Structural reliability of corroded pipeline using the so-called Separable Monte Carlo method

The evaluation of the failure probability of corroded pipelines is an important calculation to quantify the risk assessment and integrity of pipelines. Traditional Monte Carlo simulation method has been widely used to solve this type of problems, where it generates a very large number of simulations and takes longer time in computing. In this study, enhanced computational method called Separable Monte Carlo is employed to evaluate the time-dependent reliability of pipeline segments containing active corrosion defects, where a practical example was used. The results show that the Separable Monte Carlo simulation method not only minimizes the computational cost strongly but also improves the calculation precision.

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

Combining Separable Monte Carlo With Importance Sampling for Improved Accuracy

Monte-Carlo (MC) methods are often used to carry out reliability based design of structures. Methods that improve the accuracy of MC simulation include Separable Monte Carlo (SMC), Markov Chain Monte-Carlo, and importance sampling. We explore the utility of combining SMC and importance sampling for improving accuracy. The accuracy of the estimates is compared for crude MC, SMC, importance sampling and combined method for a composite plate example and a tuned mass damper example. For these examples SMC and importance sampling reduced the error individually by factors of 2 to 5, and the combination reduced it further by about a factor of 2. The results were also compared with the first order reliability method (FORM). FORM was grossly inaccurate for the tuned mass-damper example which has a failure region bounded by safe regions on either side.