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

A damage detection method is developed for nonlinear systems using model updating. The method uses a nonlinear discrete model of the system and the 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. Due to the specialized form of the augmentation, nonlinear damage causes asymmetrical damage in the updated matrices. Minimum rank perturbation theory is generalized so that it may be applied to the augmented system and can handle these asymmetrical damage scenarios. The method is demonstrated using numerical data from several nonlinear mass-spring systems.