A new distributionally robust optimization method and its application to rotor-stator clearance

Robust design optimization is crucial for ensuring the normal and stable operational performance of engineering structures by considering the effects of uncertainties inherent in the production and manufacturing processes of structural components. However, current robust design optimization methods are still relatively conservative, time-consuming, and often necessitate significant sacrifice in structural performance to achieve robustness. In response to these issues, the present study proposes a novel distributionally robust optimization (DRO) method based on a two-level Kriging surrogate model. The first-level Kriging model is constructed to replace the relationship between design variables and structural response, thereby enabling the construction of ambiguity sets based on the Euclidean norm and Kullback–Leibler (KL) divergence. This transforms the inner maximization problem into a deterministic optimization. Subsequently, the second-level Kriging model is constructed to approximate the relationship between design variables and the maximum expected value so that the outer minimization problem is also degenerated into a deterministic optimization, which is then solved by subset simulation optimization. The performance of the proposed method is preliminarily validated through a numerical examples, after which its engineering practicability is demonstrated by comparing the results of DRO with those of deterministic optimization for the variation in rotor-stator clearance in a small turbine engine.