Studies On Bregman Method For Parameter Inversion

Parameter inversion is one of very important inverse problems. Based on the data from a collaborative project of European Union, this thesis carries out the studies on solution strategy for inverse problems, particularly aiming at the parameter inversion in the control equations of transport process of contaminants in the underwater. By introducing the proximal point algorithms for convex programming into the solution of parameter inversion problem, the number of regularization functions used in the parameter inversion is greatly increased. In the thesis, a friendly user's interface for parameter inversion is developed and Bregman function based algorithm is implemented in Matlab7.0 platform. By means of simulated data, the effectiveness and convergence of proposed method is verified. The algorithm ist also used to compute the parameters based on real observed data. The thesis is organized as follows:In Chapter one, the engineering background and significance of the thesis is introduced. After surveying the state of the art of solving the inverse problems and some shortages of existing algorithms, the direction and contents of the present thesis is determined.In Chapter two, related concepts and control equations of contaminant transport process in the unsaturated soils are first introduced, and then the parameter inversion problem is proposed and the regularization approach planned to be used is also indicated.In Chapter Three, a small example is presented to demonstrate the sources of resulting ill-condition and the ways of remedying the difficulties in inverse problems. Then, the proximal point algorithms for convex programming are given in the details and potential uses of these algorithms in the solution of inverse problems are addressed. Finally, the proximal point algorithm using Bregman functions is applied to the parameter inversion problem for contaminant transport in the unsaturated soils.In Chapter Four, a user-friendly interface for the parameter inversion is developed based upon the MATLAB7.0 platform, and a computer program is implemented for inverting the parameters in contaminant-transport equations. Firstly, the proposed algorithms are verified by using simulated data. These algorithms are then applied to the data from the experimentsof soil columns for the project of European Union and penetrating curves are drawn with comparing numerical results.