Direct time-domain mass density reconstruction for RODs

Abstract

This thesis attempts to solve the inverse problem which recovers the mass density profile of thin rods based on the response at one end. The density is treated as an unknown parameter and a function of space and time. In general, the inverse problem can be considered as an optimization problem that includes the cost function and the mathematical model of the physical system. Tikhonov regularization and Lagrange multipliers are applied to tackle the problem. In addition, another approach that is based on Bayesian theory is studied. This scheme applies the Markov Chain Monte Carlo method to sample the posterior probability distribution. The numerical results are presented to show the accurateness and the effectiveness of the proposed algorithm in recovering the mass density profile