The aim of this study is to evaluate the performance of multilevel Monte Carlo (MLMC) sampling technique for uncertainty quantification in stochastic multiscale systems. Two systems, a chemical vapor deposition chamber and a catalytic flow reactor, subject to multiple parameter uncertainty, were considered. The distributions of the systems' observables were estimated using standard MC sampling and polynomial chaos expansions (PCE), where the coefficients were calculated by nonintrusive spectral projection. The MLMC technique was used to efficiently sample the two systems and accurately estimate the data necessary for constructing the PCE expressions. The results show that the usage of MLMC improved the precision of identification of PCE versus the traditional heuristic approach and lowered the computational cost of uncertainty quantification compared to standard MC.
Industrial
production of valuable chemical products often involves
the manipulation of phenomena evolving at different temporal and spatial
scales. Product properties can be captured accurately using computationally
expensive stochastic multiscale models that explicitly consider the
feedbacks between different scales. However, product design quality
is often tampered by uncertainties affecting process operation. In
this work, we used artificial neural networks (ANNs) to estimate an
uncertain parameter, accurately predict product properties under uncertainty,
and achieve orders-of-magnitude computational savings of a multiscale
model of thin film formation by chemical vapor deposition. ANNs were
trained using multiple realizations of the uncertain parameter to
capture the behavior of the thin film’s two key microscale
properties: roughness and growth rate. Next, mean square error and
maximum likelihood estimation were used for parameter estimation and
to find the ANN that could generate the closest predictions to the
real-time measurements collected from the process in the presence
of uncertainty. The chosen ANNs were employed to seek for the optimal
operating conditions to enable the fabrication process to meet product
quality specifications. ANNs are a promising technique for product
property prediction and efficient decision making in the design of
optimal operating conditions for chemical processes under uncertainty.
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