Statistical decision making for damage localization with stochastic load vectors

Abstract

Mechanical systems under vibration excitation are prime candidates for being modeled by linear time invariant systems. Damage detection in such systems relates to the monitoring of the changes in the eigenstructure of the corresponding linear system, and thus reflects changes in modal parameters (frequencies, damping, mode shapes) and finally in the finite element model of the structure. Damage localization using both finite element information and modal parameters estimated from ambient vibration data collected from sensors is possible by the Stochastic Dynamic Damage Location Vector (SDDLV) approach. Damage is related to some residual derived from the kernel of the difference between transfer matrices in both reference and damage states and a model of the reference state. Deciding that this residual is zero is up to now done using an empirically defined threshold. In this paper, we show how the uncertainty in the estimates of the state space system can be used to derive uncertainty bounds on the damage localization residuals to decide about the damage location with a hypothesis test.