Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications

Tianfeng Hou, Dirk Nuyens, Staf Roels and Hans Janssen

Reliability Engineering and System Safety, 2019, vol. 191, issue C

Abstract: In this paper, the potential benefits of quasi-Monte Carlo (QMC) methods for uncertainty propagation are assessed via two applications: a numerical case study and a realistic and complex building physical case study. The sampling efficiency of four quasi-Monte Carlo sampling strategies — Optimized Latin hypercube, Sobol’ sequence, Niederreiter–Xing sequence and lattice sequence — are quantified and the errors of these quasi-Monte Carlo methods are estimated. In addition, for getting a better understanding of the potential factors that may influence the performance of quasi-Monte Carlo methods, the effect of the different parameters and the smoothness of the target function for the building physical case study are investigated for two quantities of interest. A sensitivity analysis is performed in which first and total order Sobol’ indices are calculated and a kernel smoother is used to show the effect on the quantity of interest for certain input parameters. The outcomes show that quasi-Monte Carlo methods perform at least as well as the Monte Carlo method and are capable of outperforming the standard Monte Carlo method if the target function is sufficiently smooth and mainly depends on a limited number of parameters.

Keywords: Quasi-Monte carlo; Uncertainty propagation; Building performance; Sampling efficiency; Error estimation; Sensitivity analysis; Sobol’ Indices; Kernel smoother (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:191:y:2019:i:c:s0951832018309189

DOI: 10.1016/j.ress.2019.106549

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