Consistent regularization of nonlinear model updating for damage identification

Abstract

Even though many innovative methods have been proposed more recently, traditional sensitivity-based methods are still widely used for model updating and damage identification. Most publications, however, seem to lack rigorous mathematical treatment of some important details. A first observation is that few authors recognize the issue as an inverse problem that needs regularization. Without regularization, inherent measurement errors can lead to completely unrealistic results. Most authors who do use regularization apply it intuitively but inconsistently. In this paper, the two best-known regularization schemes—Tikhonov regularization and truncated singular value decomposition—are applied consistently to the nonlinear updating problem. Line search and stopping criteria known from numerical optimization are adapted to the regularized problem. The optimal regularization parameter is determined by generalized cross-validation. Numerical simulations are used to demonstrate the effects of some commonly encountered inconsistencies and to prove the superior behavior of the proposed algorithm. This algorithm is then successfully applied to a laboratory model with experimental data. Good agreement with actual crack patterns is observed.