Estimation of second-order statistics allows characterizing the uncertainty associated with the response of stochastic finite element models. Two common approaches for estimating these statistics are Monte Carlo simulation and perturbation. The purpose of this paper is to present a framework to aggregate the results obtained by means of these two approaches under the umbrella of Control Variates with Splitting. This allows to produce estimates of the second-order statistics of the system’s response with improved precision and accuracy. More specifically, Control Variates is implemented in such a way that the variance of the estimates of second-order statistics is minimized. In addition, the application of intervening variables for enhancing perturbation is considered as well, showing substantial advantages by increasing the accuracy of the estimates of second-order statistics. The application of the proposed framework is illustrated by means of an example involving the estimation of second-order statistics of a model involving confined seepage flow.

中文翻译：

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控制随着蒙特卡罗模拟和扰动分析的聚合结果的分裂而变化

二阶统计量的估计可以表征与随机有限元模型响应相关的不确定性。估计这些统计数据的两种常见方法是蒙特卡罗模拟和扰动。本文的目的是提出一个框架，在分裂控制变量的框架下汇总通过这两种方法获得的结果。这允许以更高的精度和准确度生成系统响应的二阶统计量的估计。更具体地说，控制变量的实现方式是使二阶统计量估计的方差最小化。此外，还考虑了应用干预变量来增强扰动，通过提高二阶统计估计的准确性而显示出巨大的优势。通过涉及有限渗流模型的二阶统计估计的示例来说明所提出的框架的应用。