Abstract
A new sampling technique referred to as the hypercube point concentration sampling technique is proposed. This sampling technique is based on the concepts of the Latin hypercube sampling technique and the point concentration method. In the proposed technique, first, the probability density function of the random variables is replaced by a sufficiently large number of probability concentrations with magnitudes and locations determined from the moments of the random variables. In other words, the probability density function is replaced by the probability mass function determined based on the point estimate method. The probability mass function is then used with the Latin hypercube sampling technique to obtain samples. For evaluating statistics of a complicated performance function of an engineering system, the proposed technique could be more efficient than the Latin hypercube sampling technique since for a given simulation cycle the required number of evaluations of the performance function in the former is less than that in the latter. The proposed sampling technique is illustrated through numerical examples.
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References
Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (Eds.) (1953) Higher transcendental functions, Bateman manuscript project, vol. II, McGraw-Hill, New York.
Hong, H. P. (1996) Point-estimate moment-based reliability analysis, Civil Engineering Systems, Vol. 13, pp. 218–294.
Hong, H. P. (1998) An efficient point estimate method for probabilistic analysis, Reliability Engineering & System Safety, vol. 59, No. 3, pp. 261–267.
Iman, R. L. and Conover, W. J. (1980) Small sample sensitivity analysis techniques for computer models, with an application to risk assessment, Commun. Statist. — Theor. Meth. A9(17):1749–1842
MacGregor, J. G. (1997) Reinforced concrete, mechanics and design, Prentice-Hall, Upper Saddle River, NJ.
Madsen, H. O., Krenk, S. and Lind, N. C. (1986) Methods of structural safety, Prentice-Hall, Englewood Cliffs, NJ.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992) Numerical recipes in FORTRAN: the art of scientific computing, Cambridge University Press, New York.
Rosenblueth, E. (1981) Two-point estimates in probability, Appl. Math. Modelling, 5: 329–335.
Rosenblueth, E. (1975) Point estimation for probability moments. Proc. Nat. Acad.. Sci. U.S.A., 72, 3812–3814.
Rubinstein, R. Y. (1981) Simulation and Monte Carlo method, John Wiley and Sons Inc., New York.
Stroud, A. H. and Secrest, D. (1966) Gaussian quadrature formulas, Prentice-Hall, Englewood Cliffs, NJ.
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Hong, H.P. (2006). Hypercube Point Concentration Sampling Technique. In: Pandey, M., Xie, WC., Xu, L. (eds) Advances in Engineering Structures, Mechanics & Construction. Solid Mechanics and Its Applications, vol 140. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4891-2_44
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DOI: https://doi.org/10.1007/1-4020-4891-2_44
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