Sparse Modeling of Energy Storage Systems in Presence of Noise

This paper presents a reduced-order modeling technique for energy storage systems such as Lithium-ion batteries (LiBs). Data-driven models offer a solution to represent the system dynamics without requiring in-situ measurements and proprietary information needed by mechanistic models. However, such models can have poor performance in unseen scenarios as they tend to overfit the training data. Here, we present a physics-inspired data-driven model to discover the governing equations of LiBs using only the excitation inputs and measured outputs. Instead of adding generic terms to discover the model, we seek physics-inspired reduced-order nonlinear models. The method is based on sparse identification of nonlinear dynamics with control, and the sparsification was achieved using sequentially thresholded ridge regression. Further, we extended the technique to work with noisy data using unscented Kalman filters, which update the terms for an enhanced state of charge (SOC) and voltage estimation. The trade-off between model accuracy and complexity is determined using threshold and regularization parameters. We formulated the problem to treat them as hyperparameters and adjust them using a training and a validation set. The model was trained on uniformly distributed electrical current signals with maximum amplitudes of 2C charge and 4C discharge rates. We used the US-highway profile as the validation set. The model's ability to predict unseen scenarios was assessed with urban dynamometer driving schedule data, where the identified model achieved the normalized root mean square error of <1.1e-3 for SOC and Voltage predictions.