Fractional-Order Physics-Informed Neural Network With Heavy-Tailed Distribution for Battery Health Prognostic

Fluctuations in battery aging process such as capacity regeneration, outliers and noise occur far more frequently than expected, with many informative fluctuation patterns being obscured during data preprocessing, making it challenging to capture its underlying patterns as well as to achieve robust battery health prognostic. Motivated by the heavy-tailed distribution of fluctuations and sub-diffusion of ions within batteries, this study pioneers a robust fractional-order battery aging model, adaptively accounting for fluctuations leveraging heavy-tailed distribution. Firstly, aging-characteristics-driven physics-informed neural network (PINN) is presented to establish an empirical battery aging model. Fractional-order partial differential equation (FOPDE) describing capacity degradation is employed to embed physical constraints into the loss function, enhancing the accuracy of battery health prognostic. Additionally, the adaptive multi-task weighting strategy based on Student-t distribution (AMW-ST) is introduced to weight the loss function terms of PINN. By assuming a heavy-tailed distribution of data labels, it adaptively captures underlying patterns from fluctuations and improves robustness of the model. Lastly, the fine-tuning method is applied to transfer aging information across batteries. By varying fractional order and selectively freezing PINN, this approach reduces time cost while maintaining high accuracy. The proposed method demonstrates effectiveness on 8 cells from two datasets, achieving average error of 0.9% with fine-tuning, 1.2% without fine-tuning and 1.4% under non-Gaussian noise.