Steady state shift damage localization

Abstract

The accuracy of the identified modal model is the weak link in many vibration based damage localization schemes. This paper presents a localization approach that avoids identification by operating with two frequency domain subspaces, one obtained by Fourier transformation of output measurements and the other from a model of the reference state and a postulated damage distribution. The approach differs from a model updating framework in that only the damage distribution, and not the extent, enters the formulation. The method operates on the premise that the loads are time limited, have an invariant distribution in space and requires that the histories be repeatable, or that the excitation be a single history, in which case repeatability is not necessary. The time histories of the excitation are not used in the technique and therefore need not be known. It is shown that multiple damages can be considered without combinatorics if $e \ge \kappa$ where e is the number of available actuators and $\kappa$ is the rank of the change in the transfer matrix due to damage. The constraint on the number of measurements, m, is $m \ge \kappa .$ The method, designated as the steady state shift damage localization (S3DL) is experimentally tested on an aluminum plate where damage is simulated by mass additions and by an edge cut.