Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

Reliability Engineering & System Safety - Tập 142 - Trang 310-325 - 2015
Michael D. Shields1,2, Kirubel Teferra1, Adam Hapij3, Raymond P. Daddazio3
1Department of Civil Engineering, Johns Hopkins University, United States
2Department of Materials Science and Engineering, Johns Hopkins University, United States
3Applied Science & Investigations, Weidlinger Associates, Inc., United States

Tóm tắt

Từ khóa


Tài liệu tham khảo

Janssen H. Monte-carlo based uncertainty analysis: sampling efficiency and sampling convergence. Reliab Eng Syst Saf 2013;109:(123–132).

Tocher K. The art of simulation. The English Universities Press, London, UK; 1963.

Helton, 2003, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliab Eng Syst Saf, 81, 23, 10.1016/S0951-8320(03)00058-9

McKay, 1979, A comparison of three methods of selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239

Olsson, 2003, On Latin hypercube sampling for structural reliability analysis, Struct Saf, 25, 47, 10.1016/S0167-4730(02)00039-5

Wang, 2003, Adaptive response surface method using inherited Latin hypercube design points, Trans ASME: J Mech Des, 125, 210, 10.1115/1.1561044

Stein, 1987, Large sample properties of simulations using Latin hypercube sampling, Technometrics, 29, 143, 10.1080/00401706.1987.10488205

Owen, 1992, A central limit theorem for Latin hypercube sampling, J R Stat Soc Ser B, 54, 541, 10.1111/j.2517-6161.1992.tb01895.x

Huntington, 1998, Improvements to and limitations of Latin hypercube sampling, Probab Eng Mech, 13, 245, 10.1016/S0266-8920(97)00013-1

Fang, 2001, Wrap-around l2-discrepancy of random sampling, Latin hypercube, and uniform designs, J Complex, 17, 608, 10.1006/jcom.2001.0589

Fang, 2002, Centered l2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs, Math Comput, 71, 275, 10.1090/S0025-5718-00-01281-3

Glasserman P, Monte Carlo Methods in financial engineering. Springer; New York, USA, 2003.

Rubinstein, 2008

Kalos M, Whitlock P. Monte Carlo methods. Wiley; Weinheim, Germany, 2008.

Gilman M. A brief survey of stopping rules for Monte Carlo In: Proceedings of the second conference on applications of simulations, New York, NY, USA; 1968.

Tong, 2006, Refinement strategies for stratified sampling methods, Reliab Eng Syst Saf, 91, 1257, 10.1016/j.ress.2005.11.027

Sallaberry, 2008, Extension of Latin hypercube samples with correlated variables, Reliab Eng Syst Saf, 93, 1047, 10.1016/j.ress.2007.04.005

Vorechovsky, 2015, Hierarchical refinement of Latin hypercube samples, Comput Aided Civil Infrastruct Eng, 30, 394, 10.1111/mice.12088

Iman R. 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, TN, USA; 1981.

McKay M. Evaluating prediction uncertainty. Technical report. NUREG/CR-6311, Los Alamos National Laboratory; 1995.

Qian, 2009, Nested Latin hypercube designs, Biometrika, 96, 957, 10.1093/biomet/asp045

Xiong, 2009, Optimizing Latin hypercube design for sequential sampling of computer experiments, Eng Optim, 41, 793, 10.1080/03052150902852999

Rennen, 2010, Nested maximin Latin hypercube designs, Struct Multidiscip Optim, 41, 371, 10.1007/s00158-009-0432-y

Lepage, 1978, A new algorithm for adaptive multidimensional integration, J Comput Phys, 27, 192, 10.1016/0021-9991(78)90004-9

Press, 1990, Recursive stratified sampling for multidimensional Monte Carlo integration, Comput Phys, 4, 190, 10.1063/1.4822899

Shields M, Sundar V. Targeted random sampling: a new approach for efficient reliability estimation of complex systems. Int J Reliab Saf.

