Abstract
This paper is concerned with the inverse problem of impact force, which is to estimate the impact forces acting on bodies from the 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 an unacceptable estimate of the true impact force. Therefore, regularization of the Laplace inversion is necessary to obtain a good estimate of the impact force. In this paper Tikhonov regularization is applied to the numerical Laplace inversion using FFT. Both numerical simulation and experimental results verify that the Tikhonov regularization is effective for improving the accuracy of the estimated impact force. In addition, it is shown that Hansen's L-curve method can be employed to determine appropriately the regularization parameter.
