Multiple crack identification in frame structures using a hybrid Bayesian model class selection and swarm-based optimization methods

Crack identification in engineering structures has been widely investigated by researchers. Most of the literature on multiple crack identification, however, has focused on rather simple structures like beams and it is often assumed that the number of cracks is known while this is not a practical assumption. In this article, multiple crack identification in frame structures is investigated based on experimental vibration data using the Bayesian model class selection and swarm-based optimization methods to identify both the number of cracks and their characteristics. To this end, first, the numerical model of the intact frame is updated based on the natural frequencies of the intact state using the particle swarm inspired multi-elitist artificial bee colony algorithm. After updating the intact model of the structure, a set of numerical models of the cracked frame with different numbers of cracks is constructed. Since the number of cracks is not known a priori, the Bayesian model class selection is employed to find the most plausible model class in order to predict the number of cracks. Then, the parameters of the cracks are identified using the particle swarm inspired multi-elitist artificial bee colony algorithm. Instead of pinpointing to one optimal solution obtained after a large number of function evaluations, a set of best solutions whose objective values are less than 10⁻⁵are recorded and the regions where the best solutions are concentrated are identified to see how the solution would differ if less number of function evaluations is employed. To fully assess the effectiveness of this approach, both numerical and experimental examples are utilized. The results confirm the effectiveness of the proposed method for identifying multiple cracks in the frames using a few experimental natural frequencies of the structure. The effect of using more natural frequencies on the accuracy of the location and depth of the cracks is also studied.