795 research outputs found
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 âlow energyâ 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
A Description of Multiscale Modeling for the Head-Disk Interface Focusing on Bottom-Level Lubricant and Carbon Overcoat Models
The challenges in designing future head disk interface (HDI) demand efficient theoretical modeling tools with flexibility in investigating various combinations of perfluoropolyether (PFPE) and carbon overcoat (COC) materials. For broad range of time and length scales, we developed multiscale/multiphysical modeling approach, which can bring paradigm-shifting improvements in advanced HDI design. In this paper, we introduce our multiscale modeling methodology with an effective strategic framework for the HDI system. Our multiscale methodology in this paper adopts a bottom to top approach beginning with the high-resolution modeling, which describes the intramolecular/intermolecular PFPE-COC degrees of freedom governing the functional oligomeric molecular conformations on the carbon surfaces. By introducing methodology for integrating atomistic/molecular/mesoscale levels via coarse-graining procedures, we investigated static and dynamic properties of PFPE-COC combinations with various molecular architectures. By bridging the atomistic and molecular scales, we are able to systematically incorporate first-principle physics into molecular models, thereby demonstrating a pathway for designing materials based on molecular architecture. We also discussed future materials (e.g., graphene for COC, star-like PFPEs) and systems (e.g., heat-assisted magnetic recording (HAMR)) with higher scale modeling methodology, which enables the incorporation of molecular/mesoscale information into the continuum scale models
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
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