A study on the influence of measurement location and regularization on the evaluation of boundary tractions by inverse finite element method

This work is concerned with an inverse approach to determine boundary tractions from displacements measured on a remote surface. The influence of measurement location and regularization on the evaluation of unknown tractions is mainly investigated through numerical experiments. The finite element method is employed in the inversion process, and the Tikhonov and the truncated singular value decomposition techniques are used to regularize an ill-conditioned system. The analytical relation between measurement location and the conditioning of a spring inverse problem is presented in this paper. Numerical results show that the solutions of inverse problems using the finite element method are very sensitive to measurement location. In addition, the effects of regularization and noise added to measured displacements are discussed through numerical examples.