Load vectors for damage localization

A technique to localize damage in structures that can be treated as linear in the pre- and postdamage states is presented. Central to the approach is the computation of a set of vectors, designated as damage locating vectors (DLVs) that have the property of inducing stress fields whose magnitude is zero in the damaged elements (small in the presence of truncations and approximations). The DLVs are associated with sensor coordinates and are computed systematically as the null space of the change in measured flexibility. The localization approach based on the use of DLVs is not structure type dependent and can be applied to single or multiple element damage scenarios. Knowledge about the system is restricted to that needed for a static analysis in the undamaged state, namely, the undamaged topology and, if the structure is indeterminate, the relative stiffness characteristics. Numerical simulations carried out with realistic levels of noise and modeling error illustrate the robustness of the technique.