Damage Localization from Transmission Zeros of Delta Systems

Conditioning difficulties often thwart the characterization of damage by model updating. Methods that can provide information on damage location without explicit selection of free parameters are important for improving the likelihood of success. A technique that satisfies this objective known as the dynamic damage locating vector method locates damage as regions where a stress field that is computed in a model of the reference state, using loads extracted from changes in the transfer matrix, is identically zero. Central to the present paper is the fact that existence of the noted loads requires that the change in the transfer matrix be rank deficient everywhere in $\mathbb{C}$ . Specifically, the paper examines the situation where the change in the transfer matrix is full normal rank and shows that although zero stress excitations are not generally feasible, useful surrogates can often be obtained from conditions defined by the invariant zero triplets (i.e., zero, zero direction, and zero input) of a mathematical structure, designated as the delta system, which maps inputs to changes in the output. The paper discusses the formulation of the delta system, the extraction of the invariant zeros, and the computation of the associated stress fields. Selection of the potentially damaged set of elements is based on a decision logic that uses the aggregate information from all (or any subset) of the identified zeros.