Global sensitivity analysis for stochastic processes with independent increments

• Published in: Probabilistic engineering mechanics Vol. 62; p. 103098
• Main Authors: Gayrard, Emeline, Chauvière, Cédric, Djellout, Hacène, Bonnet, Pierre, Zappa, Don-Pierre
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.10.2020; Elsevier Science Ltd; Elsevier
• Series: Probabilistic Engineering Mechanics
• Subjects: Applications; Brownian motion; Chaos expansions; Exact solutions; Gaussian process; Mathematics; Methodology; Normal distribution; Numerical analysis; Orthogonal polynomial; Probability; Random variables; Sensitivity analysis; Sobol’ indices; Statistics; Stochastic models; Stochastic processes; 90B22; Chaos expansions; Sobol’ indices; Stochastic processes; 60K25; 65C05; 65C50; Orthogonal polynomial; Orthogonal polynomial AMS 2010 subject classifications 90B22; Sobol' indices
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2020.103098

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.