Crack Assessment of Beam Structures from Changes in Natural Frequencies Using Meta-heuristic Approaches

Abstract

The existence of a crack in the machine and structural components has a severe impact on the performance and integrity of the engineering structure. Failure to identify cracks has several outcomes and sometimes may lead to potential failures of the whole structure. The contributed research work addresses the theoretical and experimental assessment of the influence of a surface open crack on vibration responses of cantilever aluminum beam with rectangular geometry and an inverse analysis to evaluate and to estimate the position and intensity of crack magnitude of the cracked cantilever beam using different metaheuristic approaches. In the theoretical study, variation of natural frequencies due to the presence of crack are determined using the local stiffness matrix resulting from the matrix inversion of flexibility coefficients that the crack develops in its vicinity. Several experiments are performed in the laboratory to verify results obtained from the theoretical study. The results obtained revealed that the variation of the natural frequency could be employed as a viable parameter to show the crack existence and magnitude. The focus of the present thesis work is to carry out an inverse analysis to determine the position and intensity of crack using natural frequency data. The solution of the inverse problem is to obtain crack details by minimizing an objective function based on natural frequencies. The frequency based objective function is solved by employing different simple and reliable meta-heuristic algorithms. The differential evolution (DE) and its modified version, called modified differential evolution (MDE) have been employed to estimate the position and depth of a crack. Particle swarm optimization (PSO), a population-based meta-heuristic approach, utilizes swarm intelligence to determine the position and depth of a crack. Two different variants of PSO algorithm is employed in the area of crack detection to estimate the crack details. The first variant investigates the influence of variation of inertia weight parameter in predicting the position and severity of a crack present in the cantilever beam. The second variant embedded a squeezing strategy in the PSO mechanism, called modified PSO (MPSO) to accelerate the convergence speed for obtaining optimal crack variables. The velocity update equation of PSO is further refined by employing the concept of game theory, called as game theoretic PSO (GTPSO). The last part of the thesis work presents the design of hybrid algorithm by merging the desirable characteristics of DE and PSO to alleviate their individual shortcomings. Two different strategies are adopted to integrate DE and PSO for estimation of crack position and crack depth. The first case employs a cooperative strategy between DE and PSO and called DEPSO algorithm. In the second case, a differential parameter borrowed from DE is embedded in the velocity equation of PSO and called PSODV algorithm. A comparative analysis of the proposed techniques implemented in the current research is critically examined. The outcome of comparative analysis reveals that the hybridized DEPSO algorithm outperforms other proposed techniques explored in the area of crack detection in terms of predicting the crack position and crack depth with reasonable accuracy.