{"title":"罗森布拉特变换在一阶系统可靠性近似中的应用","authors":"","doi":"10.1016/j.strusafe.2024.102521","DOIUrl":null,"url":null,"abstract":"<div><p>The reliability assessment of structural systems presents a significant challenge in structural engineering. A commonly employed approximation is the First-Order System Reliability Method (FOSRM), which estimates system reliability using the FORM component reliabilities and sensitivity factors. An essential step in FORM involves transforming the random vector <span><math><mi>X</mi></math></span> into the standard vector <span><math><mi>U</mi></math></span>, often using the Rosenblatt transformation (RT). Several studies demonstrated that different conditioning orders in the RT yield different FORM component results. This study investigates how these differences on component level propagate into the FOSRM system level. We conducted several typical engineering case studies with various failure probabilities, system sizes, and dependency structures (Gaussian and Frank Copula). For the Frank Copula, different Rosenblatt conditioning orders systematically yielded different FOSRM results, with most cases showing differences between 10% and 30% in estimated failure probability. For some systems, these differences increased with system size, suggesting that greater variations might be observed for larger systems. Notably, systems with Gaussian Copula functions also proved vulnerable to the Rosenblatt conditioning order when different components were assessed with different conditioning orders. The observed differences were larger than previously reported and should be carefully considered in uniform safety assessments.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":null,"pages":null},"PeriodicalIF":5.7000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167473024000924/pdfft?md5=b4507d4cb5d4385894a28e828f5bc5ee&pid=1-s2.0-S0167473024000924-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Application of the Rosenblatt transformation in First-Order System Reliability approximations\",\"authors\":\"\",\"doi\":\"10.1016/j.strusafe.2024.102521\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The reliability assessment of structural systems presents a significant challenge in structural engineering. A commonly employed approximation is the First-Order System Reliability Method (FOSRM), which estimates system reliability using the FORM component reliabilities and sensitivity factors. An essential step in FORM involves transforming the random vector <span><math><mi>X</mi></math></span> into the standard vector <span><math><mi>U</mi></math></span>, often using the Rosenblatt transformation (RT). Several studies demonstrated that different conditioning orders in the RT yield different FORM component results. This study investigates how these differences on component level propagate into the FOSRM system level. We conducted several typical engineering case studies with various failure probabilities, system sizes, and dependency structures (Gaussian and Frank Copula). For the Frank Copula, different Rosenblatt conditioning orders systematically yielded different FOSRM results, with most cases showing differences between 10% and 30% in estimated failure probability. For some systems, these differences increased with system size, suggesting that greater variations might be observed for larger systems. Notably, systems with Gaussian Copula functions also proved vulnerable to the Rosenblatt conditioning order when different components were assessed with different conditioning orders. The observed differences were larger than previously reported and should be carefully considered in uniform safety assessments.</p></div>\",\"PeriodicalId\":21978,\"journal\":{\"name\":\"Structural Safety\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.7000,\"publicationDate\":\"2024-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0167473024000924/pdfft?md5=b4507d4cb5d4385894a28e828f5bc5ee&pid=1-s2.0-S0167473024000924-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Structural Safety\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167473024000924\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, CIVIL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Structural Safety","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167473024000924","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
引用次数: 0
摘要
结构系统的可靠性评估是结构工程中的一项重大挑战。常用的近似方法是一阶系统可靠性法(FOSRM),该方法利用 FORM 组件可靠性和敏感性系数估算系统可靠性。FORM 的一个基本步骤是将随机向量 X 转换为标准向量 U,通常使用罗森布拉特转换(RT)。多项研究表明,RT 中不同的调节顺序会产生不同的 FORM 分量结果。本研究探讨了这些组件层面的差异如何传播到 FOSRM 系统层面。我们进行了几项典型的工程案例研究,涉及不同的故障概率、系统规模和依赖结构(高斯和 Frank Copula)。对于 Frank Copula,不同的罗森布拉特条件阶数系统地产生了不同的 FOSRM 结果,大多数情况下,估计故障概率的差异在 10% 到 30% 之间。对于某些系统,这些差异随着系统规模的扩大而增大,这表明对于较大的系统可能会观察到更大的差异。值得注意的是,当使用不同的调节阶数对不同的组件进行评估时,使用高斯 Copula 函数的系统也很容易受到 Rosenblatt 调节阶数的影响。观察到的差异比以前报告的要大,在统一安全评估中应仔细考虑。
Application of the Rosenblatt transformation in First-Order System Reliability approximations
The reliability assessment of structural systems presents a significant challenge in structural engineering. A commonly employed approximation is the First-Order System Reliability Method (FOSRM), which estimates system reliability using the FORM component reliabilities and sensitivity factors. An essential step in FORM involves transforming the random vector into the standard vector , often using the Rosenblatt transformation (RT). Several studies demonstrated that different conditioning orders in the RT yield different FORM component results. This study investigates how these differences on component level propagate into the FOSRM system level. We conducted several typical engineering case studies with various failure probabilities, system sizes, and dependency structures (Gaussian and Frank Copula). For the Frank Copula, different Rosenblatt conditioning orders systematically yielded different FOSRM results, with most cases showing differences between 10% and 30% in estimated failure probability. For some systems, these differences increased with system size, suggesting that greater variations might be observed for larger systems. Notably, systems with Gaussian Copula functions also proved vulnerable to the Rosenblatt conditioning order when different components were assessed with different conditioning orders. The observed differences were larger than previously reported and should be carefully considered in uniform safety assessments.
期刊介绍:
Structural Safety is an international journal devoted to integrated risk assessment for a wide range of constructed facilities such as buildings, bridges, earth structures, offshore facilities, dams, lifelines and nuclear structural systems. Its purpose is to foster communication about risk and reliability among technical disciplines involved in design and construction, and to enhance the use of risk management in the constructed environment