Abstract
Four generic methods for quantile estimation have been compared: Monte Carlo (MC), Monte Carlo with Harrel-Davis weighting (WMC), quasi-Monte Carlo with Sobol sequence (QMC) and quasi-random splines (QRS). The methods are combined with RBF metamodel and applied to the analysis of morphodynamic—hydrodynamic simulations of the river bed evolution. The following results have been obtained. Harrel-Davis weighting gives a moderate 10–20 % improvement of precision at small number of samples N ~ 100. Quasi-Monte Carlo methods provide significant improvement of quantile precision, e.g. the number of function evaluations necessary to achieve rms ~ 10−4 precision is reduced from 1,000,000 for MC to 100,000 for QMC and to 6,000 for QRS. On the other hand, RBF metamodeling of bulky data allows to speed up the computation of one complete result in the considered problem from 45 min (on 32CPU) to 20 s (on 1CPU), providing rapid quantile estimation for the whole set of bulky data.
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References
Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge University Press, Cambridge
Clees T, Nikitin I, Nikitina L, Thole C-A (2012) Analysis of bulky crash simulation results: deterministic and stochastic aspects. In: Pina N et al (eds) Simulation and modeling methodologies, technologies and applications, AISC 197, Springer 2012, pp 225–237
Clees T, Nikitin I, Nikitina L, Kopmann R (2012) Reliability analysis of river bed simulation models. In: Herskovits J (ed) CDROM Proceedings of EngOpt 2012, 3rd international conference on engineering optimization, Rio de Janeiro, Brazil, #267.
Halton JH (1964) Algorithm 247: radical-inverse quasi-random point sequence. Commun ACM 7(12):701–702
Harell FE, Davis CE (1982) A new distribution-free quantile estimator. Biometrika 69:635–640
Hervouet J-M (2007) Hydrodynamics of free surface flows: modelling with the finite element method. Wiley, Chichester
Jones MC (1990) The performance of kernel density functions in kernel distribution function estimation. Stat Probabil Lett 9(2):129–132
Kopmann R, Schmidt A (2010) Comparison of different reliability analysis methods for a 2D morphodynamic numerical model of River Danube. In: Dittrich A, Koll K, Aberle J, Geisenhainer P (eds) Proceedings of River Flow 2010—international conference on fluvial hydraulics, Braunschweig, 8–10. Sept. 2010, pp 1615–1620.
Nikitin I, Nikitina L, Clees T (2012) Nonlinear metamodeling of bulky data and applications in automotive design. In: Günther M et al (eds) Progress in industrial mathematics at ECMI 2010, Mathematics in Industry (17), Springer, 2012, pp 295–301
Press WH, Teukolsky S, Vetterling WT, Flannery BP (1992) Numerical Recipes in C, Cambridge University Press 1992, Chap. 7.7
Rhein B, Clees T, Ruschitzka M (2012) Robustness measures and numerical approximation of the cumulative density function of response surfaces. Commun Stat B-Simul
Riehme J, Kopmann R, Naumann U (2010) Uncertainty quantification based on forward sensitivity analysis in Sisyphe. In: Pereira JCF, Sequeira A (eds) Proceedings of V European conference on computational fluid dynamics ECCOMAS CFD 2010, Lisbon, Portugal, 14–17 June 2010
Sfakianakis ME, Verginis DG (2008) A new family of nonparametric quantile estimators. Commun Stat B-Simul 37:337–345
Sobol IM (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comp Math Math Phy 7(4):86–112
Sudret B (2012) Meta-models for structural reliability and uncertainty quantification. In: Phoon K et al (eds) Proceedings of 5th Asian-Pacific symposium on structural reliability APSSRA 2012, Singapure, pp 53–76
van Bühren G, Clees T, Hornung N, Nikitina L (2012) Aspects of adaptive hierarchical RBF metamodels for optimization. J Comput Methods Sci Eng JCMSE 12(2012), Nr.1–2:5–23
Villaret C (2010) Sisyphe 6.0 user manual H-P73-2010-01219-FR, department national hydraulics and environment laboratory, Electricité de France
Acknowledgments
We are grateful to Rebekka Kopmann from Federal Waterways Engineering and Research Institute, Karlsruhe, Germany for providing us with simulation data. We also thank Slawomir Koziel and Leifur Leifsson from Reykjavik University for fruitful discussions at the conference SIMULTECH 2013, Reykjavik, Iceland.
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Clees, T., Nikitin, I., Nikitina, L., Pott, S. (2015). Quasi-Monte Carlo and RBF Metamodeling for Quantile Estimation in River Bed Morphodynamics. In: Obaidat, M., Koziel, S., Kacprzyk, J., Leifsson, L., Ören, T. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-319-11457-6_15
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DOI: https://doi.org/10.1007/978-3-319-11457-6_15
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