Bayesian calibrated physics-informed neural networks for second-life battery SOH estimation

Second-life lithium-ion batteries (SL-LIBs) from electric vehicles offer significant potential for extending battery life and reducing environmental impact. Accurate state-of-health (SOH) estimation is critical for ensuring their safe and efficient reuse, but it is challenging due to the heterogeneous aging process and incomplete first-life data. To overcome these challenges, we propose a Bayesian calibrated physics-informed neural network (PINN) framework for SOH estimation, integrating physical degradation models, data-driven calibration techniques and uncertainty quantification. The framework uses simulation data generated by the porous electrode theory-based degradation models to train a governing equation approximator, which serves as a constraint in the PINN for SOH estimation. The Bayesian SOH estimator is trained on real-world data under the guidance of the pretrained governing equation, and leverages Monte Carlo Dropout for uncertainty quantification. Additionally, a physics model calibrator is introduced to bridge the gap between the physics-based model and real-world data, ensuring a more precise representation of actual degradation. Experimental results on a self-designed SL-LIB dataset, consisting of 84 retired batteries across 21 different working conditions, demonstrate that the proposed framework significantly outperforms existing methods.