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

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

Numerical Methods for Mixed-Integer Optimal Control with Combinatorial Constraints

This thesis is concerned with numerical methods for Mixed-Integer Optimal Control Problems with Combinatorial Constraints. We establish an approximation theorem relating a Mixed-Integer Optimal Control Problem with Combinatorial Constraints to a continuous relaxed convexified Optimal Control Problems with Vanishing Constraints that provides the basis for numerical computations. We develop a a Vanishing- Constraint respecting rounding algorithm to exploit this correspondence computationally. Direct Discretization of the Optimal Control Problem with Vanishing Constraints yield a subclass of Mathematical Programs with Equilibrium Constraints. Mathematical Programs with Equilibrium Constraint constitute a class of challenging problems due to their inherent non-convexity and non-smoothness. We develop an active-set algorithm for Mathematical Programs with Equilibrium Constraints and prove global convergence to Bouligand stationary points of this algorithm under suitable technical conditions. For efficient computation of Newton-type steps of Optimal Control Problems, we establish the Generalized Lanczos Method for trust region problems in a Hilbert space context. To ensure real-time feasibility in Online Optimal Control Applications with tracking-type Lagrangian objective, we develop a Gauß-Newton preconditioner for the iterative solution method of the trust region problem. We implement the proposed methods and demonstrate their applicability and efficacy on several benchmark problems

Book of abstracts of the 10th International Chemical and Biological Engineering Conference: CHEMPOR 2008

This book contains the extended abstracts presented at the 10th International Chemical and Biological Engineering Conference - CHEMPOR 2008, held in Braga, Portugal, over 3 days, from the 4th to the 6th of September, 2008. Previous editions took place in Lisboa (1975, 1889, 1998), Braga (1978), Póvoa de Varzim (1981), Coimbra (1985, 2005), Porto (1993), and Aveiro (2001). The conference was jointly organized by the University of Minho, “Ordem dos Engenheiros”, and the IBB - Institute for Biotechnology and Bioengineering with the usual support of the “Sociedade Portuguesa de Química” and, by the first time, of the “Sociedade Portuguesa de Biotecnologia”. Thirty years elapsed since CHEMPOR was held at the University of Minho, organized by T.R. Bott, D. Allen, A. Bridgwater, J.J.B. Romero, L.J.S. Soares and J.D.R.S. Pinheiro. We are fortunate to have Profs. Bott, Soares and Pinheiro in the Honor Committee of this 10th edition, under the high Patronage of his Excellency the President of the Portuguese Republic, Prof. Aníbal Cavaco Silva. The opening ceremony will confer Prof. Bott with a “Long Term Achievement” award acknowledging the important contribution Prof. Bott brought along more than 30 years to the development of the Chemical Engineering science, to the launch of CHEMPOR series and specially to the University of Minho. Prof. Bott’s inaugural lecture will address the importance of effective energy management in processing operations, particularly in the effectiveness of heat recovery and the associated reduction in greenhouse gas emission from combustion processes. The CHEMPOR series traditionally brings together both young and established researchers and end users to discuss recent developments in different areas of Chemical Engineering. The scope of this edition is broadening out by including the Biological Engineering research. One of the major core areas of the conference program is life quality, due to the importance that Chemical and Biological Engineering plays in this area. “Integration of Life Sciences & Engineering” and “Sustainable Process-Product Development through Green Chemistry” are two of the leading themes with papers addressing such important issues. This is complemented with additional leading themes including “Advancing the Chemical and Biological Engineering Fundamentals”, “Multi-Scale and/or Multi-Disciplinary Approach to Process-Product Innovation”, “Systematic Methods and Tools for Managing the Complexity”, and “Educating Chemical and Biological Engineers for Coming Challenges” which define the extended abstracts arrangements along this book. A total of 516 extended abstracts are included in the book, consisting of 7 invited lecturers, 15 keynote, 105 short oral presentations given in 5 parallel sessions, along with 6 slots for viewing 389 poster presentations. Full papers are jointly included in the companion Proceedings in CD-ROM. All papers have been reviewed and we are grateful to the members of scientific and organizing committees for their evaluations. It was an intensive task since 610 submitted abstracts from 45 countries were received. It has been an honor for us to contribute to setting up CHEMPOR 2008 during almost two years. We wish to thank the authors who have contributed to yield a high scientific standard to the program. We are thankful to the sponsors who have contributed decisively to this event. We also extend our gratefulness to all those who, through their dedicated efforts, have assisted us in this task. On behalf of the Scientific and Organizing Committees we wish you that together with an interesting reading, the scientific program and the social moments organized will be memorable for all.Fundação para a Ciência e a Tecnologia (FCT

