| This dissertation is comprised of three chapters, each of which describes various methods of inverse problem solutions for the purpose of estimating structural damage parameters. Each chapter is either published in a research journal, or is in the process of being published. The first chapter describes a modification to a type of evolutionary algorithm, differential evolution, for estimating damage parameters that maximize a likelihood function, resulting in a solution in fewer numerical computations. The second chapter employs a Bayesian approach to solving the inverse problem, in which the uncertainty surrounding the damage parameter estimates as well as the convergence of multiple Markov chains are quantified. Finally, the third chapter demonstrates the efficacy of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method to identify and characterize structural damage parameters on a representative ship bow hull section, when the damage model is not known a priori . The Monte Carlo Standard Error (MCSE) is computed for each of the chains' estimates of the parameters as a means of assessing the precision of the results. As these chapters have been prepared as published papers in research journals, there is a separate abstract that has been prepared for the respective journal publication that introduces each project in detail at the beginning of each chapter. |
