通过可识别性改进对相关未知模型变量进行统计模型校准

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
{"title":"通过可识别性改进对相关未知模型变量进行统计模型校准","authors":"","doi":"10.1016/j.probengmech.2024.103670","DOIUrl":null,"url":null,"abstract":"<div><p>A statistical model calibration problem is known to have unstable or non-unique optimal solutions due to its ill-posed inverse nature, which is further complicated by limited test data availability due to time and cost constraints. To overcome these challenges and improve the identifiability of calibration parameters, this study proposes a novel statistical model calibration framework. The proposed method integrates input test data for unknown model variables and output test data for a system response, employing a bivariate form of copula function to model the probability distribution while accounting for the correlations between unknown model variables. Furthermore, a sample-averaged log-likelihood is used as a calibration metric, assuming conditional independence to reflect input and output test data evenly in a single metric. Optimization-based model calibration (OBMC) is performed to identify the probability models that maximize the calibration metric for a given set of input and output test data, among candidates of marginal probability distributions and copula functions. Consequently, this proposed method enhances the identifiability of calibration parameters and overcomes insufficient data issues by taking observations of unknown model variables into account in the statistical model calibration procedure. The proposed framework is validated using numerical examples.</p></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Statistical model calibration of correlated unknown model variables through identifiability improvement\",\"authors\":\"\",\"doi\":\"10.1016/j.probengmech.2024.103670\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A statistical model calibration problem is known to have unstable or non-unique optimal solutions due to its ill-posed inverse nature, which is further complicated by limited test data availability due to time and cost constraints. To overcome these challenges and improve the identifiability of calibration parameters, this study proposes a novel statistical model calibration framework. The proposed method integrates input test data for unknown model variables and output test data for a system response, employing a bivariate form of copula function to model the probability distribution while accounting for the correlations between unknown model variables. Furthermore, a sample-averaged log-likelihood is used as a calibration metric, assuming conditional independence to reflect input and output test data evenly in a single metric. Optimization-based model calibration (OBMC) is performed to identify the probability models that maximize the calibration metric for a given set of input and output test data, among candidates of marginal probability distributions and copula functions. Consequently, this proposed method enhances the identifiability of calibration parameters and overcomes insufficient data issues by taking observations of unknown model variables into account in the statistical model calibration procedure. The proposed framework is validated using numerical examples.</p></div>\",\"PeriodicalId\":54583,\"journal\":{\"name\":\"Probabilistic Engineering Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probabilistic Engineering Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0266892024000924\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892024000924","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

摘要

众所周知,统计模型校准问题具有不稳定或非唯一的最优解,这是因为它的反问题性质,而由于时间和成本的限制,测试数据的可用性有限,使得问题变得更加复杂。为了克服这些挑战并提高校准参数的可识别性,本研究提出了一种新型统计模型校准框架。该方法整合了未知模型变量的输入测试数据和系统响应的输出测试数据,采用双变量形式的 copula 函数来模拟概率分布,同时考虑未知模型变量之间的相关性。此外,使用样本平均对数似然作为校准指标,假定条件独立,以单一指标均匀反映输入和输出测试数据。通过基于优化的模型校准(OBMC),可从边际概率分布和共轭函数的候选模型中,找出能使给定输入和输出测试数据集的校准指标最大化的概率模型。因此,通过在统计模型校准过程中考虑对未知模型变量的观测,该方法提高了校准参数的可识别性,并克服了数据不足的问题。所提出的框架通过数值示例进行了验证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical model calibration of correlated unknown model variables through identifiability improvement

A statistical model calibration problem is known to have unstable or non-unique optimal solutions due to its ill-posed inverse nature, which is further complicated by limited test data availability due to time and cost constraints. To overcome these challenges and improve the identifiability of calibration parameters, this study proposes a novel statistical model calibration framework. The proposed method integrates input test data for unknown model variables and output test data for a system response, employing a bivariate form of copula function to model the probability distribution while accounting for the correlations between unknown model variables. Furthermore, a sample-averaged log-likelihood is used as a calibration metric, assuming conditional independence to reflect input and output test data evenly in a single metric. Optimization-based model calibration (OBMC) is performed to identify the probability models that maximize the calibration metric for a given set of input and output test data, among candidates of marginal probability distributions and copula functions. Consequently, this proposed method enhances the identifiability of calibration parameters and overcomes insufficient data issues by taking observations of unknown model variables into account in the statistical model calibration procedure. The proposed framework is validated using numerical examples.

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
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
×
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