基于改进的混合粒子群算法的变循环发动机模型求解 *

Solving Variable Cycle Engine Model Based on Improved Hybrid Particle Swarm Optimization

关键词:  变循环发动机  数学建模  牛顿-拉夫森算法  粒子群算法  非线性方程组

Key words:  Variable cycle engine  Mathematical modeling  Newton-raphson method  Particle swarm optimization  Nonlinear equations

摘要:

为了降低变循环发动机模型求解时对初始值的依赖性，提升算法的全局收敛性，同时提高模型求解的效率，提出了一种基于改进的混合粒子群算法的变循环发动机模型求解思路。首先建立了变循环发动机的部件级模型，并建立了发动机的共同工作方程组；然后采用Broyden法对牛顿-拉夫森算法中的雅可比矩阵进行更新计算，在经典粒子群算法的基础上引入粒子中心，作为干扰项，并引入限制因子和自适应时变惯性系数；最后，综合了两种改进的算法，提出改进的混合粒子群算法。实验结果表明:该算法不仅继承了牛顿-拉夫森算法的高计算效率，还吸收了改进的粒子群算法的全局收敛优点，可实现模型大范围收敛。

Abstract:

In order to reduce the dependence on the initial value，promote convergence of the algorithm and improve the efficiency of solving the Variable Cycle Engine (VCE) model，an improved hybrid particle swarm optimization (PSO) algorithm was put forward. Firstly，a component-level mathematical model and co-operating equations of VCE were constructed. Then the Jacobian matrix of Newton-Raphson method using the Broyden method was updated. The particle center as distractors，limiting factor and adaptive time-varying inertia weight on the basis of classic PSO were introduced. Finally，the two improved algorithms were combined，and then the improved hybrid PSO algorithm was proposed. The experimental results show that the algorithm not only can inherit Newton-Raphson computing efficiency，but also improve convergence obviously.