Uncertainty Analysis by Point Estimate Methods Incorporating Marginal Distributions
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 3
Abstract
The model performance of an engineering system is affected by many variables subject to uncertainty. Point estimate (PE) methods are practical tools to assess the uncertainty features of a model involving multivariate stochastic parameters. Two PE methods have been developed for engineering applications. One is Rosenblueth's PE method, which preserves the first three moments of random variables and the other is Harr's PE method, which reduces the computations of Rosenblueth's method but only as appropriate for application to random variables with normal distributions. In this study, two algorithms are proposed to encompass the advantages of the two PE methods: computational practicality and the handling of mixture distributions. Through a numerical experiment, the proposed methods yielded more accurate estimations than those of Rosenblueth's method with about the same amount of computation as Harr's method. The two proposed methods were also applied to estimate statistical moments of a pier scouring model output to demonstrate their performance in an engineering application.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chang, C. H. (1994). “Incorporate information of non-normal distributions in uncertainty analysis of hydrosystems,” PhD dissertation, Inst. of Civ. Engrg., Nat. Chiao-Tung Univ., Taiwan, ROC, 58–75.
2.
Chang, C. H., Tung, Y. K., and Yang, J. C.(1994). “Monte Carlo simulation for correlated variables with marginal distributions.”J. Hydr. Engrg., ASCE, 120(3), 313–331.
3.
Chang, C. H., Tung, Y. K., and Yang, J. C.(1995). “Evaluation of probability point estimate methods.”Appl. Math. Modelling, 19(2), 95–105.
4.
Der Kiureghian, A., and Liu, P. L.(1985). “Structural reliability under incomplete probability information.”J. Engrg. Mech., ASCE, 112(1), 85–104.
5.
Harr, M. E.(1989). “Probabilistic estimates for multivariate analyses.”Appl. Math. Modelling, 13(5), 313–318.
6.
Hill, I. D., Hill, R., and Holder, R. L. (1976)l. “Algorithm AS 99: fitting Johnson curves by moments.”Appl. Statistics, 25, 180–189.
7.
Johnson, P. A.(1992). “Reliability-based pier scour engineering.”J. Hydr. Engrg., ASCE, 118(10), 1344–1358.
8.
Johnson, N. L., and Kotz, S. (1970). Continuous univariate distributions—1. John Wiley & Sons, Inc., New York, N.Y.
9.
Karmeshu, and Lara-Rosano(1987). “Modelling data uncertainty in growth forecasts.”Appl. Math. Modelling, 11(2), 62–68.
10.
Li, K. S.(1992). “Point-estimate method for calculating statistical moments.”J. Engrg. Mech., ASCE, 118(7), 1506–1511.
11.
Rosenblueth, E.(1975). “Point estimates for probability moments.”Proc. Nat. Acad. Sci. USA, 72(10), 3812.
12.
Rosenblueth, E.(1981). “Two-point estimates in probabilities.”Appl. Math. Modelling, 5(10), 329–335.
13.
Yeh, K. C., and Tung, Y. K.(1993). “Uncertainty and sensitivity of a pit migration model.”J. Hydr. Engrg., ASCE, 119(2), 262–281.
14.
Zoppou, C., and Li, K. S.(1993). “New point estimate method for water resources modeling.”J. Hydr. Engrg., ASCE, 119(11), 1300–1307.
Information & Authors
Information
Published In
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Mar 1, 1997
Published in print: Mar 1997
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.