Interval arithmetic operations for uncertainty analysis with correlated interval variables

A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analy-sis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional par-allelepiped 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 addi-tion, 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.