Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/13/4/90 |
| _version_ | 1797570788008656896 |
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| author | Kyriakos Dimitrios Kantarakias George Papadakis |
| author_facet | Kyriakos Dimitrios Kantarakias George Papadakis |
| author_sort | Kyriakos Dimitrios Kantarakias |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-03-10T20:30:21Z |
| format | Article |
| id | doaj.art-c09f5c37515b4174beb286d140c96faa |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T20:30:21Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-c09f5c37515b4174beb286d140c96faa2023-11-19T21:27:41ZengMDPI AGAlgorithms1999-48932020-04-011349010.3390/a13040090Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic SystemsKyriakos Dimitrios Kantarakias0George Papadakis1Department of Aeronautics, Imperial College London, London SW7 2AZ, UKDepartment of Aeronautics, Imperial College London, London SW7 2AZ, UKIn 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).https://www.mdpi.com/1999-4893/13/4/90uncertainty quantificationchaosgeneralized polynomial chaosmultiple shooting shadowingsensitivity analysisMonte–Carlo |
| spellingShingle | Kyriakos Dimitrios Kantarakias George Papadakis Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems Algorithms uncertainty quantification chaos generalized polynomial chaos multiple shooting shadowing sensitivity analysis Monte–Carlo |
| title | Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems |
| title_full | Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems |
| title_fullStr | Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems |
| title_full_unstemmed | Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems |
| title_short | Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems |
| title_sort | application of generalized polynomial chaos for quantification of uncertainties of time averages and their sensitivities in chaotic systems |
| topic | uncertainty quantification chaos generalized polynomial chaos multiple shooting shadowing sensitivity analysis Monte–Carlo |
| url | https://www.mdpi.com/1999-4893/13/4/90 |
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