基于混合混沌粒子群算法求解变循环发动机数学模型问题

发布时间：2018-03-12 08:01

本文选题：VCE数学模型　切入点：部件级建模　出处：《山东大学》2015年硕士论文　论文类型：学位论文

【摘要】：求解变循环发动机(Variable Cycle Engines,VCE)数学模型问题是近几年国内航空和军工领域开始重点研究的课题,其核心问题是首先通过建立合理的数学模型模拟其工作状态,然后提出适当的算法求解维持其工作状态的非线性平衡方程组。对于数学模型建立问题,部件级建模方法一直占据主流,本文通过分析气体流动和能量消耗两个方向,整理各部件的特性量及关系,建立了VCE部件级模型；对于提出算法求解非线性平衡方程组问题,近些年来许多学者提出了很多非常重要的方法,例如,使用传统的牛顿-拉夫森(Newton-Raphson)迭代算法、遗传算法(Genetic Algorithm, GA)、混合遗传算法以及BP神经网络算法解决此类问题等等,在本文中,我们在目前解决此问题较为前沿的方法——粒子群算法(Particle Swarm Optimization,PSO)基础上,提出了混合混沌粒子群算法(Hybrid Chaos-Particle Swarm Optimization,HCPSO),即,在解决本问题时,针对PSO算法对初始值较为依赖的特点,采用带随机初始值修正的穷举搜索法确定初始值的具体范围；针对PSO算法初期收敛快后期陷入局部最优的特点,将混沌的思想引入模型,使PSO算法在后期局部收敛后能够跳出稳定状态,继续寻找更优解；同时在混沌与稳定状态之间加入半混沌状态,使得算法在混沌程度相对较低时也能进行很好地计算。最后我们将通过实际数据实验验证该方法的可行性与有效性。从数值实验中我们可以看到,上述方法的全局寻优能力很好。
[Abstract]:Solving the mathematical model of variable Cycle engine (VCE) is an important research topic in the field of aviation and military industry in China in recent years. The core problem is to simulate the working state of VCE by establishing reasonable mathematical model. Then an appropriate algorithm is proposed to solve the nonlinear equilibrium equations that maintain its working state. For the problem of mathematical modeling, the part-level modeling method has been the mainstream. In this paper, gas flow and energy consumption are analyzed in two directions: gas flow and energy consumption. In recent years, many scholars have put forward a lot of important methods for solving nonlinear equilibrium equations, for example, in recent years, many scholars have put forward many very important methods, for example, The traditional Newton-Raphson iterative algorithm, genetic algorithm, hybrid genetic algorithm and BP neural network algorithm are used to solve these problems. On the basis of particle Swarm optimization algorithm (PSO), a hybrid chaotic particle swarm optimization algorithm (hybrid Chaos-Particle Swarm optimization) is proposed. In order to solve this problem, we propose a hybrid Chaos-Particle Swarm optimization algorithm, which is based on the characteristic that the PSO algorithm depends on the initial value. The exhaustive search method with random initial value correction is used to determine the specific range of initial value, and the idea of chaos is introduced into the model in view of the characteristic that PSO algorithm falls into local optimum at the beginning and late stage of convergence. After local convergence, the PSO algorithm can jump out of the stable state and continue to find a better solution. At the same time, the semi-chaotic state is added between the chaos and the stable state. Finally, we will verify the feasibility and effectiveness of the method through the actual data experiments. We can see from the numerical experiments, The global optimization ability of the above method is very good.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：V231

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