用同伦方法反演非饱和土中溶质迁移参数  

A HOMOTOPY METHOD FOR PARAMETER INVERSION OF SOLUTE TRANSPORT THROUGH UNSATURATED SOILS

作　　者：崔凯[1] 杨国伟[1] 李兴斯[2] 李宝元[2] 

机构地区：[1]中国科学院力学研究所高温气体动力学重点实验室,北京100080 [2]大连理工大学工程力学系,大连116023

出　　处：《力学学报》2005年第3期307-312,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家重点基础性研究发展规划资助项目(G1999032805)

摘　　要：非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题.将同伦方法引入该问题的求解,通过构造线性同伦将原问题转化为求解同伦函数最小值的无约束优化问题.同时在分析了同伦参数正则化效应的基础上,提出一种两段同伦参数修正方法.即在求解的初始阶段,根据拟Sigmoid函数调整同伦参数, 以追踪同伦路径,保证计算稳定地进行;在迭代的后期,采用与残差相关的同伦参数修正方法,以抵抗观测噪声对求解的影响.数值算例为求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移模型参数反演问题, 计算结果表明了该方法的大范围收敛性及较强的抵抗观测噪声的能力.Parameter inversion of solute transport inside unsaturated soils was generally solved through a nonlinear operator equation. In this paper, we propose a homotopy method to deal with this problem. The original problem is finally transformed into an unconstrained optimization problem of minimizing the homotopy function. Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter. In the early stage, a quasi-sigmoid method is used to assure the stability of computation, while in the later stage, the calibration of the homotopy parameter is governed by the computational residuals in order to compensate the error of observed data. Problems of parameter inversion of solute transport coupled with equilibrium and non-equilibrium effects through one-dimensional unsaturated soils are carried out as numerical examples and the computational results clearly demonstrate the feature of global convergence of the homotopy method. Moreover, even though experimental quantities are contaminated heavily by noise, a favorable solution is still obtained.

关 键 词：非饱和土 迁移参数 同伦方法 Sigmoid函数 非线性算子方程 无约束优化问题 大范围收敛性 反演问题 修正方法 观测噪声 函数最小值 求解问题 问题转化 初始阶段 同伦路径 模型参数 溶质迁移 吸附效应 数值算例 计算结果 

分 类 号：O221.2[理学—运筹学与控制论] TU43[理学—数学]