An improved iterative model reduction technique to estimate the unknown responses using limited available responses

Abstract

A major challenge in structural health monitoring (SHM) is the availability of responses at limited degrees of freedom (DOFs). This requires the determination of the transformation parameter to expand the available DOFs to the full size of a model. The present study proposes an improved iterative model reduction algorithm by eliminating the stiffness terms from the transformation equation. The modified equation is a function of measured modal responses and mass matrices. This enables obtaining the unknown responses without repeated evaluations in case of stiffness reductions typically involved in SHM problems. The transformation parameter is solved using an improved Levenberg-Marquardt (LM) based iterative least-squares optimization technique. Specifically, the LM algorithm is enhanced by introducing an adaptive damping term in the least-squares problem. The proposed approach is further integrated into the substructuring scheme so that it can be readily applied for large finite element models. The algorithm is numerically demonstrated by considering a beam and a ten-storey building model using modal data with Gaussian noise. The effectiveness of the proposed reduced-order model is studied for a gradually decreasing number of modes and available responses for various measurement configurations by comparing with the results of the existing model reduction techniques.