非线性二维导热反问题的混沌-正则化混合解法  

Chaos-Regularization Hybrid Algorithm for Nonlinear Two-Dimensional Inverse Heat Conduction Problem

作　　者：王登刚[1] 刘迎曦[2] 李守巨[2] 

机构地区：[1]同济大学建筑工程系,上海200092 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《应用数学和力学》2002年第8期864-870,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目 (10 0 72 0 14 )

摘　　要：考虑热传导系数随温度变化 ,建立了非线性二维稳态导热反问题数值计算模型·　并把混沌优化方法和梯度正则化方法相结合 ,构成一种混沌_正则化混合算法求该计算模型的全局解·　以热传导系数随温度线性变化为例 ,由布置在结构边界上的观测点温度信息确定了结构材料热传导系数及其随温度变化规律·　结果表明混合算法计算结果与初值无关 ,具有很好的全局寻优性能 ,而且计算量远比经典遗传算法和单纯采用混沌优化方法小·A numerical model of nonlinear two_dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature. Combining the chaos optimization algorithm with the gradient regularization method, a chaos_regularization hybrid algorithm was proposed to solve the established numerical model. The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature_dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.

关 键 词：逆问题 导热反问题 导热系数 全局最优 混合法/混沌优化方法 梯度正则化方法 

分 类 号：O39[理学—工程力学] O482.2[理学—力学]