Stiffness Identification and Damage Localization via Differential Evolution Algorithms

The goal of structural health monitoring is to identify which discrepancies between the actual behaviour of a structure and its reference undamaged state are indicative of damage. For this purpose, an objective function, which minimizes the difference between the measured and theoretical modal characteristics of the structure, is formulated. By selecting the stiffness parameters as optimization variables, a differential evolution algorithm is applied to create successive generations that better reflect the measured response, until a certain tolerance is met. At each step of the algorithm, the current modal parameters are recalculated from the new generation of stiffness matrices to estimate the value of the objective function. This procedure represents a favourable path to solve the so-called 'inverse problem'. Furthermore, the comparison of the identified stiffness matrix with the initial one allows for damage detection and localization. A numerical example, where a generic structure is discretized into finite elements, is provided.