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Latin hypercube sampling with inequality constraints

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Abstract

In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical welding simulation, where the inequality constraints are caused by the physical decreasing of some material properties in function of the temperature.

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References

  • Asserin, O., Loredo, A., Petelet, M., Iooss, B.: Global sensitivity analysis in welding simulations—What are the material data you really need? Finite Elem. Anal. Des. (2009, submitted). Available at URL: http://hal.archives-ouvertes.fr/hal-00419162/fr/

  • Borgonovo, E.: Sensitivity analysis of model output with input constraints: A generalized rationale for local methods. Risk Anal. 28, 667–680 (2008)

    Article  Google Scholar 

  • Bursztyn, D., Steinberg, D.: Comparison of designs for computer experiments. J. Stat. Plan. Inference 136, 1103–1119 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • De Rocquigny, E., Devictor, N., Tarantola, S. (eds.): Uncertainty in Industrial Practice. Wiley, New York (2008)

    Google Scholar 

  • Fang, K.-T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, London (2006)

    MATH  Google Scholar 

  • Gentle, J.: Random Number Generation and Monte Carlo Methods. Springer, Berlin (2003)

    MATH  Google Scholar 

  • Helton, J., Davis, F.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Eng. Syst. Saf. 81, 23–69 (2003)

    Article  Google Scholar 

  • Iman, R., Conover, W.: A distribution-free approach to inducing rank correlation among input variables. Commun. Stat. 11(3), 311–334 (1982)

    MATH  Google Scholar 

  • Iooss, B., Boussouf, L., Feuillard, V., Marrel, A.: Numerical studies of the metamodel fitting and validation processes. Int. J. Adv. Syst. Meas. 3, 11–21 (2010)

    Google Scholar 

  • Jourdan, A., Franco, J.: Optimal Latin hypercube designs for the Kullback-Leibler criterion. Adv. Stat. Anal. 94(4), 341–351 (2010)

    Article  Google Scholar 

  • Kleijnen, J.: Design and Analysis of Simulation Experiments. Springer, Berlin (2008)

    MATH  Google Scholar 

  • Kurowicka, D., Cooke, R.: Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley, New York (2006)

    Book  MATH  Google Scholar 

  • Levy, S., Steinberg, D.: Computer experiments: A review. Adv. Stat. Anal. 94(4), 311–324 (2010)

    Article  Google Scholar 

  • McKay, M., Beckman, R., Conover, W.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • Owen, A.: A central limit theorem for Latin hypercube sampling. J. R. Stat. Soc. B 16, 140–149 (1992)

    Google Scholar 

  • Park, J.-S.: Optimal Latin-hypercube designs for computer experiments. J. Stat. Plan. Inference 39, 95–111 (1994)

    Article  MATH  Google Scholar 

  • Petelet, M.: Analyse de sensibilité globale de modèles thermomécaniques de simulation numérique du soudage. Thèse de l’Université de Bourgogne (2007)

  • Petelet, M., Asserin, O., Iooss, B., Loredo, A.: Echantillonnage LHS des propriétés matériau des aciers pour l’analyse de sensibilité globale en simulation numérique du soudage. In: Actes de MATERIAUX, Dijon, France, 2006

    Google Scholar 

  • Pistone, G., Vicario, G.: Comparing and generating Latin Hypercube designs in Kriging models. Adv. Stat. Anal. 94(4), 353–366 (2010)

    Article  Google Scholar 

  • Saltelli, A., Chan, K., Scott, E. (eds.): Sensitivity Analysis. Wiley Series in Probability and Statistics. Wiley, New York (2000)

    MATH  Google Scholar 

  • Simpson, T., Lin, D., Chen, W.: Sampling strategies for computer experiments: Design and analysis. Int. J. Reliab. Appl. 2, 209–240 (2001a)

    Google Scholar 

  • Simpson, T., Peplinski, J., Kock, P., Allen, J.: Metamodel for computer-based engineering designs: Survey and recommendations. Eng. Comput. 17, 129–150 (2001b)

    Article  MATH  Google Scholar 

  • Sobol, I.: Uniformly distributed sequences with additional uniformity property. USSR Comput. Math. Math. Phys. 16, 236–242 (1976)

    Article  MathSciNet  Google Scholar 

  • Stein, M.: Large sample properties of simulations using Latin hypercube sampling. Technometrics 29, 143–151 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Volkova, E., Iooss, B., Van Dorpe, F.: Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site. Stoch. Environ. Res. Risk Assess. 22, 17–31 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Bertrand Iooss.

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Petelet, M., Iooss, B., Asserin, O. et al. Latin hypercube sampling with inequality constraints. AStA Adv Stat Anal 94, 325–339 (2010). https://doi.org/10.1007/s10182-010-0144-z

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  • DOI: https://doi.org/10.1007/s10182-010-0144-z

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