Quantifying Uncertainty in Li-ion Battery Aging due to Unknown Usage with Hybrid Physics-Informed Neural Networks

Lithium-ion batteries are a popular choice to electric and hybrid power vehicles. When dealing with safety-critical and costly applications, such as in urban air mobility, the ability to model and forecast the state of charge and state of health is very important. When managing fleets of electric/hybrid vehicles, the lack of complete datasets, in which battery usage is recorded since first commissioning, adds a layer of complexity to building models for diagnosis, prognosis, and risk management. Building accurate models based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. These simplifications lead to residual discrepancy between model predictions and observed data. Alternatively, machine learning is attractive, but obtaining large and well curated datasets is often unfeasible due to safety constraints or costs. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We then overcome the limitation of requiring the full historical usage of individual batteries through Bayesian update. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with limited and partially observed data.