Crack Prediction in Stepped Circular Arches Through Optimization Algorithms

ABSTRACT The purpose of this study is to demonstrate the effectiveness of using optimization algorithms to predict the locations and depths of cracks in stepped circular arches. The cracked zone is modeled as a rotational spring that connects the two adjacent sections. The theoretical model of Euler–Bernoulli is employed to derive the equation of motion for circular arches. By applying boundary conditions as well as the cracks and stepped continuity conditions, a homogeneous system is obtained and resolved through a Newton–Raphson algorithm. The optimization algorithms, coded in MATLAB, are designed for estimating the location and severity of a crack by minimizing the gap between the measured and calculated frequencies. The algorithms utilized in this study encompass the Particle Swarm Optimization (PSO), Firefly hybrid‐Genetic algorithm (FF‐GA), and Particle Swarm Optimization combined with genetic algorithm (PSO‐GA). The predicted values of crack depths and locations obtained via the three algorithms are compared with the exact results by means of a parametric approach. This later leads to ascertaining which of these algorithms demonstrates greater reliability in detecting cracks along the edge of the lateral surface of the arch. The outcomes obtained have been thoroughly deliberated and analyzed.