Quadrature as applied to computer models for robust design: theoretical and empirical assessment
This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2021-01-01
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| Series: | Design Science |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S205347012100024X/type/journal_article |
| _version_ | 1811156429015351296 |
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| author | Daniel D. Frey Yiben Lin Petra Heijnen |
| author_facet | Daniel D. Frey Yiben Lin Petra Heijnen |
| author_sort | Daniel D. Frey |
| collection | DOAJ |
| description | This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, this paper proves that the method gives exact transmitted variance if the response is a fourth-order separable polynomial response. It is also proven that the relative error mean and variance of the method decrease with the dimensionality m if the response is separable. To further assess the proposed method, a probability model based on the effect hierarchy principle is used to generate sets of polynomial response functions. For typical populations of problems, it is shown that the proposed method has less than 5% error in 90% of cases. Simulations of five engineering systems were developed and, given parametric alternatives within each case study, a total of 12 case studies were conducted. A comparison is made between the cumulative density function for the hierarchical probability models and a corresponding distribution function for case studies. The data from the case-based evaluations are generally consistent with the results from the model-based evaluation. |
| first_indexed | 2024-04-10T04:51:26Z |
| format | Article |
| id | doaj.art-58b47ccea2fa458184819673d797a07e |
| institution | Directory Open Access Journal |
| issn | 2053-4701 |
| language | English |
| last_indexed | 2024-04-10T04:51:26Z |
| publishDate | 2021-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Design Science |
| spelling | doaj.art-58b47ccea2fa458184819673d797a07e2023-03-09T12:32:01ZengCambridge University PressDesign Science2053-47012021-01-01710.1017/dsj.2021.24Quadrature as applied to computer models for robust design: theoretical and empirical assessmentDaniel D. Frey0https://orcid.org/0000-0002-9886-7512Yiben Lin1Petra Heijnen2MIT, Department of Mechanical Engineering, Cambridge, MA, USAMorgan Stanley, New York, NY, USADelft University of Technology, Technology Policy and Management, Delft, NetherlandsThis paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, this paper proves that the method gives exact transmitted variance if the response is a fourth-order separable polynomial response. It is also proven that the relative error mean and variance of the method decrease with the dimensionality m if the response is separable. To further assess the proposed method, a probability model based on the effect hierarchy principle is used to generate sets of polynomial response functions. For typical populations of problems, it is shown that the proposed method has less than 5% error in 90% of cases. Simulations of five engineering systems were developed and, given parametric alternatives within each case study, a total of 12 case studies were conducted. A comparison is made between the cumulative density function for the hierarchical probability models and a corresponding distribution function for case studies. The data from the case-based evaluations are generally consistent with the results from the model-based evaluation.https://www.cambridge.org/core/product/identifier/S205347012100024X/type/journal_articleRobust designuncertainty quantificationdesign of computer experiments |
| spellingShingle | Daniel D. Frey Yiben Lin Petra Heijnen Quadrature as applied to computer models for robust design: theoretical and empirical assessment Design Science Robust design uncertainty quantification design of computer experiments |
| title | Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| title_full | Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| title_fullStr | Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| title_full_unstemmed | Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| title_short | Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| title_sort | quadrature as applied to computer models for robust design theoretical and empirical assessment |
| topic | Robust design uncertainty quantification design of computer experiments |
| url | https://www.cambridge.org/core/product/identifier/S205347012100024X/type/journal_article |
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