{"title":"从多项式混沌展开论分数矩估计","authors":"","doi":"10.1016/j.ress.2024.110594","DOIUrl":null,"url":null,"abstract":"<div><div>Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic coefficients of polynomial chaos expansion are used for an estimation of arbitrary fractional moments via Hölder’s inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in four numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.</div></div>","PeriodicalId":54500,"journal":{"name":"Reliability Engineering & System Safety","volume":null,"pages":null},"PeriodicalIF":9.4000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On fractional moment estimation from polynomial chaos expansion\",\"authors\":\"\",\"doi\":\"10.1016/j.ress.2024.110594\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic coefficients of polynomial chaos expansion are used for an estimation of arbitrary fractional moments via Hölder’s inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in four numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.</div></div>\",\"PeriodicalId\":54500,\"journal\":{\"name\":\"Reliability Engineering & System Safety\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":9.4000,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reliability Engineering & System Safety\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0951832024006653\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, INDUSTRIAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reliability Engineering & System Safety","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0951832024006653","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
On fractional moment estimation from polynomial chaos expansion
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic coefficients of polynomial chaos expansion are used for an estimation of arbitrary fractional moments via Hölder’s inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in four numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.
期刊介绍:
Elsevier publishes Reliability Engineering & System Safety in association with the European Safety and Reliability Association and the Safety Engineering and Risk Analysis Division. The international journal is devoted to developing and applying methods to enhance the safety and reliability of complex technological systems, like nuclear power plants, chemical plants, hazardous waste facilities, space systems, offshore and maritime systems, transportation systems, constructed infrastructure, and manufacturing plants. The journal normally publishes only articles that involve the analysis of substantive problems related to the reliability of complex systems or present techniques and/or theoretical results that have a discernable relationship to the solution of such problems. An important aim is to balance academic material and practical applications.