No Cover Image

Journal article 609 views 340 downloads

Hermite polynomial normal transformation for structural reliability analysis

Jinsheng WANG, Muhannad Aldosary, Song Cen, Chenfeng Li Orcid Logo

Engineering Computations, Volume: 38, Issue: 8, Pages: 3193 - 3218

Swansea University Authors: Jinsheng WANG, Muhannad Aldosary, Chenfeng Li Orcid Logo

  • 56558.pdf

    PDF | Accepted Manuscript

    Released under the terms of a Creative Commons Attribution Non-commercial International License 4.0 (CC BY-NC 4.0)

    Download (15.03MB)

Check full text

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...

Full description

Published in: Engineering Computations
ISSN: 0264-4401
Published: Emerald 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56558
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2021-03-25T13:29:00Z
last_indexed 2021-10-30T03:20:30Z
id cronfa56558
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2021-10-29T18:13:12.5273757</datestamp><bib-version>v2</bib-version><id>56558</id><entry>2021-03-25</entry><title>Hermite polynomial normal transformation for structural reliability analysis</title><swanseaauthors><author><sid>559f85fdaadb1652f2e5fd07a2d2772a</sid><firstname>Jinsheng</firstname><surname>WANG</surname><name>Jinsheng WANG</name><active>true</active><ethesisStudent>false</ethesisStudent></author><author><sid>0d9c3ff4d593820671007306ab95c216</sid><firstname>Muhannad</firstname><surname>Aldosary</surname><name>Muhannad Aldosary</name><active>true</active><ethesisStudent>false</ethesisStudent></author><author><sid>82fe170d5ae2c840e538a36209e5a3ac</sid><ORCID>0000-0003-0441-211X</ORCID><firstname>Chenfeng</firstname><surname>Li</surname><name>Chenfeng Li</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2021-03-25</date><deptcode>FGSEN</deptcode><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 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.</abstract><type>Journal Article</type><journal>Engineering Computations</journal><volume>38</volume><journalNumber>8</journalNumber><paginationStart>3193</paginationStart><paginationEnd>3218</paginationEnd><publisher>Emerald</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0264-4401</issnPrint><issnElectronic/><keywords>Structural reliability analysis, Polynomial normal transformation, Hermite polynomials, Statistical moments</keywords><publishedDay>17</publishedDay><publishedMonth>8</publishedMonth><publishedYear>2021</publishedYear><publishedDate>2021-08-17</publishedDate><doi>10.1108/ec-05-2020-0244</doi><url/><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-10-29T18:13:12.5273757</lastEdited><Created>2021-03-25T13:22:44.1106830</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering</level></path><authors><author><firstname>Jinsheng</firstname><surname>WANG</surname><order>1</order></author><author><firstname>Muhannad</firstname><surname>Aldosary</surname><order>2</order></author><author><firstname>Song</firstname><surname>Cen</surname><order>3</order></author><author><firstname>Chenfeng</firstname><surname>Li</surname><orcid>0000-0003-0441-211X</orcid><order>4</order></author></authors><documents><document><filename>56558__19560__5efc043b31684f30aa9db06ea375ade8.pdf</filename><originalFilename>56558.pdf</originalFilename><uploaded>2021-03-25T14:12:43.6560686</uploaded><type>Output</type><contentLength>15760545</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><documentNotes>Released under the terms of a Creative Commons Attribution Non-commercial International License 4.0 (CC BY-NC 4.0)</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by-nc/4.0/</licence></document></documents><OutputDurs/></rfc1807>
spelling 2021-10-29T18:13:12.5273757 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 FGSEN 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 Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-10-29T18:13:12.5273757 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
author_id_fullname_str_mv 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
format Journal article
container_title Engineering Computations
container_volume 38
container_issue 8
container_start_page 3193
publishDate 2021
institution Swansea University
issn 0264-4401
doi_str_mv 10.1108/ec-05-2020-0244
publisher Emerald
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description 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 2021-08-17T04:11:36Z
_version_ 1763753797327257600
score 11.012678

Similar Items