Probabilistic interval analysis for structures with uncertainty

A hybrid probabilistic and interval method for engineering problems described by a mixture of random and interval variables is presented. Random interval arithmetic for carrying out basic operations between random and interval variables is developed by extending interval arithmetic rules. The uncertainty of a random interval variable is represented by probabilistic as well as interval information. A random interval moment method is proposed to calculate the mean and variance of random interval variables. The solution strategy and associated numerical tool are developed by using perturbation theory and Taylor expansion for linear equations with random and interval variables. Engineering applications in structures with analytical or semi-analytical solutions are used to demonstrate the accuracy and effectiveness of the proposed method.