Damage detection from the variation of parameter matrices estimated by incomplete FRF data

Abstract

It is not easy to experimentally obtain the FRF (Frequency Response Function) matrix corresponding to a full set of DOFs (degrees of freedom) for a dynamic system. Utilizing FRF data measured at specific positions, with DOFs less than that of the system, as constraints to describe a damaged system, this study identifies parameter matrices such as mass, stiffness and damping matrices of the system, and provides a damage identification method from their variations. The proposed parameter identification method is compared to Lee and Kim's method and Fritzen's method. The validity of the proposed damage identification method is illustrated in a simple dynamic system. An accurate dynamic finite element model of a structure is very important for structural design and analysis. The modes of vibration and frequency response of the finite element model are compared to experimental measurements to test its accuracy. If a discrepancy between the two is found, the analytical model should be modified to satisfy the experimental measurements, and then the model should be updated for subsequent simulation and design studies. An FRF matrix of the full set of DOFs measured by experiments is used to predict parameter matrices of the dynamic system. The FRFs have been used directly to update condensed analytical models for obtaining the proper modal model. A single FRF measured at several frequencies, along with a correlated analytical model of the structure in its original state, is used for updating structural parameters. There have been many attempts to update the unknown physical parameters directly from the FRFs (Mottershead and Stanway 1986). It has been reported (Lee and Shin 2002) that FRF data provide more information than modal data, as the latter are extracted from a very limited frequency range related to resonance. Friswell and Penny (1990) proposed an approach to reduce the model order so that the stated estimation process reduces to a least squares problem based on the FRFs. Fanning and Carden (2004) presented a method for detecting added mass in structural systems from a single FRF measured at several frequencies in an identification algorithm. Cha and