Impact-Force Estimation by Quadratic Spline Approximation

Abstract

This paper focuses on a solution of the ill-posed inverse problem of the impact-force reconstruction. The solution approximates the impact-force with a regularized quadratic spline having an uniform distribution of knots along the time domain of analysis. The approximation results in a small size, ill-posed, and rank-deficient system equation, which is then solved by the truncated singular value decomposition and L-curve methods. The proposal that is verified by three impact-force problems provides acceptable estimated impact-forces. However, the estimated impact-force in the unloading part rather oscillates in particular when the data are severely contaminated with the noise. Therefore, the present method needs to be further developed to allow a non-uniform knots distribution such that the regularization in the unloading part can be increased.