A new interval uncertain optimization method for structures using Chebyshev surrogate models

•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.

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.