A statistics and optimization-based approach for crack parameter identification in curved beams

This article presents a study for detecting crack parameters (crack location and crack-depth ratio) in horizontally curved thin-walled channel section beams utilizing only dynamic information from a post-damage event based on combined statistical and optimization tools. A combined response surface methodology and genetic algorithm have been utilized in the present research work. Finite element computations based on design of experiment have been used in order to obtain the coefficients of a second-order polynomial model for the response surface function. Genetic algorithm is then used as a searching tool to determine the optimum parameters by minimizing an objective function which is formed as the root mean square of the errors between the computed responses from response surface functions and measured responses. Two cases of different subtended central angles are considered to illustrate the approach. Each case required 18 laboratory experiments to provide measured input to the proposed integrated approach. It was found that large variation can occur in the calculation of natural frequencies of thin-walled beams, when the effect of warping stiffness is neglected in mathematical model. This study reveals that the precision of the localization and quantification of cracks are dependent on subtended angle. The present method has great potential in crack detection as it does not require the response of an uncracked beam as baseline criteria.