Abstract
In recent years, new, intelligent and efficient sampling techniques for Monte Carlo simulation have been developed. However, when such new techniques are introduced, they are compared to one or two existing techniques, and their performance is evaluated over two or three problems. A literature survey shows that benchmark studies, comparing the performance of several techniques over several problems, are rarely found. This article presents a benchmark study, comparing Simple or Crude Monte Carlo with four modern sampling techniques: Importance Sampling Monte Carlo, Asymptotic Sampling, Enhanced Sampling and Subset Simulation; which are studied over six problems. Moreover, these techniques are combined with three schemes for generating the underlying samples: Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling. Hence, a total of fifteen sampling strategy combinations are explored herein. Due to space constrains, results are presented for only three of the six problems studied; conclusions, however, cover all problems studied. Results show that Importance Sampling using design points is extremely efficient for evaluating small failure probabilities; however, finding the design point can be an issue for some problems. Subset Simulation presented very good performance for all problems studied herein. Although similar, Enhanced Sampling performed better than Asymptotic Sampling for the problems considered: this is explained by the fact that in Enhanced Sampling the same set of samples is used for all support points; hence a larger number of support points can be employed without increasing the computational cost. Finally, the performance of all the above techniques was improved when combined with Latin Hypercube Sampling, in comparison to Simple or Antithetic Variates sampling.
Highlights
Since the early beginnings in the sixties and seventies, structural reliability analysis has reached a mature stage encompassing solid theoretical developments and increasing practical applications
The reference probability of failure is evaluated by Crude and by Importance Sampling Monte Carlo simulation, using Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling. 1×105 samples are employed for each solution
The original solution via Crude Monte Carlo took approximately 11 hours to compute a probability of failure with coefficient of variation of 0.27 and relative deviations of: 28.68% (Simple Sampling), 1.1% (Latin Hypercube Sampling) and 37.87% (Antithetic Variates Sampling)
Summary
Since the early beginnings in the sixties and seventies, structural reliability analysis has reached a mature stage encompassing solid theoretical developments and increasing practical applications. Several intelligent sampling techniques for Monte Carlo simulation have been proposed in recent years (Au and Beck, 2001; Au, 2005; Au et al, 2007; Bucher, 2009; Sichani et al, 2011a; Sichani et al, 2011b; Sichani et al, 2014; Naess et al, 2009; Naess et al, 2012) When such techniques are introduced, they are generally compared with one or two existing techniques, and their performance is evaluated over two or three problems. This article presents a benchmark study, comparing Simple or Crude Monte Carlo with four modern sampling techniques: Importance Sampling Monte Carlo, Asymptotic Sampling, Enhanced Sampling and Subset Simulation over six problems These techniques are combined with three schemes for generating the underlying samples: Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
