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<p>This thesis is submitted by Weiping Tang on August 2, 2011.</p> / <p>Several control schemes for monitoring process mean shifts, including cumulative sum (CUSUM), weighted cumulative sum (WCUSUM), adaptive cumulative sum (ACUSUM) and exponentially weighted moving average (EWMA) control schemes, display high performance in detecting constant process mean shifts. However, a variety of dynamic mean shifts frequently occur and few control schemes can efficiently work in these situations due to the limited window for catching shifts, particularly when the mean decreases rapidly. This is precisely the case when one uses the residuals from autocorrelated data to monitor the process mean, a feature often referred to as forecast recovery. This thesis focuses on detecting a shift in the mean of a time series when a forecast recovery dynamic pattern in the mean of the residuals is observed. Specifically, we examine in detail several particular cases of the Autoregressive Integrated Moving Average (ARIMA) time series models. We introduce a new upper-sided control chart based on the Exponentially Weighted Moving Average (EWMA) scheme combined with the Fast Initial Response (FIR) feature. To assess chart performance we use the well-established Average</p> <p>Run Length (ARL) criterion. A non-homogeneous Markov chain method is developed for ARL calculation for the proposed chart. We show numerically that the proposed procedure performs as well or better than the Weighted Cumulative Sum (WCUSUM) chart introduced by Shu, Jiang and Tsui (2008), and better than the conventional CUSUM, the ACUSUM and the Generalized Likelihood Ratio Test (GLRT) charts. The methods are illustrated on molecular weight data from a polymer manufacturing process.</p> / Master of Science (MSc)

<p>This thesis deals with combinatorial and geometric aspects of linear optimization, and consists of two parts.</p> <p>In the first part, we address a conjecture formulated in 2008 and stating that the largest possible average diameter of a bounded cell of a simple hyperplane arrangement of n hyperplanes in dimension d is not greater than the dimension d. The average diameter is the sum of the diameters of each bounded cell divided by the total number of bounded cells, and then we consider the largest possible average diameter over all simple hyperplane arrangements. This quantity can be considered as an indication of the average complexity of simplex methods for linear optimization. Previous results in dimensions 2 and 3 suggested that a specific type of extensions, namely the covering extensions, of the cyclic arrangement might achieve the largest average diameter. We introduce a method for enumerating the covering extensions of an arrangement, and show that covering extensions of the cyclic arrangement are not always among the ones achieving the largest diameter.</p> <p>The software tool we have developed for oriented matroids computation is used to exhibit a counterexample to the hypothesized minimum number of external facets of a simple arrangement of n hyperplanes in dimension d; i.e. facets belonging to exactly one bounded cell of a simple arrangement. We determine the largest possible average diameter, and verify the conjectured upper bound, in dimensions 3 and 4 for arrangements defined by no more than 8 hyperplanes via the associated uniform oriented matroids formulation. In addition, these new results substantiate the hypothesis that the largest average diameter is achieved by an arrangement minimizing the number of external facets.</p> <p>The second part focuses on the colourful simplicial depth, i.e. the number of colourful simplices in a colourful point configuration. This question is closely related to the colourful linear programming problem. We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in R^d is contained in at least (d+1)²/2 simplices with one vertex from each set. This improves the previously established lower bounds for d>=4 due to Barany in 1982, Deza et al in 2006, Barany and Matousek in 2007, and Stephen and Thomas in 2008.</p> <p>We also introduce the notion of octahedral system as a combinatorial generalization of the set of colourful simplices. Configurations of low colourful simplicial depth correspond to systems with small cardinalities. This construction is used to find lower bounds computationally for the minimum colourful simplicial depth of a configuration, and, for a relaxed version of the colourful depth, to provide a simple proof of minimality.</p> / Doctor of Philosophy (PhD)

