Application of R2PSO Algorithm in Crack Detection of Functionally Graded Beams

Abstract

A fault diagnosis procedure based on r2PSO algorithm-a newly developed version of particle swarm optimization (PSO)-is presented for detecting crack depth and location in a functionally graded material (FGM) cantilever beam. The governing equation and boundary conditions are obtained by using the extended Hamilton's principle, and the characteristic equation is obtained as a function of position ratio and depth ratio of crack. Identification of the crack is formulated as an optimization problem. The r2PSO algorithm is used to find the optimal solution of the cost function, which is based on the summation of the absolute value of the characteristic equation for three natural frequencies. The position ratio and depth ratio of crack are computed by algorithm, when three natural frequencies of FGM beam are entered to algorithm as inputs. The obtained results confirm the applicability and efficiency of r2PSO to calculate the parameters of crack with high accuracy and suitable convergence rate.