In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging from risk management to utility optimisation. In practice, this distribution usually cannot be derived analytically and has to be obtained numerically by simulations. To this end, standard Monte Carlo simulations are often used, however, they cannot efficiently reconstruct the tail of the distribution which is essential in many applications. One possible remedy is to use the Multicanonical Monte Carlo method, an adaptive importance sampling scheme. In this method, one draws samples from an importance sampling distribution in a nonstandard form in each iteration, which is usually done via Markov chain Monte Carlo (MCMC). MCMC is inherently serial and therefore struggles with parallelism. In this paper, we present a new approach, which uses the Sequential Monte Carlo sampler to draw from the importance sampling distribution, which is particularly suited for parallel implementation. With both mathematical and practical examples, we demonstrate the competitive performance of the proposed method.
翻译:在许多现实世界工程系统中,系统的性能或可靠性都以星标参数为特征。这种性能参数的分布在许多不确定的量化问题中很重要,从风险管理到公用事业优化等,从许多不确定的量化问题中都有重要之处。实际上,这种分布通常不能通过分析得出,而必须通过模拟数字获得。为此,常常使用标准的蒙特卡洛模拟,但是,它们无法有效地重建在许多应用中至关重要的分布的尾部。一种可能的补救办法是使用多卡尼卡蒙特卡洛方法,即适应性重要性取样办法。在这种方法中,人们从每种迭代中以非标准形式进行的重要抽样分布中抽取样本,通常通过Markov链蒙特卡洛(MCConte Carlo)(MC)进行。MCMC具有内在的序列性,因此与平行性相抗争。在本文件中,我们提出了一个新方法,即使用定序的蒙特卡洛取样器从重要性抽样分布中提取出,特别适合平行执行的重要数据。我们用数学和实用的例子来展示拟议方法的竞争性性。