Distributional Uncertainty Analysis of a Batch Crystallization Process Using Power Series and Polynomial Chaos Expansions

Computationally efficient approaches are presented that quantify the influence of parameter uncertainties upon the states and outputs of finite-time control trajectories for nonlinear systems. In the first approach, the worst-case values of the states and outputs due to model parameter uncertainties are computed as a function of time along the control trajectories. The approach uses an efficient contour mapping technique to provide an estimate of the distribution of the states and outputs as a function of time. To increase the estimation accuracy of the shape of the distribution, an approach that uses second order power series expansion in combination with Monte Carlo simulations is proposed. Another approach presented here is based on the approximate representation of the model via polynomial chaos expansion. A quantitative and qualitative assessment of the approaches is performed in comparison to the Monte Carlo simulation technique that uses the nonlinear model. It is shown that the power series and polynomial chaos expansion based approaches require a significantly lower computational burden compared to Monte Carlo approaches, while give good approximation of the shape of the distribution. The techniques are applied to the crystallization of an inorganic chemical with uncertainties in the nucleation and growth parameters. Copyright © 2003 IFAC