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Hermite polynomial normal transformation for structural reliability analysis
Engineering Computations, Volume: 38, Issue: 8, Pages: 3193 - 3218
Swansea University Authors: Jinsheng WANG, Muhannad Aldosary, Chenfeng Li
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DOI (Published version): 10.1108/ec-05-2020-0244
Abstract
PurposeNormal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the...
Published in: | Engineering Computations |
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ISSN: | 0264-4401 |
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2021
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URI: | https://cronfa.swan.ac.uk/Record/cronfa56558 |
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The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables.Design/methodology/approachThe new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies.FindingsComprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems.Originality/valueThis study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. 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2025-01-16T11:12:04.3343679 v2 56558 2021-03-25 Hermite polynomial normal transformation for structural reliability analysis 559f85fdaadb1652f2e5fd07a2d2772a Jinsheng WANG Jinsheng WANG true false 0d9c3ff4d593820671007306ab95c216 Muhannad Aldosary Muhannad Aldosary true false 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2021-03-25 PurposeNormal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables.Design/methodology/approachThe new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies.FindingsComprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems.Originality/valueThis study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy. Journal Article Engineering Computations 38 8 3193 3218 Emerald 0264-4401 Structural reliability analysis, Polynomial normal transformation, Hermite polynomials, Statistical moments 17 8 2021 2021-08-17 10.1108/ec-05-2020-0244 COLLEGE NANME COLLEGE CODE Swansea University Not Required 2025-01-16T11:12:04.3343679 2021-03-25T13:22:44.1106830 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Jinsheng WANG 1 Muhannad Aldosary 2 Song Cen 3 Chenfeng Li 0000-0003-0441-211X 4 56558__19560__5efc043b31684f30aa9db06ea375ade8.pdf 56558.pdf 2021-03-25T14:12:43.6560686 Output 15760545 application/pdf Accepted Manuscript true Released under the terms of a Creative Commons Attribution Non-commercial International License 4.0 (CC BY-NC 4.0) true eng https://creativecommons.org/licenses/by-nc/4.0/ |
title |
Hermite polynomial normal transformation for structural reliability analysis |
spellingShingle |
Hermite polynomial normal transformation for structural reliability analysis Jinsheng WANG Muhannad Aldosary Chenfeng Li |
title_short |
Hermite polynomial normal transformation for structural reliability analysis |
title_full |
Hermite polynomial normal transformation for structural reliability analysis |
title_fullStr |
Hermite polynomial normal transformation for structural reliability analysis |
title_full_unstemmed |
Hermite polynomial normal transformation for structural reliability analysis |
title_sort |
Hermite polynomial normal transformation for structural reliability analysis |
author_id_str_mv |
559f85fdaadb1652f2e5fd07a2d2772a 0d9c3ff4d593820671007306ab95c216 82fe170d5ae2c840e538a36209e5a3ac |
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559f85fdaadb1652f2e5fd07a2d2772a_***_Jinsheng WANG 0d9c3ff4d593820671007306ab95c216_***_Muhannad Aldosary 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li |
author |
Jinsheng WANG Muhannad Aldosary Chenfeng Li |
author2 |
Jinsheng WANG Muhannad Aldosary Song Cen Chenfeng Li |
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Engineering Computations |
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Emerald |
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PurposeNormal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables.Design/methodology/approachThe new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies.FindingsComprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems.Originality/valueThis study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy. |
published_date |
2021-08-17T14:09:59Z |
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1822139664805396480 |
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11.541055 |