The system of sparse gridpoints was used to propagate uncertainty forward in time through orbital mechanics simulations. Propagation of initial uncertainty through a nonlinear dynamic model is examined in regards to the uncertainty of orbit estimation. The necessary underlying mechanics of orbital mechanics, probability, and nonlinear estimation theory are reviewed to allow greater understanding of the problem. The sparse grid method itself and its implementation is covered in detail, along with the necessary properties and how to best it to a given problem based on inputs and desired outputs. Three test cases were run in the form of a restricted two-body problem, a perturbed two-body problem, and a three-body problem in which the orbiting body is positioned at a Lagrange point. It is shown that the sparse grid method shows sufficient accuracy for all mean calculations in the given problems and that higher accuracy levels allow for accurate estimation of higher moments such as the covariance.

Call number: LD2668 .T4 1984 B76 / Master of Science

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively absorb energy. Unlike a traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy from a wide range of frequencies. However, each NES is only efficient over a limited range of excitations. In addition, NES efficiency is extremely sensitive to perturbations in design parameters or loading, demonstrating a nearly discontinuous efficiency. Therefore, in order to optimally design a NES, uncertainties must be accounted for. This thesis focuses on optimally selecting parameters to design an effective NES system through optimization under uncertainty. For this purpose, a specific algorithm is introduced that makes use of clustering techniques to segregate efficient and inefficient NES behavior. SVM and Kriging approximations as well as new adaptive sampling techniques are used for the optimization under uncertainty. The variables of the problems are either random design variables or aleatory variables. For example, the excitation applied to the main vibrating system is treated as aleatory. In an effort to increase the range of excitations for which NESs are effective, a combination of NESs configured in parallel is considered. Optimization under uncertainty is performed on several examples with varying design parameters as well as different numbers of NESs (from 1 to 10). Results show that combining NESs in parallel is an effective method to increase the excitation range over which a NES is effective.

Using survey-based measures of future interest rate expectations from the Blue Chip Economic Indicators and the Survey of Professional Forecasters, we examine the relationship between monetary policy uncertainty, captured as the dispersion of interest rate forecasts, and fluctuations in real economic activity and core inflation. We use a flexible time-varying parameter vector autoregression (TVP-VAR) model to clearly isolate the dynamic effects of shocks to monetary policy uncertainty. To further study possible a possible nonlinear relationship between monetary policy uncertainty and the macroeconomic aggregates, we extract the impulse-response functions (IRF’s) estimated at each quarter in the time series, and use a multi-variate regression with various measures of the shape of the IRF’s and the level of monetary policy uncertainty at that quarter in the TVP-VAR model to gauge the relationship between the effectiveness of traditional monetary policy (shocks to the Federal Funds rate), forward guidance (shocks to expected interest rates) and uncertainty. The results show that monetary policy uncertainty can have a quantitatively significant impact on output, with a one standard deviation shock to uncertainty associated with a 0.6% rise in unemployment. The indirect effects are more substantial, with a one standard deviation increase in monetary policy uncertainty associated with a 23% decrease in the maximum response of unemployment to a forward guidance episode (interest rate expectations shock). This evidence points to the importance of managing monetary policy uncertainty (clear and direct forward guidance) as a key policy tool in both stimulating economic activity as well as propagating other monetary policy through the macroeconomy.

Traditionally, transportation road networks have been designed for minimal congestion. Unfortunately, such approaches do not guarantee minimal vehicle emissions. Given the negative impacts of vehicle pollutants as well as tighter national air quality standards, it is critical for regions to be able to identify capacity modifications to road networks such that vehicle emissions are minimal. This ability combined with land use changes and opportunities for non-auto travel are paramount in helping regions improve air quality. However, network design research has yet to directly address this topic. To fill this apparent gap in network design research, an emissions network design problem and solution method are proposed in this thesis. Three air pollutants are considered: hydrocarbons, nitrogen oxides, and carbon monoxide. The proposed model is applied to two road networks: Sioux Falls, ND and Anaheim, CA. The model is a bi-level optimization problem solved using a genetic algorithm and incorporates the influence of demand uncertainty. Findings indicate designing for minimal congestion tends to increase emissions of criteria air pollutants. However, not adding capacity to a road network also increases emissions of pollutants. Therefore, an optimization problem and solution method, such as the model presented here, is useful for identifying capacity additions that reduce vehicle emissions. It is also useful for understanding the tradeoffs between designing a network for minimal congestion versus minimal vehicle emissions. / text

