On High-Dimensional Time-Variant Reliability Analysis with the Maximum Entropy Principle

Abstract

The structural reliability analysis suffers from the curse of dimensionality if the associated limit state function involves a large number of inputs. This study develops a reliability analysis method that deals with high-dimensional inputs over time. The probability distribution of the structural response is reconstructed by the maximum entropy principle which is achieved by solving an optimization problem derived from the concept of relative entropy. The optimization problem is transformed into a convex one with respect to the orders of fractional moments and the Lagrange multipliers. Additionally, considering the associated computational issues, it is reformulated with side constraints on the parameters of the maximum entropy distribution. Then, a global optimization procedure is performed. The proposed method is successfully applied to the reliability analysis of a linear and a nonlinear structural system, which involves a large number of inputs deriving from the discretization of the input random processes.