Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

SINGLE STAGE LED DRIVER TECHNOLOGY WITH LOW FREQUENCY RIPPLE CANCELLATION

Because of high efficacy, long lifespan, and environment-friendly operation, LED lighting devices become more and more popular in every part of our life, such as ornament/interior lighting, outdoor lightings and flood lighting. The LED driver is the most critical part of the LED lighting fixture. It heavily affects the purchasing cost, operation cost as well as the light quality. Design a high efficiency, low component cost and flicker-free LED driver is the goal. The conventional single-stage LED driver can achieve low cost and high efficiency. However, it inevitably produces significant twice-line-frequency lighting flicker, which adversely affects our health. The conventional two-stage LED driver can achieve flicker-free LED driving at the expenses of significantly adding component cost, design complexity and low the efficiency. The basic ripple cancellation LED driving method has been proposed in chapter three. It achieves a high efficiency and a low component cost as the single-stage LED driver while also obtaining flicker-free LED driving performance. The basic ripple cancellation LED driver is the foundation of the entire thesis. As the research evolving, another two ripple cancellation LED drivers has been developed to improve different aspects of the basic ripple cancellation LED driver design. The primary side controlled ripple cancellation LED driver has been proposed in chapter four to further reduce cost on the control circuit. It eliminates secondary side compensation circuit and an opto-coupler in design while at the same time maintaining flicker-free LED driving. A potential integrated primary side controller can be designed based on the proposed LED driving method. The energy channeling ripple cancellation LED driver has been proposed in chapter five to further reduce cost on the power stage circuit. In previous two ripple cancellation LED drivers, an additional DC-DC converter is needed to achieve ripple cancellation. A power transistor has been used in the energy channeling ripple cancellation LED driving design to successfully replace a separate DC-DC converter and therefore achieved lower cost. The detailed analysis supports the theory of the proposed ripple cancellation LED drivers. Simulation and experiment have also been included to verify the proposed ripple cancellation LED drivers.

Parallel nonconvex generalized Benders decomposition for natural gas production network planning under uncertainty

A scenario-based two-stage stochastic programming model for gas production network planning under uncertainty is usually a large-scale nonconvex mixed-integer nonlinear programme (MINLP), which can be efficiently solved to global optimality with nonconvex generalized Benders decomposition (NGBD). This paper is concerned with the parallelization of NGBD to exploit multiple available computing resources. Three parallelization strategies are proposed, namely, naive scenario parallelization, adaptive scenario parallelization, and adaptive scenario and bounding parallelization. Case study of two industrial natural gas production network planning problems shows that, while the NGBD without parallelization is already faster than a state-of-the-art global optimization solver by an order of magnitude, the parallelization can improve the efficiency by several times on computers with multicore processors. The adaptive scenario and bounding parallelization achieves the best overall performance among the three proposed parallelization strategies.

Robust scenario formulations for strategic supply chain optimization under uncertainty

Strategic supply chain optimization (SCO) problems are often modelled as a two-stage optimization problem, in which the first-stage variables represent decisions on the development of the supply chain and the second-stage variables represent decisions on the operations of the supply chain. When uncertainty is explicitly considered, the problem becomes an intractable infinite-dimensional optimization problem, which is usually solved approximately via a scenario or a robust approach. This paper proposes a novel synergy of the scenario and robust approaches for strategic SCO under uncertainty. Two formulations are developed, namely, naïve robust scenario formulation and affinely adjustable robust scenario formulation. It is shown that both formulations can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded with the infinity-norm, and the uncertain equality constraints can be reformulated into deterministic constraints without assumption of the uncertainty region. Case studies of a classical farm planning problem and an energy and bioproduct SCO problem demonstrate the advantages of the proposed formulations over the classical scenario formulation. The proposed formulations not only can generate solutions with guaranteed feasibility or indicate infeasibility of a problem, but also can achieve optimal expected economic performance with smaller numbers of scenarios.

