Print Email Facebook Twitter An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals Title An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals Author Chen, Xiaoqian (National University of Defense Technology) Yao, W (TU Delft Flow Physics and Technology; National University of Defense Technology) Zhao, Yong (National University of Defense Technology) Ouyang, Qi (National University of Defense Technology) Department Flow Physics and Technology Date 2016-12-01 Abstract The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing well-developed and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem. Subject Aleatory uncertaintyEpistemic uncertaintyFlexible intervalMeasure theoryReliability analysis To reference this document use: http://resolver.tudelft.nl/uuid:921fe4c1-19b3-4de2-8469-544e83815ea1 DOI https://doi.org/10.1007/s00158-016-1509-z ISSN 1615-147X Source Structural and Multidisciplinary Optimization, 54 (6), 1641-1652 Part of collection Institutional Repository Document type journal article Rights © 2016 Xiaoqian Chen, W Yao, Yong Zhao, Qi Ouyang Files PDF 10.1007_s00158_016_1509_z.pdf 1.03 MB Close viewer /islandora/object/uuid:921fe4c1-19b3-4de2-8469-544e83815ea1/datastream/OBJ/view