Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique

Abstract

Compared with the probability approach, the non-probabilistic convex model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters, and whereby makes the reliability analysis very convenient and economical. In this paper, we attempt to propose and create a correlation analysis technique mathematically for the non-probabilistic convex model, and based on it develop an effective method to construct the multidimensional ellipsoids on the uncertainty. A marginal convex model is defined to describe the variation range of each uncertain parameter, and a covariance is defined to represent the correlation degree of two uncertain parameters. For a multidimensional problem, the covariance matrix and correlation matrix can be created through all marginal convex models and covariances, based on which the required ellipsoid on the uncertainty can be conveniently achieved. By combining the correlation analysis technique and the reliability index approach, a non-probabilistic reliability analysis method is also developed for uncertain structures. Six numerical examples are presented to demonstrate the effectiveness of the present method.