Damage detection and identification of parameter matrices using residual force vector

Abstract

Beginning with incomplete mode shape measurement data, this study presents analytical equations to predict the actual stiffness and mass matrices. The measured modal data, including the measurement, manufacturing and modeling errors, should be updated for subsequent analysis. In this study, the incomplete mode shape data are expanded to a full set of degrees-of-freedom (DOFs) based on the generalized inverse method and the concept of residual force vector. The corrected parameter matrices are straightforwardly derived using the estimated mode shape data and the pseudo inverse method. The validity of the proposed method is evaluated based on the number of measured modes in an application, and its limitations are investigated