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| Title: | Efficient sampling for non-intrusive polynomial chaos applications With multiple uncertain input variables | |
| Author (s): | Hosder, Serhat Walters, R.W. Balch, M. | |
| Department/Lab Affiliations: | Mechanical & Aerospace Engineering | |
| Keywords: | Collocation points Efficient sampling NIPC Non-intrusive polynomial chaos | |
| Issue Date: | 2007-04 | |
| Publisher: | American Institute of Aeronautics and Astronautics | |
| Citation: | S. Hosder, R.W. Walters, and M. Balch “Efficient Sampling For Non-Intrusive Polynomial Chaos Applications With Multiple Uncertain Input Variables,” 9th AIAA Non-Deterministic Approaches Conference, Paper No. AIAA-2007-1939. Waikiki, Hawaii, April 2007. | |
| Abstract: | The accuracy and the computational efficiency of a Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) method applied to stochastic problems with multiple uncertain input variables has been investigated. Two stochastic model problems with multiple uniform random variables were studied to determine the effect of different sampling methods (Random, Latin Hypercube, and Hammersley) for the selection of the collocation points. The effect of the number of collocation points on the accuracy of polynomial chaos expansions were also investigated. The results of the stochastic model problems show that all three sampling methods exhibit a similar performance in terms of the the accuracy and the computational efficiency of the chaos expansions. It has been observed that using a number of collocation points that is twice more than the minimum number required gives a better approximation to the statistics at each polynomial degree. This improvement can be related to the increase of the accuracy of the polynomial coefficients due to the use of more information in their calculation. The results of the stochastic model problems also indicate that for problems with multiple random variables, improving the accuracy of polynomial chaos coefficients in NIPC approaches may reduce the computational expense by achieving the same accuracy level with a lower order polynomial expansion. To demonstrate the application of Point-Collocation NIPC to an aerospace problem with multiple uncertain input variables, a stochastic computational aerodynamics problem which includes the numerical simulation of steady, inviscid, transonic flow over a three-dimensional wing with an uncertain free-stream Mach number and angle of attack has been studied. For this study, a 5th degree Point-Collocation NIPC expansion obtained with Hammersley sampling was capable of estimating the statistics at an accuracy level of 1000 Latin Hypercube Monte Carlo simulations with a significantly lower computational cost. | |
| Type: | Article - Conference proceedings text | |
| In Title: | 9th AIAA Non-Deterministic Approaches Conference | |
| Copyright Notice: | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. FULL COPYRIGHT INFORMATION: | |
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| title | Efficient sampling for non-intrusive polynomial chaos applications With multiple uncertain input variables | |
| contributor.author | Hosder, Serhat | |
| contributor.author | Walters, R.W. | |
| contributor.author | Balch, M. | |
| contributor.deptlab | Mechanical & Aerospace Engineering | |
| subject | Collocation points | |
| subject | Efficient sampling | |
| subject | NIPC | |
| subject | Non-intrusive polynomial chaos | |
| date.issued | 2007-04 | |
| publisher | American Institute of Aeronautics and Astronautics | |
| identifier.URI | ||
| identifier.URI | ||
| identifier.citation | S. Hosder, R.W. Walters, and M. Balch “Efficient Sampling For Non-Intrusive Polynomial Chaos Applications With Multiple Uncertain Input Variables,” 9th AIAA Non-Deterministic Approaches Conference, Paper No. AIAA-2007-1939. Waikiki, Hawaii, April 2007. | |
| description.abstract | The accuracy and the computational efficiency of a Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) method applied to stochastic problems with multiple uncertain input variables has been investigated. Two stochastic model problems with multiple uniform random variables were studied to determine the effect of different sampling methods (Random, Latin Hypercube, and Hammersley) for the selection of the collocation points. The effect of the number of collocation points on the accuracy of polynomial chaos expansions were also investigated. The results of the stochastic model problems show that all three sampling methods exhibit a similar performance in terms of the the accuracy and the computational efficiency of the chaos expansions. It has been observed that using a number of collocation points that is twice more than the minimum number required gives a better approximation to the statistics at each polynomial degree. This improvement can be related to the increase of the accuracy of the polynomial coefficients due to the use of more information in their calculation. The results of the stochastic model problems also indicate that for problems with multiple random variables, improving the accuracy of polynomial chaos coefficients in NIPC approaches may reduce the computational expense by achieving the same accuracy level with a lower order polynomial expansion. To demonstrate the application of Point-Collocation NIPC to an aerospace problem with multiple uncertain input variables, a stochastic computational aerodynamics problem which includes the numerical simulation of steady, inviscid, transonic flow over a three-dimensional wing with an uncertain free-stream Mach number and angle of attack has been studied. For this study, a 5th degree Point-Collocation NIPC expansion obtained with Hammersley sampling was capable of estimating the statistics at an accuracy level of 1000 Latin Hypercube Monte Carlo simulations with a significantly lower computational cost. | |
| type | Article - Conference proceedings | |
| type.DCMIType | text | |
| relation.isPartOf | 9th AIAA Non-Deterministic Approaches Conference | |
| rights | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. | |
| rights.URI | ||
| date.accessioned | 2007-04-11T17:00:48Z | |
| date.available | 2007-04-11T17:00:48Z | |
| identifier.persist.URI | ||
| Full Text |
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