Distribution-Free Monte Carlo Simulation: Premise and Refinement
Publication: Journal of Construction Engineering and Management
Volume 134, Issue 5
Abstract
From cost estimation to reliability analysis, Monte Carlo simulation has found its niche in a wide variety of applications in civil engineering. With recognition of correlations among variables, recent efforts have been devoted to model the correlations more accurately and with no restriction on the form of marginal distributions, i.e., being distribution free. Yet, the conventional method introduced by Iman and Conover, although widely accepted, is bound to have errors: The generated correlation matrix may bear no resemblance to the desired correlation matrix. The purposes of this study are to shed light on the underlying premises of the conventional method and to refine the method by reducing the errors to an acceptable level automatically. A particle swarm optimization algorithm is proposed to repair invalid (nonpositive definite) correlation matrices and to bring the generated correlation matrix into conformity with the desired target. The effectiveness of the proposed algorithm has been verified in estimating cost of electrical services based on historical data.
Get full access to this article
View all available purchase options and get full access to this article.
References
AbouRizk, S. M., Halpin, D. W., and Wilson, J. R. (1994). “Fitting beta distributions based on sample data.” J. Constr. Eng. Manage., 120(2), 288–305.
Bonett, D. G., and Wright, T. A. (2000). “Sample size requirements for estimating Pearson, Kendall and Spearman correlations.” Psychometrika, 65, 23–28.
Chau, K. W. (1995). “Monte Carlo simulation of construction costs using subjective data.” Constr. Manage. Econom., 13, 369–383.
Chou, J. S., Wang, L. L., Chou, W. K., and O’Conner, J. (2005). “Preliminary cost estimates using probabilistic simulation for highway bridge replacement projects.” Proc., Construction Research Congress 2005, San Diego, Calif., April 5–7, 467–471.
Clemen, R. T., and Reilly, T. (1999). “Correlations and copulas for decision and risk analysis.” Manage. Sci., 45, 208–224.
Clerc, M., and Kennedy, J. (2002). “The particle swarm-explosion, stability, and convergence in a multidimensional complex space.” IEEE Trans. Evol. Comput., 6, 58–73
Elbeltagi, E., Hegazy, T., and Grierson, D. (2005). “Comparison among five evolutionary-based optimization algorithms.” Adv. Eng. Inf., 19(1), 43–53.
Hamm, N. A. S., Hall, J. W., and Anderson, M. G. (2006). “Variance-based sensitivity analysis of the probability of hydrologically induced slope instability.” Comput. Geosci., 32(6), 803–817.
Iman, R. L., and Conover, W. J. (1982). “A distribution-free approach to inducing rank correlations among input variables.” Comm. in Statistics, 11(3), 311–334.
Kennedy, J., Eberhart, R. C., and Shi, Y. (2001). Swarm intelligence, Morgan Kaufmann, San Francisco.
Krishnamoorthy, K. (2006). Handbook of statistical distributions with applications, Chapman and Hall, Boca Raton, Fla.
Kupiec, P. H. (1998). “Stress testing in a value at risk framework.” J. Derivatives, 6(1), 7–24.
Kurowicka, D., and Cooke, R. M. (2006). Uncertainty analysis with high dimensional dependence, Wiley, New York, 107–109.
Liu, M., and Frangopol, D. M. (2005). “Bridge annual maintenance prioritization under uncertainty by multiobjective combinatorial optimization.” Comput. Aided Civ. Infrastruct. Eng., 20(5), 343–353.
Lupoi, G., Franchin, P., Lupoi, A., and Pinto, P. E. (2006). “Seismic fragility analysis of structural systems.” J. Eng. Mech., 132(4), 385–395.
Lurie, P. M., and Goldberg, M. S. (1998). “An approximate method for sampling correlated random variables from partially specified distributions.” Manage. Sci., 44, 203–218.
Maio, C., Schexnuayder, C., Knutson, K., and Weber, S. (2000). “Probability distribution functions for construction simulation.” J. Constr. Eng. Manage., 126(4), 285–292.
Moonan, W. J. (1957). “Linear transformation to a set of stochastically dependent normal variables.” J. Am. Stat. Assoc., 52, 247–252.
Mrawira, D., Welch, W. J., Schonlau, M., and Haas, R. (1999). “Sensitivity analysis of computer models: World Bank HDM-III model.” J. Transp. Eng., 125(5), 421–428.
Olsson, A. M., and Sandberg, G. E. (2002). “Latin hypercube sampling for stochastic finite-element analysis.” J. Eng. Mech., 128(1), 121–125.
Ranasinghe, M. (2000). “Impact of correlation and induced correlation on the estimation of project cost of buildings.” Constr. Manage. Econom., 18, 395–406.
Rebonato, R., and Jackel, P. (1999). “The most general methodology to create a valid correlation matrix for risk management and option pricing purposes.” J. Risk, 2(2), 17–27.
Schmeiser, B. W., and Lal, R. (1982). “Bivariate gamma random vectors.” Oper. Res., 30(2), 355–374.
Scollard, C. R., and Bartlett, F. M. (2004). “Impact of new ACI 318 flexural resistance factor on bond failures.” J. Struct. Eng., 130(1), 138–146.
Shen, L. Y., and Wu, Y. Z. (2005). “Risk concession model for build/operate/transfer contract projects.” J. Constr. Eng. Manage., 131(2), 211–220.
Touran, A. (1993). “Probabilistic cost estimation with subjective correlations.” J. Constr. Eng. Manage., 119(1), 58–71.
Touran, A., and Lopez, R. (2006). “Modeling cost escalation in large infrastructure projects.” J. Constr. Eng. Manage., 132(8), 853–860.
Touran, A., and Suphot, L. (1997). “Rank correlation in simulating construction costs.” J. Constr. Eng. Manage., 123(3), 297–301.
Vale, C. D., and Maurelli, V. A. (1983). “Simulating multivariate nonnormal distributions.” Psychometrika, 48, 465–471.
van den Bergh, F., and Engelbrecht, A. P. (2006). “A study of particle swarm optimization particle trajectories.” Inform. Science, 176(8), 937–971.
Vose, D. (2000). Risk analysis: A quantitative guide, 2nd Ed., Wiley, Chichester, U.K., 296–299.
Wang, W. C. (2002). “Simulation-facilitated model for assessing cost correlations.” Comput. Aided Civ. Infrastruct. Eng., 17(5), 368–380.
Yang, I. T. (2005). “Simulation-based estimation for correlated cost elements.” Int. J. Proj. Manage., 23(4), 275–282.
Yang, I. T. (2006). “Using Gaussian copula to simulate repetitive projects.” Constr. Manage. Econom., 24(9), 899–909.
Yang, I. T. (2007). “Risk modeling of dependence between project task durations.” Comput. Aided Civ. Infrastruct. Eng., 22(6), 419–429.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: Mar 21, 2007
Accepted: Jun 7, 2007
Published online: May 1, 2008
Published in print: May 2008
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.