A new interval uncertain optimization method for structures using Chebyshev surrogate models. (January 2015) - Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing
Highlights: An interval uncertainty optimization methodology, considering both the robustness and reliability. Interval arithmetic is introduced to replace the inner loop optimization, to improve efficiency. High-order Taylor inclusion function is proposed to compress overestimation in interval arithmetic. Chebyshev surrogate model is proposed to approximate the coefficients of the inclusion function. Abstract: This paper proposes a new non-probabilistic interval uncertain optimization methodology for structures. The uncertain design problem is often formulated as a double-loop optimization. Interval arithmetic is introduced to directly evaluate the bounds of interval functions and eliminate the inner loop optimization. A high-order Taylor inclusion function is proposed to compress the overestimation of interval arithmetic. A Chebyshev surrogate model is proposed to approximate the high-order coefficients of the inclusion function. A metaheuristic optimization algorithm is combined with the mathematical programming to search the global optimum. Two numerical examples are used to demonstrate the effectiveness of this method.