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Article

Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems

Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
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Algorithms 2020, 13(4), 90; https://doi.org/10.3390/a13040090
Received: 3 February 2020 / Revised: 25 March 2020 / Accepted: 8 April 2020 / Published: 13 April 2020
In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are very costly, while traditional methods for sensitivity analysis, such as the adjoint, fail in chaotic systems. In this work, we employ the non-intrusive generalized Polynomial Chaos (gPC) for UQ, coupled with the Multiple-Shooting Shadowing (MSS) algorithm for sensitivity analysis of chaotic systems. It is shown that the gPC, coupled with MSS, is an appropriate method for conducting UQ in chaotic systems and produces results that match well with those from MC and Finite-Differences (FD). View Full-Text
Keywords: uncertainty quantification; chaos; generalized polynomial chaos; multiple shooting shadowing; sensitivity analysis; Monte–Carlo uncertainty quantification; chaos; generalized polynomial chaos; multiple shooting shadowing; sensitivity analysis; Monte–Carlo
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MDPI and ACS Style

Kantarakias, K.D.; Papadakis, G. Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems. Algorithms 2020, 13, 90. https://doi.org/10.3390/a13040090

AMA Style

Kantarakias KD, Papadakis G. Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems. Algorithms. 2020; 13(4):90. https://doi.org/10.3390/a13040090

Chicago/Turabian Style

Kantarakias, Kyriakos D.; Papadakis, George. 2020. "Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems" Algorithms 13, no. 4: 90. https://doi.org/10.3390/a13040090

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