Detection of crack location via a global minimization approach

A global minimization method is presented for determining the approximate location of a crack in a beam-type structure based on vibration data. The exact modal deflection and the corresponding modal inertia force of the cracked structure are first computed using a measured eigencouple (frequency and mode shape) of the structure. A reduced stiffness model is then adopted in the finite element formulation of the cracked structure to simulate the dynamic behavior and compute the approximate modal deflection of the structure subjected to the exact modal inertia force. An error function measuring the difference between the exact and approximate modal deflections of the cracked structure is constructed and minimized in a global minimization process for identifying the cracked element from which the approximate location of the crack in the structure is determined. The applications of the proposed global minimization method for crack location identification are illustrated by means of several examples.