Research On Parameter Inversion Method Applied To Water Environment Mathematical Model

The mathematical models of water environment are designed to describe how the variables indicating the quality of a body of water evolve with time under a variety of influence such as spacial variation and other control condition. It is of important significance to study the parameters in the established mathematical model. One can predict the water quality by determine the underlying parameters in the model. One can even induce the water system to evolve to more favorable configuration by adjusting the corresponding parameters. Therefore, it has been a focus in the research community that how to determine these parameter precisely. Without the reliable parameters in the model, it is impossible to make any reliable calculation on the reality problem, regardless some very powerful prediction and control methods that are already developed. In conclusion, it is very important to understand the parameter inversion problem, judged from both the theoretical and practical point of view.Mathematics is the language of science and is the basis of natural science and engineering. In order to quantitatively describe the phenomena, mathematics is indispensable in the practice of science and technology. In this thesis, we study the well established BOD-DO water quality model. We numerically solve the problem and apply the regularized iteration method and genetic algorithm to solve the parameter inversion problem. This work focuses on the parameter determining in the water quality model. In the first time, we study several parameter inversions in the unstable BOD-DO water quality model, developed a rigorous mathematical basis for inversion problem of this model.We introduce the theory and method of genetic algorithm to the inversion problem of water quality model. The numeral simulation and practical calculations reveals that the genetic algorithm is very effective in solving the inversion problem in the water quality problem. About various calculations that we intention before, we also compile computer codes to numerically study this problem.