On The Theories And Methods Of Mechanisms And Global Optimization Based On Chaos & Fractal

Chaos and Fractals, as the important fields of nonlinear system science, have been paid great attention in recent years, and a great deal of achievements has been made both in the theory and application in engineering. In this dissertation Chaotic and Fractal theory have been studied thoroughly and systematically, and the chaotic and fractal phenomenas of problems in mechanisms, robotics and design optimization have been detailed analyzed, and the application for computational kinematics, design optimization and evolution computation have been investigated in a creative way. The researches are all oriented to the difficulty problems in mechanisms and global optimization. The main researches and contributions of this dissertation are as follows:Definitions and theorems pertaining to the chaotic and fractal dynamics are investigated systematically. The relation between Li-Yorke chaotic and Devaney chaotic definitions and the related propositions are demonstrated and proved, and the chaotic characteristics of Julia set are studied and key propositions of Julia set are proved. Two new methods toward the chaos are proposed which provides an effective tool for the application of chaos to mechanisms and design optimization: method of computing the bifurcation accurately based on genetic algorithms and method of finding the Julia set point of iteration function. Lyapunov exponent for discrete and continuous dynamic systems are investigated, and an effective criteria for determining chaos based on computing the largest Lyapunov exponent using variation method is proposed.Chaotic and fractal technique is used as a tool for solving problems of mechanism synthesis for the first time, and the advantages and disadvantages of several computational kinematics theories are analyzed. The phenomena of chaos and fractals in computational kinematics are investigated, and the phenomena that chaos and fractal does exist in Newton-Raphson iterative method are proved both in theory and numerical simulation. The optimization model for finding Julia set point of Newton-Raphson iteration function is proposed and solved by evolutionary programming. Based on that Julia set is the boundaries of basins of attractions(roots) a novel method for obtaining all solutions of system of nonlinear equations arising from mechanism synthesis problem by utilizing sensitive fractal areas to locate the Julia set point is proposed, and planar rigid body guidance with five precision positions and planar path generation with nine precision points are solved by the method, and more meaningful solutions have been found compared with that by Homotopy method.An unconstrained optimization method for global solution based on chaos and fractal is proposed for the first time. The chaotic and fractal dynamic characteristics of discrete nonlinear system in Newton technique optimization are studied deeply, and reasons that sensitivity of Newton technique optimization heavily dependents on the initial guess point are investigated by means of chaosand fractal theory. Based on that Julia set is the boundaries of basins of attractions (optimal) a new global optimization method of finding all local optima in nonlinear optimization problem is proposed by utilizing sensitive fractal areas to locate the Julia set point. The developed technique uses an important feature of fractals to preserve shape of basins of attraction(optima) on infinitely small scales. The method has been applied to the approximate synthesis of planar function generation and planar rigid body guidance effectively.The chaotic global optimization method based on continuous time variables is also proposed for the first time. That the continuous inertial system has optimization ability is proved. By adjusting compelling force adequately the chaos motion generated by inertial dissipative system is controlled to let the system migrating among the local minima and finally converging to global minimum. The proposed method is aplicated to the problem of point-to-point motion of redundant robot manipulators working in the...