A Two-Step Damage Diagnostic Approach Based on Static Strain Energy and Model-Updating via the Equilibrium Optimizer

Despite the great achievements accomplished so far in the field of damage detection, the need for a more comprehensive damage detection approach that effectively functions despite several real-world obstacles still exists. Among different methods suggested so far, model-updating holds the most appeal; however, its accuracy and efficiency are seriously challenged when the problem size grows as it fails to solve the problem with an increase in the number of variables. In this paper, a two-step approach is suggested that reduces the problem size in model updating-based damage detection methods by identifying potentially damaged elements using a static strain-based damage identification index over the first step. Therefore, only a few unknown variables will be introduced to the next step, which involves an iterative model-updating process that includes a novel damage-sensitive objective function to determine damage severities in the located elements of the previous step. In this stage, a meta-heuristic optimizer, the Equilibrium Optimizer, is utilized to detect the unknown variables, i.e., damage values. This optimization algorithm is used given that it has not been applied to damage detection problems before. The method is also tested on a number of numerical examples to be validated and the effects of external factors such as measurement noise can be taken into account. Apart from that, a comparative study is also carried out to compare the efficacy of the present work with previous references. Interestingly, the method is capable of detecting damaged elements with great speed and accuracy, and the quality of the results has not been seriously affected in the presence of perturbing factors. Moreover, information from even a limited number of first modes has been enough to solve the problem, which means that the approach does not require all vibration modes. Finally, an experimental verification study is also carried out to demonstrate the capability of the method in detecting damaged elements in real structures. It is shown that the method can detect the damaged element successfully, which is indicative of the practicality of the suggested technique in real-world applications.