Distribution with Independent Components for Uncertainty Quantification and Structural Reliability Analysis

Abstract

This paper presents a novel method based on the Information Theory, Machine Learning and Independent Component analysis for Uncertainty Quantification and Structural Reliability Analysis. At first, it is shown that the optimal probabilistic model may be determined through minimum relative entropy and the theory of statistical learning

it is also discussed that methods based on the maximum entropy may perform well for the evaluation of the marginal distributions, including the tails. To determine the joint distribution of the basic random variables it is introduced the multivariate probabilistic model of Distributions with Independent Components (DIC). It has same computational simplicity of Nataf, but it is more accurate, since it does not pursue any assumption about the tail dependency. The proposed framework is applied to determine the joint distribution of wave height and period of wave data. Its extension for high dimensional reliability analysis of complex structural systems is straightforward.