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

Eun-Taik Lee,Hee-Chang Eun

doi:10.1177/1687814019890806

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.

Highlights

It is difficult to accurately describe the responses of an actual system using the structural model established at the design stage because of inaccurate constructions, inhomogeneous properties of the structural materials, environmental effects, and measurement errors
This study investigates the effect of external noise contained in the measured mode shapes
Assuming the invariant mass matrix, this example evaluates the numerical results of the updated methods by the lowest two modal data sets depending on the external noise

Summary

Introduction

It is difficult to accurately describe the responses of an actual system using the structural model established at the design stage because of inaccurate constructions, inhomogeneous properties of the structural materials, environmental effects, and measurement errors. This article presents the mathematical forms of the updated parameter matrices to satisfy the flexibility matrix and eigenfunction established by the measured modal data using the least-squares approach.

Results

Conclusion