Estimation of small failure probabilities in high dimensions by subset simulation
Estimation of small failure probabilities in high dimensions by subset simulation
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DOI：
10.1016/s0266-8920(01)00019-4
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发表时间：
2001-10-01
影响因子：
2.6
通讯作者：
Beck, JL
中科院分区：
文献类型：
--
作者：
Au, SK;Beck, JL
提出了一种称为“子集模拟”的新模拟方法来计算工程系统可靠性分析中遇到的小故障概率。基本思想是通过引入中间故障事件将故障概率表示为较大条件故障概率的乘积。通过适当选择条件事件，可以使条件失效概率足够大，以便可以通过少量样本的模拟来估计它们。计算小故障概率的原始问题（计算要求较高）被简化为计算一系列条件概率，可以通过模拟轻松有效地估计这些概率。然而，条件概率无法通过标准蒙特卡罗程序有效估计，因此提出了基于 Metropolis 算法的马尔可夫链蒙特卡罗模拟 (MCS) 技术来进行估计。所提出的方法对不确定参数的数量具有鲁棒性，并且在计算小概率时有效。通过计算受到白噪声激励的线性振荡器和不确定地震激励下的五层非线性滞回剪力建筑的首次偏移概率，证明了该方法的效率。 (C) 2001 Elsevier Science Ltd. 保留所有权利。
A new simulation approach, called 'subset simulation', is proposed to compute small failure probabilities encountered in reliability analysis of engineering systems. The basic idea is to express the failure probability as a product of larger conditional failure probabilities by introducing intermediate failure events. With a proper choice of the conditional events, the conditional failure probabilities can be made sufficiently large so that they can be estimated by means of simulation with a small number of samples. The original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which can be readily and efficiently estimated by means of simulation. The conditional probabilities cannot be estimated efficiently by a standard Monte Carlo procedure, however, and so a Markov chain Monte Carlo simulation (MCS) technique based on the Metropolis algorithm is presented for their estimation. The proposed method is robust to the number of uncertain parameters and efficient in computing small probabilities. The efficiency of the method is demonstrated by calculating the first-excursion probabilities for a linear oscillator subjected to white noise excitation and for a five-story nonlinear hysteretic shear building under uncertain seismic excitation. (C) 2001 Elsevier Science Ltd. All rights reserved.