A multi-objective approach to solve the damage detection problem

Optimization-based damage detection methodologies require the definition of an objective function in terms of a given structural response. Often, such functions rely on the difference between the experimental and analytical dynamic parameters for the current structure and are generally plagued by the difficulty of assigning weight factors to the terms of the linear combination. The present study obviates issues of this nature by formulating the problem so that each term corresponds to an individual objective. Therefore, the problem comes to entail multiple-objectives, for which the Non-Dominated Sorting Genetic Algorithm II can be fruitfully employed. Similarly, a heuristic mutation operator helps take into account the unstructured nature of the damage detection problem. As a sort of case study, the methodology proposed herein is applied to 100 random damage detection scenarios in a beam structure divided into 60 finite elements. Although results demonstrate that the algorithm reliably locates damaged elements approximately 80% of the time, the amount of error with regard to damage extent occasionally proved high. Despite this fact, most computed damage scenarios contained few misidentified damaged elements (less than six 49% of the time) with low damage extents generally.