Crack identification of beam structures using homotopy continuation algorithm

Abstract

An approach based on homotopy continuation algorithm is presented to identify the parameters of a cracked beam. Euler–Bernoulli finite beam element with a fully opened crack model is adopted to establish the dynamic equation of the structural system. In the inverse problem, the homotopy equation is derived from minimizing the error between the calculated and the simulated measured acceleration responses. The range of homotopy parameter is divided into a number of divisions. Newton iterative method is employed to estimate the solution at each of these division points. The solution at the last division point corresponds to the homotopy equation matching the objective function. Numerical simulations with a simply supported beam and two-span beam show that the proposed method is very accurate compared to an existing method for both single and multiple cracks identification. The effects of type of excitation, division of the homotopy parameter and measurement noise on the identified results are discussed. It is noted that there is no need for an accurate set of initial values with the proposed approach.