【作者】 高飞；

【导师】 童恒庆；

【作者基本信息】 武汉理工大学 ， 流体力学， 2006， 博士

【摘要】 湍流的产生机制之迷在百年来一直吸引着数代科学家为之倾倒和献身，曾被称为“经典物理学最后的疑团”，但是对湍流的研究进展甚缓，至今还停留在半经验理论的水平上。其中描述液体力学和等离子体的基本方程Navier-Stokes方程，在2000年被巴黎国际数学大会列为21世纪世界数学的七大难题之一。 从混沌来考察湍流发生的机制已引起国内外学者的广泛重视，为揭开湍流的产生机制提供了新思路和新途径。迄今已提出的很多有效的混沌控制与同步方法，不仅为混沌理论走向应用准备必要的手段，而且在理论上促进了混沌理论和流体力学特别是湍流理论等方面的深入研究。 对混沌系统的未知参数估计与在线估计和高阶不稳定的周期轨道(UPO)及其相关算法的深入研究，必将对混沌系统的控制及和基于UPO的混沌系统特征变量的表达产生深远影响。然而现有算法，如牛顿类算法，在探索UPO和系统参数在线识别方面的局限性，与混沌控制与同步的发展、要求形成了鲜明的反差。 本论文主要从演化算法(EA)的角度，以其新进展差异演化(DE)和粒子群优化(PSO)为基本算法，辅以合理的改进策略，对于Navier-Stokes的简化模型lorenz混沌系统和其二维平面上的简化Hénon混沌系统，通过模型转化构造合适的函数优化问题，讨论这些系统的参数估计、控制与同步等问题。 第一章首先介绍混沌学的研究背景和意义。其次探讨了与湍流、多相流及N-S方程等相关的混沌系统的历史与现状，分析存在的问题和解决的方案。而后介绍本文的研究内容、拟解决的关键问题和主要的创新点。 第二章首先从算法的理论、应用等角度，对EA的实质、特点、发展现状作概述。然后对其中的进化规划、模拟退火算法，特别是EA领域最为常见、影响最为广泛的GA的算法框架、组成和收敛性做出详尽的探讨。最后，鉴于EA类算法易收敛到局部最优的特点，介绍几类通用的算法改进策略。 第三章主要讨论DE和PSO两种典型的EA类算法。首先对DE和PSO的内在思想、实现方式、特点等进行详细的论述，分析其优缺点，探讨改进的策略。而后分别在基于最大公约数的思想求解电子基本电荷和非线性方程求根这更多还原

【Abstract】 So many scientists are being infatuated with the enigma of creation mechanism of turbulence in several centuries, which was named the last puzzle of the classical Physics. But researches on turbulence are not progressing smoothly and remain at the level of half experience and immature theory. In which the fundamental Navier-Stokes equation for the fluid and plasma is regarded as one of the seven greatest hard nuts to crack in Parisian international mathematics conference for 21 centuries in 2000.Investigating the enigma of creation mechanism of turbulence from chaos provides s novel way of thinking and the new approach for uncovering the enigma and control the turbulence, and it is attached great importance both in domestic and abroad now. Up to now lots of valid methods have been put forward to chaos control and synchronization. These not only provide necessary approach for the applications of chaos theory but also promote the thorough study in theories of chaos and fluid mechanics especially in turbulence.The deep investigations and studies in chaos’ unknown system parameters estimation and higher order unstable periodic orbits (UPO) and related algorithms will exert a deep influence on both chaos control and chaotic characteristics based on UPO. However, the limitations of the existing algorithms, such as methods in Newton kind, in detecting UPO and estimating system parameters online and the developments and demands of chaos control and synchronization form a sharp contrast.In view of above mentioned reasons, the simplified model of Navier-Stokes equation Lorenz chaos system and their reducing in 2 dimensions Henon system is considered in unknown parameter estimation, control and synchronization. Through appropriate functions’ minimizations of correspondent models transforming, the proposed evolutionary algorithms recent achievements Differential Evolution (DE) and Particle Swarm Optimization (PSO) with the proper improvements are adopted. The rest of this paper is organized as follows.In Chapter 1, we introduce the research background and meaning of chaos firstly. Then the history and current situation of the chaos system related to turbulence, multi-phase flows and Navier-Stokes equation are probed and analyzed. Thirdly the main aspects, the key problems to be solved and the main innovations we have researched are introduced.更多还原