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Data-Efficient Sensitivity Analysis with Surrogate Modeling

  • Tom Van SteenkisteEmail author
  • Joachim van der Herten
  • Ivo Couckuyt
  • Tom Dhaene
Chapter
Part of the PoliTO Springer Series book series (PTSS)

Abstract

As performing many experiments and prototypes leads to a costly and long analysis process, scientists and engineers often rely on accurate simulators to reduce costs and improve efficiency. However, the computational demands of these simulators are also growing as their accuracy and complexity keeps increasing. Surrogate modeling is a powerful framework for data-efficient analysis of these simulators. A common use-case in engineering is sensitivity analysis to identify the importance of each of the inputs with regard to the output. In this work, we discuss surrogate modeling, sequential design, sensitivity analysis and how these three can be combined into a data-efficient sensitivity analysis method to accurately perform sensitivity analysis.

Keywords

Surrogate modeling Sequential design Sensitivity analysis Data-efficient 

References

  1. 1.
    Borgonovo E (2007) A new uncertainty importance measure. Reliab Eng Syst Saf 92:771–784CrossRefGoogle Scholar
  2. 2.
    Broomhead DS, Lowe D (1988) Radial basis functions, multi-variable functional interpolation and adaptive networks. Technical report, DTIC DocumentGoogle Scholar
  3. 3.
    Crestaux T, Le Maıtre O, Martinez JM (2009) Polynomial chaos expansion for sensitivity analysis. Reliab Eng Syst Saf 94(7):1161–1172CrossRefGoogle Scholar
  4. 4.
    Crombecq K, Gorissen D, Deschrijver D, Dhaene T (2010) A novel hybrid sequential design strategy for global surrogate modelling of computer experiments. SIAM J Sci Comput 33(4):1948–1974CrossRefGoogle Scholar
  5. 5.
    Cukier R, Levine H, Shuler K (1978) Nonlinear sensitivity analysis of multiparameter model systems. J Comput Phys 26(1):1–42MathSciNetCrossRefGoogle Scholar
  6. 6.
    van Dam ER, Rennen G, Husslage B (2009) Bounds for maximin latin hypercube designs. Oper Res 57(3):595–608MathSciNetCrossRefGoogle Scholar
  7. 7.
    Degroote J, Hojjat M, Stavropoulou E, Wüchner R, Bletzinger KU (2013) Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem. Struct Multidiscip Optim 47(1):77–94MathSciNetCrossRefGoogle Scholar
  8. 8.
    Goethals K, Couckuyt I, Dhaene T, Janssens A (2012) Sensitivity of night cooling performance to room/system design: surrogate models based on CFD. Build Environ 58:23–36CrossRefGoogle Scholar
  9. 9.
    Gorissen D (2010) Grid-enabled adaptive surrogate modeling for computer aided engineering. PhD thesis, Universiteit GentGoogle Scholar
  10. 10.
    Gorissen D, Couckuyt I, Laermans E, Dhaene T (2010a) Multiobjective global surrogate modeling, dealing with the 5-percent problem. Eng Comput 26(1):81–98CrossRefGoogle Scholar
  11. 11.
    Gorissen D, Crombecq K, Couckuyt I, Demeester P, Dhaene T (2010b) A surrogate modeling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11:2051–2055Google Scholar
  12. 12.
    van der Herten J, Couckuyt I, Deschrijver D, Dhaene T (2015) A fuzzy hybrid sequential design strategy for global surrogate modeling of high-dimensional computer experiments. SIAM J Sci Comput 37(2):1020–1039MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hughes G (1968) On the mean accuracy of statistical pattern recognizers. IEEE Trans Inf Theory 14(1):55–63CrossRefGoogle Scholar
  14. 14.
    Ishigami T, Homma T (1990) An importance quantification technique in uncertainty analysis for computer models. In: Proceedings of first international symposium on uncertainty modeling and analysis. IEEE, pp 398–403Google Scholar
  15. 15.
    Jin R (2004) Enhancements of metamodeling techniques in engineering design. PhD thesis, University of Illinois at ChicagoGoogle Scholar
  16. 16.
    Lehmensiek R, Meyer P, Muller M (2002) Adaptive sampling applied to multivariate, multiple output rational interpolation models with applications to microwave circuits. Int J RF Microw Comput Aided Eng 12(4):332–340CrossRefGoogle Scholar
  17. 17.
    Liu Q, Feng B, Liu Z, Zhang H (2017) The improvement of a variance-based sensitivity analysis method and its application to a ship hull optimization model. J Mar Sci Technol 22(4):694–709CrossRefGoogle Scholar
  18. 18.
    Morris M (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174CrossRefGoogle Scholar
  19. 19.
    Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT PressGoogle Scholar
  20. 20.
    Sacks J, Welch W, Mitchell T, Wynn H (1989) Design and analysis of computer experiments. Stat Sci 409–423MathSciNetCrossRefGoogle Scholar
  21. 21.
    Saltelli A (2002a) Making best use of model valuations to compute sensitivity indices. Comput Phys Commun 145:280–297CrossRefGoogle Scholar
  22. 22.
    Saltelli A (2002b) Sensitivity analysis for importance assessment. Risk Anal 22(3):579–590CrossRefGoogle Scholar
  23. 23.
    Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice: a guide to assessing scientific models. WileyGoogle Scholar
  24. 24.
    Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. WileyGoogle Scholar
  25. 25.
    Santner T, Williams B, Notz W (2003) The design and analysis of computer experiments. Springer series in statistics. Springer-Verlag, New YorkCrossRefGoogle Scholar
  26. 26.
    Sobol I (1993) Sensitivity analysis for nonlinear mathematical models. Math Model Comput Exp 1:407–414zbMATHGoogle Scholar
  27. 27.
    Sobol I (2001) Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Math Comput Simul 55(1–3):271–280MathSciNetCrossRefGoogle Scholar
  28. 28.
    Sobol I, Kucherenko S (2009) Derivative based global sensitivity measures and their link with global sensitivity indices. Math Comput Simul 79(10):3009–3017MathSciNetCrossRefGoogle Scholar
  29. 29.
    Sudret B, Mai C (2015) Computing derivative-based global sensitivity measures using polynomial chaos expansions. Reliab Eng Syst Saf 134:241–250CrossRefGoogle Scholar
  30. 30.
    Suykens J, Gestel TV, Brabanter JD, Moor BD, Vandewalle J (2002) Least squares support vector machines. World Scientific Publishing Co. Pte Ltd, SingaporeCrossRefGoogle Scholar
  31. 31.
    Van Steenkiste T, van der Herten J, Couckuyt I, Dhaene T (2016) Sensitivity analysis of expensive black-box systems using metamodeling. In: 2016 winter simulation conference (WSC). IEEE, pp 578–589Google Scholar
  32. 32.
    Van Steenkiste T, van der Herten J, Couckuyt I, Dhaene T (2018) Sequential sensitivity analysis of expensive black-box simulators with metamodelling. Appl Math Model 61:668–681MathSciNetCrossRefGoogle Scholar
  33. 33.
    Vu KK, D’Ambrosio C, Hamadi Y, Liberti L (2017) Surrogate-based methods for black-box optimization. Int Trans Oper Res 24(3):393–424MathSciNetCrossRefGoogle Scholar
  34. 34.
    Wang G, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Design 129(4):370–380CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tom Van Steenkiste
    • 1
    Email author
  • Joachim van der Herten
    • 1
  • Ivo Couckuyt
    • 1
  • Tom Dhaene
    • 1
  1. 1.IDLab, Department of Information TechnologyGhent University - imecGentBelgium

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