A Study on Multiobjective Optimization Technique for Inverse and Crack Identification Problems

Abstract

It is well known that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a structure, a variety of techniques were developed. However, these approaches are not enough to identify the crack profiles because the crack identification problem is heavily ill-posed (the existence, uniqueness and stability of solutions cannot be assured). A method is presented in this article which uses Pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization (MOPCEAs), which are deriving solutions without weighting factors such as a regularization parameter and can work effectively for problems of concern. With finite element model of the structure to calculate eigenfrequencies, it is possible to formulate the inverse problem in multiobjective optimization format. MOPCEAs are used to identify the crack location and depth by minimizing three objective functions, which are defined by the difference of the calculated eigenfrequency and the measured/reference one, respectively. We have tried this new idea on beam structures and the results are promising.