Research And Application Of Differential Evolution Algorithm In Inverse Problems

Differential Evolution Algorithm is a new simple intelligence of random swarm evolution, which is closely related to artificial life and developed on the basic of Genetic Algorithm. The DEA own many advantages, analysis from the structure, such as the simple theory of the DEA, little parameters, that is why it is easy to master; analysis from the capability, DEA own the ability of fast convergence and the strong capability of global searching; Compare with Genetic Algorithm, DEA can overcome the complex progresses of decoding and encoding in binary, the select operator will lead to later stagnation under the selection method of roulette wheel, DEA also can improve the search precision.During the twenty years since DEA was proposed, so that its theories are not fruitful. Most scholars are working on improving the deficiencies in the performance improvements in some aspect, and proposed a number of improvements, including the analysis of parameters, research on DEA in different strategies and in complicated environment, capability of convergence and algorithm’s application research. It turns out that the improved algorithms have better capability of local search and stronger ability of analysis than normal algorithm, for that the improved DEA are widely used in different kinds of complex optimization problems. On the other hand, the inverse problems whose characters are randomness, nonlinear, fuzzy and uncertain, would lead to the unsteady and imperfect results of parameters inversion. So how to solve inverse problems of parameters in both theory and practical application with intelligent algorithms has a great deal of significance.Some work have been done for the deficiencies of DEA in performance, and improved DEA are applied in different areas, includes less linear system, nonlinear system and highly non-linear degrees of freedom robot, to solve the optimization problem, namely parameter inverse problem in a broad sense. And all proposed above are the core of the thesis, mainly research are about following aspects:(1) Under the inspiration of GA whose theory is bio-genetic, elaborate the theory and principle of DEA.(2) Proposed different improved algorithms on the basis of general DEA. Test each improved algorithm using basic standard functions, such as Sphere function, Generalized-Rastrigin function and banana function, and verify the effectiveness and rapid convergence of improved algorithms by comparing simulation results with general DEA.(3) For the study of linear systems in the field of parameter inverse problem, analyze some continuous linear matrix equation in control system by using improved DEA, the results of experiment show that the improved DEA is a new approach to solve matrix problem by comparing the general DEA with the improved one.(4) For the research on the nonlinear system in the field of parameter inverse problems, make a study on how to use the general and improved DEA to identity the Hammerstein system which is one of the typical nonlinear system. The simulation results show that the improved algorithm is a new method for analyzing nonlinear system identification.(5) for the study on parameter inverse problem of parallel robots, using an improved mixed DEA to solve kinematics equations of a typical 3-RPS lower-mobility parallel manipulator and get the pose parameters. Compared with the general DEA, the improved DEA search performance is superior.