对流－扩散方程反问题的控制论求解方法  

Numerical Solution to the Inverse Problems Governed by Convection-Diffusion Equations Using Cybernetics Method

作　　者：王佳鹤[1] 金忠青[1] 

机构地区：[1]河海大学

出　　处：《水动力学研究与进展（A辑）》1996年第2期229-235,共7页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金

摘　　要：本文从控制论角度将对流－扩散方程反问题提为分布参数系统的最优控制问题，并提出用计算机辅助优化法实现求解。针对环境工程中的污染排放控制问题，应用计算机辅助优化法分别求解了二维非恒定河道边界及源项控制反问题。计算结果表明，计算机辅助优化法对求解对流－扩散方程反问题是行之有效的；应用于污染排放控制计算，可基本解决多个或单个污染源反演问题；与现有的反问题求解方法相比，其优点是求解过程简单、通用性好。The cybernetics method for solving inverse problems governed by convection-diffusion equations is presented in the paper. It is pointed that from the point of view of controlling a system, inverse problem is identical with cybernetics. It is suggested that bringing inverse probleminto cybernetics, a new way to solve inverse problems can be found. The inverse problems of boundary condition control and source control in 2-d unsteady rivers are solved by computer-aided optimization method. Numerical results show that the present method is efficient in solving inverse problems governed by convection-diffusion equations. It can be a new way in solving practical engineeing inverse problems in the fields of environmental science.

关 键 词：对流-扩散方程 反问题 控制论 最优控制 

分 类 号：O352[理学—流体力学] TV131.2[理学—力学]