Detection of structural damages by model updating based on singular value decomposition of transfer function subsets

Abstract

In this paper, a sensitivity-based finite element (FE) model updating method using singular value decomposition (SVD) of frequency response function (FRF) is introduced. An exact sensitivity equation is proposed by incorporating measured responses of a damaged structure in the mathematical formulations. A set of incompletely measured natural frequencies of a damaged structure and mode shapes of the intact structure are used to deal with incomplete measurement without the implementation of FE model reduction or data expansion algorithms. The insights provided from the variation of SVD of transfer functions are used for the selection of proper updating frequency ranges. The appropriate arrangement and assembly of SVD-based sensitivity equations are discussed to achieve more accurate model updating results. The solution of the developed sensitivity equation is obtained by the linear least-square (LS) method and imposing unbiased side constraints on the design variables. The proposed method was examined numerically on the FE model of a 2D truss model and experimentally on a concrete beam. Low-frequency ranges, including ranges around the first sixth vibration modes for numerical cases and ranges around the first three vibration modes for experimental cases, are successfully implemented for damage detection. The numerical and experimental results prove its high sensitivity for the cases of low severity and distributed damages and its robustness against high levels of measurement, natural frequency, and mass modeling errors.