A stable elemental decomposition for dynamic process optimization

AbstractIn Cervantes and Biegler (A.I.Ch.E.J. 44 (1998) 1038), we presented a simultaneous nonlinear programming problem (NLP) formulation for the solution of DAE optimization problems. Here, by applying collocation on finite elements, the DAE system is transformed into a nonlinear system. The resulting optimization problem, in which the element placement is fixed, is solved using a reduced space successive quadratic programming (rSQP) algorithm. The space is partitioned into range and null spaces. This partitioning is performed by choosing a pivot sequence for an LU factorization with partial pivoting which allows us to detect unstable modes in the DAE system. The system is stabilized without imposing new boundary conditions. The decomposition of the range space can be performed in a single step by exploiting the overall sparsity of the collocation matrix but not its almost block diagonal structure. In order to solve larger problems a new decomposition approach and a new method for constructing the quadratic programming (QP) subproblem are presented in this work. The decomposition of the collocation matrix is now performed element by element, thus reducing the storage requirements and the computational effort. Under this scheme, the unstable modes are considered in each element and a range-space move is constructed sequentially based on decomposition in each element. This new decomposition improves the efficiency of our previous approach and at the same time preserves its stability. The performance of the algorithm is tested on several examples. Finally, some future directions for research are discussed

Conflict-Based Model Predictive Control for Scalable Multi-Robot Motion Planning

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners

Equation-oriented Optimization of Cryogenic Systems for Coal Oxycombustion Power Generation

AbstractEfficient separation systems are essential to the development of economical CO2 capture system for fossil flue power plants. Air Separation Units (ASU) and CO2 Processing Units (CPU) are considering the best commercially available technologies for the O2/N2 and CO2/N2, O2, Ar separations in coal oxycombustion processes. Both of these systems operate at cryogenic temperatures and include self-integrated refrigeration cycles, making their design challenging. Several researchers have applied sensitivity tools available in the commercial flow sheet simulators to study and improve ASU and CPU systems for oxy-fired coal power plants. These studies are limited, however, as they neglect important interactions between design variables.In this paper, we apply an advanced equation-based flowsheet optimization framework to design these cryogenic separations systems. The key advantage of this approach is the ability to use state-of-the-art nonlinear optimization solvers that are capable of considering 100,000+ variables and constraints. This allows for multi-variable optimization of these cryogenic separations systems and their accompanying multi-stream heat exchangers. The effectiveness of this approach is demonstrated in two case studies. The optimized ASU designs requires 0.196 kWh/kg of O2, which are similar to a “low energy” design from American Air Liquide and outperforms other academic studies. Similarly, the optimized CPU requires 18% less specific separation energy than an academic reference case. Pareto (sensitivity) curves for the ASU and CPU systems are also presented. Finally, plans to apply the framework to simultaneously optimize an entire oxycombustion process are discussed

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.http://www.sciencedirect.com/science/article/B6V4N-4R7F42T-2/1/7729956156701c2970c6a488f929884

An optimization model for assessment of membrane-based post-combustion gas upcycling into hydrogen or syngas

In this work, we present an optimization model and techno-economic analysis aimed at assessing the viability of employing membrane technology to recover value-added compounds from post-combustion gases of the process industry. In particular, the tail gas generated in carbon black manufacturing process is targeted. The content of hydrogen (H2) and carbon monoxide (CO) in this waste gas stream is relatively high, thus the possibility of increasing the sustainability of the process by recovering either H2 or both compounds simultaneously (syngas) is addressed. A comparison is performed between the optimal process designs for each recovery scenario based on the separation characteristics provided by state-of-the-art and prospective membrane materials. To that end, a two-stage membrane separation process using hollow-fiber membranes is implemented in the General Algebraic Modeling System (GAMS) as a nonlinear programming model (NLP). The optimal process design for each recovery scenario is found determining the feed pressure, membrane area, power consumption and composition of all process streams that meet the specified H2 recovery and product purity targets at the minimum net present value cost. Results indicate that membrane technology can drive the recovery of significant amounts of H2 from this unconventional source using the separation potential of current polymeric membranes. Moreover, novel ionic liquid-based membranes may be seen as promising candidates providing the required separation properties to obtain a syngas-rich product stream at a lower cost. In this way, the recovery of value-added products is intensified and the carbon dioxide emissions related to the conventional thermal treatment of the tail gas are partially mitigated, thus also reducing the environmental impact of carbon black manufacturing process.Financial support from the Spanish Ministry of Economy and Competitiveness (CTQ2015-66078) is gratefully acknowledged

3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: III. Thermochemical tomography in the Western-Central U.S.

