Determination of an optimal regularization factor in system identification with Tikhonov regularization for linear elastic continua

This paper presents a geometric mean scheme (GMS)to determine an optimal regularization factor for Tikhonov regularization technique in the system identi0cation problems of linear elastic continua. The characteristics of non-linear inverse problems and the role of the regularization are investigated by the singular value decomposition of a sensitivity matrix of responses. It is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution. Based on this observation, the optimal regularization factor is de0ned as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses. The validity of the GMS is demonstrated through two numerical examples with measurement errors and modelling errors