Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models

被引:12
作者
Pan, Qiyun [1 ]
Byon, Eunshin [1 ]
Ko, Young Myoung [2 ]
Lam, Henry [3 ]
机构
[1] Univ Michigan, Dept Ind & Operat Engn, Ann Arbor, MI 48109 USA
[2] Pohang Univ Sci & Technol, Dept Ind & Management Engn, Pohang, South Korea
[3] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA
基金
美国国家科学基金会; 新加坡国家研究基金会;
关键词
Monte Carlo sampling; reliability; variance reduction; NESTED SIMULATION; DESIGN; APPROXIMATION; VARIANCE;
D O I
10.1002/nav.21938
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.
引用
收藏
页码:524 / 547
页数:24
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