Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence

Reliability Engineering and System Safety

Volumn 109, Issue , 2013, Pages 123-132

  Janssen, Hans ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Monte Carlo; Sample splitting; Sampling convergence; Sampling efficiency; Space filling Latin hypercube; Uncertainty analysis

Indexed keywords

EFFICIENCY; SAMPLING; UNCERTAINTY ANALYSIS;

COMPUTATIONAL COSTS; COMPUTATIONAL EXPENSE; CORE SIMULATIONS; LATIN HYPERCUBE; LATIN HYPERCUBE DESIGNS; LATIN HYPERCUBE SAMPLING; MAXIMIN; MONTE CARLO; MONTE CARLO ANALYSIS; MONTE CARLO SIMULATION; RELIABILITY AND ROBUSTNESS; SAMPLE-SPLITTING; SAMPLING EFFICIENCY; SAMPLING STRATEGIES; SPACE-FILLING;

MONTE CARLO METHODS;

EID: 84866502551     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2012.08.003     Document Type: Article

References (82)

1. J.C. Helton, and D.E. Burmaster Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems Reliability Engineering and System Safety 54 1996 91 94
2. W.L. Oberkampf, S.M. DeLand, R.M. Rutherford, K.V. Diegert, and K.F. Alvin Error and uncertainty in modeling and simulation Reliability Engineering and System Safety 75 2002 333 357
3. J.C. Helton Treatment of uncertainty in performance assessments of complex system Risk Analysis 14 2004 483 511
4. H. Karadeniz, and T. Vrouwenvelder Overview reliability methods C. Guedes Soares, Safety and reliability of industrial products, systems and structures 2010 Taylor & Francis Group London, United Kingdom 181 189
5. D.E. Burmaster, and P.D. Anderson Principles of good practice for the use of monte carlo techniques in human health and ecological risk assessments Risk Analysis 14 1994 477 481
6. S. Ferson What Monte Carlo methods cannot do Human and Ecological Risk Assessment 2 1996 990 1007
7. D.R.J. Moore Using Monte Carlo analysis to quantify uncertainty in ecological risk assessment: are we gilding the lily or bronzing the dandelion? Human and Ecological Risk Assessment 2 1996 628 633
8. A. Singhee, and R.A. Rutenbar Why quasi-Monte Carlo is better than Monte Carlo or Latin hypercube sampling for statistical circuit analysis IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 29 2010 1763 1776
9. J.B. Cardoso, J.R. de Almeida, J.M. Diasa, and P.G. Coelho Structural reliability analysis using Monte Carlo simulation and neural networks Advances in Engineering Software 39 2008 505 513
10. Helton JC, Hansen CW, Sallaberry CJ. Uncertainty and sensitivity analysis in performance assessment for the proposed repository for high-level radioactive waste at Yucca Mountain, Nevada. Reliability Engineering and System Safety, 10.1016/j.ress.2011.07.002, in press.
11. P. Rugen, and B. Callahan An overview of Monte Carlo - a fifty year perspective Human and Ecological Risk Assessment 2 1996 671 680
12. C. Dehlendorff, M. Kulahci, and K.K. Andersen Designing simulation experiments with controllable and uncontrollable factors for applications in healthcare Journal of the Royal Statistical Society C 60 2011 31 49
13. W.J.H. Van Groenendaal, and J.P.C. Kleijnen On the assessment of economic risk: factorial design versus Monte Carlo methods Reliability Engineering and System Safety 57 1997 91 102
14. T.M. Cioppa, and T.W. Lucas Efficient nearly orthogonal and space-filling Latin hypercubes Technometrics 49 2007 45 55
15. Yin L, Smith MAJ, Trivedi KS. Uncertainty analysis in reliability modeling. In: Proceedings of annual reliability & maintainability symposium. Philadelphia, Pennsylvania, USA; 2001.
16. K. Durga Rao, V. Gopika, V.V.S. Sanyasi Rao, H.S. Kushwaha, A.K. Verma, and A. Srividya Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment Reliabilitiy Engineering and System Safety 94 2009 872 883
17. J.M. Hammersley Monte Carlo methods for solving multivariable problems Annals of the New York Academy of Sciences 86 1960 844 874
18. Z. Li, W. Chen, S. Deng, and Z. Lin The characteristics of space cooling load and indoor humidity control for residences in the subtropics Building and Environment 41 2006 1137 1147
19. A.-L. Pasanen, J.-K. Kasanen, S. Rautiala, M. Ikäheimo, J. Rantamäki, and H. Kääriäinen Fungal growth and survival in building materials under fluctuating moisture and temperature conditions International Biodeterioration and Biodegradation 46 2000 117 127
20. D. Mudarri, and W.J. Fisk Public health and economic impact of dampness and mold Indoor Air 17 2007 226 235
21. L. Fang, G. Clausen, and P.O. Fanger Impact of temperature and humidity on the perception of indoor air quality Indoor Air 8 1998 80 90
22. S. Hokoi, and M. Matsumoto An analysis of stochastic properties of the heating load in an intermittently air-conditioned building Energy and Buildings 11 1988 259 266
23. K.J. Lomas, and H. Eppel Sensitivity analysis techniques for building thermal simulation programs Energy and Buildings 19 1992 21 44
