To avoid an over-conservative design and ensure desired performance in an optimal way, the product quality and robustness are considered in terms of the product performance mean and variance. In this paper, to facilitate robust design exploration under uncertainty, a new sequential subspace robustness assessment method is presented to assess not only the mean and variance of performance, but also their sensitivities with respect to design parameters. The proposed method is based on the computational framework that integrates the Univariate Revolving Integration (URI) and surrogate modeling of univariate integral functions. The proposed framework enables consideration of bivariate interaction effects approximately by the aggregation of multiple URIs in a partial set of bivariate subspaces. It is found that the proposed method provides better accuracy with comparable computational cost in assessing the statistical moments and sensitivities of product performance than existing methods such as dimension reduction method. Several numerical examples including mathematical and structural problems are presented to demonstrate the efficiency and accuracy of the method.
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