Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Investigating Uncertainty with Fungible Parameter Estimate Analysis(2020) Prendez, Jordan Yee; Harring, Jeffrey R; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Researchers need methods for evaluating whether statistical results are worthy of interpretation. Likelihood functions contain large amounts of information regarding the support for differing estimates. However, maximum likelihood estimates (MLE) are typically the only set of estimates interpreted. Previous research has indicated that these alternative estimates can often be computed and represent data approximately as well as their MLE counterparts. The close fit between these alternative estimates are said to make them fungible. While similar in fit, fungible estimates are in some cases different enough (from the MLE) that they would support alternative substantive interpretations of the data. By calculating fungible parameter estimates (FPEs) one can either strengthen or weaken one’s inference by exploring the degree in which diverging estimates are supported. This dissertation has two contributions. First, it proposes a new method for generating FPEs under a broader definition of what should constitute fungible parameter estimates. This method allows for flexible computation of FPEs. Second, this method allows for an exploration of research inquiries that have been largely unexplored. What are the circumstances in which FPEs would convey uncertainty in the parameter estimates? That is, what are the causes of uncertainty that are measured by FPEs. Understanding the causes of this uncertainty are important for utilizing FPEs in practice. This dissertation uses a simulation study in order to investigate several factors that might be encountered in applied data analytic scenarios and affect the range of fungible parameter estimates including model misfit. The results of this study indicate the importance of interactions when examining FPEs. For some conditions, FPE ranges indicate that there was less uncertainty when the model was correctly specified. Under alternative conditions, FPE ranges suggest greater uncertainty for the correctly specified model. This example is mirrored in several results that suggest that a simple prediction of the level of uncertainty is difficult for likelihoods characterizing real world modeling scenarios.Item Stochastic Simulation: New Stochastic Approximation Methods and Sensitivity Analyses(2015) Chau, Marie; Fu, Michael C.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we propose two new types of stochastic approximation (SA) methods and study the sensitivity of SA and of a stochastic gradient method to various input parameters. First, we summarize the most common stochastic gradient estimation techniques, both direct and indirect, as well as the two classical SA algorithms, Robbins-Monro (RM) and Kiefer-Wolfowitz (KW), followed by some well-known modifications to the step size, output, gradient, and projection operator. Second, we introduce two new stochastic gradient methods in SA for univariate and multivariate stochastic optimization problems. Under a setting where both direct and indirect gradients are available, our new SA algorithms estimate the gradient using a hybrid estimator, which is a convex combination of a symmetric finite difference-type gradient estimate and an average of two associated direct gradient estimates. We derive variance minimizing weights that lead to desirable theoretical properties and prove convergence of the SA algorithms. Next, we study the finite-time performance of the KW algorithm and its sensitivity to the step size parameter, along with two of its adaptive variants, namely Kesten's rule and scale-and-shifted KW (SSKW). We conduct a sensitivity analysis of KW and explore the tightness of an mean-squared error (MSE) bound for quadratic functions, a relevant issue for determining how long to run an SA algorithm. Then, we propose two new adaptive step size sequences inspired by both Kesten's rule and SSKW, which address some of their weaknesses. Instead of us- ing one step size sequence, our adaptive step size is based on two deterministic sequences, and the step size used in the current iteration depends on the perceived proximity of the current iterate to the optimum. In addition, we introduce a method to adaptively adjust the two deterministic sequences. Lastly, we investigate the performance of a modified pathwise gradient estimation method that is applied to financial options with discontinuous payoffs, and in particular, used to estimate the Greeks, which measure the rate of change of (financial) derivative prices with respect to underlying market parameters and are central to financial risk management. The newly proposed kernel estimator relies on a smoothing bandwidth parameter. We explore the accuracy of the Greeks with varying bandwidths and investigate the sensitivity of a proposed iterative scheme that generates an estimate of the optimal bandwidth.Item Sensitivity Analysis Based Approaches for Mitigating the Effects of Reducible Interval Input Uncertainty on Single- and Multi-Disciplinary Systems using Multi-Objective Optimization(2010) Hamel, Joshua Matthew; Azarm, Shapour; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Uncertainty is an unavoidable aspect of engineering systems and will often degrade system performance or perhaps even lead to system failure. As a result, uncertainty must be considered as a part of the design process for all real-world engineering systems. The presence of reducible uncertainty further complicates matters as designers must not only account for the degrading effects of uncertainty but must also determine what levels of uncertainty can be considered as acceptable. For these reasons, methods for determining and effectively mitigating the effects of uncertainty are necessary for solving engineering design problems. This dissertation presents several new methods for use in the design of engineering systems under interval input uncertainty. These new approaches were developed over the course of four interrelated research thrusts and focused on the overall goal of extending the current research in the area of sensitivity analysis based design under reducible interval uncertainty. The first research thrust focused on developing an approach for determining optimal uncertainty reductions given multi-disciplinary engineering systems with multiple output functions at both the system and sub-system levels. The second research thrust extended the approach developed during the first thrust to use uncertainty reduction as a means for both reducing output variations and simultaneously ensuring engineering feasibility. The third research thrust looked at systems where uncertainty reduction alone is insufficient for ensuring feasibility and thus developed a sensitivity analysis approach that combined uncertainty reductions with small design adjustments in an effort to again reduce output variations and ensure feasibility. The fourth and final