Pathways to Water Sector Decarbonization, Carbon Capture and Utilization

The water sector is in the middle of a paradigm shift from focusing on treatment and meeting discharge permit limits to integrated operation that also enables a circular water economy via water reuse, resource recovery, and system level planning and operation. While the sector has gone through different stages of such revolution, from improving energy efficiency to recovering renewable energy and resources, when it comes to the next step of achieving carbon neutrality or negative emission, it falls behind other infrastructure sectors such as energy and transportation. The water sector carries tremendous potential to decarbonize, from technological advancements, to operational optimization, to policy and behavioural changes. This book aims to fill an important gap for different stakeholders to gain knowledge and skills in this area and equip the water community to further decarbonize the industry and build a carbon-free society and economy. The book goes beyond technology overviews, rather it aims to provide a system level blueprint for decarbonization. It can be a reference book and textbook for graduate students, researchers, practitioners, consultants and policy makers, and it will provide practical guidance for stakeholders to analyse and implement decarbonization measures in their professions

Pathways to Water Sector Decarbonization, Carbon Capture and Utilization

The water sector is in the middle of a paradigm shift from focusing on treatment and meeting discharge permit limits to integrated operation that also enables a circular water economy via water reuse, resource recovery, and system level planning and operation. While the sector has gone through different stages of such revolution, from improving energy efficiency to recovering renewable energy and resources, when it comes to the next step of achieving carbon neutrality or negative emission, it falls behind other infrastructure sectors such as energy and transportation. The water sector carries tremendous potential to decarbonize, from technological advancements, to operational optimization, to policy and behavioural changes. This book aims to fill an important gap for different stakeholders to gain knowledge and skills in this area and equip the water community to further decarbonize the industry and build a carbon-free society and economy. The book goes beyond technology overviews, rather it aims to provide a system level blueprint for decarbonization. It can be a reference book and textbook for graduate students, researchers, practitioners, consultants and policy makers, and it will provide practical guidance for stakeholders to analyse and implement decarbonization measures in their professions

Pathways to Water Sector Decarbonization, Carbon Capture and Utilization

The water sector is in the middle of a paradigm shift from focusing on treatment and meeting discharge permit limits to integrated operation that also enables a circular water economy via water reuse, resource recovery, and system level planning and operation. While the sector has gone through different stages of such revolution, from improving energy efficiency to recovering renewable energy and resources, when it comes to the next step of achieving carbon neutrality or negative emission, it falls behind other infrastructure sectors such as energy and transportation. The water sector carries tremendous potential to decarbonize, from technological advancements, to operational optimization, to policy and behavioural changes. This book aims to fill an important gap for different stakeholders to gain knowledge and skills in this area and equip the water community to further decarbonize the industry and build a carbon-free society and economy. The book goes beyond technology overviews, rather it aims to provide a system level blueprint for decarbonization. It can be a reference book and textbook for graduate students, researchers, practitioners, consultants and policy makers, and it will provide practical guidance for stakeholders to analyse and implement decarbonization measures in their professions

Pathways to Water Sector Decarbonization, Carbon Capture and Utilization

The water sector is in the middle of a paradigm shift from focusing on treatment and meeting discharge permit limits to integrated operation that also enables a circular water economy via water reuse, resource recovery, and system level planning and operation. While the sector has gone through different stages of such revolution, from improving energy efficiency to recovering renewable energy and resources, when it comes to the next step of achieving carbon neutrality or negative emission, it falls behind other infrastructure sectors such as energy and transportation. The water sector carries tremendous potential to decarbonize, from technological advancements, to operational optimization, to policy and behavioural changes. This book aims to fill an important gap for different stakeholders to gain knowledge and skills in this area and equip the water community to further decarbonize the industry and build a carbon-free society and economy. The book goes beyond technology overviews, rather it aims to provide a system level blueprint for decarbonization. It can be a reference book and textbook for graduate students, researchers, practitioners, consultants and policy makers, and it will provide practical guidance for stakeholders to analyse and implement decarbonization measures in their professions

A contribution to support decision making in energy/water sypply chain optimisation

