Damage location and assessment along structural elements using damage submatrices

A new method to locate and determine the magnitude of damage, expressed as the loss of stiffness, along structural elements of buildings, called Damage Submatrices Method is presented. The method uses information related to the stiffness of both states of the structure: undamaged and damaged, utilizing iterative eigenvalue computations. The novelty of the method relies on its capability to identify damage in specific zones of structural elements depending on how the undamaged model of the structure was discretized. Another advantage of the proposed method is its convergence. This paper also contributes a new approach to simulate noise perturbing stiffness matrices. This technique can be useful for realistic damage detection investigations. Also, the proposed technique used to expand condensed damaged stiffness matrices, to global coordinates, may be useful for system identification projects. Two examples taken from the literature are studied involving limited modal measurements and noise effects to calibrate the method and corroborate its capability for damage assessment. Application of the proposed method to these structures corroborates its efficiency for identifying stiffness degradation of structural elements.