Quantile surrogates and sensitivity by adaptive Gaussian process for efficient reliability-based design optimization

Abstract

To obtain the optimal structural design satisfying probabilistic requirements, reliability-based design optimization (RBDO) has been widely studied and applied. However, its practical applications have been often hampered by huge computational costs. To address the challenge, the authors recently developed an RBDO method termed quantile surrogates by adaptive Gaussian process (QS-AGP), which approximates the quantiles of the performance functions adaptively using Gaussian process models to check whether the pre-generated design samples satisfy the reliability requirements. It has been shown that QS-AGP requires much fewer evaluations of performance functions than existing RBDO methods. However, the approach could be computationally expensive in high-dimensional applications since it may require an insurmountable memory to handle the pre-generated design samples. To alleviate this difficulty, a new quantile surrogate based RBDO framework is proposed in this paper. To this end, a non-sampling-based procedure is proposed for an efficient estimation of the quantile surrogates based on both input uncertainties and model error of surrogates. Moreover, to perform quantile-surrogate-based RBDO without relying on pre-generated design samples, the parameter sensitivity of the quantile surrogate is implemented. The computational efficiency of the proposed RBDO method, termed quantile surrogates and sensitivity by adaptive Gaussian process (QS2-AGP), is demonstrated by a variety of RBDO examples featuring up to 15 design parameters. The supporting source codes are available for download at https://github.com/Jungh0Kim/QS2-AGP.