Update of parameter matrices of the dynamic system using the least-squares approach

Abstract

Model-based responses rarely coincide with the actual responses owing to modeling and measurement errors, deterioration of structural performance, and presence of damages in the structure. The parameter matrices should be updated for successful subsequent analysis and design efforts. This study derives the mathematical forms of variations in the parameter matrices between the actual system and the analytical model. A method using the least-squares principle constrained by the measured modal data is presented. The method is directly derived by minimizing the performance indices expressed by the norm of the variation in the parameter matrices between the actual system and the analytical model. The proposed update methods predict the updated parameter matrices depending on the prescribed weighting matrices and detect damages from the predicted parameter matrix variations. Examples compare the methods depending on the established weighting matrices, the number of measurement data sets of the first modal data only and the lowest two modal data. This study also investigates the effect of external noise contained in the measured data.