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    Sequential Sampling-Based Asymptotic Probability Estimation of High-Dimensional Rare Events

    Source: Journal of Mechanical Design:;2023:;volume( 145 ):;issue: 010::page 101701-1
    Author:
    Xu, Yanwen
    ,
    Wang, Pingfeng
    DOI: 10.1115/1.4062790
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Accurate analysis of rare failure events with an affordable computational cost is often challenging in many engineering applications, particularly for problems with high-dimensional system inputs. The extremely low probabilities of occurrence often lead to large probability estimation errors and low computational efficiency. Thus, it is vital to develop advanced probability analysis methods that are capable of providing robust estimations of rare event probabilities with narrow confidence bounds. The general method of determining confidence intervals of an estimator using the central limit theorem faces the critical obstacle of low computational efficiency. This is a side effect of the widely used Monte Carlo method, which often requires a large number of simulation samples to derive a reasonably narrow confidence interval. In this paper, a new probability analysis approach is developed which can be used to derive the estimates of rare event probabilities efficiently with narrow estimation bounds simultaneously for high-dimensional problems and complex engineering systems. The asymptotic behavior of the developed estimator is proven theoretically without imposing strong assumptions. An asymptotic confidence interval is established for the developed estimator. The presented study offers important insights into the robust estimations of the probability of occurrences for rare events. The accuracy and computational efficiency of the developed technique are assessed with numerical and engineering case studies. Case study results have demonstrated that narrow bounds can be obtained efficiently using the developed approach with the true values consistently located within the estimation bounds.
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      Sequential Sampling-Based Asymptotic Probability Estimation of High-Dimensional Rare Events

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4294784
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    contributor authorXu, Yanwen
    contributor authorWang, Pingfeng
    date accessioned2023-11-29T19:28:16Z
    date available2023-11-29T19:28:16Z
    date copyright7/19/2023 12:00:00 AM
    date issued7/19/2023 12:00:00 AM
    date issued2023-07-19
    identifier issn1050-0472
    identifier othermd_145_10_101701.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4294784
    description abstractAccurate analysis of rare failure events with an affordable computational cost is often challenging in many engineering applications, particularly for problems with high-dimensional system inputs. The extremely low probabilities of occurrence often lead to large probability estimation errors and low computational efficiency. Thus, it is vital to develop advanced probability analysis methods that are capable of providing robust estimations of rare event probabilities with narrow confidence bounds. The general method of determining confidence intervals of an estimator using the central limit theorem faces the critical obstacle of low computational efficiency. This is a side effect of the widely used Monte Carlo method, which often requires a large number of simulation samples to derive a reasonably narrow confidence interval. In this paper, a new probability analysis approach is developed which can be used to derive the estimates of rare event probabilities efficiently with narrow estimation bounds simultaneously for high-dimensional problems and complex engineering systems. The asymptotic behavior of the developed estimator is proven theoretically without imposing strong assumptions. An asymptotic confidence interval is established for the developed estimator. The presented study offers important insights into the robust estimations of the probability of occurrences for rare events. The accuracy and computational efficiency of the developed technique are assessed with numerical and engineering case studies. Case study results have demonstrated that narrow bounds can be obtained efficiently using the developed approach with the true values consistently located within the estimation bounds.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleSequential Sampling-Based Asymptotic Probability Estimation of High-Dimensional Rare Events
    typeJournal Paper
    journal volume145
    journal issue10
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.4062790
    journal fristpage101701-1
    journal lastpage101701-12
    page12
    treeJournal of Mechanical Design:;2023:;volume( 145 ):;issue: 010
    contenttypeFulltext
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