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A Dimension-Reduction Interval Analysis Method for Uncertain Problems

J.C. Tang1, C.M. Fu1,2

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City, 410082, P. R. China
College of Mechanical Engineering, University of South China, Hengyang 421001, P. R. China
* Corresponding author. E-mail address: tangjiachang@hnu.edu.cn (J.C. Tang).

Computer Modeling in Engineering & Sciences 2017, 113(3), 239-259. https://doi.org/10.3970/cmes.2017.113.249

Abstract

In this paper, an efficient interval analysis method called dimension-reduction interval analysis (DRIA) method is proposed to calculate the bounds of response functions with interval variables, which provides a kind of solution method for uncertainty analysis problems of complex structures and systems. First, multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem. Second, all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method. As a result, the multi-dimensional function is approximately represented by the functions that each interval variable occurs once, and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation. Finally, three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.

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Cite This Article

Tang, J., Fu, C. (2017). A Dimension-Reduction Interval Analysis Method for Uncertain Problems. CMES-Computer Modeling in Engineering & Sciences, 113(3), 239–259. https://doi.org/10.3970/cmes.2017.113.249



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