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Structural and Multidisciplinary Optimization

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06.02.2020 | Research Paper

Hybrid metamodel of radial basis function and polynomial chaos expansions with orthogonal constraints for global sensitivity analysis

verfasst von: Zeping Wu, Donghui Wang, Wenjie Wang, Kun Zhao, Houcun Zhou, Weihua Zhang

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 2/2020

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Abstract

In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for the global sensitivity analysis of time-consuming models. Firstly, the orthogonal conditions of radial basis functions (RBF) and polynomial chaos expansions (PCE) were derived to construct the hybrid metamodel. Then, the variance of the metamodel was decoupled into the variances of the RBF and PCE independently by using the orthogonal condition. Furthermore, the analytical formulations of Sobol indices for the hybrid metamodel were derived according to the orthogonal decomposition. Thus, the interaction items of radial basis function and polynomial chaos expansions were eliminated, which significantly simplifies the Sobol indices. Two analytical cases were employed to investigate the influence of the number of the polynomial chaos expansions items, and several analytical and engineering cases were tested to demonstrate the accuracy and efficiency of the proposed method. In the engineering cases, the proposed method yielded significant improvements in terms of both accuracy and efficiency comparing with the existing global sensitivity analysis approaches, which indicates that the proposed method is more appropriate to the global sensitivity analysis of time-consuming engineering problems.

Vorheriger Artikel System reliability analysis with small failure probability based on active learning Kriging model and multimodal adaptive importance sampling

Nächster Artikel An optimization method based on the evolutionary and topology approaches to reduce the mass of composite wind turbine blades

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Blatman G, Sudret B (2008) Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach. Comptes Rendus - Mec 336:518–523. https://doi.org/10.1016/j.crme.2008.02.013 CrossRefMATH

Blatman G, Sudret B (2010a) Efficient computation of global sensitivity indices using sparse polynomial chaos expansions. Reliab Eng Syst Saf 95:1216–1229. https://doi.org/10.1016/j.ress.2010.06.015 CrossRef

Blatman G, Sudret B (2010b) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Eng Mech 25:183–197. https://doi.org/10.1016/j.probengmech.2009.10.003 CrossRef

Borgonovo E, Tarantola S (2012) Advances in sensitivity analysis. Reliab Eng Syst Saf 107:1–2. https://doi.org/10.1016/j.ress.2012.09.001 CrossRef

Borgonovo E, Castaings W, Tarantola S (2012) Model emulation and moment-independent sensitivity analysis: an application to environmental modelling. Environ Model Softw 34:105–115. https://doi.org/10.1016/j.envsoft.2011.06.006 CrossRef

Buzzard GT (2012) Global sensitivity analysis using sparse grid interpolation and polynomial chaos. Reliab Eng Syst Saf 107:82–89. https://doi.org/10.1016/j.ress.2011.07.011 CrossRef

Chakraborty S, Chowdhury R (2017) A hybrid approach for global sensitivity analysis. Reliab Eng Syst Saf 158:50–57. https://doi.org/10.1016/j.ress.2016.10.013 CrossRef

Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127:875. https://doi.org/10.1115/1.1904642 CrossRef

Cheng K, Lu Z, Wei Y et al (2017) Mixed kernel function support vector regression for global sensitivity analysis. Mech Syst Signal Process 96:201–214. https://doi.org/10.1016/j.ymssp.2017.04.014 CrossRef

Cressie N (1990) The origins of kriging. Math Geol 22:239–252. https://doi.org/10.1007/bf00889887

Crestaux T, Le Maître O, Martinez JM (2009) Polynomial chaos expansion for sensitivity analysis. Reliab Eng Syst Saf 94:1161–1172. https://doi.org/10.1016/j.ress.2008.10.008 CrossRef

Efron B, Stein C (1981) The jackknife estimate of variance. Source Ann Stat Ann Stat 9:586–596. https://doi.org/10.1137/1.9781611970319 MathSciNetCrossRefMATH

Gaspar B, Teixeira AP, Guedes Soares C (2017) Adaptive surrogate model with active refinement combining Kriging and a trust region method. Reliab Eng Syst Saf 165:277–291. https://doi.org/10.1016/j.ress.2017.03.035

Garcia-Cabrejo O, Valocchi A (2014) Global sensitivity analysis for multivariate output using polynomial chaos expansion. Reliab Eng Syst Saf 126:25–36. https://doi.org/10.1016/j.ress.2014.01.005 CrossRef

Ge Q, Ciuffo B, Menendez M (2015) Combining screening and metamodel-based methods: an efficient sequential approach for the sensitivity analysis of model outputs. Reliab Eng Syst Saf 134:334–344. https://doi.org/10.1016/j.ress.2014.08.009 CrossRef

