Distributional uncertainty analysis using polynomial chaos expansions

A computationally efficient approach is presented that quantifies the influence of parameter uncertainties on the states and outputs of finite-time control trajectories for nonlinear systems, based on the approximate representation of the model via polynomial chaos expansion. The approach is suitable for studying the uncertainty propagation in open-loop or closed-loop systems. A quantitative and qualitative assessment of the method is performed in comparison to the Monte Carlo simulation technique that uses the nonlinear model for uncertainty propagation. The polynomial chaos expansion-based approach is characterized by a significantly lower computational burden compared to Monte Carlo approaches, while providing a good approximation of the shape of the uncertainty distribution of the process outputs. The techniques are applied to the crystallization of an inorganic chemical with uncertainties in the nucleation and growth parameters.