Refine your search
Collections
Co-Authors
Year
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Yao, Zengquan
- A PC-Kriging-HDMR Integrated with an Adaptive Sequential Sampling Strategy for High-Dimensional Approximate Modeling
Abstract Views :135 |
PDF Views:84
Authors
Affiliations
1 School of Systems Science and Engineering, Sun Yat-Sen University, Guangzhou, Guangdong 510275, CN
1 School of Systems Science and Engineering, Sun Yat-Sen University, Guangzhou, Guangdong 510275, CN
Source
AIRCC's International Journal of Computer Science and Information Technology, Vol 15, No 3 (2023), Pagination: 63-79Abstract
High-dimensional complex multi-parameter problems are ubiquitous in engineering, as traditional surrogate models are limited to low/medium-dimensional problems (referred to p≤10). They are limited to the dimensional disaster that greatly reduce the modelling accuracy with the increase of design parameter space. Moreover, for the case of high nonlinearity, the coupling between design variables fail to be identified due to the lack of parameter decoupling mechanism. In order to improve the prediction accuracy of high-dimensional modeling and reduce the sample demand, this paper considered embedding the PC-Kriging surrogate model into the high-dimensional model representation framework of Cut- HDMR. Accordingly, a PC-Kriging-HDMR approximate modeling method based on the multi-stage adaptive sequential sampling strategy (including first-stage adaptive proportional sampling criterion and second stage central-based maximum entropy criterion) is proposed. This method makes full use of the high precision of PC-Kriging and optimizes the layout of test points to improve the modeling efficiency. Numerical tests and a cantilever beam practical application are showed that: (1) The performance of the traditional single-surrogate model represented by Kriging in high-dimensional nonlinear problems is obviously much worser than that of the combined- surrogate model under the framework of Cut-HMDR (mainly including Kriging-HDMR, PCE-HDMR, SVR-HDMR, MLS-HDMR and PC-Kriging-HDMR);(2)The number of samples for PC-Kriging-HDMR modeling increases polynomially rather than exponentially with the expansion of the parameter space, which greatly reduces the computational cost;(3)None of the existing Cut-HDMR can be superior to any in all aspects. Compared with PCEHDMR and Kriging-HDMR, PC-Kriging-HDMR has improved the modeling accuracy and efficiency within the expected improvement range, and also has strong robustness.Keywords
Multiparameter Decoupling, PC-Kriging-HDMR, Surrogate Model, Adaptive Sequential Sampling, Highdimensional Modeling.Full Text
References
- Eldred M, Dunlavy D. Formulations for surrogate-based optimization with data fit, multifidelity, and reduced-order models[C]//11th AIAA/ISSMO multidisciplinary analysis and optimization conference. 2006: 7117.
- Queipo N V, Haftka R T, Shyy W, etal. Surrogate-based analysis and optimization[J]. Progress in Aerospace Sciences, 2005, 41(1): 1-28.
- Koch P N, Simpson T W, Allen J K, et al. Statistical approximations for multidisciplinary design optimization: the problem of size[J]. Journal of aircraft, 1999, 36(1): 275-286.
- Sobol' I M. Sensitivity Estimates for Nonlinear Mathematical Models [J]. Mathematical Modelling and Computational Experiments, 1993, 1(4): 407-414.
- Rabitz H, Aliş Ö F. General foundations of high-dimensional model representations[J]. Journal of Mathematical Chemistry, 1999, 25(2-3): 197-233.
- Li G, Rosenthal C, Rabitz H. High dimensional model representations[J]. The Journal of Physical Chemistry A, 2001, 105(33): 7765-7777.
- Sobol I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and computers in simulation, 2001, 55(1-3): 271-280.
- Banerjee I, Ierapetritou M G. Design optimization under parameter uncertainty for general black-box models[J]. Industrial & engineering chemistry research, 2002, 41(26): 6687-6697.
- Li E, Wang H, Li G. High dimensional model representation (HDMR) coupled intelligent sampling strategy for nonlinear problems[J]. Computer Physics Communications, 2012, 183(9): 1947-1955.
- Tang L, Lee K Y, Wang H. Kriging-HDMR Nonlinear approximate model method[J]. Chinese Journal of Theoretical and Applied Mechani, 2011, 43(4): 780-784.
- Li G, Xing X, Welsh W, et al. High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions[J]. Journal of Mathematical Chemistry, 2017, 55: 278-303.
- Cai X, Qiu H, Gao L, et al. An enhanced RBF-HDMR integrated with an adaptive sampling method for approximating high dimensional problems in engineering design[J]. Structural and Multidisciplinary Optimization, 2016, 53: 1209-1229.
- Ju Y, Parks G, Zhang C. A bisection-sampling-based support vector regression–high-dimensional model representation metamodeling technique for high-dimensional problems[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017, 231(12): 2173-2186.
- Cai X, Qiu H, Gao L, et al. Metamodeling for high dimensional design problems by multi-fidelity simulations[J]. Structural and multidisciplinary optimization, 2017, 56: 151-166
- Zhang N, Wang P, Dong H. Research on high-dimensional model representation with various metamodels[J]. Engineering Optimization, 2018.
- Shan S, Wang G G. Metamodeling for high dimensional simulation-based design problems[J]. 2010.
- Schobi R, Sudret B, Wiart J. Polynomial-chaos-based Kriging[J]. International Journal for Uncertainty Quantification, 2015, 5(2).
- Schöbi R, Marelli S, Sudret B. UQLab user manual–PC-Kriging[J]. Report UQLab-V1, 2017: 1-109.
- Sudret B. Global sensitivity analysis using polynomial chaos expansions[J]. Reliability engineering & system safety, 2008, 93(7): 964-979.
- Kleijnen J P C. Kriging metamodeling in simulation: A review[J]. European journal of operational research, 2009, 192(3): 707-716.
- Boomsma W, Ferkinghoff-Borg J, Lindorff-Larsen K. Combining experiments and simulations using the maximum entropy principle[J]. PLoS computational biology, 2014, 10(2): e1003406.
- Ji L, Chen G, Qian L, et al. An iterative interval analysis method based on Kriging-HDMR for uncertainty problems[J]. Acta Mechanica Sinica, 2022, 38(7): 521378.
- Li E, Ye F, Wang H. Alternative Kriging-HDMR optimization method with expected improvement sampling strategy[J]. Engineering Computations, 2017.
- Huang Z, Qiu H, Zhao M, et al. An adaptive SVR-HDMR model for approximating high dimensional problems[J]. Engineering Computations, 2015.
- Ji L, Chen G, Qian L, et al. An iterative interval analysis method based on Kriging-HDMR for uncertainty problems[J]. Acta Mechanica Sinica, 2022, 38(7): 521378.
- Kim D, Lee I. Efficient high-dimensional metamodeling strategy using selectively high-ordered kriging HDMR (SH-K-HDMR)[J]. Journal of Mechanical Science and Technology, 2021, 35: 5099-5105.
- Zhang Q, Wu Y, Lu L, et al. An adaptive dendrite-HDMR metamodeling technique for high-dimensional problems[J]. Journal of Mechanical Design, 2022, 144(8): 081701.