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The study focuses on the sensitivity and uncertainty analysis of occupancy-related parameters using Energyplus modeling method. The model is based on a real building Zero Energy Lab in Discovery Park, at University of North Texas. Four categories of parameters are analyzed: heating/cooling setpoint, lighting, equipment and occupancy. Influence coefficient (IC) is applied in the sensitivity study, in order to compare the impact of individual parameter on the overall building energy consumption. The study is conducted under Texas weather file as well as North Dakota weather file in order to find weather’s influence of sensitivity. Probabilistic collocation method (PCM) is utilized for uncertainty analysis, with an aim of predicting future energy consumption based on history or reference data set. From the study, it is found that cooling setpoint has the largest influence on overall energy consumption in both Texas and North Dakota, and occupancy number has the least influence. The analysis also indicates schedule’s influence on energy consumption. PCM is able to accurately predict future energy consumption with limited calculation, and has great advantage over Monte Carlo Method. The polynomial equations are generated in both 3-order and 6-order, and the 6-order equation is proved to have a better result, which is around 0.1% compared with real value.

Uncertainty principle, which was first introduced by Werner Heisenberg in 1927, forms a fundamental component of quantum mechanics. A graceful aspect of quantum mechanics is that the uncertainty relations between incompatible observables allow for succinct quan- titative formulations of this revolutionary idea: it is impossible to simultaneously measure two complementary variables of a particle in precision. In particular, information theory offers two basic ways to express the Heisenberg’s principle: variance-based uncertainty relations and entropic uncertainty relations. We first investigate the uncertainty relations based on the sum of variances and derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations. Our work indicates that it seems unreasonable to assume a priori that incompatible observables have equal contribution to the variance-based sum form uncertainty relations. We also study the role of mutually exclusive physical states in the recent work and generalize the variance-based uncertainty relations to mutually exclusive uncertainty relations. Next, we develop a new kind of entanglement detection criteria within the framework of marjorization theory and its matrix representation. By virtue of majorization uncertainty bounds, we are able to construct the entanglement criteria which have advantage over the scalar detect- ing algorithms as they are often stronger and tighter. Furthermore, we explore various expression of entropic uncertainty relations, including sum of Shannon entropies, majorization uncer- tainty relations and uncertainty relations in presence of quantum memory. For entropic uncertainty relations without quantum side information, we provide several tighter bounds for multi-measurements, with some of them also valid for Rényi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an admixture bound for entropic uncertainty relations with multi-measurements. Comparisons among existing bounds for multi-measurements are also given. However,classical entropic uncertainty relations assume there has only classical side information. For modern uncertainty relations, those who allowed for non-trivial amount of quantum side information, their bounds have been strengthened by our recent result for both two and multi- measurements. Finally, we propose an approach which can extend all uncertainty relations on Shannon entropies to allow for quantum side information and discuss the applications of our entropic framework. Combined with our uniform entanglement frames, it is possible to detect entanglement via entropic uncertainty relations even if there is no quantum side in- formation. With the rising of quantum information theory, uncertainty relations have been established as important tools for a wide range of applications, such as quantum cryptography, quantum key distribution, entanglement detection, quantum metrology, quantum speed limit and so on. It is thus necessary to focus on the study of uncertainty relations.

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Thesis advisor: Noah P. Snyder / Estimating annual phosphorus (P) loading in impaired fresh water bodies is necessary to identify and prioritize management activities. A variety of monitoring programs and water quality models have been developed to estimate P loading in impaired watersheds. However, uncertainty associated with annual riverine P loads tends to receive less attention. This study addresses this gap by exploring the range in annual total phosphorus (TP) loads from two common load estimation methods using data collected in the Charles River watershed (CRW) in eastern Massachusetts. The CRW has two P Total Maximum Daily Load (TMDL) reports due to impairments with respect to excessive summer algal growth. Three estimation methods are used in this thesis to quantify annual TP loads (LY): the concentration-discharge relationship (CQ), the land use coefficient (LUC) method, and the average concentration, continuous discharge (ACQ) method. LY derived using the LUC method spanned an average relative percent range of 214% at each site, whereas LY results from the concentration-discharge method spanned an average relative percent range of 56%. While results of the CQ method produced a narrower range of LY, the CQ relationship is subject to seasonal dependencies and inconsistency through time. Seasonal terms in the LOADEST program, a publicly available and commonly used statistics tool, do allow the model estimates to capture trends through time, an advantage over the LUC method. Results of an interlaboratory comparison of P concentrations demonstrate the potentially large role of analytical uncertainty in LY estimation. Significant discrepancies between the results of each method for a single location and time suggest that loading estimates and consequently management priorities may be dependent on the estimation technique employed. / Thesis (MS) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.