Multivariate Simulation and Multimodal Dependence Modeling of Vehicle Axle Weights with Copulas
Publication: Journal of Transportation Engineering
Volume 132, Issue 12
Abstract
Safety assessment and rational design of bridge structures requires the uncertainty associated with vehicle loads to be modeled as accurately as possible. This modeling is rendered difficult by the presence of vehicle axle weights that involve different combinations of unimodal and multimodal probability distributions with different dependence structures. In this paper, a transformation invariant approach using copula functions is proposed for the multivariate simulation of dependent axle weights of different vehicle classes. Copula based dependence modeling, which is widely used in the financial risk analysis, is applied to model and simulate three different vehicle cases with different combinations of marginal probability distributions for axle weights. The database of observed vehicle weights is based on the data collected at five locations on national highways in India. The dependence between multimodal distributions of axle weights is accurately considered and simulations are carried out. The simulated axle weights are found to be in very good agreement with the observed data. This type of simulation is useful in carrying out simulation-based reliability analysis of bridges and pavements.
Get full access to this article
View all available purchase options and get full access to this article.
References
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, AC-19(6), 716–723.
Ali, M. M., Mikhail, N. N., and Haq, M. S. (1978). “A class of bivariate distributions including the bivariate logistic.” J. Multivariate Anal., 8(3), 405–412.
Anderson, D. R., Burnham, K. P., and Thompson, W. L. (2000). “Null hypothesis testing: Problems, prevalence, and an alternative.” J. Wildlife Management, 64(4), 912–923.
Bailey, S. F. (1996). “Basic principles and load models for the structural safety evaluation of existing bridges.” Doctoral thesis No. 1467, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula methods in finance, Wiley, New York.
Clayton, D. G. (1978). “A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.” Biometrika, 65(1), 141–151.
Crespo-Minguillon, C., and Casas, J. R. (1997). “A comprehensive traffic load model for bridge safety checking.” Struct. Safety, 19(4), 339–359.
Ditlevsen, O., and Madsen, H. O. (1996). Structural reliability methods, Wiley, Chichester, U.K.
Edgeman, R. L. (1990). “Assessing the inverse Gaussian distribution assumption.” IEEE Trans. Reliab., 39(3), 352–355.
Embrechts, P., Lindskog, F., and McNeil, A. (2003). “Modeling dependence with copulas and applications to risk management.” Handbook of heavy tailed distributions in finance, S. Rachev, ed., Elsevier, Amsterdam, The Netherlands, Chap. 8, 329–384.
Frank, M. J. (1979). “On the simultaneous associativity of and .” Aequ. Math., 19(2-3), 194–226.
Frees, E. W., and Valdez, E. A. (1998). “Understanding relationships using copulas.” North American Actuarial J., 2(1), 1–25.
Genest, C., and MacKay, J. (1986). “The joy of copulas: Bivariate distributions with uniform marginals.” Am. Stat., 40(4), 280–283.
Genest, C., and Rivest, L.-P. (1993). “Statistical inference procedures for bivariate Archimedean copulas.” J. Am. Stat. Assoc., 88(423), 1034–1043.
Genest, C., Ghoudi, K., and Rivest, L. (1995). “A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions.” Biometrika, 82(3), 543–552.
Gumbel, E. J. (1960). “Bivariate exponential distributions.” J. Am. Stat. Assoc., 55(292), 698–707.
Huang, W.-H., Sung, Y.-L., and Lin, J.-D. (2002). “Development of axle load distribution for heavy vehicles.” Preprints, 81st Annual Meeting, Transportation Research Board, Washington, D.C.
Joe, H. (1997). Multivariate models and dependence concepts, Chapman and Hall, London.
Johnson, M. E. (1987). Multivariate statistical simulation, Wiley, New York.
Liu, P.-L., and Der Kiureghian, A. (1986). “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech., 1(2), 105–112.
Mohammadi, J., and Shah, N. (1992). “Statistical evaluation of truck overloads.” J. Transp. Eng., 118(5), 651–665.
Nelsen, R. B. (1999). An introduction to copulas, Lecture notes in statistics 139, Springer, New York.
Nowak, A. S. (1995). “Calibration of LRFD bridge code.” J. Struct. Eng., 121(8), 1245–1251.
Patton, A. (2002). “Applications of copula theory in financial econometrics.” Ph.D. dissertation, Dept. of Economics, Univ. of California, San Diego.
Schweizer, B. (1991). “Thirty years of copulas.” Advances in probability distributions with given marginals: Beyond the copulas (Mathematics and its applications), G. Dall’Aglio, S. Kotz, and G. Salinetti, eds., Kluwer Academic, Dordrecht, The Netherlands, 13–50.
Schweizer, B., and Wolff, E. F. (1981). “On nonparametric measures of dependence for random variables.” Ann. Stat., 9(4), 879–885.
Sklar, A. (1959). “Fonctions de repa’rticion a’ n dimensions et leurs marges.” Publications de l’Institut de Statistique de l’Université de Paris, Paris, 8, 229–231.
Timm, D. H., Newcomb, D. E., and Galambos, T. V. (2000). “Incorporation of reliability into mechanistic-empirical pavement design.” Transportation Research Record. 1730, Transportation Research Board, Washington, D.C., 73–80.
Timm, D. H., Tisdale, S. M., and Turochy, R. E. (2005). “Axle load spectra characterization by mixed distribution modeling.” J. Transp. Eng., l31(2), 83–88.
Srinivas, S. (2006). “Copula based dependence and probabilistic load modeling of highway bridges.” Ph.D. thesis, Indian Institute of Technology, Chennai, India.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 132 • Issue 12 • December 2006
Pages: 945 - 955
Copyright
© 2006 ASCE.
History
Received: Jul 7, 2005
Accepted: Mar 20, 2006
Published online: Dec 1, 2006
Published in print: Dec 2006
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.