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Interval arithmetic operations for uncertainty analysis with correlated interval variables

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Abstract

A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.

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Acknowledgments

This work was supported by the National Natural Science Foundation for Excellent Young Scholars (Grant 51222502), the National Natural Science Foundation of China (Grant 11172096), and the Funds for State Key Laboratory of Construction Machinery (SKLCM2014-1).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

    Chao Jiang, Chun-Ming Fu, Bing-Yu Ni & Xu Han

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  1. Chao Jiang
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  2. Chun-Ming Fu
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  3. Bing-Yu Ni
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  4. Xu Han
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Correspondence to Chao Jiang.

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Jiang, C., Fu, CM., Ni, BY. et al. Interval arithmetic operations for uncertainty analysis with correlated interval variables. Acta Mech. Sin. 32, 743–752 (2016). https://doi.org/10.1007/s10409-015-0525-3

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  • DOI: https://doi.org/10.1007/s10409-015-0525-3

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