Vibration-based updating method for structural health monitoring using Moth-Flame optimization algorithm

Structural damage not only changes the dynamic characteristics of the structure, but also it may lead to complete destruction of the structure in some cases. Since early identification of damage can prevent such catastrophic events, structural health monitoring and damage detection has absorbed the attention of the civil, mechanical and aerospace engineers in the last decades. An effective health monitoring methodology not only can provide information about the global serviceability of the monitored structure, but also it can help the engineers to prepare cost-effective rehabilitation programs based on the obtained details about the health of the structure and its members. Different methods have been proposed for structural damage identification and estimation. Vibration-based methods consider the changes in the structural modal parameters, like natural frequencies and associated mode shapes, and/or their derivatives, like modal flexibility and residual force vector, for damage identification and quantification. Considering their acceptable sensitivity to wide-range of structural damages, vibration-based methods are considered as one of the most practical approaches for structural fault prognosis. Employing vibration parameters to define the damage detection problem as a model updating problem, is one of the well-known strategies that can return both the damage location and extent in different types of engineering structures. Such methods can be solved with optimization algorithms to find and report the structural damage in terms of the global extremums of a damage-sensitive objective function.
In this paper a new model updating approach for health monitoring and damage localization and quantification in engineering structures is presented. At first, a damage-sensitive objective function, which is based on the error function between the modal data of the monitored structure and its analytical model, is proposed. This objective function is formulated by means of the point-by-point matching strategy to minimize the difference between two models. Modal natural frequencies and the associated mode shape vectors are directly fed to the objective function and this can result in an easy assessment methodology to check the convergence rate of the function. Moreover, in such a case, the objective function uses the sensitivity of both these parameters for damage identification. The proposed inverse problem is solved using Moth-Flame Optimization (MFO) algorithm which has been inspired form spiral convergence of moths toward artificial lights. From mathematical point of view, updating the position of the moths with respect to the flames –which are the best solutions obtained during iterations–, reduces the probability of being trapped in the local extremum points and also, ensures the convergence of the algorithm to its global optimal solution. The applicability of the method was evaluated by studying different damage patterns on three numerical examples of engineering structures: a seven-story shear frame, a simple beam with 10 elements, and a planar truss with 29 elements. In all these studies, damages were simulated as reduction in the stiffness matrix of the damaged elements. Different issues, like noise effects, were considered and their impacts on the performance of the proposed method were investigated. Furthermore, comparative studies were carried out to discuss the advantages and drawbacks of the introduced method as well as the employed techniques. The obtained results indicate that the method is an effective strategy for vibration-based damage detection and localization in engineering structures.