Efficiency of uncertainty propagation methods for moment estimation of uncertain model outputs

Uncertainty quantification and propagation play a crucial role in designing and operating chemical processes. This study computationally evaluates the performance of commonly used uncertainty propagation methods based on their ability to estimate the first four statistical moments of model outputs with uncertain inputs. The metric used to assess the performance is the minimum number of model evaluations required to reach a certain confidence level for the moment estimates. The methods considered include Monte-Carlo simulation, numerical integration, and expansion-based methods. The true values of the moments were calculated by high-density sampling with Monte-Carlo simulations. Ninety-five functions with different characteristics were used in the computational experiments. The results reveal that, despite their accuracy, numerical integration methods' performance deteriorates quickly with increases in the number of uncertain inputs. The Monte-Carlo simulation methods converge to the moments' true values with the minimum number of model evaluations if model characteristics are not considered or known.

Automated summary

This study computationally evaluates the performance of commonly used uncertainty propagation methods in estimating the statistical moments of model outputs with uncertain inputs, revealing that numerical integration methods deteriorate with an increase in uncertain inputs, while Monte-Carlo simulation methods converge to the true values of moments with minimal model evaluations.