A regularization method for the linear error localization of models of elastomechanical systems

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Abstract
The parametric updating of models of elastomechanical systems leads to inverse problems which are generally ill-posed in the sense of Hadamard. In order to reduce the ill-posedness, regularization techniques can be applied, which means taking additional information into account. One possible piece of regularizing information is the knowledge of those parameters which are associated with submodels to which the model error can be mainly restricted, since the reduction of the problem to these parameters improves the condition of the associated solution operator. The aim of error localization is to find out those parameters mainly affected, and this still leads to an ill-posed inverse problem especially due to the sensitivity of the parameter estimates with respect to the data. A regularization of the Tikhonov type is presented in order to overcome this ill-posedness. This regularization mainly depends on a special choice of the weighting matrix of the penalty term in the formulation of the extended least squares method. It is proposed here to choose this weighting matrix proportional to the data sensitivity of the normal solution. The effectiveness of this regularization is demonstrated by an example with simulated measurements.

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