Damage detection in nonlinear systems using system augmentation and generalizedminimum rank perturbation theory

Abstract

A damage detection method is developed for nonlinear systems using model updating. Themethod uses a nonlinear discrete model of the system and the form of the nonlinearities tocreate an augmented linear model of the system. A modal analysis technique that usesforcing that is known but not prescribed is then used to solve for the modal properties ofthe augmented linear system after the onset of damage. Due to the specialized form of theaugmentation, nonlinear damage causes asymmetrical damage in the updated matrices.Minimum rank perturbation theory is generalized so that it may be applied to theaugmented system and can handle these asymmetrical damage scenarios. Themethod is demonstrated using numerical data from several nonlinear mass–springsystems.