Model Based Damage Identification Using Output Spectral Densities

Abstract

A damage identification method utilizing an existing computational model and output spectral densities is presented. The problem covered here is the detection, localization and quantification of damage in real vibrating elastomechanical structures. The damages are localized by means of changes in the dynamic characteristics between a reference model and the actual, measured system. The main contribution is that the exact measurement of the input signals is ignored. These signals are assumed to be an ergodic random process, whose statistical properties such as mean and covariances must be estimated. Power spectral densities allow random excitations to be dealt with. The lack of measurement information is treated by means of the dynamic condensation technique and the Kalman Bucy filter technique. In the first case the size of the model matrices are reduced to the number of measured degrees of freedom (dof). In the second procedure the measured responses are expanded to the size of the model matrices. With equally sized measurement and model matrices a linear equation system for the desired parameter changes is derived by using the sensitivity approach. The equation system for this inverse problem is usually ill-conditioned and must be regularized in some way. One possibility is to reduce the subset of parameters to be in error. The algorithm is applied to a beam structure and a measured laboratory structure, a multi story frame, in which artificial damage is introduced by weakening one column between two stories. So, it is shown that the location and the size of the corresponding stiffness decrease can be detected.