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Structural and Multidisciplinary Optimization

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01-04-2019 | Review Article

Distance correlation-based method for global sensitivity analysis of models with dependent inputs

Authors: Yicheng Zhou, Zhenzhou Lu, Sinan Xiao, Wanying Yun

Published in: Structural and Multidisciplinary Optimization | Issue 3/2019

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Abstract

Global sensitivity analysis (GSA) plays an important role to quantify the relative importance of uncertain parameters to the model response. However, performing quantitative GSA directly is still a challenging problem for complex models with dependent inputs. A novel method is proposed for screening dependent inputs in the study. The proposed method inherits the capability of easily handing multivariate dependence from the distance correlation. With the help of a projection operator in the Hilbert space, it can work without knowing the specific conditional distribution of inputs. The advantages of the proposed method are discussed and demonstrated through applications to numerical and environmental modeling examples containing many dependent variables. Compared to classical GSA methods with dependent variables, the proposed method can be easily used, while the accuracy of inputs screening is well maintained.

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Borgonovo E (2007) A new uncertainty importance measure. Reliab Eng Syst Saf. 92(6):771–784CrossRef

Botev ZI, Grotowski JF, Kroese DP (2010) Kernel density estimation via diffusion. Ann Stat 38(5):2916–2957MathSciNetCrossRefMATH

Brell G, Li G, Rabitz H (2010) An efficient algorithm to accelerate the discovery of complex material formulations. J Chem Phys 132(17):174103CrossRef

Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22(10):1509–1518CrossRef

Campolongo F, Saltelli A, Cariboni J (2011) From screening to quantitative sensitivity analysis. A Unifi- Approach. Comput Phys Commun 182(4):978–988CrossRefMATH

Da Veiga S (2015) Global sensitivity analysis with dependence measures. J Stat Comput Simul 85(7):1283–1305MathSciNetCrossRef

Da Veiga S, Wahl F, Gamboa F (2009) Local polynomial estimation for sensitivity analysis on models with correlated inputs. Technometrics. 51(4):452–463MathSciNetCrossRef

De Lozzo M, Marrel A (2016) New improvements in the use of dependence measures for sensitivity analysis and screening. J Stat Comput Simul 86(15):3038–3058MathSciNetCrossRef

De Lozzo M, Marrel A (2017) Sensitivity analysis with dependence and variance-based measures for spatio-temporal numerical simulators. Stoch Env Res Risk A 31(6):1437–1453CrossRef

Feng K, Lu Z, Yun W (2018) Aircraft icing severity analysis considering three uncertainty types. AIAA J. https://doi.org/10.2514/1.J057529. Accessed 25 March 2019

Ge Q, Menendez M (2014) An efficient sensitivity analysis approach for computationally expensive microscopic traffic simulation models. Int J Transp 2(2):49–64CrossRef

Ge Q, Menendez M (2017) Extending Morris method for qualitative global sensitivity analysis of models with dependent inputs. Reliab Eng Syst Saf 162:28–39CrossRef

Ge Q, Ciuffo B, Menendez M (2014) An exploratory study of two efficient approaches for the sensitivity analysis of computationally expensive traffic simulation models. IEEE Trans Intell Transp Syst 15(3):1288–1297CrossRef

Gretton A, Bousquet O, Smola A, Schölkopf B (2005) Measuring statistical dependence with Hilbert-Schmidt norms. In: Jain S, Simon H, Tomita E (eds) Algorithmic learning theory. Lecture Notes in Computer Science, vol 3734. Springer, Berlin, pp 63–77CrossRef

Hamilton AS, Hutchinson DG, Moore RD (2000) Estimating winter streamflow using conceptual streamflow model. J Cold Reg Eng 14(4):158–175CrossRef

Huo X, Székely GJ (2016) Fast computing for distance covariance. Technometrics. 58(4):435–447MathSciNetCrossRef

Iman RL (2008) Latin hypercube sampling. Encyclopedia of Quantitative Risk Analysis and Assessment. Wiley, Hoboken

Iman RL, Conover WJ (1982) A distribution-free approach to inducing rank correlation among input variables. Commun Stat Simul Comput 11(3):311–334CrossRefMATH

Janon A, Klein T, Lagnoux A, Nodet M, Prieur C (2014) Asymptotic normality and efficiency of two Sobol’ index estimators. ESAIM-Probab Stat 18:342–364

Joeph H, Pierre G (2018) An approximation theoretic perspective of the Sobol’ indices with dependent variables. Int J Uncertain Quan 8(6):483–493

Kala Z, Valeš J (2017) Global sensitivity analysis of lateral-torsional buckling resistance based on finite element simulations. Eng Struct 134:37–47CrossRef

Kala Z, Valeš J (2018) Imperfection sensitivity analysis of steel columns at ultimate limit state. Arch Civ Mech Eng 18:1207–1218

Kollat JB, Reed PM, Wagener T (2012) When are multiobjective calibration trade-offs in hydrologic models meaningful? Water Resour Res 48(3)

Kucherenko S (2009) Derivative based global sensitivity measures and their link with global sensitivity indices. Math Comput Simul 79(10):3009–3017MathSciNetCrossRefMATH

Lambert RS, Lemke F, Kucherenko SS, Song S, Shah N (2016) Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling. Math Comput Simul 128:42–54MathSciNetCrossRef

