多交界面热传导方程模型的数值解与参数估计

本文研究了多交界面热传导模型的数值解以及参数估计. 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算法在参数估计时的性能差异.

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

This paper mainly studies the numerical solution and parameter estimation of a multi-interface heat conduction equation. Firstly, the heat conduction equation and interface conditions are discretized to tridiagonal linear equations by using the finite difference method. Then a chasing algorithm is used to obtain the numerical solution. Furthermore, an 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 sink into the local extreme values prematurely and thus improve the optimization accuracy. Finally, the performance of the proposed algorithm is compared to the standard PSO algorithm and some classical nonlinear optimization algorithms such as Active Set ( AS ), Interior Point ( IP ) and SQP by using a numerical example.