Relative contributions of aleatory and epistemic uncertainty sources in time series prediction

Abstract This paper develops a novel computational framework to compute the Sobol indices that quantify the relative contributions of various uncertainty sources towards the system response prediction uncertainty. In the presence of both aleatory and epistemic uncertainty, two challenges are addressed in this paper for the model-based computation of the Sobol indices: due to data uncertainty, input distributions are not precisely known; and due to model uncertainty, the model output is uncertain even for a fixed realization of the input. An auxiliary variable method based on the probability integral transform is introduced to distinguish and represent each uncertainty source explicitly, whether aleatory or epistemic. The auxiliary variables facilitate building a deterministic relationship between the uncertainty sources and the output, which is needed in the Sobol indices computation. The proposed framework is developed for two types of model inputs: random variable input and time series input. A Bayesian autoregressive moving average (ARMA) approach is chosen to model the time series input due to its capability to represent both natural variability and epistemic uncertainty due to limited data. A novel controlled-seed computational technique based on pseudo-random number generation is proposed to efficiently represent the natural variability in the time series input. This controlled-seed method significantly accelerates the Sobol indices computation under time series input, and makes it computationally affordable.