Wang Xiaoyi, Chang Xinyue, Meng Pengfei, Wang Wenxuan
{"title":"基于乘法降维法和泰勒级数展开的高效方差全局敏感性分析方法","authors":"Wang Xiaoyi, Chang Xinyue, Meng Pengfei, Wang Wenxuan","doi":"10.1177/1748006x241240815","DOIUrl":null,"url":null,"abstract":"In this study, the detailed derivation of unconditional and conditional statistical moments for calculating two variance-based global sensitivity indices is presented based on the multiplicative dimensional reduction method. Furthermore, an efficient calculation method for the statistical moment of performance function is proposed using Taylor series expansion, transforming it into a calculation of the statistical moment of random variable. Additionally, a recursive formula for the raw moment of normally distributed random variables is derived and a calculation formula for non-normally distributed random variables’ raw moment is provided. Finally, by combining the multiplicative dimensional reduction method with Taylor series expansion, two more effective methods are proposed for variance-based global sensitivity index. Compared with the reference method, the two proposed methods increase efficiency by 66.66% and 33.33%, respectively. The accuracy and efficiency of this approach are verified by a low-dimensional roof truss and a high-dimensional ten-bar truss structure in conjunction with finite element software. Moreover, its engineering application value is demonstrated by applying it to a high-dimensional complex hydraulic piping system containing 28 input variables.","PeriodicalId":51266,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An efficient variance-based global sensitivity analysis method based on multiplicative dimensional reduction method and Taylor series expansion\",\"authors\":\"Wang Xiaoyi, Chang Xinyue, Meng Pengfei, Wang Wenxuan\",\"doi\":\"10.1177/1748006x241240815\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, the detailed derivation of unconditional and conditional statistical moments for calculating two variance-based global sensitivity indices is presented based on the multiplicative dimensional reduction method. Furthermore, an efficient calculation method for the statistical moment of performance function is proposed using Taylor series expansion, transforming it into a calculation of the statistical moment of random variable. Additionally, a recursive formula for the raw moment of normally distributed random variables is derived and a calculation formula for non-normally distributed random variables’ raw moment is provided. Finally, by combining the multiplicative dimensional reduction method with Taylor series expansion, two more effective methods are proposed for variance-based global sensitivity index. Compared with the reference method, the two proposed methods increase efficiency by 66.66% and 33.33%, respectively. The accuracy and efficiency of this approach are verified by a low-dimensional roof truss and a high-dimensional ten-bar truss structure in conjunction with finite element software. Moreover, its engineering application value is demonstrated by applying it to a high-dimensional complex hydraulic piping system containing 28 input variables.\",\"PeriodicalId\":51266,\"journal\":{\"name\":\"Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1177/1748006x241240815\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, INDUSTRIAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/1748006x241240815","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
An efficient variance-based global sensitivity analysis method based on multiplicative dimensional reduction method and Taylor series expansion
In this study, the detailed derivation of unconditional and conditional statistical moments for calculating two variance-based global sensitivity indices is presented based on the multiplicative dimensional reduction method. Furthermore, an efficient calculation method for the statistical moment of performance function is proposed using Taylor series expansion, transforming it into a calculation of the statistical moment of random variable. Additionally, a recursive formula for the raw moment of normally distributed random variables is derived and a calculation formula for non-normally distributed random variables’ raw moment is provided. Finally, by combining the multiplicative dimensional reduction method with Taylor series expansion, two more effective methods are proposed for variance-based global sensitivity index. Compared with the reference method, the two proposed methods increase efficiency by 66.66% and 33.33%, respectively. The accuracy and efficiency of this approach are verified by a low-dimensional roof truss and a high-dimensional ten-bar truss structure in conjunction with finite element software. Moreover, its engineering application value is demonstrated by applying it to a high-dimensional complex hydraulic piping system containing 28 input variables.
期刊介绍:
The Journal of Risk and Reliability is for researchers and practitioners who are involved in the field of risk analysis and reliability engineering. The remit of the Journal covers concepts, theories, principles, approaches, methods and models for the proper understanding, assessment, characterisation and management of the risk and reliability of engineering systems. The journal welcomes papers which are based on mathematical and probabilistic analysis, simulation and/or optimisation, as well as works highlighting conceptual and managerial issues. Papers that provide perspectives on current practices and methods, and how to improve these, are also welcome