Ghanem RG, Spanos PD (1991) Stochastic finite elements: a spectral approach. 7795. https://doi.org/10.1007/978-1-4612-3094-6

Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1905–1915. https://doi.org/10.1029/JB076i008p01905 CrossRef

Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52:1–17. https://doi.org/10.1016/0951-8320(96)00002-6 CrossRef

Ishigami T, Homma T (1990) An importance quantification technique in uncertainty analysis for computer models. Proc ISUMA 90’, First Int Symp Uncertain Model Anal 398–403. https://doi.org/10.1109/ISUMA.1990.151285

Jourdan A (2012) Global sensitivity analysis using complex linear models. Stat Comput 22:823–831. https://doi.org/10.1007/s11222-011-9239-y MathSciNetCrossRefMATH

Kersaudy P, Sudret B, Varsier N et al (2015) A new surrogate modeling technique combining Kriging and polynomial chaos expansions - application to uncertainty analysis in computational dosimetry. J Comput Phys 286:103–117. https://doi.org/10.1016/j.jcp.2015.01.034 MathSciNetCrossRefMATH

Liu H, Hervas J-R, Ong Y-S et al (2018) An adaptive RBF-HDMR modeling approach under limited computational budget. Struct Multidiscip Optim 57:1233–1250. https://doi.org/10.1007/s00158-017-1807-0 CrossRef

Oakley JE, O'Hagan A (2004) Probabilistic sensitivity analysis of complex models: a Bayesian approach. J R Stat Soc B 66:751–769. https://doi.org/10.2307/3647504

Rabitz H, Alis Ö, Alış ÖF (1999) General foundations of high-dimensional model representations. J Math Chem 25:197–233. https://doi.org/10.1023/A:1019188517934 MathSciNetCrossRefMATH

Ratto M, Pagano A (2010) Using recursive algorithms for the efficient identification of smoothing spline ANOVA models. AStA Adv Stat Anal 94:367–388. https://doi.org/10.1007/s10182-010-0148-8 MathSciNetCrossRef

Ratto M, Pagano A, Young P (2007) State dependent parameter metamodelling and sensitivity analysis. Comput Phys Commun 177:863–876. https://doi.org/10.1016/j.cpc.2007.07.011 CrossRef

Sacks J, Welch WJ, Mitchell T, Wynn H (1989) Design and analysis of computer experiments. Stat Sci 4:409–435. https://www.jstor.org/stable/2245858

Saltelli A (2002) Making best use of model valuations to compute sensitivity indices. Comput Phys Commun 145:280–297. https://doi.org/10.1016/S0010-4655(02)00280-1 CrossRefMATH

Saltelli A, Ratto M, Andres T et al (2008) Global sensitivity analysis: The Primer

Schöbi R, Sudret B, Wiart J (2015) Polynomial-chaos-based Kriging. Int J Uncertainty Quantification 5:171–193

Schöbi R, Sudret B, Marelli S (2017) Rare event estimation using polynomial-chaos Kriging. ASCE-ASME J Risk Uncertain Eng Syst Part A Civ Eng 3:D4016002. https://doi.org/10.1061/AJRUA6.0000870 CrossRef

Shao Q, Younes A, Fahs M, Mara TA (2017) Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Comput Methods Appl Mech Eng 318:474–496. https://doi.org/10.1016/j.cma.2017.01.033 MathSciNetCrossRefMATH

Sobieczky H (1999) Parametric Airfoils and Wings. 68:71–87. https://doi.org/10.1007/978-3-322-89952-1_4

Sobol’ IM (1990) Sensitivity analysis for nonlinear mathematical models. Mat Model 2:112–118. https://doi.org/10.18287/0134-2452-2015-39-4-459-461 MathSciNetCrossRefMATH

Sobol’ IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280. https://doi.org/10.1016/S0378-4754(00)00270-6 MathSciNetCrossRefMATH

Sobol’ IM (2003) Theorems and examples on high dimensional model representation. Reliab Eng Syst Saf 79:187–193. https://doi.org/10.1016/S0951-8320(02)00229-6 CrossRef

Sobol’ IM, Kucherenko S (2009) Derivative based global sensitivity measures and their link with global sensitivity indices. Math Comput Simul 79:3009–3017. https://doi.org/10.1016/j.matcom.2009.01.023 MathSciNetCrossRefMATH

Sobol’ IM, Kucherenko S (2010) A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Comput Phys Commun 181:1212–1217. https://doi.org/10.1016/j.cpc.2010.03.006 MathSciNetCrossRefMATH

Sobol’ IM, Levitan YL (1999) On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index. Comput Phys Commun 117:52–61. https://doi.org/10.1016/S0010-4655(98)00156-8 CrossRefMATH

Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93:964–979. https://doi.org/10.1016/j.ress.2007.04.002 CrossRef

Sudret B, Mai CV (2015) Computing derivative-based global sensitivity measures using polynomial chaos expansions. Reliab Eng Syst Saf 134:241–250. https://doi.org/10.1016/j.ress.2014.07.009 CrossRef

Todri E, Amenaghawon AN, Del Val LJ, et al (2014) Global sensitivity analysis and meta-modeling of an ethanol production process. Chem Eng Sci 114:114–127. https://doi.org/10.1016/j.ces.2014.04.027

Wang P, Lu Z, Tang Z (2013) An application of the Kriging method in global sensitivity analysis with parameter uncertainty. Appl Math Model 37:6543–6555. https://doi.org/10.1016/j.apm.2013.01.019 MathSciNetCrossRefMATH

Wang D, Fei Y, Hu F, Zhang WH (2014a) An integrated framework for solid rocket motor grain design optimization. Proc Inst Mech Eng Part G J Aerosp Eng 228:1156–1170. https://doi.org/10.1177/0954410013486589 CrossRef

Wang D, Wu Z, Fei Y, Zhang W (2014b) Structural design employing a sequential approximation optimization approach. Comput Struct 134:75–87. https://doi.org/10.1016/j.compstruc.2013.12.004 CrossRef

Wang F, Xiong F, Chen S, Song J (2019) Multi-fidelity uncertainty propagation using polynomial chaos and Gaussian process modeling. Struct Multidiscip Optim 60:1583–1604. https://doi.org/10.1007/s00158-019-02287-7

Wiener N (1938) The homogeneous chaos. Am J Math 60:897. https://doi.org/10.2307/2371268 MathSciNetCrossRefMATH

Wu Z, Wang D, Patrick Okolo N et al (2016a) Unified estimate of Gaussian kernel width for surrogate models. Neurocomputing 203:41–51. https://doi.org/10.1016/j.neucom.2016.03.039 CrossRef

Wu Z, Wang D, Okolo NP et al (2016b) Global sensitivity analysis using a Gaussian radial basis function metamodel. Reliab Eng Syst Saf 154:171–179. https://doi.org/10.1016/j.ress.2016.06.006 CrossRef

Wu Z, Wang D, Okolo PN et al (2017a) Efficient space-filling and near-orthogonality sequential Latin hypercube for computer experiments. Comput Methods Appl Mech Eng 324:348–365. https://doi.org/10.1016/j.cma.2017.05.020 MathSciNetCrossRefMATH

Wu Z, Wang D, Zhang W et al (2017b) Solid-rocket-motor performance-matching design framework. J Spacecr Rocket 54:1–10CrossRef

Wu J, Zhang D, Liu J, Han X (2019a) A moment approach to positioning accuracy reliability analysis for industrial robots. IEEE Trans Reliab 1–16. https://doi.org/10.1109/TR.2019.2919540

Wu Z, Wang D, Wang W et al (2019b) Solid rocket motor design employing an efficient performance matching approach. Proc Inst Mech Eng Part G J Aerosp Eng 233:4052–4065. https://doi.org/10.1177/0954410018814037 CrossRef

Wu Z, Wang W, Wang D et al (2019c) Global sensitivity analysis using orthogonal augmented radial basis function. Reliab Eng Syst Saf 185:291–302. https://doi.org/10.1016/j.ress.2018.12.028 CrossRef

Xiao S, Lu Z, Xu L (2016) A new effective screening design for structural sensitivity analysis of failure probability with the epistemic uncertainty. Reliab Eng Syst Saf 156:1–14. https://doi.org/10.1016/j.ress.2016.07.014 CrossRef

Zhang D, Han X (2020) Kinematic reliability analysis of robotic manipulator. J Mech Des 142:5–21. https://doi.org/10.1115/1.4044436 CrossRef

Zhang X, Pandey MD (2014) An effective approximation for variance-based global sensitivity analysis. Reliab Eng Syst Saf 121:164–174. https://doi.org/10.1016/j.ress.2013.07.010 CrossRef

Zhang D, Han X, Jiang C et al (2017) Time-dependent reliability analysis through response surface method. J Mech Des Trans ASME 139. https://doi.org/10.1115/1.4035860

Titel: Hybrid metamodel of radial basis function and polynomial chaos expansions with orthogonal constraints for global sensitivity analysis
verfasst von: Zeping Wu
Donghui Wang
Wenjie Wang
Kun Zhao
Houcun Zhou
Weihua Zhang
Publikationsdatum: 06.02.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 2/2020
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-020-02516-4

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