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Meccanica

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05-09-2022

A subinterval bivariate dimension-reduction method for nonlinear problems with uncertainty parameters

Authors: Feng Li, Heng Zhao, Tonghui Wei, Hongfeng Li

Published in: Meccanica | Issue 9/2022

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Abstract

A subinterval bivariate dimension-reduction method is proposed to predict the upper and lower bounds of nonlinear problems with uncertain-but-bounded parameters, especially for nonmonotonic problems. The existing interval function decomposition method solves the dimensional curse problem, but is only suitable for the monotone case. To address this limitation, the original structural response function with multidimensional interval parameters is decomposed by the bivariate dimension-reduction method into a set of univariate and bivariate interval response functions, and then the interval parameters are partitioned into some subintervals with low uncertainty. The upper and lower bounds of the structural response are approximately predicted not by analyzing all discrete points in the entire uncertain domain, but by calculating the responses at bivariate points, univariate points, and the midpoint, which can improve the computational efficiency. Finally, the accuracy and efficiency of the proposed method are verified using several numerical examples and engineering applications.

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Title: A subinterval bivariate dimension-reduction method for nonlinear problems with uncertainty parameters
Authors: Feng Li
Heng Zhao
Tonghui Wei
Hongfeng Li
Publication date: 05-09-2022
Publisher: Springer Netherlands
Published in: Meccanica / Issue 9/2022
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-022-01570-0

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