Data-Driven Method to Quantify Correlated Uncertainties

Polynomial chaos (PC) has been proven to be an efficient method for uncertainty quantification, but its applicability is limited by two strong assumptions: the mutual independence of random variables and the requirement of exact knowledge about the distribution of the random variables. We describe a new data-driven method for dealing with correlated multivariate random variables for uncertainty quantification that requires only observed data of the random variables. It is based on the transformation of correlated random variables into independent random variables. We use singular value decomposition as a transformation strategy that does not require information about the probability distribution. For the transformed random variables, we can construct the PC basis to build a surrogate model. This approach provides an additional benefit of quantifying high-dimensional uncertainties by combining our method with the analysis-of-variance (ANOVA) method. We demonstrate in several numerical examples that our proposed approach leads to accurate solutions with a much smaller number of simulations compared to the Monte Carlo method.