Multiple augmentations of nonlinear systems and generalized minimum rank perturbations for damage detection

Abstract

A generalized minimum rank perturbation theory for identifying damage location and extent in nonlinear systems using a model-based approach is presented. This model updating method is able to handle changes in the mass, damping and stiffness parameters arising from the damage. The method uses a nonlinear discrete model of the system and the functional form of the nonlinearities to create an augmented linear model of the system. A modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage. The methodology has been demonstrated for cubic spring nonlinearities. In this work, the class of nonlinearities is expanded to include Coulomb friction. Several new algorithms are presented, including an iterative generalized minimum rank perturbation theory and a technique based on multiple augmentations to determine damages in linear and nonlinear parameters when there is an incomplete set of eigenvectors. Finally, two eigenvector filtering algorithms, which reduce the effects of measurement noise, are presented.