Optimization algorithm for uncertain model updating based on interval overlap ratios and Chebyshev polynomials

This study proposes an interval model updating method based on interval overlap ratios and Chebyshev polynomials. The interval midpoints and interval radii of the uncertain parameters are determined by solving optimization problems separately. The objective function for determining the interval midpoints is constructed based on predicted and measured data. To determine the interval radii, Chebyshev polynomials are used to construct the uncertainty propagation between the updated and modal parameters. A small number of samples is required for Chebyshev polynomials, which improves the computing efficiency of the proposed method. Based on the interval overlap ratio, the objective function for determining the interval radii is constructed. The interval overlap ratio can effectively quantify the agreement between the intervals of modal parameters obtained from simulation and experimental models. Additionally, a surrogate model is used in the proposed method instead of a finite element model, which can be selected as needed. The proposed method is applied to a three-degree-of-freedom mass-spring system, and its computational accuracy in cases of well-separated and close modes is discussed in detail. Furthermore, the method is used in an engineering example, the GARTEUR aircraft model. The results show that the proposed method is effective for interval model updating with high accuracy.