Date of Completion


Embargo Period



optimal battery charging algorithm, battery life management algorithm, capacity fade, power fade, state-of-charge (SOC), time-to-charge (TTC), Li-ion battery, battery capacity modeling, CC-CV, linear quadratic optimal control, fault detection and diagnosis (FDD), leaky noisy OR, logistic regression (LR), test model, maximum a posteriori (MAP), Bayesian inference, decision-making, Bayes' rule

Major Advisor

Krishna R. Pattipati

Associate Advisor

Yaakov Bar-Shalom

Associate Advisor

Shengli Zhou

Field of Study

Electrical Engineering


Doctor of Philosophy

Open Access

Open Access


The focus of this dissertation is on using optimization and Bayesian inference in model-based decision making. We discuss two problems: (a) optimal battery charging and battery life management; (b) fault diagnosis using probabilistic graphical models. In the first part of this thesis, we address the optimal charging problem using a two-time-scale algorithm which performs fast-charging at the lower-level (fast time-scale), while managing the battery life at the higher-level (low time-scale). At the lower-level, we derive optimal charging algorithms for Li-ion batteries using equivalent electrical circuit models and quadratic optimization approaches. The objective function is considered as a linear combination of time-to-charge, energy-loss, temperature rise index, and any other arbitrary function of state-of-charge (SOC). A generic algorithm, which is applicable to any equivalent electrical circuit model of a battery, is derived for calculating the optimal current profile. At the higher-level, we propose a battery life management algorithm to determine the optimal values for the control parameters of the charging process, namely, maximum allowable current and maximum allowable terminal voltage. As a precursor to the battery life management algorithm, we propose two new battery capacity fade models that are shown to be statistically superior to the bi-exponential capacity fade model. In the second part of the thesis, we consider the fault diagnosis problem using probabilistic graphical models. We discuss the Detection-False Alarm (DFA), the Leaky Noisy OR (LNOR), and the logistic regression (LR)-based test models. Here, we prove the equivalence of DFA and LNOR test models. Then, we propose a unified test model that includes both the LNOR and the LR test models as special cases, and derive a Maximum \textit{a posteriori} solution for the multiple fault diagnosis problem based on the unified test model using the Lagrangian relaxation method and deriving a dual cost function for the problem.