Inclusion of correlation effects in model prediction under data uncertainty

Abstract

In probabilistic representation and propagation of uncertainty, it is likely that the marginal distribution types for the input variables are not known or cannot be specified accurately due to the presence of sparse point or interval data. This paper proposes a methodology for multivariate input modeling of random variables by using a four parameter flexible Johnson family of distributions for the marginals that also accounts for data uncertainty. Semi-empirical formulas in terms of the Johnson marginals and covariances are presented to estimate the model parameters (reduced correlation coefficients). This multivariate input model is particularly suitable for uncertainty quantification problems that contain both aleatory and data uncertainty. In this paper, a computational framework is developed to consider correlations among basic random variables as well as among their distribution parameters. We present a methodology for propagating both aleatory and data uncertainty arising from sparse point data through computational models of system response that assigns probability distributions to the distribution parameters and quantifies the uncertainty in correlation coefficients by use of computational resampling methods. For interval data, the correlations among the input variables are unknown. We formulate the optimization problems of deriving bounds on the cumulative probability distribution of system response, using correlations among the input variables that are described by interval data.