Bounds for uncertain structural problems with large-range interval parameters

A novel bivariate interval function decomposition method is proposed and applied to predict the bounds of structural response with large-range interval parameters. When the existing interval methods solve large uncertainty problems, either the calculation accuracy is poor or better accuracy is often achieved at the cost of more computational effort. To overcome this drawback, the bivariate interval function decomposition (BIFD) is first constructed for the approximation of the original response function. The univariate and the bivariate points are substituted into the second-order Taylor expansion to derive BIFD; thus, the expression of BIFD contains only the one- and two-dimensional functions. Particularly, the response function is decomposed into the sum of multiple low-dimensional functions, and solving the bounds of multi-dimensional original response can be transformed into solving those of low-dimensional interval functions. Then, the sensitivity information of structural response with respect to uncertain parameters is utilized to save computational consumption. Finally, the precision and effectiveness of the method are validated by comparing it with the other six existing interval analysis methods through several numerical examples and engineering applications.