Methods Development For Parameters Inversion Of Contaminant Transport Through Unsaturated Soils

Nonlinear inverse problem arises from many areas of scientific and engineering applications. Up to date, various methods have been applied to solving this problem, of which iterative regularization method is the frequently used one. This dissertation takes the parameter inversion problem of contaminant transport through unsaturated soils as its platform and is mainly devoted to improve iterative regularization methods for solving nonlinear inverse problems. The emphases are focused on the following aspects: widen the convergence region, efficiently update the homotopy parameter, choice the appropriate regularization functional as well as test the other error function. Consequently, some efficient methods are proposed and a toolbox for solving general inverse problems is developed, in particular it has been successfully applied to solving the inverse problem of parameter inversion of contaminant transport through unsaturated soils.Main contents of this dissertation are as follows:In chapter 1, the background of this dissertation is introduced and some existing methods for solving linear/nonlinear inverse problems are surveyed. Main research areas and structure of this dissertation are discussed.The background of this dissertation, named the non-equilibrium process of contaminant transport through unsaturated soils, is introduced in chapter 2. Taking the transport process of Cadmium through unsaturated soils as the example, corresponding mathematical models and laboratory soil-column testing method is introduced as well.In chapter 3, the aim is targeted at widening the convergence region of the method. To this end, a homotopy method is employed for solving the inverse problem of parameter inversion of contaminant transport. At the same time, the effect of the homotopy parameter is studied and some efficient methods for updating the homotopy parameter are presented.In chapter 4, the effect of regularization functional is studied. By employing the D-Function as the regularization functional, a new method, named HLB method for solving nonlinear inverse problems is presented and applied to solvingthe inverse problem of parameter inversion of contaminant transport through unsaturated soils. The feasibility of the HLB method is justified with numerical computations.In chapter 5, the nonlinear least square problem is replaced by a minmax problem in the formulation of inverse problem, and the HMB method is presented in which the aggregate function is used to smoothen the infinity norm and the D-Function and homotopy methods are also incorporated.In chapter 6, a toolbox for solving nonlinear inverse problems, named NIP is developed. Methods discussed above are all integrated in NIP toolbox.The last chapter gives a summary of the dissertation and some possible extensions of the present work.Appendix A contains the experimental results and fitting curves referenced by this dissertation.Appendix B briefly introduces the functionality of NIP toolbox.Appendix C is a tutorial of NIP toolbox.