portable equipment. We propose a bi-directional long short-term memory recurrent neural network with an attention mechanism (BILSTM-AT) model to predict the voltage degradation of the PEMFC stack. Random forest regression model is used to extract essential variables as inputs in the model. The prediction interval is derived by using the dropout method. Model parameters are determined by an optimization method. The test data of the two PEMFC stacks are used to compare the proposed model with some existing models. The prediction results show that BILSTM-AT outperforms other models. Moreover, the proposed model with a sliding window method on remaining useful life (RUL) prediction can achieve more accurate results, with a relative error of about 0.09%~0.29%.

Vichard L., Harel F., Ravey A., Venet P., Hissel D.

In the last years, Proton Exchange Membrane Fuel Cells (PEMFC) became a promising energy converter for both transportation and stationary applications. However, durability of fuel cells still needs to be improved to achieve a widespread deployment. Degradation mechanisms and aging laws are not yet fully understood. Therefore, long-term durability tests are necessary to get more information. Moreover, degradation models are requested to estimate the remaining useful life of the system and take adequate corrective actions to optimize durability and availability. This paper presents in a first part the results of a long-term durability test performed on an open cathode fuel cell system operated during 5000 h under specific operating conditions including start/stop and variable ambient temperature. Performance evolution and degradation mechanisms are then analyzed to understand influence of operating conditions and how to extend the durability. In a second part of the paper, the results are used to build a degradation model based on echo state neural network in order to predict the performance evolution. Results of the degradation prediction are very promising as the normalized root mean square error remains very low with a prediction time over 2000 h.

Liu J., Li Q., Chen W., Yan Y., Qiu Y., Cao T.

To solve the prediction problem of proton exchange membrane fuel cell (PEMFC) remaining useful life (RUL), a novel RUL prediction approach of PEMFC based on long short-term memory (LSTM) recurrent neural networks (RNN) has been developed. The method uses regular interval sampling and locally weighted scatterplot smoothing (LOESS) to realize data reconstruction and data smoothing. Not only the primary trend of the original data can be preserved, but noise and spikes can be effectively removed. The LSTM RNN is adopted to estimate the remaining life of test data. 1154-hour experimental aging analysis of PEMFC shows that the prediction accuracy of the novel method is 99.23%, the root mean square error (RMSE) and mean absolute error (MAE) is 0.003 and 0.0026 respectively. The comparison analysis shows that the prediction accuracy of the novel method is 28.46% higher than that of back propagation neural network (BPNN). Root mean square error, relative error (RE) and mean absolute error are all much smaller than that of BPNN. Therefore, the novel method can quickly and accurately forecast the residual service life of the fuel cell.