Hierarchical bayesian model for probabilistic analysis of electric vehicle battery degradation

Document Type


Publication Date



Department of Electrical and Computer Engineering, Department of Computer Science


This article proposes a hierarchical Bayesian model for probabilistic estimation of the electric vehicle (EV) battery capacity fade. Deterministic estimation of the EV battery degradation is not reliable, as its aging factors are mostly external and varies by time, location, and the driver's usage pattern, while probabilistic models can address the observations uncertainties and provide more accurate estimations. We have developed a comprehensive Bayesian network model that incorporates two main aspects of the EV battery aging: hierarchy and variety of external effectual factors. Multiple levels of hierarchical relationship with intermediate hidden variables connect the external factors, such as driving behavior and habits, charging options, and grid services to the battery capacity fade. The mathematical expression of the model is extracted based on Bayes' theorem, the probability distributions for all variables are carefully chosen, and the Metropolis-Hastings Markov chain Monte Carlo sampling method is applied to generate the posterior distributions. The model is trained with a subset of experimental data (85%) and tested with the other 15% of data to prove its accuracy. Also, three case studies for different drivers, different grid services' repetitions, and different climates are explored to show model's flexibility with different input data.

Publication Title

IEEE Transactions on Transportation Electrification