The seeking of process sustainability forces enterprises to change their operations. Additionally, the industrial globalization implies a very dynamic market that, among other issues, promotes the enterprises competition. Therefore, the efficient control and use of their Key Performance Indicators, including profitability, cost reduction, demand satisfaction and environmental impact associated to the development of new products, is a significant challenge. All the above indicators can be efficiently controlled through the Supply Chain Management. Thus, companies work towards the optimization of their individual operations under competitive environments taking advantage of the flexibility provided by the virtually inexistent world market restrictions. This is achieved by the coordination of the resource flows, across all the entities and echelons belonging to the system network. Nevertheless, such coordination is significantly complicated if considering the presence of uncertainty and even more if seeking for a win-win outcome. The purpose of this thesis is extending the current decision making strategies to expedite these tasks in industrial processes. Such a contribution is based on the development of efficient mathematical models that allows coordinating large amount of information synchronizing the production and distribution tasks in terms of economic, environmental and social criteria. This thesis starts presents an overview of the requirements of sustainable production processes, describing and analyzing the current methods and tools used and identifying the most relevant open issues. All the above is always within the framework of Process System Engineering literature. The second part of this thesis is focused in stressing the current Multi-Objective solution strategies. During this part, first explores how the profitability of the Supply Chain can be enhanced by considering simultaneously multiple objectives under demand uncertainties. Particularly, solution frameworks have been proposed in which different multi-criteria decision making strategies have been combined with stochastic approaches. Furthermore, additional performance indicators (including financial and operational ones) have been included in the same solution framework to evaluate its capabilities. This framework was also applied to decentralized supply chains problems in order to explore its capabilities to produce solution that improves the performances of each one of the SC entities simultaneously. Consequently, a new generalized mathematical formulation which integrates many performance indicators in the production process within a supply chain is efficiently solved. Afterwards, the third part of the thesis extends the proposed solution framework to address the uncertainty management. Particularly, the consideration of different types and sources of uncertainty (e.g. external and internal ones) where considered, through the implementation of preventive approaches. This part also explores the use of solution strategies that efficiently selects the number of scenarios that represent the uncertainty conditions. Finally, the importance and effect of each uncertainty source over the process performance is detailed analyzed through the use of surrogate models that promote the sensitivity analysis of those uncertainties. The third part of this thesis is focused on the integration of the above multi-objective and uncertainty approaches for the optimization of a sustainable Supply Chain. Besides the integration of different solution approaches, this part also considers the integration of hierarchical decision levels, by the exploitation of mathematical models that assess the consequences of considering simultaneously design and planning decisions under centralized and decentralized Supply Chains. Finally, the last part of this thesis provides the final conclusions and further work to be developed.La globalización industrial genera un ambiente dinámico en los mercados que, entre otras cosas, promueve la competencia entre corporaciones. Por lo tanto, el uso eficiente de las los indicadores de rendimiento, incluyendo rentabilidad, satisfacción de la demanda y en general el impacto ambiental, representa un area de oportunidad importante. El control de estos indicadores tiene un efecto positivo si se combinan con la gestión de cadena de suministro. Por lo tanto, las compañías buscan definir sus operaciones para permanecer activas dentro de un ambiente competitivo, tomando en cuenta las restricciones en el mercado mundial. Lo anterior puede ser logrado mediante la coordinación de los flujos de recursos a través de todas las entidades y escalones pertenecientes a la red del sistema. Sin embargo, dicha coordinación se complica significativamente si se quiere considerar la presencia de incertidumbre, y aún más, si se busca exclusivamente un ganar-ganar. El propósito de esta tesis es extender el alcance de las estrategias de toma de decisiones con el fin de facilitar estas tareas dentro de procesos industriales. Estas contribuciones se basan en el desarrollo de modelos matemáticos eficientes que permitan coordinar grandes cantidades de información sincronizando las tareas de producción y distribución en términos económicos, ambientales y sociales. Esta tesis inicia presentando una visión global de los requerimientos de un proceso de producción sostenible, describiendo y analizando los métodos y herramientas actuales así como identificando las áreas de oportunidad más relevantes dentro del marco de ingeniería de procesos La segunda parte se enfoca en enfatizar las capacidades de las estrategias de solución multi-objetivo, durante la cual, se explora el mejoramiento de la rentabilidad de la cadena de suministro considerando múltiples objetivos bajo incertidumbres en la demanda. Particularmente, diferentes marcos de solución han sido propuestos en los que varias estrategias de toma de decisión multi-criterio han sido combinadas con aproximaciones estocásticas. Por otra parte, indicadores de rendimiento (incluyendo financiero y operacional) han sido incluidos en el mismo marco de solución para evaluar sus capacidades. Este marco fue aplicado también a problemas de cadenas de suministro descentralizados con el fin de explorar sus capacidades de producir soluciones que mejoran simultáneamente el rendimiento para cada uno de las entidades dentro de la cadena de suministro. Consecuentemente, una nueva formulación que integra varios indicadores de rendimiento en los procesos de producción fue propuesta y validada. La tercera parte de la tesis extiende el marco de solución propuesto para abordar el manejo de incertidumbres. Particularmente, la consideración de diferentes tipos y fuentes de incertidumbre (p.ej. externos e internos) fueron considerados, mediante la implementación de aproximaciones preventivas. Esta parte también explora el uso de estrategias de solución que elige eficientemente el número de escenarios necesario que representan las condiciones inciertas. Finalmente, la importancia y efecto de cada una de las fuentes de incertidumbre sobre el rendimiento del proceso es analizado en detalle mediante el uso de meta modelos que promueven el análisis de sensibilidad de dichas incertidumbres. La tercera parte de esta tesis se enfoca en la integración de las metodologías de multi-objetivo e incertidumbre anteriormente expuestas para la optimización de cadenas de suministro sostenibles. Además de la integración de diferentes métodos. Esta parte también considera la integración de diferentes niveles jerárquicos de decisión, mediante el aprovechamiento de modelos matemáticos que evalúan lasconsecuencias de considerar simultáneamente las decisiones de diseño y planeación de una cadena de suministro centralizada y descentralizada. La parte final de la tesis detalla las conclusiones y el trabajo a futuro necesario sobre esta línea de investigaciónPostprint (published version