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- Title
An adaptive PCE-HDMR metamodeling approach for high-dimensional problems.
- Authors
Yue, Xinxin; Zhang, Jian; Gong, Weijie; Luo, Min; Duan, Libin
- Abstract
Metamodel-based high-dimensional model representation (HDMR) has recently been developed as a promising tool for approximating high-dimensional and computationally expensive problems in engineering design and optimization. However, current stand-alone Cut-HDMRs usually come across the problem of prediction uncertainty while combining an ensemble of metamodels with Cut-HDMR results in an implicit and inefficient process in response approximation. To this end, a novel stand-alone Cut-HDMR is proposed in this article by taking advantage of the explicit polynomial chaos expansion (PCE) and hierarchical Cut-HDMR (named PCE-HDMR). An intelligent dividing rectangles (DIRECT) sampling method is adopted to adaptively refine the model. The novelty of the PCE-HDMR is that the proposed multi-hierarchical algorithm structure by integrating PCE with Cut-HDMR can efficiently and robustly provide simple and explicit approximations for a wide class of high-dimensional problems. An analytical function is first used to illustrate the modeling principles and procedures of the algorithm, and a comprehensive comparison between the proposed PCE-HDMR and other well-established Cut-HDMRs is then made on fourteen representative mathematical functions and five engineering examples with a wide scope of dimensionalities. The results show that the proposed PCE-HDMR has much superior accuracy and robustness in terms of both global and local error metrics while requiring fewer number of samples, and its superiority becomes more significant for polynomial-like functions, higher-dimensional problems, and relatively larger PCE degrees.
- Subjects
HIGH-dimensional model representation; MATHEMATICAL functions; POLYNOMIAL chaos; ENGINEERING design
- Publication
Structural & Multidisciplinary Optimization, 2021, Vol 64, Issue 1, p141
- ISSN
1615-147X
- Publication type
Article
- DOI
10.1007/s00158-021-02866-7