Perturbation-invariant eigenvalue assignment for statistical damage localization

Abstract

Abstract The present paper reviews a recently proposed eigenvalue assignment scheme for structural damage localization. The eigenvalue assignment is, under the assumption of system controllability and observability, formulated with the objective of rendering an eigenspectrum subset invariant to low-rank perturbations in the considered system. Damage localization follows with the perturbations being realized as damage patterns postulated in different subdomains using a model of the system. The damage location can thus be inferred from the damage-induced shifts in the assigned eigenvalues, which, ideally, will be zero when postulating a pattern that entails the physical damage distribution. In real applications, eigenvalue invariance is unattainable due to, among other phenomena, stochastic disturbances, so the localization is conducted by hypothesis testing with the assigned eigenvalues and their uncertainty bounds. The paper reviews the proposed damage localization method and tests its applicability in the context of a numerical example.