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Global sensitivity analysis for stochastic processes with independent increments
Probabilistic Engineering Mechanics ( IF 2.6 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.probengmech.2020.103098
Emeline Gayrard , Cédric Chauvière , Hacène Djellout , Pierre Bonnet , Don-Pierre Zappa

Abstract This paper is a first attempt to develop a numerical technique to analyze the sensitivity and the propagation of uncertainty through a system with stochastic processes having independent increments as input. Similar to Sobol’ indices for random variables, a meta-model based on Chaos expansions is used and it is shown to be well suited to address such problems. New global sensitivity indices are also introduced to tackle the specificity of stochastic processes. The accuracy and the efficiency of the proposed method is demonstrated on an analytical example with three different input stochastic processes: a Wiener process; an Ornstein–Uhlenbeck process and a Brownian bridge process. The considered output, which is function of these three processes, is a non-Gaussian process. Then, we apply the same ideas on an example without known analytical solution.

中文翻译:

具有独立增量的随机过程的全局敏感性分析

摘要 本文首次尝试开发一种数值技术,通过具有独立增量的随机过程作为输入的系统来分析不确定性的敏感性和传播。与 Sobol 的随机变量指数类似,使用了基于混沌扩展的元模型,它被证明非常适合解决此类问题。还引入了新的全局敏感性指数来解决随机过程的特殊性。所提出方法的准确性和效率在具有三个不同输入随机过程的分析示例中得到证明:维纳过程;Ornstein-Uhlenbeck 过程和布朗桥过程。作为这三个过程的函数的所考虑的输出是非高斯过程。然后,
更新日期:2020-10-01
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