Evolutionary Reliable Regional Kriging Surrogate and Soft Outer Array for Robust Engineering Optimization

Robust optimization seeks designs with optimized performance and low sensitivity to possible variations in a product's life-cycle. As a popular robust design scheme in industry, Taguchi method uses the signal-to-noise ratio (SNR) as a metric of robustness. However, the Taguchi experimental design includes an inner orthogonal arrays (OA) for control factors and an outer OA for noise factors in estimating SNR-based robustness, raising a serious cost concern, especially if expensive samples are involved. Furthermore, rigorous control of noise factors to prespecified levels in the outer OA is impractical in engineering applications. This paper presents a novel approach, robust optimization using evolving reliable Kriging surrogate (ROERKS) that uses an evolving surrogate model to approximate the actual system, and uses a soft outer array to estimate the robustness. Both control variables and noise factors are merged into a combined experimental design served as the training samples to construct a Kriging-based surrogate model. An evolutionary optimizer is applied to search of the subspace of the design variables for a robust optimal solution, and a soft outer array is introduced to estimate the fitness function consisted of the mean and the variance response of evolving individual. To accommodate reduced accuracy of the surrogate model owing to an inadequate sample size, an issue that commonly arises in expensive optimization, the proposed algorithm uses a reliable region to constrain the genetic algorithm search. The verification result of the quasi-optimum is then added to the training samples to refine the evolving surrogate and to adjust the reliable region. A hybrid infilling strategy is then introduced to prevent the early convergence of the quasi-optimum. If the predicted optimum is in close proximity to current samples, the infilling strategy switches to an alternative sample with maximum expected improvement to improve sample efficiency. The iteration process continues until it converges to a robust optimum. The robust optimization of a numerical example for minimization and the robust optimization of a micro accelerometer design with a nominal-the-best sensitivity are presented to demonstrate the effectiveness of the proposed method. ROERKS outperforms Taguchi method and the RSM-based robust optimization, and derives a superior robust optimum using many fewer experiments.