Closed-Loop Damage-Locating Vectors

The present paper considers localization of stiffness-related damage in minimum-phase structural systems for which input and output data is collected both prior and posterior to damage formation. In an idealized setting, such damage induces a rank-deficient transfer matrix perturbation, whose null space carries information on the spatial damage distribution. The information can be materialized by applying the null vectors, referred to as dynamic damage-locating vectors (DDLVs), as loads to the given system, which will confine damage to the subdomain exhibiting rigid-body motion. In real systems, where the transfer matrix perturbation will not be rank-deficient, the DDLVs must be extracted from a quasi-null space, and this will impair the discrimination between undamaged and damaged subdomains. This paper explores the merit of adding flexibility in the design of the DDLVs by implementing virtual output feedback with the aim of ameliorating the discrimination problem. The virtual implementation allows one to design and realize closed-loop systems, and hereby closed-loop DDLVs, from the identified open-loop system. Different design criteria, each theoretically amenable to enhance the damage resolution provided by the closed-loop DDLVs, are proposed and subsequently tested in a numerical example.