A comparison of gain design criteria for closed-loop model updating

A conventional procedure for structural model updating is to solve an inverse problem with the aim of minimizing the discrepancy between an experimental target feature vector and a model-predicted one. The inverse problem to be solved is often ill-posed as the number of model parameters to be updated typically exceeds the number of target features. One way to confront this issue is to expand the target feature vector through closed-loop model updating, where gains are used to form multiple closed-loop eigenstructures from which target features are obtained. Besides confronting the ill-posedness of the inverse problem, the closed-loop model updating procedure also allows one to tailor the sensitivities of the target features by adequate design of the feedback gains. The present paper offers a comparative study in which the merit of different gain design criteria is examined for closed-loop sensitivity-based model updating. More specifically, the gains will be designed through eigenstructure assignment in an optimization setting where different cost functions, including the nuclear norm and the condition number of the sensitivity matrix, will be tested. Updating results will be shown for a numerical model of a shear building.