Load Vectors for Damage Localization

Abstract

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.

Damage localization under ambient vibration using changes in flexibility

“…The Damage Location Vector (DLV) method, first proposed by Bernal (2002a), is based upon determination of a special set of vectors, the so-called damage location vectors (DLVs). The DLVs have the property that when they are applied to the structure as static forces at the sensor locations, no stress is induced in the damaged elements.…”

“…(16), because of noise and computational errors, the singular values corresponding to are generally not exactly zero. To select the DLVs from the SVD of the matrix , an index svn was proposed by Bernal (2002a) and defined as (19) in which = the ith singular value of the matrix ; = constant that is used to normalize the maximum stress in the structural element, which is induced by the static load , to have a value of one; and is the right singular vector of . Each of the DLVs is then applied to an undamaged analytical model of the structure, and the stress in each structural element is calculated.…”

“…Toksoy and Aktan (1994) and Biswas (1994, 1995) employed the flexibility matrix to detect damage in structures. Most recently, Bernal (2002a) proposed a flexibility-based damage localization method.…”

“…Biswas (1994, 1995) presented a damage detection and localization method based on the flexibility changes in the structure. Bernal (2002a) computed a set of load vectors from the flexibility matrix change, designated as damage location vectors to localize damage.…”

“…Ambient vibration has become an important source of excitation for SHM. Bernal (2002b) presented an initial study to extend the Damage Location Vector (DLV) method (Bernal 2002a) to handle the ambient vibration case.…”