Adaptive Robust Design Optimization

Robust design optimization (RDO) seeks optimal solutions that exhibit minimal sensitivity to input uncertainties, making it highly valuable for engineering structural design. Conventional RDO formulations typically involve a computationally prohibitive nested double-loop procedure, particularly when high-fidelity finite element simulations are required. This work proposes a fully decoupled adaptive RDO framework based on Kriging surrogate modeling that completely eliminates the nested structure by transforming the original uncertainty-based optimization into an equivalent deterministic one. Closed-form expressions for the mean and standard deviation of the performance function with respect to arbitrary design variables are derived and directly embedded into the uncertainty propagation phase, thereby eliminating approximation errors inherent in traditional post-processing numerical integration schemes. Furthermore, metamodeling uncertainty is rigorously quantified and incorporated into the uncertainty propagation process. An adaptive sampling strategy is developed to sequentially refine the Kriging model in regions critical to robust optimality, significantly enhancing the accuracy of uncertainty quantification while maintaining computational efficiency. The effectiveness and superiority of the proposed fully decoupled adaptive RDO approach are demonstrated through several benchmark numerical examples and practical engineering problems. Results confirm that the method achieves comparable or superior robustness and reliability with only a small fraction of the computational cost required by traditional nested or semi-decoupled RDO methods.