Statistical confidence using minimum rank perturbation theory

In this paper, the effect of measurement noise on damage detection performance of the minimum rank perturbation theory is investigated. Closed-form solutions for the sensitivity of the minimum rank perturbation theory damage vectors and calculated stiffness perturbations with respect to errors in the measured modes shapes or frequency response functions are developed. This sensitivity allows one to establish confidence in damage existence, location and extent assessment. The use of this information in interpreting damage detection results is discussed in the context of an experimental study.