MEDIUM-CHAIN-LENGTH POLY(3-HYDROXYALKANOATE) NANOPARTICLE SUSPENSIONS

The main goal of this thesis was to prepare medium-chain-length poly-3-hydroxyalkanoate (mcl-PHA) nanoparticle suspensions at high solids content (≥ 10 % w/v). A two-stage emulsification-solvent evaporation process was employed to produce poly-3-hydroxydecanoate (PHD) suspensions. The formulation and processing conditions including ultrasonication time and amplitude, selection of solvent, and selection of surfactants and their concentrations were investigated to make concentrated suspensions (10 and 30 % (w/v)) of PHD with particles less than 300 nm. Among the ionic surfactants tested to stabilize the suspension, the anionic, sodium dodecyl sulphate (SDS), and the cationic, dodecyltrimethylammonium bromide (DTAB) surfactants produced the smallest particle sizes (~100 nm). However, more stabilized nanoparticles were obtained when the ionic surfactant, SDS, was combined with any of the non-ionic surfactants tested, with polyoxyethylene octyl phenyl ether (Triton X-100) or polyoxyethylene (20) sorbitan monooleate (Tween 80) resulting in a slight increase in zeta potential over 30 days while the zeta potential with other non-ionic surfactants decreased. Mcl-PHA containing 11 and 18 % of carboxyl groups was synthesized via free radical addition reaction of 11-mercaptoundecanoic acid to the pendant double bonds of unsaturated poly-3-hydroxynonanoate (PHNU). Colloidal suspensions prepared by ultrasonication needed a surfactant to maintain stability, even at 0.4 % solids of mcl-PHA containing 11 % carboxylation (PHNC-1) unlike the stable suspensions prepared without surfactants by the titration method. Similar particle sizes (155.6 ± 8.4 to 163.4 ± 11.3 nm) and polydispersity indices (0.42 ± 0.03 to 0.49 ± 0.04) were obtained when several non-ionic surfactants were tested to minimize particle agglomeration, with the smallest particles obtained with Triton X-100. When Triton X-100 was combined with a variety of ionic surfactants, smaller nanoparticles (97.1 ± 1.1 to 121.7 ± 5.7 nm) with a narrower particle size distribution (0.21 ± 0.001 to 0.25 ± 0.003) were produced. The SDS and Triton X-100 combination was chosen to evaluate other mcl-PHAs at 10 % (w/v) solids content. Slightly smaller nanoparticles were formed with carboxylated mcl-PHAs compared to mcl-PHAs having aliphatic pendant side chains. Mcl-PHA consisting of 18 % carboxylation (PHNC-2) formed a much smaller nanoparticles and higher zeta potential.

The Flotation of Niobium Oxide Minerals from Carbonatite Ores

Global niobium production is presently dominated by three operations, Araxá and Catalão (Brazil), and Niobec (Canada). Although Brazil accounts for over 90% of the world’s niobium production, a number of high grade niobium deposits exist worldwide. The advancement of these deposits depends largely on the development of operable beneficiation flowsheets. Pyrochlore, as the primary niobium mineral, is typically upgraded by flotation with amine collectors at acidic pH following a complicated flowsheet with significant losses of niobium. This research compares the typical two stage flotation flowsheet to a direct flotation process (i.e. elimination of gangue pre-flotation) with the objective of circuit simplification. In addition, the use of a chelating reagent (benzohydroxamic acid, BHA) was studied as an alternative collector for fine grained, highly disseminated pyrochlore. For the amine based reagent system, results showed that while comparable at the laboratory scale, when scaled up to the pilot level the direct flotation process suffered from circuit instability because of high quantities of dissolved calcium in the process water due to stream recirculation and fine calcite dissolution, which ultimately depressed pyrochlore. This scale up issue was not observed in pilot plant operation of the two stage flotation process as a portion of the highly reactive carbonate minerals was removed prior to acid addition. A statistical model was developed for batch flotation using BHA on carbonatite ore (0.25% Nb2O5) that could not be effectively upgraded using the conventional amine reagent scheme. Results showed that it was possible to produce a concentrate containing 1.54% Nb2O5 with 93% Nb recovery in ~15% of the original mass. Fundamental studies undertaken included FT-IR and XPS, which showed the adsorption of both the protonized amine and the neutral amine onto the surface of the pyrochlore (possibly at niobium sites as indicated by detected shifts in the Nb3d binding energy). The results suggest that the preferential flotation of pyrochlore over quartz with amines at low pH levels can be attributed to a difference in critical hemimicelle concentration (CHC) values for the two minerals. BHA was found to be absorbed on pyrochlore surfaces by a similar mechanism to alkyl hydroxamic acid. It is hoped that this work will assist in improving operability of existing pyrochlore flotation circuits and help promote the development of niobium deposits globally. Future studies should focus on investigation into specific gangue mineral depressants and inadvertent activation phenomenon related to BHA flotation of gangue minerals.