Optimization and Bayesian Inference in Model-based Decision Making

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.