3 research outputs found
Multilevel Monte Carlo for noise estimation in stochastic multiscale systems
The final publication is available at Elsevier via https://doi.org/10.1016/j.cherd.2018.10.006� 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The purpose of this study is to adapt Multilevel Monte Carlo (MLMC) sampling technique for random noise estimation in stochastic multiscale systems and evaluate the performance of this method. The system under consideration was a simulation of thin film formation by chemical vapour deposition, where a kinetic Monte Carlo solid-on-solid model was coupled with partial differential equations that represented mass, energy and momentum transport. The noise in the expected value of the system�s observable (film roughness) was estimated using MLMC and standard Monte Carlo (MC) sampling. The MLMC technique achieved conservative estimates of noise in the observable at an order of magnitude lower computational cost than standard MC sampling. This study highlights the nuances of adapting the MLMC technique to the stochastic multiscale system and provides insight on the benefits and challenges of using MLMC for noise estimation in stochastic multiscale systems.Natural Sciences and Engineering Research Council of Canad
Recommended from our members
Characterization of Continuous Spatial Particle Atomic Layer Deposition
By continuously conveying powder through alternating regions of precursor gas via linear vibration, continuous spatial particle ALD reactors were developed to satisfy the low cost and high throughput requirements of large-scale powder processing applications. While mesoscale and atomic-scale simulations have revealed details about the kinetics and molecular transport behavior of ALD processes, models which resolve the coupled gas-solid flow dynamics within particle ALD reactors are still lacking in the literature. This thesis introduces a series of models and experimental measures, in order of increasing complexity, to investigate the multiphase fluid dynamics, heat and mass transfer, and chemical reactions in continuous spatial particle ALD reactors.
A combined experimental and continuum-scale modeling campaign was developed to investigate the gas-solids flow behavior during particle ALD. Discrete element method (DEM) simulations with a fluctuating gravity model for vibration revealed solids plug flow behavior and hopping convection of the powder bed during linear vibration. By kinematically driving a layer of particles approximating the porous baseplate, the gas phase was incorporated in a computational fluid dynamics-discrete element method (CFD-DEM) model to explore the effects of aeration velocity and particle cohesion on the solids flow behavior. To improve powder bed agitation and mixing during convection, different porous mesh baffle designs were explored and incorporated into the baseplate. High speed videography and particle imaging velocimetry (PIV) captured the particle trajectories during vibration to determine the best design for powder mixing. Incorporating insights from the DEM simulations, the high computational expense associated with reactor-scale CFD simulations of particle ALD was reduced significantly by treating the powder bed as a moving porous media (MPM). The new MPM model approach revealed material properties and operating conditions that impact the final product uniformity and the species fractions in the effluent stream. Experimental characterization of the powder substrates and porous reactor baseplates using optical microscopy, surface profilometry, x-ray computed tomography (XRCT), powder rheometry, porometry, porosimetry, and particle size analysis provided application-specific inputs to the CFD-DEM and MPM models.</p
On the Techniques for Efficient Sampling, Uncertainty Quantification and Robust Control of Stochastic Multiscale Systems
In order to better understand and leverage natural phenomena to design materials and devices (e.g. biomedical coatings, catalytic reactors, thin conductive films for microprocessors, etc.), stochastic multiscale models have been developed that explicitly model the interactions and feedbacks between the electronic, atomistic/molecular, mesoscopic and macroscopic scales. These models attempt to use the accurate results from the fine scales to inform industrially relevant domain sizes and thereby improve product quality through optimal control actions during industrial manufacturing. However, the presence of stochastic calculations increases the computational cost of such modeling approaches and makes their direct application in uncertainty quantification, optimization and online control challenging. Uncertainty cannot be ignored from simulations, otherwise there will be model-plant mismatch and loss in performance. The added computational intensity necessitates the development of more efficient computational methods that can leverage the accurate predictions of stochastic multiscale models in the industrial setting where accuracy, efficiency and speed are of utmost importance.
A lot of research has been done in the area of stochastic multiscale models over the past few decades, but some gaps in knowledge remain. For instance, the performance of traditional uncertainty quantification techniques such as power series (PSE) and polynomial chaos expansions (PCE) has not been compared in the context of stochastic multiscale systems. Furthermore, a novel sampling technique called Multilevel Monte Carlo (MLMC) sampling emerged from the field of computational finance with the aim of preserving accuracy of estimation of model observables while decreasing the required computational cost. However, its applications in the field of chemical engineering and in particular for stochastic multiscale systems remain limited. Also, the advancements in computing power caused the usefulness of machine learning methods such as Artificial Neural Networks (ANNs) to increase. Because of their flexibility, accuracy and computational efficiency, ANNs are experiencing a resurgence of research interest, but their application for stochastic multiscale chemical engineering systems are still limited at the moment.
This thesis aims to fill the identified gaps in knowledge. The results of the conducted research indicate that PCE can be more computationally efficient and accurate than PSE for stochastic multiscale systems, but it may be vulnerable to the effects of stochastic noise. MLMC sampling provides an attractive advantage over the heuristic methods for uncertainty propagation in stochastic multiscale systems because it allows to estimate the level of noise in the observables. However, the stochastic noise imposes a limit on the maximum achievable MLMC accuracy, which was not observed for continuous systems that were originally used in MLMC development. ANNs appear to be a very promising method for online model predictive control of stochastic multiscale systems because of their computational efficiency, accuracy and robustness to large disturbances not seen in the training data