Author(s): D. J. Lee; J. H. Heo
Linked Author(s): Jun-Haeng Heo
Keywords: Uncertainty; Risk of failure; Asymptotic variance; Gumbel; Monte-Carlo simulation
Abstract: To assess and quantify uncertainty of the risk of failure of hydraulic structures, the concept of asymptotic variance is considered in this study. The variances of the risk of failure are derived based on the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood method (ML) by using Taylor expansion assuming the underlying model is the Gumbel probability distribution. The 1st and 2nd order approximations of variance of the risk of failure are derived as a function of sample size, design life, and nonexceedance probability and comparative analysis is carried out in various conditions. For the derived variances, it is shown that MOM gives the largest variances in all cases while ML does the smallest ones for relatively high nonexceedance probabilities. In addition, PWM gives the smallest variances for low nonexceedance probabilities. The 1st and 2nd approximations show almost same variances in most cases but the 2nd approximation gives the negative values in some cases of lower nonexceedance probability and higher design life. To verify the performance of the derived variances, Monte-Carlo simulation experiments are performed. The simulation results show that MOM gives the largest variances while ML does the smallest ones in most cases. And the derived variances converge to the simulation ones as sample size increases for all nonexceedance probability and design life considered herein.
Year: 2003