Regularization of Numerical Inversion of Laplace Transform for the Inverse Analysis of Impact Force.

Abstract

This paper is concerned with the inverse problem of impact force, which is to estimate impact force acting on bodies from measurement of their impact responses. As the authors have shown previously, both numerical Laplace transformation and its inversion are required to solve the inverse problem. Since the inverse analysis is based on experimental data and, in addition, the Laplace inversion is typical of ill-posed problems, straightforward computation tends to provide unacceptable estimate of impact force. Therefore, regularization of the Laplace inversion is necessary to obtain a good estimate of the impact force. In this paper, Tikhonov regularization in applied to the numerical Laplace inversion by using FFT. Both numerical simulation and experimental verification show that the Tikhonov regularization is effective for improving estimation accuracy of the impact force. In addition, to appropriately determine the regularization parameter, Hansen's L-curve method is found to be effective.