A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters
The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computationa...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/7471460 |
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| author | Rugao Gao Keping Zhou Yun Lin |
| author_facet | Rugao Gao Keping Zhou Yun Lin |
| author_sort | Rugao Gao |
| collection | DOAJ |
| description | The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. But in gPCEM, a nonlinear transformation of random variables should always be used to adapt the generalized Polynomial Chaos theory for the analysis of random problems with complicated probability distributions, which may introduce nonlinearity in the procedure of random uncertainty propagation as well as leading to approximation errors on the probability distribution function (PDF) of random variables. This paper aims to develop a flexible polynomial expansion method for response analysis of the finite element system with bounded random variables following arbitrary probability distributions. Based on the large family of Jacobi polynomials, an Improved Jacobi Chaos Expansion Method (IJCEM) is proposed. In IJCEM, the response of random system is approximated by the Jacobi expansion with the Jacobi polynomial basis whose weight function is the closest to the probability density distribution (PDF) of the random variable. Subsequently, the moments of the response can be efficiently calculated though the Jacobi expansion. As the IJCEM avoids the necessity that the PDF should be represented in terms of the weight function of polynomial basis by using the variant transformation, neither the nonlinearity nor the errors on random models will be introduced in IJCEM. Numerical examples on two random problems show that compared with gPCEM, the IJCEM can achieve better efficiency and accuracy for random problems with complex probability distributions. |
| format | Article |
| id | doaj-art-6a77eecc5fac47bd8212dc9f4d34d31e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-6a77eecc5fac47bd8212dc9f4d34d31e2025-02-03T06:00:36ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/74714607471460A Flexible Polynomial Expansion Method for Response Analysis with Random ParametersRugao Gao0Keping Zhou1Yun Lin2Central south university, School of resources and safety engineering, Hunan Changsha, Hunan, 410083, ChinaCentral south university, School of resources and safety engineering, Hunan Changsha, Hunan, 410083, ChinaCentral south university, School of resources and safety engineering, Hunan Changsha, Hunan, 410083, ChinaThe generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. But in gPCEM, a nonlinear transformation of random variables should always be used to adapt the generalized Polynomial Chaos theory for the analysis of random problems with complicated probability distributions, which may introduce nonlinearity in the procedure of random uncertainty propagation as well as leading to approximation errors on the probability distribution function (PDF) of random variables. This paper aims to develop a flexible polynomial expansion method for response analysis of the finite element system with bounded random variables following arbitrary probability distributions. Based on the large family of Jacobi polynomials, an Improved Jacobi Chaos Expansion Method (IJCEM) is proposed. In IJCEM, the response of random system is approximated by the Jacobi expansion with the Jacobi polynomial basis whose weight function is the closest to the probability density distribution (PDF) of the random variable. Subsequently, the moments of the response can be efficiently calculated though the Jacobi expansion. As the IJCEM avoids the necessity that the PDF should be represented in terms of the weight function of polynomial basis by using the variant transformation, neither the nonlinearity nor the errors on random models will be introduced in IJCEM. Numerical examples on two random problems show that compared with gPCEM, the IJCEM can achieve better efficiency and accuracy for random problems with complex probability distributions.http://dx.doi.org/10.1155/2018/7471460 |
| spellingShingle | Rugao Gao Keping Zhou Yun Lin A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters Complexity |
| title | A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters |
| title_full | A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters |
| title_fullStr | A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters |
| title_full_unstemmed | A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters |
| title_short | A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters |
| title_sort | flexible polynomial expansion method for response analysis with random parameters |
| url | http://dx.doi.org/10.1155/2018/7471460 |
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