Identification of system matrices based on experimental modal analysis and its application in structural health monitoring

Abstract

This paper presents a system matrices identification approach directly from the real-time measured structural responses. Based on the experimental modal analysis, the identified system matrices are expected to represent the system behaviours as same as the experimentally measured ones. Due to the fact that the system matrices, i.e. the mass, stiffness, and damping matrices, are the direct reflection of the inherent properties of the structure, they can be naturally served as the indicator of structural damages. The identification approach utilizes the state space representation for the equation development to construct the system matrices using the complex modes (i.e. the complex eigenvalues and eigenvectors). The complex modes, however, requires a calibration process to enforce the so-called properness condition, which is not generally fulfilled by the modes because of the inevitable experimental noise. An efficient method based on the Riccati equation is proposed to calibrate the complex eigenvectors so that they can be safely used to construct the system matrices. A scalar quantity based on the norm of the matrices is defined as the indicator for structural health monitoring. The overall approach is performed on a numerical model of a structure with controllable modifications (i.e. artificial damages). The difference between the identified matrices of the original and modified structures clearly demonstrates the approachs feasibility in structural health monitoring.