System Augmentation and Matrix Updating for Damage Detection in Nonlinear Systems

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, the augmented system matrices may not be symmetric, also nonlinear damage causes asymmetrical damage in the updated matrices. A generalized minimum rank perturbation theory is developed to handle the asymmetrical damage scenarios. The damage extent algorithm becomes an iterative process when damage occurs simultaneously in the mass and stiffness matrices. The method is demonstrated using numerical data from two nonlinear mass spring systems and a nonlinear truss. Various damage scenarios of the three nonlinear systems are used to explore the effectiveness of the method. The nonlinearities explored include cubic springs and Coulomb friction.