A dimension-wise method and its improvement for multidisciplinary interval uncertainty analysis

Considering that uncertain factors widely exist in practical engineering, this study develops an improved dimension-wise method for multidisciplinary interval uncertainty analysis, in which the extremums of each interval variable for determining systematical response bounds are solved using the Chebyshev polynomial approximation and iterative criterion. First, Chebyshev basis functions are involved to construct the approximate relation between the system output variables and initial interval parameters dimension by dimension in multidisciplinary frameworks. The Gauss-Chebyshev quadrature formulas are then utilized to confirm coefficients of the fitting function. Due to the weakness of traditional dimension-wise method, that is, it ignores the coupling effects of uncertain variables, a new iterative dimension-wise method (IDWM) where the nominal states of intervals can be updated in each iteration, is proposed. Discussions on efficiency and accuracy are further expounded. Both numerical and engineering examples are eventually given to demonstrate the usage and validity of the developed methodology, and results indicate that the presented IDWM has a superiority in uncertainty propagation problems of multidisciplinary issues.