Estimating Parameters of Physics-Based Battery Models – What Machine Learning Can and Cannot Do

With the widespread use of Lithium-ion (Li-ion) batteries in multiple industries, the design space for the electrochemical cells has increased drastically. Li-ion batteries’ design parameters and material properties, such as porosity, electrode thickness, active material loading, and solid phase diffusivities, typically vary substantially due to different design goals and variation in the manufacturing process. Due to the difficulty in obtaining these and other battery cell parameters, many battery management systems used to control and monitor Li-ion batteries opt for the simplified resistor-capacitor circuit-based battery cell representation over using physics-based battery models. However, if these parameters become obtainable, scientists could implement advanced battery management systems using physics-based battery models to capture precisely how the battery performs and degrades in a wide variety of applications. Multiple methods, such as genetic algorithms, statistics, and machine learning, have been attempted for the parametrization and characterization of battery cells to enable accurate battery simulations using physics-based models 1, 2. However, there are inherent limitations to the type and number of parameters that can be estimated using these methods if only the standard battery cell cycling data is utilized for this purpose. The present work elucidates and quantifies these limitations specifically in the case of machine learning based approach and provides deeper insights into these limitations that may help develop more robust cell characterization protocols. In the present work, model parameters are varied in a continuum-level physics-based model and simulations are performed for: (1) constant current-constant voltage (CC-CV) charging and constant current discharge at different C-rates, and (2) electrochemical impedance spectroscopy (EIS) in the relevant frequency range at multiple states of charge (SOCs). The Single Particle Model (SPM) is used for performing these simulations due to its relative simplicity and small number of parameters. At first, the charge and discharge data are input as training data in a long short-term memory neural network (LSTM NN), and EIS data is input as training data in a convolutional neural network (CNN). Once trained, the machine learning (ML) model uses charge, discharge, and EIS data withheld from the original training data set to predict SPM parameters. The estimated parameters are compared with the true parameters used for SPM charge, discharge, and EIS simulations, and the error in parameter estimation is quantified. A rigorous grid convergence analysis is performed to highlight the importance of ensuring that the spatial discretization error of the model does not influence the parameter estimation accuracy. For the first error quantification, all parameters are varied concurrently to obtain the parameter estimation error that arises from a large, undetermined parameter set. Parameters are then analyzed individually and in clusters related to diffusion, kinetics, and stoichiometric limitations. Further analysis is performed on parameters that could not be estimated with sufficient accuracy, including theoretical explanations for the incurred error and the effect of this error on the internal state predictions. References: Dawson-Elli, N., et al., On the creation of a chess-ai-inspired problem-specific optimizer for the pseudo two-dimensional battery model using neural networks. Journal of The Electrochemical Society, 2019. 166 (6): p. A886. Berliner, M.D., et al., Nonlinear identifiability analysis of the porous electrode theory model of lithium-ion batteries. Journal of The Electrochemical Society, 2021. 168 (9): p. 090546.