基于遗传算法的Tikhonov正则参数优化计算

OPTIMAL CALCULATION OF TIKHONOV REGULARIZATION PARAMETER BASED ON GENETIC ALGORITHM

Tikhonov正则化方法是求解不适定问题的最有效方法之一,而正则参数的计算是这一方法实施的关键。当测量误差水平未知时,通常是采用迭代求解,然而,其正则解对参数的迭代初始值选择具有敏感性,因而不能保证最优。该文视正则参数的计算为优化问题,分别以广义交叉准则(GCV)、L-曲线准则和Engl误差极小化准则为目标函数,基于遗传算法,从全域内获得正则参数的最优值。并对一桁架的荷载分布进行了重构,结果表明,这一方法是寻求最优正则解的一条有效途经。

Tikhonov regularization approach has been accepted as one of the most effective ways to solve ill-posed problems. In the approach, the key step is the calculation of a regularization parameter. Usually, iterative methods are used to obtain the parameter. However, the obtained iterative solutions are sensitive to the initial choice of the parameter, and different initial values may lead to quite different solutions. Presently, the optimal calculation of Tikhonov regulafization parameter is discussed. A method based on the Genetic Algorithm （GA） is proposed, which uses the generalized cross-validation （GCV）, L-curve and Engl＇s error criterion as an optimal function, respectively. Numerical analysis is carried out for the load distribution model of a pin-jointed truss. It is shown that the method can achieve an optimal value of the parameter in the whole range, and therefore provides an efficient way for obtaining an optimal regularization solution.