Invariant eigenvalue assignment and uncertainty quantification for damage localization

Abstract

A scheme is presented for damage localization in linear and time-invariant (LTI) systems using static output feedback eigenstructure assignment. The feedback is realized through signal processing of open-loop input–output data, and the assignment is formulated to render an eigenvalue subset invariant to a number of perturbations that define the spatial domain of the plausible damage distribution. For each perturbation, a feedback gain is designed to realize the eigenvalue invariance, whereby the damage location can be inferred from the shifts in the assigned eigenvalues. The interrogation is posed as a statistical hypothesis test with eigenvalue uncertainty bounds derived from an asymptotic analysis of the assignment formulation. Numerical and experimental examples are presented to validate the theoretical developments and convey the details of the damage localization application.