Training of physics-informed Bayesian neural networks with ABC-SS for prognostic of Li-ion batteries

The current surge in the need for Li-ion batteries to power electric vehicles has also translated in a need for more advanced models that can predict their behavior, but also quantify the uncertainty in their predictions, given the amount of variables involved and the varying operating conditions. This manuscript proposes a new Bayesian physics-informed recurrent neural network, where the battery discharge curve is described using the Nernst and Butler-Volmer equations, the activity correction term within such equations is modeled with two multilayer perceptrons, and approximate Bayesian computation by subset-simulation is used to train the weights, bias and the physical parameters representing the maximum charge available and the internal resistance. The challenges found during the adaptation and implementation of the Bayesian training algorithm to the recurrent physics-informed cell are described, along with the approaches proposed to overcome them. The performance of the Bayesian hybrid model presented in this paper has also been evaluated using data from NASA Ames Prognostics Data Repository, and the results show comparable accuracy to the standard approach with backpropagation, and a flexible and realistic quantification of the uncertainty. Furthermore, the uncertainty related to the physical parameters of the hybrid model can be evaluated in semi-isolation of the weights and bias of the MLPs, providing a sensitivity tool to assess the relative importance between different parameters.