多交界面热传导模型的数值解与参数估计  

Numerical solution and parameter estimation of multi-interface heat conduction models

作　　者：陈相兵[1] 闵心畅[2] 陈晨[3] CHEN Xiang-Bing;MIN Xin-Chang;CHEN Chen(Division of Mathematics,Sichuan University Jinjiang College,Meishan 620860,China;School of Mathematics,Sichuan University,Chengdu 610064,China;College of Science,Civil Aviation Flight University of China,Guanghan 618307,China)

机构地区：[1]四川大学锦江学院数学教学部,眉山620860 [2]四川大学数学学院,成都610064 [3]中国民用航空飞行学院理学院,广汉618307

出　　处：《四川大学学报（自然科学版）》2022年第5期9-14,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技计划资助项目(2022JDRC0068,2021JDRC0080);四川省教育厅项目(18ZB0363);四川大学锦江学院校级项目(JG201727);中国民用航空飞行学院校级课题(J2021-058)。

摘　　要：本文研究了多交界面热传导模型的数值解及参数估计.首先,本文运用有限差分法对传热方程和交界面条件进行离散化,将其转换为三对角型线性方程组.然后,基于追赶算法所给出的线性方程组数值解,本文建立了方程参数的非线性规划模型,并设计自适应粒子群优化算法(Particle Swarm Optimization, PSO).本文提出的自适应PSO算法对惯性因子实施一种自适应的非线性递减调整策略,以避免群体过早陷入局部极值、提升粒子的寻优精度.最后,本文以仿真实验比较了自适应PSO算法、标准PSO算法及经典的非线性优化算法如AS(Active Set)算法,IP(Interior Point)算法和SQP算法等在参数估计时的性能差异.This paper mainly studies the numerical solution and parameter estimation of a multi-interface heat conduction model. Firstly, the heat conduction equation and interface conditions are discretized to tridiagonal linear equations by using the finite difference method.Then a chasing method is used to obtain the numerical solution. Furthermore, a adaptive Particle Swarm Optimization(PSO) algorithm is proposed for the parameter estimation. This algorithm adopts an adaptive nonlinear decreasing adjustment strategy for the inertia factor in order not to sinking into the local extreme values prematurely and the optimization accuracy. Finally, the performance of the proposed algorithm is compared to the standard PSO algorithm and the classical nonlinear optimization algorithms such as Active Set(AS), Interior Point(IP) and SQP by using a numerical example.

关 键 词：热传导方程 向后差分格式 追赶法 自适应粒子群算法 

分 类 号：O241.82[理学—计算数学]