Li R, Zhong W, Zhu L (2012) Feature screening via distance correlation learning. J Am Stat 107(499):1129–1139MathSciNetCrossRefMATH

Lindström G (1997) A simple automatic calibration routine for the HBV model. Hydrol Res 28(3):153–168MathSciNetCrossRef

Lyons R (2013) Distance covariance in metric spaces. Ann Probab 41(5):3284–3305MathSciNetCrossRefMATH

Malte K. Vine copula MATLAB toolbox, version 1.2, 2016, https://github.com/MalteKurz/VineCopulaMatlab.git. Accessed 25 Mar 2019

Mara TA, Tarantola S (2012) Variance-based sensitivity indices for models with dependent inputs. Reliab Eng Syst Saf 107:115–121CrossRef

Mara TA, Tarantola S, Annoni P (2015) Non-parametric methods for global sensitivity analysis of model output with dependent inputs. Environ Model Softw 72:173–183CrossRef

Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics. 33(2):161–174 https://www.tandfonline.com/doi/abs/10.1080/00401706.1991.10484804. Accessed 25 March 2019

Nelsen RB (2007) An introduction to copulas. Springer Science & Business Media, BerlinMATH

Owen AB (2013) Better estimation of small Sobol’ sensitivity indices. ACM T Model Comput S (TOMACS) 23(2):11

Pianosi F, Sarrazin F, Wagener T (2015) A Matlab toolbox for global sensitivity analysis. Environ Model Softw 70:80–85CrossRef

Plischke E, Borgonovo E, Smith CL (2013) Global sensitivity measures from given data. Eur J Oper Res 226(3):536–550MathSciNetCrossRefMATH

Rizzo ML, Székely GJ (2016) Energy distance. WIREs Comput Stat 8:27–38MathSciNetCrossRef

Saltelli A (2002) Sensitivity analysis for importance assessment. Risk Anal 22(3):579–590CrossRef

Saltelli A, Tarantola S (2002) On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposal. J Am Stat Assoc 97(459):702–709MathSciNetCrossRefMATH

Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, HobokenMATH

Saltelli A, Campolongo F, Cariboni J (2009) Screening important inputs in models with strong interaction properties. Reliab Eng Syst Saf 94(7):1149–1155CrossRef

Sobol IM (1976) Uniformly distributed sequences with an additional uniform property. USSR Comput Math Math Phys 16(5):236–242CrossRefMATH

Sobol’ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Modeling Comput Exp 1(4):407–414

Székely GJ, Rizzo ML (2013) The distance correlation t-test of independence in high dimension. J Multivar Anal 117:193–213MathSciNetCrossRefMATH

Szekely GJ, Rizzo ML (2014) Partial distance correlation with methods for dissimilarities. Ann Stat 42(6):2382–2412MathSciNetCrossRefMATH

Székely GJ, Rizzo ML, Bakirov NK (2007) Measuring and testing dependence by correlation of distances. Ann Stat:2769–2794

Xiao S, Lu Z, Wang P (2018) Multivariate global sensitivity analysis for dynamic models based on energy distance. Struct Multidiscip Optim 57:279–291MathSciNetCrossRef

Xu C (2013) Decoupling correlated and uncorrelated parametric uncertainty contributions for nonlinear models. Appl Math Model 37(24):9950–9969MathSciNetCrossRefMATH

Xu L, Lu Z, Xiao S (2019) Generalized sensitivity indices based on vector projection with multivariate outputs. Appl Math Model 66:592–610CrossRef

Yun W, Lu Z, Jiang X, Zhang L (2018) Borgonovo moment independent global sensitivity analysis by Gaussian radial basis function meta-model. Appl Math Model 54:378–392MathSciNetCrossRef

Yun W, Lu Z, Jiang X (2018) An efficient method for moment-independent global sensitivity analysis by dimensional reduction technique and principle of maximum entropy. Reliab Eng Syst Saf. https://doi.org/10.1016/j.ress.2018.03.029. Accessed 25 March 2019

Zadeh FK, Nossent J, Sarrazin F, Pianosi F, van Griensven A, Wagener T, Bauwens W (2017) Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model. Environ Model Softw 91:210–222CrossRef

Zhang K, Lu Z, Wu D, Zhang Y (2017) Analytical variance based global sensitivity analysis for models with correlated variables. Appl Math Model 45:748–767MathSciNetCrossRef

Zhou C, Lu Z, Zhang L, Hu J (2014) Moment independent sensitivity analysis with correlations. Appl Math Model 38(19–20):4885–4896CrossRefMATH

Zhou C, Lu Z, Li W (2015) Sparse grid integration based solutions for moment-independent importance measures. Probabilist Eng Mech 39:46–55

Zhou Y, Lu Z, Cheng K (2019a) Sparse polynomial chaos expansions for global sensitivity analysis with partial least squares and distance correlation. Struct Multidiscip Optim 59(1):229–247MathSciNetCrossRef

Zhou Y, Lu Z, Cheng K, Yun W (2019b) A Bayesian Monte Carlo-based method for efficient computation of global sensitivity indices. Mech Syst Signal Process 117(15):498–516CrossRef

Title: Distance correlation-based method for global sensitivity analysis of models with dependent inputs
Authors: Yicheng Zhou
Zhenzhou Lu
Sinan Xiao
Wanying Yun
Publication date: 01-04-2019
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 3/2019
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-019-02257-z

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