24. I.A. Macdonald, and J.A. Clarke Applying uncertainty considerations to energy conservation equations Energy and Buildings 39 2007 1019 1026
25. S. de Wit, and G. Augenbroe Analysis of uncertainty in building design evaluations and its implications Energy and Buildings 34 2002 951 958
26. K. Pietrzyk, K. Kurkinen, and C.-E. Hagentoft An example of application of limit state approach for reliability analysis of moisture performance of a building component Journal of Thermal Envelope and Building Science 28 2004 9 26
27. J. Haarhoff, and E.H.A. Mathews Monte Carlo method for thermal building simulation Energy and Buildings 38 2006 1395 1399
28. V. Corrado, and H.E. Mechri Uncertainty and sensitivity analysis for building energy rating Journal of Building Physics 33 2009 125 156
29. G.Y. Yun, P. Tuohy, and K. Steemers Thermal performance of a naturally ventilated building using a combined algorithm of probabilistic occupant behaviour and deterministic heat and mass balance models Energy and Buildings 41 2009 489 499
30. F. Domínguez-Muñoz, J.M. Cejudo-López, and A. Carrillo-Andrés Uncertainty in peak cooling load calculations Energy and Buildings 42 2010 1010 1018
31. C. Xu, H.S. He, Y. Hu, Y. Chang, X. Li, and R. Bu Latin hypercube sampling and geostatistical modeling of spatial uncertainty in a spatially explicit forest landscape model simulation Ecological Modelling 185 2005 255 269
32. M.D. McKay, R.J. Beckman, and W.J. Conover A comparison of three methods for selecting values for input variables in the analysis of output from a computer code Technometrics 21 1979 239 245
33. M.E. Johnson, L.M. Moore, and D. Ylvisaker Minimax and maximin distance designs Journal of Statistical Planning and Inference 26 1990 131 148
34. M.D. Morris, and T.J. Mitchell Exploratory designs for computational experiments Journal of Statistical Planning and Inference 43 1995 381 402
35. K.-T. Fang, C.-X. Ma, and P. Winker Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs Mathematics of Computation 71 2002 275 296
36. V.R. Joseph, and Y. Hung Orthogonal-maximin Latin hypercube designs Statistica Sinica 18 2008 171 186
37. L. Pronzato, and W.G. Müller Design of computer experiments: space filling and beyond Statistics and Computing 2011 online first
38. Gilman MJ. A brief survey of stopping rules for Monte Carlo. In: Proceedings of the second conference on applications of simulations. New York, USA; 1968.
39. Iman RL. Statistical methods for including uncertainties associated with the geologic isolation of radioactive waste which allow for comparison with licensing criteria. In: Proceedings of the symposium on uncertainties associated with the regulation of the geologic disposal of high-level radioactive waste. Gatlinburg, Tennessee, USA; 1981.
40. Hansen CW, Helton CJ, Sallaberry CJ. Use of replicated Latin hypercube sampling to estimate sampling variance in uncertainty and sensitivity analysis results for the geologic disposal of radioactive waste. Reliability Engineering and System Safety, 10.1016/j.ress.2011.12.006, in press.
41. A.F. Bielajew Fundamentals of the Monte Carlo method for neutral and charged particle transport 2001 The University of Michigan Ann Arbor, Michigan, USA
42. B.R.B. Walters, I. Kawrakow, and D.W.O. Rogers History by history statistical estimators in the BEAM code system Medical Physics 29 2002 2745 2752
43. M. Stein Large sample properties of simulations using Latin hypercube sampling Technometrics 29 1987 143 151
44. J.C. Helton, and F.J. Davis Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems 2002 Sandia National Laboratories New Mexico, USA SAND2001-0417
45. J.C. Helton, and F.J. Davis Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems Reliability Engineering and System Safety 81 2003 23 69
46. J.C. Helton, F.J. Davis, and J.D. Johnson A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling Reliability Engineering and System Safety 89 2005 305 330
47. F. Hossain, E.N. Anagnostou, and A.C. Bagtzoglou On Latin hypercube sampling for efficient uncertainty estimation of satellite rainfall observations in flood prediction Computers and Geosciences 32 2006 776 792
48. A.A. Khan, L. Lye, and T. Husain Latin hypercube sampling for uncertainty analysis in multiphase modeling Journal of Environmental Engineering and Science 7 2008 617 626
49. G.G. Pilger, J.F. Costa, and J. Koppe The benefits of Latin hypercube sampling in sequential simulation algorithms for geostatistical applications Applied Earth Science 117 2008 160 174
50. T.J. Santner, B.J. Williams, and W.I. Notz The design and analysis of computer experiments 2003 Springer-Verlag - New York New York, United States
51. K.-T. Fang, R. Li, and A. Sudjianto Design and modelling for computer experiments 2006 Taylor & Francis Group Boca Raton, Florida, United States
52. T.W. Simpson, T.K.J. Lin, and W. Chen Sampling strategies for computer experiments: design and analysis International Journal of Reliability and Applications 2 2001 209 240
