Damage Detection in Nonlinear Systems Using Optimal Feedback Auxiliary Signals and System Augmentations

Abstract

An optimal sensitivity enhancing feedback control has been proposed recently. This method differs from previous sensitivity enhancing approaches because in addition to placing the closed-loop eigenvalues of the interrogated system, the eigenvectors are also optimally placed. This technique addresses two major limitations of frequency-based damage detection methods: the low sensitivity of the frequencies to damages and the limited range of damage scenarios identifiable from frequency-only measurement data. An unresolved challenge is enhancing sensitivity for nonlinear systems. This paper addresses this challenge by using optimal feedback auxiliary signals to enhance sensitivity for damage detection in nonlinear systems. The nonlinearity is accounted for by creating augmented linear models of higher order (in a higher dimensional state space). The methodology for constructing augmented linear systems with this property has been previously proposed by the authors (2008, “ Multiple Augmentations of Nonlinear Systems and Generalized Minimum Rank Perturbations for Damage Detection,” J. Sound Vib., 316(1-5), pp. 101–121). Herein, the focus is on generalizing the previous work on sensitivity enhancing feedback and on system augmentation for enhancing sensitivity of damage detection in nonlinear systems. Results obtained by applying the optimal feedback auxiliary signals and optimal augmentation to a nonlinear mass-spring system are presented.