The Research & Application Of The Regularization Method Based On Genetic Algorithm

There are a lot of applications of inverse problems in science and engineering, inverse problem and its solution methods have been a hot research field. The difficulty in solving inverse problem is its ill-posed characteristic, that is the existence,uniqueness and stablility of the solution. For the most inverse problems in engineering, the existence of the solution is evident, there must be the reason for a kind of result. But the uniqueness and stablility of the solution are the problems. There have been lots of computational inverse techniques for solving this kind of ill-posed inverse problems. In all these methods, Tikhonov regularization method is the most popular method to solve the ill-posed inverse problems.(1) The ill-posedness is the characteristic of inverse problems, take an example of the Fredholm integral equation to illustrate the influence of ill-posedness.(2) The modified Tikhonov regularization method is presented based on genetic algorithm, the superiorities of the two algorithms are inherited. The numerical computation of the method is very important to the precision of the solution, genetic algorithm is employed to implicit the regularization algorithm numerically, as it is a kind of adaptive global algorithm based on evaluation. The validity of this combined method is proved by the inverse parameter estimation problem of a cantilever beam.(3) The method is applied to a parameter estimation of a drawbead model, the Bauschinger effect and the incline of the neutral layer are estimated by the measured drawbead restraining force.A kind of credible, effective and stable inverse solution method is presented for ill-posed inverse engineering problems in this research. We can better estimated the system or improve the efficiency by implementing the method in engineering.