An adaptive PCE-HDMR metamodeling approach for high-dimensional problems

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 pre...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 64; no. 1; pp. 141 - 162
Main Authors: Yue, Xinxin, Zhang, Jian, Gong, Weijie, Luo, Min, Duan, Libin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Design engineering
Design optimization
Dimensional analysis
Engineering
Engineering Design
Functions (mathematics)
Mathematical analysis
Mathematical functions
Metamodels
Polynomials
Rectangles
Research Paper
Robustness (mathematics)
Sampling methods
Structural hierarchy
Theoretical and Applied Mechanics
Polynomial chaos expansion (PCE)
Adaptive sampling
High-dimensional model representation (HDMR)
Metamodeling
Design optimization
ISSN:1615-147X, 1615-1488
Online Access:Get full text
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Summary: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.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-021-02866-7