The analysis and estimation for  rare events with extremely small probabilities under the acceptable computational cost are challenging in many engineering applications, especially for high dimensional problems. Those small probabilities of the engineering system often lead to the decline in the estimation accuracy and efficiency that recognizes the importance of the robust estimation of the probability with narrow bounds in rare events. Generally, confidence intervals of the estimator are established based on the central limit theorem. One of the main obstacles is that the widely used Monte Carlo method requires a huge number of samples to derive reasonably narrow confidence interval which is computationally expensive. This paper, therefore, proposes a powerful probability analysis approach that can estimate the probability of rare events in high dimensional systems efficiently and provide narrow bounds for estimations simultaneously. The asymptotic behaviors of the proposed estimator is proved theoretically without strong assumptions. Based on that, an asymptotic confidence interval is established for the proposed estimator. This study offers some important insights into the robust estimation of rare events. The efficiency of the developed technique for rare events estimation with confidence intervals is assessed with several engineering design examples. Our numerical experiments demonstrate that narrow bounds are built efficiently with probability estimations, and the real probability results are always located within the proposed estimation bounds, which indicates that the proposed approach can improve both efficiency and accuracy of the rare events estimation


Sequential Sampling Based Reliability Analysis for High Dimensional Rare Events With Confidence Intervals

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

IDETC2020 - Virtual Conference

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.