A Bayesian Inference Approach To The Inverse Problem Of Beam Models

Beam models, governed by certain partial differential equations, are the basic models in engineering mechanics. They are frequently occurred in the fields of bridge construction and aerospace. There have been extensive and thorough investigations about the forward problem of beam models, i.e., determining the deflection of a beam subject to a vertical applied force. However, there are few results on the corresponding inverse problem, i.e., determining the vertical applied force in terms of the deflection field of a beam. It is ill-posed and requires much more efforts to devise effective numerical methods for the problem.In the literature, a Bayesian inference approach has been developed to solve in-verse problems of linear systems, and the main contribution of this thesis is to extend the method to solve inverse problems of finite-dimensional linear operator equations, for the convenience of practical applications. The related existence theory of the so-lution and the convergence analysis is also established. After introducing the mathe-matical model of the forward problem of beam models and its finite element approx-imation, a Bayesian inference approach is applied to solve the corresponding inverse problem. Numerical results are provided to show the effectiveness of the method.