具有相关输入模型的数据驱动稀疏多项式混沌展开

IF 3.7 Q1 PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH
Zhanlin Liu, Youngjun Choe
{"title":"具有相关输入模型的数据驱动稀疏多项式混沌展开","authors":"Zhanlin Liu,&nbsp;Youngjun Choe","doi":"10.1016/j.jnlssr.2023.08.003","DOIUrl":null,"url":null,"abstract":"<div><p>Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm. The source code is made publicly available for reproducibility.</p></div>","PeriodicalId":62710,"journal":{"name":"安全科学与韧性(英文)","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Data-driven sparse polynomial chaos expansion for models with dependent inputs\",\"authors\":\"Zhanlin Liu,&nbsp;Youngjun Choe\",\"doi\":\"10.1016/j.jnlssr.2023.08.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm. The source code is made publicly available for reproducibility.</p></div>\",\"PeriodicalId\":62710,\"journal\":{\"name\":\"安全科学与韧性(英文)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2023-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"安全科学与韧性(英文)\",\"FirstCategoryId\":\"1087\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666449623000415\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"安全科学与韧性(英文)","FirstCategoryId":"1087","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666449623000415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH","Score":null,"Total":0}
引用次数: 0

摘要

多项式混沌展开式(pce)已在许多实际工程应用中使用,通过将输出分解为输入的多项式来量化输出的不确定性是如何从输入传播的。具有独立输入的模型的pce在文献中得到了广泛的探讨。最近,针对具有依赖输入的模型提出了不同的方法,以将pce的使用扩展到更多的实际应用中。典型的方法包括基于Gram-Schmidt算法构建pce或将依赖输入转换为独立输入。然而,这两种方法在计算效率和对输入分布的额外假设方面都有各自的局限性。在本文中,我们提出了一种数据驱动的方法来为具有依赖输入的模型构建稀疏pce,而不需要任何分布假设。该算法根据一组多项式与输出的相关性,递归地构造标准正交多项式。提出的稀疏pce构建算法不仅减少了最小观测值的数量,而且提高了数值稳定性和计算效率。算例验证了该算法的有效性。为了再现性,源代码是公开的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Data-driven sparse polynomial chaos expansion for models with dependent inputs

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm. The source code is made publicly available for reproducibility.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
安全科学与韧性(英文)
安全科学与韧性(英文) Management Science and Operations Research, Safety, Risk, Reliability and Quality, Safety Research
CiteScore
8.70
自引率
0.00%
发文量
0
审稿时长
72 days
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信