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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 optimizationdoi:10.20855/ijav.2017.22.4488 fatcat:kgcj52lnn5b3bf5rg355sasegq