Quadrature as applied to computer models for robust design: theoretical and empirical assessment
<jats:title>Abstract</jats:title> <jats:p>This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with <jats:italic>m</jats:italic> noise variables, the method...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press (CUP)
2023
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| Online Access: | https://hdl.handle.net/1721.1/150937 |
| _version_ | 1811080332210864128 |
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| author | Frey, Daniel D Lin, Yiben Heijnen, Petra |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Frey, Daniel D Lin, Yiben Heijnen, Petra |
| author_sort | Frey, Daniel D |
| collection | MIT |
| description | <jats:title>Abstract</jats:title>
<jats:p>This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with <jats:italic>m</jats:italic> noise variables, the method requires 4<jats:italic>m</jats:italic> + 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 <jats:italic>m</jats:italic> 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.</jats:p> |
| first_indexed | 2024-09-23T11:29:34Z |
| format | Article |
| id | mit-1721.1/150937 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:29:34Z |
| publishDate | 2023 |
| publisher | Cambridge University Press (CUP) |
| record_format | dspace |
| spelling | mit-1721.1/1509372023-06-23T03:30:28Z Quadrature as applied to computer models for robust design: theoretical and empirical assessment Frey, Daniel D Lin, Yiben Heijnen, Petra Massachusetts Institute of Technology. Department of Mechanical Engineering <jats:title>Abstract</jats:title> <jats:p>This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with <jats:italic>m</jats:italic> noise variables, the method requires 4<jats:italic>m</jats:italic> + 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 <jats:italic>m</jats:italic> 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.</jats:p> 2023-06-22T14:17:54Z 2023-06-22T14:17:54Z 2021 2023-06-22T14:08:09Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/150937 Frey, Daniel D, Lin, Yiben and Heijnen, Petra. 2021. "Quadrature as applied to computer models for robust design: theoretical and empirical assessment." Design Science, 7. en 10.1017/DSJ.2021.24 Design Science Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ application/pdf Cambridge University Press (CUP) CUP |
| spellingShingle | Frey, Daniel D Lin, Yiben Heijnen, Petra Quadrature as applied to computer models for robust design: theoretical and empirical assessment |
| 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 |
| url | https://hdl.handle.net/1721.1/150937 |
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