research thrust looked to relax many of the assumptions required by the first three research thrusts and developed a general sensitivity analysis inspired approach for determining optimal upper and lower bounds for reducible sources of input uncertainty. Multi-objective optimization techniques were used throughout this research to evaluate the tradeoffs between the benefits to be gained by mitigating uncertainty with the costs of making the design changes and/or uncertainty reductions required to reduce or eliminate the degrading effects of system uncertainty most effectively. The validity of the approaches developed were demonstrated using numerical and engineering example problems of varying complexity.Item Robust Optimization and Sensitivity Analysis with Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications(2007-11-21) Li, Mian; Azarm, Shapour; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Uncertainty is inevitable in engineering design optimization and can significantly degrade the performance of an optimized design solution and/or even change feasibility by making a feasible solution infeasible. The problem with uncertainty can be exacerbated in multi-disciplinary optimization whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. It is important to determine which ranges of parameter uncertainty are most important or how to best allocate investments to partially or fully reduce uncertainty under a limited budget. To address these issues, this dissertation concentrates on a new robust optimization approach and a new sensitivity analysis approach for multi-objective and multi-disciplinary design optimization problems that have parameters with interval uncertainty. The dissertation presents models and approaches under four research thrusts. In the first thrust, an approach is presented to obtain robustly optimal solutions which are as best as possible, in a multi-objective sense, and at the same time their sensitivity of objective and/or constraint functions is within an acceptable range. In the second thrust, the robust optimization approach in the first thrust is extended to design optimization problems which are decomposed into multiple subproblems, each with multiple objectives and constraints. In the third thrust, a new approach for multi-objective sensitivity analysis and uncertainty reduction is presented. And in the final research thrust, a metamodel embedded Multi-Objective Genetic Algorithm (MOGA) for solution of design optimization problems is presented. Numerous numerical and engineering examples are used to explore and demonstrate the applicability and performance of the robust optimization, sensitivity analysis and MOGA techniques developed in this dissertation. It is shown that the obtained robust optimal solutions for the test examples are conservative compared to their corresponding optimal solutions in the deterministic case. For the sensitivity analysis, it is demonstrated that the proposed method identifies parameters whose uncertainty reduction or elimination produces the largest payoffs for any given investment. Finally, it is shown that the new MOGA requires a significantly fewer number of simulation calls, when used to solve multi-objective design optimization problems, compared to previously developed MOGA methods while obtaining comparable solutions.Item MECHANISTIC-EMPIRICAL DESIGN OF FLEXIBLE PAVEMENTS: A SENSITIVITY STUDY(2006-03-14) Carvalho, Regis Luis; Schwartz, Charles W; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Pavement structural design is a daunting task. Traffic loading is a heterogeneous mix of vehicles, axle types and loads with distributions that vary daily and over the pavement design life. Pavement materials respond to these loads in complex ways influenced by stress state and magnitude, temperature, moisture, loading rate, and other factors. Environment exposure adds further complications. It should be no wonder the profession has resorted to largely empirical methods. Developments over recent decades offered an opportunity for more rational and rigorous pavement design procedures. The latest of these accomplishments is the development of the mechanistic-empirical pavement design procedure in NCHRP Project 1-37A. This study presents a comparison of flexible pavement designs between the 1993 AASHTO guide and the NCHRP 1-37A methodology and a sensitivity analysis of the NCHRP 1-37A's input parameters. Recommendations for future studies involving the application and implementation of the new mechanistic-empirical pavement design guide concludes the study.Item Analysis of Routing Strategies in Air Transportation Networks for Express Package Delivery Services(2005-07-06) Mahapatra, Subrat; Haghani, Ali; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The package delivery industry plays a dominant role in our economy by providing consistent and reliable delivery of a wide range of goods. Shipment Service Providers (SSP) offer a wide range of service levels characterized by varying time windows and modes of operation and follow different network configurations and strategies for their operations. SSP operate vast systems of aircraft, trucks, sorting facilities, equipment and personnel to move packages between customer locations. Due to the high values of the assets involved in terms of aircraft and huge operational cost implications, any small percentage savings could result in the order of savings of millions of dollars for the company. The current research focuses on the Express Package Delivery Problem and the optimization of the air transportation network. SSP must determine which routes to fly, which fleets to assign to those routes and how to assign packages to those aircraft, all in response to demand projections and operational restrictions. The objective is to find the cost minimizing movement of packages from their origins to their destinations given the very tight service windows, and limited aircraft capacity. In the current research, we formulate the air transportation network as a mixed integer program which minimizes the total operating costs subject to the demand, capacity, time, aircraft and airport constraints. We use this model to study of various operational strategies and their potential cost implications. We consider two main operational strategies: one involving no intermediate stops on pick-up and delivery sides and the other involving one intermediate stop between origin and hub on pick-up side and between hub and destination on delivery side. Under each strategy, we analyze the cost implications under a single hub network configuration and regional hub network configuration. We study the impact of various routing scenarios, various variants and logical combinations of these scenarios which gives a clear understanding of the network structure. We perform an extensive sensitivity analysis to understand the implications of variation in demand, fixed cost of operation, variable cost of operation and bounds on the number of aircraft taking off and landing in the airports.