A subinterval bivariate dimension-reduction method for nonlinear problems with uncertainty parameters

A subinterval bivariate dimension-reduction method is proposed to predict the upper and lower bounds of nonlinear problems with uncertain-but-bounded parameters, especially for nonmonotonic problems. The existing interval function decomposition method solves the dimensional curse problem, but is only suitable for the monotone case. To address this limitation, the original structural response function with multidimensional interval parameters is decomposed by the bivariate dimension-reduction method into a set of univariate and bivariate interval response functions, and then the interval parameters are partitioned into some subintervals with low uncertainty. The upper and lower bounds of the structural response are approximately predicted not by analyzing all discrete points in the entire uncertain domain, but by calculating the responses at bivariate points, univariate points, and the midpoint, which can improve the computational efficiency. Finally, the accuracy and efficiency of the proposed method are verified using several numerical examples and engineering applications.