Metamodel for Efficient Estimation of Capacity-Fade Uncertainty in Li-Ion Batteries for Electric Vehicles

This paper presents an efficient method for estimating capacity-fade uncertainty in lithium-ion batteries (LIBs) in order to integrate them into the battery-management system (BMS) of electric vehicles, which requires simple and inexpensive computation for successful application. The study uses the pseudo-two-dimensional (P2D) electrochemical model, which simulates the battery state by solving a system of coupled nonlinear partial differential equations (PDEs). The model parameters that are responsible for electrode degradation are identified and estimated, based on battery data obtained from the charge cycles. The Bayesian approach, with parameters estimated by probability distributions, is employed to account for uncertainties arising in the model and battery data. The Markov Chain Monte Carlo (MCMC) technique is used to draw samples from the distributions. The complex computations that solve a PDE system for each sample are avoided by employing a polynomial-based metamodel. As a result, the computational cost is reduced from 5.5 h to a few seconds, enabling the integration of the method into the vehicle BMS. Using this approach, the conservative bound of capacity fade can be determined for the vehicle in service, which represents the safety margin reflecting the uncertainty.lithium-ion battery; capacity fade; electrochemical model; battery management system; electric vehicles; uncertainty estimation; Markov Chain Monte Carlo; metamode