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An effective evidence theory‐based reliability analysis algorithm for structures with epistemic uncertainty
Author(s) -
Wang Wenxuan,
Xue Hai,
Gao Hangshan
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2767
Subject(s) - univariate , measure (data warehouse) , unary operation , function (biology) , monotonic function , mathematics , mathematical optimization , taylor series , quadratic equation , algorithm , reliability (semiconductor) , series (stratigraphy) , computer science , statistics , data mining , multivariate statistics , discrete mathematics , mathematical analysis , power (physics) , paleontology , physics , geometry , quantum mechanics , biology , evolutionary biology
The purpose of this article is to develop an effective method to evaluate the reliability of structures with epistemic uncertainty so as to improve the applicability of evidence theory in practical engineering problems. The main contribution of this article is to establish an approximate semianalytic algorithm, which replaces the process of solving the extreme value of performance function and greatly improve the efficiency of solving the belief measure and the plausibility measure. First, the performance function is decomposed as a combination of a series of univariate functions. Second, each univariate function is approximated as a unary quadratic function by the second‐order Taylor expansion. Finally, based on the property of the unary quadratic function, the maximum and minimum values of each univariate function are solved, and then the maximum and minimum values of performance function are obtained according to the monotonic relationship between each univariate function and their combination. As long as the first‐ and second‐order partial derivatives of the performance function with respect to each input variable are obtained, the belief measure and plausibility measure of the structure can be estimated effectively without any additional computational cost. Two numerical examples and one engineering application are investigated to demonstrate the accuracy and efficiency of the proposed method.