Theses - Computation for Design and Optimization
http://hdl.handle.net/1721.1/39116
2016-10-28T02:36:37ZTensor decomposition and parallelization of Markov Decision Processes
http://hdl.handle.net/1721.1/105018
Tensor decomposition and parallelization of Markov Decision Processes
Smart, David P. (David Paul)
Markov Decision Processes (MDPs) with large state spaces arise frequently when applied to real world problems. Optimal solutions to such problems exist, but may not be computationally tractable, as the required processing scales exponentially with the number of states. Unsurprisingly, investigating methods for efficiently determining optimal or near-optimal policies has generated substantial interest and remains an active area of research. A recent paper introduced an MDP representation as a tensor composition of a set of smaller component MDPs, and suggested a method for solving an MDP by decomposition into its tensor components and solving the smaller problems in parallel, combining their solutions into one for the original problem. Such an approach promises an increase in solution efficiency, since each smaller problem could be solved exponentially faster than the original. This paper develops this MDP tensor decomposition and parallelization algorithm, and analyzes both its computational performance and the optimality of its resultant solutions.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 85-81).
2016-01-01T00:00:00ZNumerical approaches to optimize dispatch on microgrids with energy storage
http://hdl.handle.net/1721.1/104567
Numerical approaches to optimize dispatch on microgrids with energy storage
Xie, Lutao
Microgrids and distributed generation are predicted to become extremely dominant in developing nations, and will be largely beneficial to both electricity suppliers and consumers. With the penetration of renewable energy into the electricity supply, to maintain a balance between power supply and demand is becoming more difficult. Nevertheless, it is quite feasible that large electrical storage systems such as batteries can efficiently mitigate problems caused by the intermittency of renewables, and thus enable stable adoption of such power sources. In order to understand how the energy capacity and power characteristics of batteries should be specified to optimize economic or socioeconomic benefits, an optimizing strategy for battery usage in microgrids energy scheduling was constructed. This strategy is based on the past power consumption, predictions of day-ahead power consumption, and historical trends of seasonal and daily trends, which gives a nonlinear, discontinuous and high dimensional objective function. Optimizing such an objective function is found to be very computational intensive and complex. In this paper, the nature of this large-scale optimization problem is studied. For real time dispatch, four optimization methods including active-set, interior-point method, sequential quadratic programming (SQP) and trust-region-reflective are discussed and compared to find the relatively fast and robust optimization algorithm. The computation was implemented by using the MATLAB nonlinear programming solver 'fmincon'. Three main objectives are carried out to improve the efficiency of solving this optimization problem: (1) determination of the mathematical& physical definitions of tolerances and discussion on convergence criteria with the corresponding tolerances; (2) Study and comparison on influences of the initial condition and the behavior of the objective function (highly related to peak demand charge); and (3) suggestions on modification of the model to achieve reduction of the computation time whilst maintain acceptable accuracy.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 49-50).
2016-01-01T00:00:00ZReduced-space Gaussian process regression forecast for nonlinear dynamical systems
http://hdl.handle.net/1721.1/104565
Reduced-space Gaussian process regression forecast for nonlinear dynamical systems
Wan, Zhong Yi, S.M. Massachusetts Institute of Technology
In this thesis work, we formulate a reduced-order data-driven strategy for the efficient probabilistic forecast of complex high-dimensional dynamical systems for which data-streams are available. The first step of this method consists of the reconstruction of the vector field in a reduced-order subspace of interest using Gaussian Process Regression (GPR). GPR simultaneously allows for the reconstruction of the vector field, as well as the estimation of the local uncertainty. The latter is due to i) the local interpolation error and ii) due to the truncation of the high-dimensional phase space and it analytically quantified in terms of the GPR hyperparameters. The second step involves the formulation of stochastic models that explicitly take into account the reconstructed dynamics and their uncertainty. For regions of the attractor where the training data points are not sufficiently dense for GPR to be effective an adaptive blended scheme is formulated that guarantees correct statistical steady state properties. We examine the effectiveness of the proposed method to complex systems including the Lorenz 63, Lorenz 96, the Kuramoto-Sivashinsky, as well as a prototype climate model. We also study the performance of the proposed approach as the intrinsic dimensionality of the system attractor increases in highly turbulent regimes.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 93-97).
2016-01-01T00:00:00ZChemistry models for major gas species estimation and tar prediction in fluidized bed biomass gasification
http://hdl.handle.net/1721.1/104564
Chemistry models for major gas species estimation and tar prediction in fluidized bed biomass gasification
Sridhar, Rajesh
The present work deals with the process of fluidized bed biomass gasification (FBBG), which is the thermochemical conversion of solid biomass into combustible synthetic gas using a fluidized bed. Fluidized bed gasifiers encounter high tar concentrations at the gasifier outlet necessitating expensive downstream cleaning equipment. Apart from the complex chemical pathways involved, tar production is also strongly dependent on the transport processes occurring inside the gasifier. Hence, the development of a detailed model to predict the variation of tar production under different operating conditions needs to include two important considerations: a comprehensive chemical kinetic sub-model and a detailed hydrodynamic sub-model. However, due to the huge computational expense associated with such a detailed simulation coupling the complex chemistry and hydrodynamics, there is a need to develop simplified models on both fronts. The first part of this work presents a detailed discussion on the chemistry models for biomass gasification: after introducing the existing state-of-the-art reaction mechanisms (both detailed and compact), two new global chemistry models, incorporating a global primary tar cracking reaction, for air-blown gasification and steam-blown gasification conditions are developed. The major gas species and total tar concentrations predicted using the global models in reactor network simulations of the gasifiers are compared with the corresponding predictions obtained using the detailed CRECK mechanism for biomass gasification, as well as with the available experimental observations. On the hydrodynamics front, an improved reactor network model based on the two-phase theory has been developed to better capture the mixing inhomogeneities in the bubbling fluidized bed, including mass transfer considerations between the bubble and emulsion phases. Finally, the predictions of various tar class concentrations and major gas species concentrations, obtained using the improved reactor network model in conjunction with the detailed CRECK kinetic reaction mechanism, for both air-blown gasification and steam gasification, are presented. Key words: Biomass gasification, Fluidized beds, Chemical reactor network modeling, chemical kinetics, chemistry mechanism reduction, Global chemistry model
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 133-140).
2016-01-01T00:00:00Z