System Identification, Uncertainty Quantification, and Inference of Constitutive Relations in Electrochemistry

Abstract

This thesis consists of three parts, each part addressing a challenging question as regards mathematical and computational modeling in electrochemistry, with particular applications to Lithium-ion batteries. The first problem concerns the mean-clustering approach to modeling the evolution of lattice dynamics, which finds application in describing the lattice structure of Lithium-ion cathodes. Instead of tracking the state of individual lattice sites, this approach describes the time evolution of the concentrations of different cluster types. It leads to an infinite hierarchy of ordinary differential equations which must be closed by truncation using a so-called closure condition. The pair approximation is the most common form of such closure. Here, we consider its generalization, termed the “optimal approximation”, which we calibrate using a robust data-driven strategy. The form of the obtained optimal approximation allows us to deduce a simple sparse closure model. In addition to being more accurate than the classical pair approximation, this “sparse approximation” is also physically interpretable, which allows us to a posteriori refine the hypotheses underlying construction of this class of closure models. On the other hand, parametrization of the mean-cluster model closed with the pair approximation is shown to lead to an ill-posed inverse problem. In the second problem we investigate the question of the state-of-charge estimation in cells operating under dynamic loading conditions. We use a hybrid data-driven strategy, referred to as “sparse identification of nonlinear dynamics”, in order to obtain a sparse representation of the dynamics of the system based on a provided library of candidates terms in the evolution equation. This strategy leverages the measurement data acquired using Electrochemical Impedance Spectroscopy and the sparse regression techniques. The dynamical system identified in this way is then used in combination with a suitable Kalman-type filter in order to enhance the estimates of the state of the system based on the measurement data while in operation. In the third problem we construct a data-driven model describing Lithium plating in a battery cell, which is a key process contributing to degradation of such cells. Starting from the fundamental Doyle- Fuller-Newman (DFN) model, we use asymptotic reduction and spatial averaging techniques to derive a simplified representation to track the temporal evolution of two key concentrations in the system, namely, the total intercalated Lithium on the negative electrode particles and total plated Lithium. This model depends on an a priori unknown constitutive relation representing the plating dynamics of the cell in function of the state variables. An optimal form of this constitutive relation is then deduced from experimental measurements of the time-dependent concentrations of different Lithium phases acquired through Nuclear Magnetic Resonance spectroscopy. This is done by solving an inverse problem in which this constitutive relation is found subject to minimum assumptions as a minimizer of a suitable constrained optimization problem where the discrepancy between the model predictions and experimental data is minimized. This optimization problem is solved using a state-of-the-art adjoint-based technique. In contrast to some of the earlier approaches to modeling Lithium plating, the proposed model is also able to predict non-trivial evolution of the concentrations in the relaxation regime when no current is applied to the cell. When equipped with an optimal constitutive relation, the model provides accurate predictions of the time evolution of both intercalated and plated Lithium across a wide range of charging/discharging rates. It can therefore serve as a useful tool for prediction and control of degradation mechanism in battery cells.