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.