Acknowledgments We are indebted to F. Darbyshire and J. von Hunen for useful comments on earlier versions of this work. This manuscript benefited from thorough and constructive reviews by W. Levandowski and an anonymous reviewer. We also thank J. Connolly, M. Sambridge, B. Kennett, S. Lebedev, B. Shan, U. Faul, and M. Qashqai for insightful discussions about, and contributions to, some of the concepts presented in this paper. The work of J.C.A. has been supported by two Australian Research Council Discovery grants (DP120102372 and DP110104145). Seismic data are from the IRIS DMS. D.L.S. acknowledges support from NSF grant EAR-135866. This is contribution 848 from the ARC Centre of Excellence for Core to Crust Fluid Systems (http://www.ccfs.mq.edu.au) and 1106 in the GEMOC Key Centre (http://www.gemoc.mq.edu.au).Peer reviewedPublisher PD

Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models

Computational inverse problems related to partial differential equations (PDEs) often contain nuisance parameters that cannot be effectively identified but still need to be considered as part of the problem. The objective of this work is to show how to take advantage of a reduced order framework to speed up Bayesian inversion on the identifiable parameters of the system, while marginalizing away the (potentially large number of) nuisance parameters. The key ingredients are twofold. On the one hand, we rely on a reduced basis (RB) method, equipped with computable a posteriori error bounds, to speed up the solution of the forward problem. On the other hand, we develop suitable reduction error models (REMs) to quantify in an inexpensive way the error between the full-order and the reduced-order approximation of the forward problem, in order to gauge the effect of this error on the posterior distribution of the identifiable parameters. Numerical results dealing with inverse problems governed by elliptic PDEs in the case of both scalar parameters and parametric fields highlight the combined role played by RB accuracy and REM effectivity

Optimization of multistage olefin/paraffin membrane separation processes through rigorous modeling

In this work, we explore the capabilities of an NLP optimization model to determine the viability of facilitated transport membrane processes intended to replace traditional distillation currently employed for propane/propylene separation. An NLP optimization model for multistage membrane processes has been formulated, introducing the mathematical description of the facilitated transport mechanisms in the PVDF‐HFP/BMImBF4/AgBF4 membranes previously developed by our research group. For the first time, a simultaneous optimization of the process and the membrane material (i.e., carrier concentration) has been performed, thanks to the implementation of the governing equations for the fixed site and mobile carrier mechanisms. Once the model is solved in GAMS it returns the optimal membrane area, carrier loading and permeate pressure of each stage based on Net Present Value Cost (NPVC) minimization. Different process flow sheets were evaluated and the results show prominent reductions on NPVC for facilitated transport multistage processes when compared to distillation.Financial support from the Spanish Ministry of Science under the pro-jects CTQ2015-66078-R and CTQ2016-75158-R (MINECO, Spain-FEDER 2014–2020) is gratefully acknowledged. Raúl Zarca also thanks the Universidad de Cantabria for the postgraduate fellowship

Estudi sobre les hores més conflictives en un institut de secundària

Aquest Treball Final de Màster analitza la conflictivitat existent a les aules d'un institut de secundària. S'ha fet un estudi, amb dades reals de dos centres, sobre les incidències produïdes segons tres paràmetres que són la franja horària o hora lectiva, el curs i la matèria. Aquestes dades s'han representat i analitzat mitjançant taules i gràfics per poder fer una comparació. Els resultats obtinguts en els dos centres són sorprenentment coincidents pel que fa a conflictivitat per cursos i franges horàries, que es concentra al primer cicle i a la segona franja horària. Les diferències són una mica més grans pel que fa referència a les assignatures. Un cop identificada la franja horària més conflictiva del dia, s'ha dissenyat una proposta d'aplicació a l'aula relacionada amb tècniques de relaxació. Per desenvolupar la proposta s'ha fet un estudi de les tècniques existents a l'actualitat