Proper engine selection for Reusable Launch Vehicles (RLVs) is a key factor in the design of low cost reusable launch systems for routine access to space. RLVs typically use combinations of different types of engines used in sequence over the duration of the flight. Also, in order to properly choose which engines are best for an RLV design concept and mission, the optimal trajectory that maximizes or minimizes the mission objective must be found for that engine configuration. Typically this is done by the designer iteratively choosing engine combinations based on his/her judgment and running each individual combination through a full trajectory optimization to find out how well the engine configuration performed on board the desired RLV design. This thesis presents a new method to reliably predict the optimal engine configuration and optimal trajectory for a fixed design of a conceptual RLV in an automated manner. This method is accomplished using the original code Steele-Flight. This code uses a combination of a Genetic Algorithm (GA) and a Non-Linear Programming (NLP) based trajectory optimizer known as GPOPS II to simultaneously find the optimal engine configuration from a user provided selection pool of engine models and the matching optimal trajectory. This method allows the user to explore a broad range of possible engine configurations that they wouldn't have time to consider and do so in less time than if they attempted to manually select and analyze each possible engine combination. This method was validated in two separate ways. The codes ability to optimize trajectories was compared to the German trajectory optimizer suite known as ASTOS where only minimal differences in the output trajectory were noticed. Afterwards another test was performed to verify the method used by Steele-Flight for engine selection. In this test, Steele-Flight was provided a vehicle model based on the German Saenger TSTO RLV concept and models of turbofans, turbojets, ramjets, scramjets and rockets. Steele-Flight explored the design space through the use of a Genetic Algorithm to find the optimal engine combination to maximize payload. The results output by Steele-Flight were verified by a study in which the designer manually chose the engine combinations one at a time, running each through the trajectory optimization routine to determine the best engine combination. For the most part, these methods yielded the same optimal engine configurations with only minor variation. The code itself provides RLV researchers with a new tool to perform conceptual level engine selection from a gathering of user provided conceptual engine data models and RLV structural designs and trajectory optimization for fixed RLV designs and fixed mission requirement. / Master of Science

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<p>In this thesis deposit and loan rate-setting equations for chartered banks are derived on the premise that these rates are set so as to maximize the banking industry's profits. Because of the oligopolistic nature of the Canadian banking industry and because explicit collusion is illegal an optimizing model of chartered bank ratesetting behaviour was integrated into the institutional framework of the Canadian banking industry.</p> <p>To do this a two-stage model of the Canadian banking industry is proposed. At the first stage, the prime rate on loans and the rate on non-chequing personal savings deposits are set so as to maximize the collective profits of the industry. To circumvent the illegality of explicit collusion a price leadership model is developed. In this model it is not one of the individual banks which is a price leader, but rather changes in the bank rate act as a signal for all of the individual banks to change their rates. The formulation proposed was tested and the hypothesis accepted for both rates. The second stage of the two-stage model is concerned with asset and liability management and is not developed in this thesis.</p> <p>A second contribution of this thesis is to take into account chartered bank rate-setting behaviour when estimating demand equations for both business loans and nonchequing personal savings deposits. When the estimation procedure used reflects these problems it is found that there are large changes in the values of the estimated coefficients in the demand functions for loans and deposits, compared to the simple O.L.S. estimates of the parameter values.</p> / Doctor of Philosophy (PhD)

Bayesian optimal designs have received increasing attention in recent years, especially in biomedical and clinical trials. Bayesian design procedures can utilize the available prior information of the unknown parameters so that a better design can be achieved. However, a difficulty in dealing with the Bayesian design is the lack of efficient computational methods. In this research, a hybrid computational method, which consists of the combination of a rough global optima search and a more precise local optima search, is proposed to efficiently search for the Bayesian D-optimal designs for multi-variable generalized linear models. Particularly, Poisson regression models and logistic regression models are investigated. Designs are examined for a range of prior distributions and the equivalence theorem is used to verify the design optimality. Design efficiency for various models are examined and compared with non-Bayesian designs. Bayesian D-optimal designs are found to be more efficient and robust than non-Bayesian D-optimal designs. Furthermore, the idea of the Bayesian sequential design is introduced and the Bayesian two-stage D-optimal design approach is developed for generalized linear models. With the incorporation of the first stage data information into the second stage, the two-stage design procedure can improve the design efficiency and produce more accurate and robust designs. The Bayesian two-stage D-optimal designs for Poisson and logistic regression models are evaluated based on simulation studies. The Bayesian two-stage optimal design approach is superior to the one-stage approach in terms of a design efficiency criterion. / Ph. D.

The trend in isolated DC/DC bus converters is to increase the output power in the same brick form factors that have been used in the past. Traditional intermediate bus converters (IBCs) use silicon power metal oxide semiconductor field effect transistors (MOSFETs), which recently have reached the limit in terms of turn on resistance (RDSON) and switching frequency. In order to make the IBCs smaller, the switching frequency needs to be pushed higher, which will in turn shrink the magnetics, lowering the converter size, but increase the switching related losses, lowering the overall efficiency of the converter. Wide-bandgap semiconductor devices are becoming more popular in commercial products and gallium nitride (GaN) devices are able to push the switching frequency higher without sacrificing efficiency. GaN devices can shrink the size of the converter and provide better efficiency than its silicon counterpart provides. A survey of current IBCs was conducted in order to find a design point for efficiency and power density. A two-stage converter topology was explored, with a multiphase buck converter as the front end, followed by an LLC resonant converter. The multiphase buck converter provides regulation, while the LLC provides isolation. With the buck converter providing regulation, the switching frequency of the entire converter will be constant. A constant switching frequency allows for better electromagnetic interference (EMI) mitigation. This work includes the details to design and implement a hard-switched multiphase buck converter with planar magnetics using GaN devices. The efficiency includes both the buck efficiency and the overall efficiency of the two-stage converter including the LLC. The buck converter operates with 40V - 60V input, nominally 48V, and outputs 36V at 1 kW, which is the input to the LLC regulating 36V – 12V. Both open and closed loop was measured for the buck and the full converter. EMI performance was not measured or addressed in this work. / Master of Science / Traditional silicon devices are widely used in all power electronics applications today, however they have reached their limit in terms of size and performance. With the introduction of gallium nitride (GaN) field effect transistors (FETs), the limits of silicon can now be passed with GaN providing better performance. GaN devices can be switched at higher switching frequencies than silicon, which allows for the magnetics of power converters to be smaller. GaN devices can also achieve higher efficiency than silicon, so increasing the switching frequency will not hurt the overall efficiency of the power converter. GaN devices can handle higher switching frequencies and larger currents while maintaining the same or better efficiencies over their silicon counterparts. This work illustrates the design and implementation of GaN devices into a multiphase buck converter. This converter is the front end of a two-stage converter, where the buck will provide regulation and the second stage will provide isolation. With the use of higher switching frequencies, the magnetics can be decreased in size, meaning planar magnetics can be used in the power converter. Planar magnetics can be placed directly inside of the printing circuit board (PCB), which allows for higher power densities and easy manufacturing of the magnetics and overall converter. Finally, the open and closed loop were verified and compared to the current converters that are on the market in the 48V – 12V area of intermediate bus converters (IBCs).