Robust design optimisation under lack-of-knowledge uncertainty

Abstract

Design optimization is common practice in engineering where the goal is to find the optimal combination of design parameters under prescribed constraints. However, some parameters may be impossible to define in a deterministic sense and may only be known with significant uncertainty. This limitation has led to an alternative definition of design optimality called robustness, where attention is payed to the variation around the optimal performance. Straightforward methods to solve robust optimization problems are usually limited in two ways: (1) the computation burden of the so-called ‘double-loop’ optimization problem hinders application to realistic models, and (2) the formalisms are typically limited to probabilistic descriptions of the uncertainty. This paper presents a formulation of the robust optimization problem under interval uncertainty and proposes a new approach taking advantage of the so-called adaptive Gaussian processes to solve it efficiently. The proposed surrogate approach mitigates the computational burden of the resolution, and a dedicated learning function is proposed to ensure iterative minimization of the surrogate modelling error and convergence towards the robust optimum. The algorithm uses a stopping criterion related to the level of confidence associated with the optimality of the solution. The approach is illustrated on six analytical and engineering benchmark problems.