53. Giunta AA, Wojtkiewicz Jr. SF, Eldred MS. Overview of modern design of experiments methods for computational simulations. In: Proceedings of 41st AIAA aerospace sciences meeting and exhibit. Reno, Nevada, USA; 2003.
54. V.C.P. Chen, K.-L. Tsui, R.R. Barton, and J.K. Allen A review of design and modeling in computer experiments Handbook of Statistics 22 2003 231 261
55. R.T. Johnson, D.C. Montgomery, J. Bradley, and P.A. Parker Comparing computer experiments for fitting high-order polynomial metamodels Journal of Quality Technology 42 2010 86 102
56. F.M. Alam, K.R. McNaught, and T.J. Ringrose A comparison of experimental designs in the development of a neural network simulation metamodel Simulation Modelling Practice and Theory 12 2004 559 578
57. Simlab - software package for uncertainty and sensitivity analysis. Joint research centre of the European commission. Downloadable for free at: simlab.jrc.ec.europa.eu; [last accessed 4.11.11].
58. ® Excel. Version 5.7. Ithaca, New York, USA; 2010.
59. Frontline Systems. Frontline solvers user guide. Incline village. Nevada, USA; 2011.
60. Oracle crystal ball. www.oracle.com/technetwork/middleware/crystalball/ overview/precision-control-133236.pdf; [last accessed on 4.11.11].
61. B. Efron, and R. Tibshirani Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy Statistical Science 1 1986 54 75
62. J.G. Booth, and S. Sarkar Monte Carlo approximation of bootstrap variances American Statistical Association 52 1998 354 357
63. P.J. Bickel, F. Götze, and W.R. van Zwet Resampling fewer than n observations: gains, losses, and remedies for losses Statistica Sinica 7 1997 1 31
64. R. Pino Mej, M.D. Jimenez Gamero, and A.A. Enguix Gonzalez Monte Carlo comparison of three consistent bootstrap procedures Journal of Statistical Computation and Simulation 79 2009 323 334
65. C.J. Sallaberry, J.C. Helton, and S.C. Hora Extension of Latin hypercube samples with correlated variables Reliability Engineering and System Safety 93 2008 1047 1059
66. F. Xiong Optimizing Latin hypercube design for sequential sampling of computer experiments Engineering Optimization 41 2009 793 810
67. C.-E. Hagentoft, A.S. Kalagasidis, B. Adl-Zarrabi, S. Roels, J. Carmeliet, and H. Hens Assessment method of numerical prediction models for combined heat, air and moisture transfer in building components: benchmarks for one-dimensional cases Journal of Thermal Envelope and Building Science 27 2004 327 352
68. Hagentoft CE. HAMSTAD WP2 benchmarking package. Final report. Document chalmers 2002-h14. Göteborg, Sweden: Chalmers University of Technology; 2002.
69. H. Janssen, B. Blocken, and J. Carmeliet Conservative modelling of the moisture and heat transfer in building components under atmospheric excitation International Journal of Heat and Mass Transfer 50 2007 1128 1140
70. H. Janssen Adaptive Kronrod-Patterson integration of non-linear finite-element matrices International Journal for Numerical Methods in Engineering 81 2010 1455 1474
71. H. Janssen Thermal diffusion of water vapour in porous materials: fact or fiction? International Journal of Heat and Mass Transfer 54 2011 1548 1562
72. H. Janssen, B. Blocken, S. Roels, and J. Carmeliet Wind-driven rain as a boundary condition for HAM simulations: analysis of simplified modelling approaches Building and Environment 42 2007 1555 1567
73. R.L. Iman, and W.J.A. Conover Distribution-free approach to inducing rank correlation among input variables Communications in Statistics - Simulation and Computation B11 1982 311 334
74. A.B. Owen Controlling correlations in Latin hypercube samples Journal of the American Statistical Association 89 1994 1517 1522
75. R. Jin, W. Chen, and A. Sudjianto An efficient algorithm for constructing optimal design of computer experiments Journal of Statistical Planning and Inference 134 2005 268 287
76. Wikipedia. en.wikipedia.org/wiki/Variance; [last accessed on 4.11.11].
77. Macdonald IA. Comparison of sampling techniques on the performance of Monte Carlo based sensitivity analysis In: Proceedings of building simulation 2009. 11th international IBPSA conference. Glasgow, United Kingdom; 2009.
78. Niederreiter H. Random number generation and quasi-Monte Carlo methods. Society for industrial and applied mathematics. Philadelphia, Pennsylvania; 1192.
79. McKay MD. Evaluating prediction uncertainty. Los Alamos National Laboratory. Report NUREG/CR-6311. Los Alamos, New Mexico, USA; 1995.
80. K. Pietrzyk, and C.E. Hagentoft Probabilistic analysis of air infiltration in low-rise buildings Building and Environment 43 2008 537 549
81. K. Pietrzyk, and C.E. Hagentoft Reliability analysis in building physics design Building and Environment 43 2008 558 568
82. E.R. van Dam, D den Hertog, B.G.M. Husslage, and G. Rennen Space-filling Latin hypercube designs for computer experiments Optimization and Engineering 12 2011 611 630