Modeling and simulation of sodium-ion batteries based on the combination of electrochemical mechanism and machine learning

Sodium-ion batteries have gained increasing attention due to their advantages, such as abundant raw material reserves and low costs. As a new battery system, the electrochemical and thermal properties of its electrodes and the entire cell, as well as their variations over both short and long periods, still contain many unknowns. Similar to lithium-ion batteries, sodium-ion batteries also experience performance degradation over time. To ensure the long-term, safe, and stable operation of batteries in service, health and safety management are necessary. Modeling and simulation can accurately predict the multi-scale behavior of battery characteristics, and thus, serve as an important theoretical foundation for battery management. Therefore, modeling and simulation of sodium-ion batteries are crucial. This paper first considers the temperature changes during battery operation and, based on the fundamental working principles of the battery, develops an electrochemical-thermal coupling model by retaining the main physical processes while ignoring secondary processes. Then, to identify and optimize the highly sensitive model parameters, a weighted particle swarm optimization algorithm is used, ensuring that the parameters are valid and reasonable. Finally, to address the differences among individual cells and the uncertainties in the measured data, machine learning algorithms are introduced into battery mechanism modeling. Specifically, a dynamic residual forest model (DRF) for sodium-ion batteries is constructed using random forest and incremental learning algorithms, which iteratively learns from errors to reduce simulation errors in voltage and temperature. In the DRF model, the random forest algorithm initially performs a preliminary prediction, followed by the use of incremental learning algorithms to correct prediction errors, thereby continuously optimizing the prediction accuracy of battery terminal voltage and temperature. The key feature of this model is its ability to handle real-time data streams, adapt to dynamic changes in data distribution, and reduce the need for retraining on new data, all while maintaining high prediction accuracy. This allows the model to simulate the complex operating conditions during the actual use of the battery. By using the DRF model to correct the outputs of the electrochemical-thermal coupling model, the final predictions of terminal voltage and temperature are obtained. Validation results show that the hybrid model provides better predictions of terminal voltage and temperature for different individual cells with higher accuracy.