A Solution of the Ill-Posed Impact-Force Inverse Problems by the Weighted Least Squares Method

Abstract

This paper deals with an inverse problem of impact-force prediction. The force is expressed in a set of expansion functions; hence, the original governing equation is reformulated to a problem of finding the weight of each expansion function. The expansion function is designed to best approximate the impact-force profile. The approach allows us to take into account more priori information of the solution; consequently, a better solution can be obtained. A numerical verification shows the estimation error of the present method is 3%, while the error of the Tikhonov solution is 18.5%.