Johnson, 1990, Minimax and maximin distance designs, J Stat Plan Inference, 26, 131, 10.1016/0378-3758(90)90122-B

Morris, 1995, Exploratory designs for computational experiments, J Stat Plan Inference, 43, 381, 10.1016/0378-3758(94)00035-T

Ye, 2000, Algorithmic construction of optimal symmetric Latin hypercube designs, J Stat Plan Inference, 90, 145, 10.1016/S0378-3758(00)00105-1

Joseph V, Hung Y. Orthogonal-maximin Latin hypercube designs. Stat Sin 2008;18(171–186).

Liefvendahl, 2006, A study on algorithms for optimization of Latin hypercubes, J Stat Plan Inference, 136, 3231, 10.1016/j.jspi.2005.01.007

Park, 1994, Optimal Latin-hypercube designs for computer experiments, J Stat Plan Inference, 39, 95, 10.1016/0378-3758(94)90115-5

Iman, 1982, A distribution-free approach to inducing rank correlation among input variables, Commun Stat: Simul Comput, 11, 311, 10.1080/03610918208812265

Florian, 1992, An efficient sampling scheme, Probab Eng Mech, 7, 123, 10.1016/0266-8920(92)90015-A

Vorechovsky, 2009, Correlation control in small-sample monte carlo type simulations i, Probab Eng Mech, 24, 452, 10.1016/j.probengmech.2009.01.004

Tang, 1993, Orthogonal array-based Latin hypercubes, J Am Stat Assoc, 88, 1392, 10.1080/01621459.1993.10476423

Ye, 1998, Orthogonal column Latin hypercubes and their application in computer experiments, J Am Stat Assoc, 93, 1430, 10.1080/01621459.1998.10473803

Cioppa, 2007, Efficient nearly orthogonal and space-filling Latin hypercubes, Technometrics, 49, 45, 10.1198/004017006000000453

Fang K-T, Li R, Sudjianto A. Design and modeling for computer experiments. London, UK: Chapman and Hall/CRC; Boca Roton, FL, USA, 2006.

Dalbey K, Karystinos G. Fast generation of space-filling Latin hypercube sample designs. In: Proceedings of the 13th AIAA/ISSMO multidisciplinary analysis and optimization conference; 2010.

Hickernell F. Lattice rules: how well do they measure up? In: random and quasi-random point sets. Springer; New York, USA, 1998.

Aurenhammer, 1991, Voronoi diagrams—a survey of a fundamental geometric data structure, ACM Comput Surv, 23, 345, 10.1145/116873.116880

Wu C, Hamada M. Experiments: planning, analysis, and parameter design optimization. New York: Wiley; Hoboken, NJ, USA, 2000.

Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, et al. Global sensitivity analysis: the primer. Wiley; 2008.

Grigoriu, 2009, Reduced order models for random function. application to stochastic problems, Appl Math Model, 33, 161, 10.1016/j.apm.2007.10.023

Roy, 2011, A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing, Comput Methods Appl Mech Eng, 200, 2131, 10.1016/j.cma.2011.03.016

Teferra, 2014, Mapping model validation metrics to subject matter expert scores for model adequacy assessment, Reliab Eng Syst Saf, 132, 9, 10.1016/j.ress.2014.07.010

Bleich, 1970, Interaction between structures and bilinear fluids, Int J Solids Struct, 6, 617, 10.1016/0020-7683(70)90034-X

DiMaggio, 1981, Uncoupling approximations in fluid–structure interaction problems with cavitation, J Appl Mech, 48, 753, 10.1115/1.3157728

Sprague, 2001, Computational treatments of cavitation effects in near-free-surface underwater shock, Shock Vib, 7, 105, 10.1155/2001/853074

Sprague, 2003, Spectral elements and field separation for an acoustic field subject to cavitation, J Comput Phys, 184, 149, 10.1016/S0021-9991(02)00024-4

Stultz K, Daddazio R. The applicability of fluid–structure interaction approaches to the analysis of floating targets subjected to undex loading In: Proceedings of the 73rd shock and vibration symposium, Newport, RI; 2002.

Efron, 1979, Bootstrap methods: another look at the jackknife, Ann Stat, 7, 1, 10.1214/aos/1176344552