Accurate and reliable mathematical modeling is essential for the optimal control and performance analysis of polymer electrolyte membrane fuel cell (PEMFC) systems, which are mainly implemented based on accurate parameter estimation. In this paper, a multi-strategy tuna swarm optimization (MS-TSO) is proposed to estimate the parameters of PEMFC voltage models and compare them with other optimizers such as differential evolution, the whale optimization approach, the salp swarm algorithm, particle swarm optimization, Harris hawk optimization and the slime mould algorithm. In the optimizing routine, the unidentified factors of the PEMFCs are used as the decision variables, which are optimized to minimize the sum of square errors between the estimated and measured data. The optimizers are examined based on three PEMFC datasets including BCS500W, NedStackPS6 and harizon500W as well as a set of experimental data which are measured using the Greenlight G20 platform with a 25 cm² single cell at 353 K. It is confirmed that MS-TSO gives better performance in terms of convergence speed and accuracy than the competing algorithms. Furthermore, the results achieved by MS-TSO are compared with other reported approaches in the literature. The advantages of MS-TSO in ascertaining the optimum factors of various PEMFCs have been comprehensively demonstrated.

Proton exchange membrane fuel cells have attracted widespread attention due to their cleanliness and high energy density, but the performance degradation during operation greatly limits their commercialization. Therefore, the reliable degradation prediction of fuel cell performance is of great significance. The recovery phenomenon of the reversible voltage loss that occurs during the operation of fuel cells has posed great difficulties for model training and prediction. Moreover, the models may easily and erroneously learn the combined trends in the recovery of reversible voltage loss and performance degradation. To address this issue, this paper employs the Transformer model to predict the performance degradation of fuel cells. By utilizing the unique self-attention structure and masking mechanism of the Transformer model, the signal for the recovery of the reversible voltage loss is adopted as the input for the model to avoid interference from information before voltage recovery on subsequent predictions. Experimental results show that the model has the highest prediction accuracy at various prediction starting points. Meanwhile, it can predict the accelerated performance degradation of fuel cells, which has positive implications for health management.

To establish a reliable long-term estimation and prognosis for the state of health (SOH) and voltage degradation prediction of fuel cell stacks (FCSs), this paper initiates a fusion prognostic strategy and a rolling prediction framework for long-term SOH estimation for FCSs based on the designed 2500-hour prolonged durability experiment on vehicular FCS. Specifically, a time-varying dynamic degradation model is first developed to track the dynamic performance deterioration of FCSs based on the electrochemical mechanism and dynamic equivalent circuit model of the fuel cell. Subsequently, an improved Informer model is proposed for SOH estimation and voltage degradation prediction. The experimental results validate that the proposed model can effectively monitor the dynamic degradation behavior of the proton exchange membrane FCS, exhibiting superior accuracy in forecasting long-term voltage degradation. Moreover, the model can precisely predict the long-term aging trend and voltage periodic recovery of FCSs, with a Root Mean Square Error ranging from 0.33 to 1.04V and a Mean Absolute Percentage Error below 0.5%. Finally, a rolling prediction framework for SOH estimation of FCSs, applicable to cloud-based implementation schemes, is developed to provide quantitative SOH estimation for each operational period, facilitating the development of FCS design and control strategies.

To develop an energy management strategy (EMS) that adapts to the state-of-health (SOH) of the fuel cell stack (FCS) to keep the output of the powertrain of fuel cell hybrid electric vehicles optimal all the time, a degradation adaptive EMS is proposed. The proposed EMS is based on a hierarchical framework, where the upper layer involves a degradation rate model to estimate the SOH of the FCS online and acquire performance characteristics at different SOH levels. In the lower layer, an EMS using the Rule-DDPG algorithm is developed. The results prove that the proposed method outperforms existing mainstream EMSs and aligns closely with the dynamic programming approach regarding economic and durability indicators. Compared to non-adaptive EMSs across various driving cycles, the proposed degradation adaptive EMS can consistently achieve the lowest energy consumption and optimal durability performance, tailored to the current SOH of the powertrain. In addition, a comparison between offline simulation and hard-in-the-loop testing validates the computational efficiency and real-time applicability of the proposed strategy in practical environments. Specifically, the calculation time for each sample during the WLTC cycle is shown to be less than 213.214ms, with an average calculation time of 168.637ms and a minimum calculation time of 150.618ms.

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.