This dissertation describes the development of an intelligent non-invasive thermal energy flow rate sensor for laminar and turbulent pipe flows. Energy flow rate is the thermal energy that is carried by a fluid, for example, in a pipe to heat or cool a space in a building. It can be measured by an energy flow rate sensor which consists of a volume flow rate meter and supply and return fluid temperature sensors to bill the users for their energy usage. A non-invasive, low-cost, and easy to install thermal energy flow rate sensor based on thermal interrogation transient heat flux and temperature measurements has been developed to measure fluid velocity and fluid temperature in pipes. This sensor can be used for different pipe diameters, different pipe materials, and different viscous fluids. The transient measurements are made on the outer surface of a pipe by using a heat flux sensor and a thin-film thermocouple which are covered by a thin-film heater. A one-dimensional transient thermal model is applied before and during activation of the external heater along with a parameter estimation code to provide estimates of the fluid heat transfer coefficient and apparent thermal resistance between the thermocouple and the pipe surface. This dissertation contributes to the sensor's development in three ways. First, a new design is developed by using a single layer of Kapton tape with an adhesive (dielectric material) between the thermocouple foils and the pipe wall to isolate the thermocouple electrically from the pipe surface. This new design gives accurate and reliable estimates of the internal mean fluid temperature without environmental interference. Second, this new sensor design is tested for turbulent pipe flows with two different pipe diameters ( = 25.4 mm and = 12.7 mm) and two different viscous fluids (diesel oil and water). Experiments are completed over a large range of fluid velocity from 0.2 m/s to 5.5 m/s and a range of fluid temperature from 20 ℃ to 50 ℃. The estimated parameters, heat transfer coefficient and apparent thermal resistance, are correlated with the fluid velocity and fluid temperature. This sensor gives a good correlation, repeatability, and sensitivity between the estimated parameters and the fluid velocities with an accurate estimation of the fluid temperatures without environmental interference. Third, this sensor is tested for laminar flow in pipes over a range of fluid velocity from 0.049 m/s to 0.45 m/s and a range of fluid temperature from 20 ℃ to 50 ℃. A new empirical correlation between the estimated parameters and the laminar fluid velocity has been developed. The results show that this sensor gives lower sensitivity and accuracy between the estimated parameters and the fluid velocity and fluid temperature for the laminar flow. / Doctor of Philosophy / Heating or cooling is responsible for approximately 50% of the total energy consumption in a building. Budlings' energy consumption can be measured by energy flow rate sensors (measuring both fluid velocity and fluid temperature). Current energy flow rate sensors are invasive (requiring installation inside the system and disturbing the flow) which create unacceptable risks, such as fluid leaks and damage the equipment. Other energy flow rate sensors based on ultrasonic and electromagnetic technologies are non-invasive which can be installed on the outside of the pipe without disturbing the flow, however, they are expensive to buy, difficult to install, and hard to calibrate. Therefore, developing new sensor techniques is necessary, preferably non-invasive, low-cost, and easy to install. In this dissertation, a new non-invasive, low-cost, and easy to install thermal energy flow rate sensor has been designed, developed, and tested. This thermal sensor is based on transient heat flux and temperature measurements which are made on the outside of a copper pipe surface by using a heat flux sensor and a thermocouple. This sensor is used to estimate the energy consumption by measuring a fluid velocity and a fluid temperature in heating and cooling pipe applications for different pipe diameters, different fluids, and different pipe materials. A parameter estimation code is developed to match the analytical and experimental sensor temperature values and to estimate the unknown system parameters. These parameters are correlated with the fluid velocity and fluid temperature. Experiments are completed over a large range of fluid velocity from 0.049 m/s to 5.5 m/s and a range of fluid temperature from 20℃ to 50℃. The encouraging measurement results show that this sensor gives a good correlation, repeatability, accuracy, and sensitivity between the estimated parameters and the fluid velocities with an accurate estimation of the fluid temperatures to allow calculation of the thermal energy consumption.

A systematic and versatile method to derive accurate and efficient Circuit Oriented Large Signal Average Models (COLSAMs) that approximate the slow dynamics manifold of the moving average values of the relevant state variables for Pulse-Width Modulated (PWM) dc to dc and three-phase to dc power converters is developed. These COLSAMs can cover continuous conduction mode (CCM) as well as discontinuous conduction mode (DCM) of operation and they are over one order of magnitude cheaper, computation wise, than the switching models. This method leads primarily to simple and effective input-output oriented models that represent transfer as well as loading characteristics of the converter. Sine these models consist of time invariant continuous functions they can be linearized at an operating point in order to obtain small-signal transfer functions that approximate the dynamics of the original PWM system around an orbit. The models are primarily intended for software circuit simulators (i.e. Spice derived types, Saber, Simplorer, etc), to take advantage of intrinsic features such as transient response, linearization, transfer function, harmonic distortion calculations, without having to change simulation environment. Nevertheless, any mathematics simulator for ordinary differential equations can be used with the set of equations obtained through application of Kirchoff's laws to the COLSAMs. Furthermore, the COLSAMs provide physical insight to help with power stage and control design, and they allow easy interconnection among themselves, as well as with switching models, for complete analysis at different scales (time, signal level, complexity; interconnectivity). A new average model for the Zero-Voltage Switched Full-Bridge (ZVS-FB) PWM Converter is developed with the above method and its high accuracy is verified with simulations from a switching behavioral model for several circuit component values for both CCM and DCM. Intrinsic positive damping effects and special delay characteristics created by an energy holding element in a saturable reactor-based Zero-Voltage Zero-Current Switched Full-Bridge (ZVZCS-FB) PWM converter are explained for the first time by a new average model. Its large signal predictions match very well those from switch model simulations whereas its small-signal predictions are verified with experimental results from 3.5 kW prototype modules. The latter are used in a multi-module converter to supply the DC power bus in and aircraft. The design of control loops for the converter is based on the new model and its linearization. The ZVZCS-FB PWM converter's average model above is extended to deal with interconnection issues and constraints in a Quasi-Single Stage (QSS) Zero-Voltage Zero-Current Switched (ZVZCS) Three-Phase Buck Rectifier. The new model reveals strong nonlinear transfer characteristics for standard Space Vector Modulation (SVM), which lead to high input current distortion and output voltage ripple inadmissible in telecommunications applications. Physical insight provided by this average model led to the development of a combined modified SVM and feed-forward duty-cycle compensation scheme to reliably minimize the output voltage ripple. Experimental results from a 6 kW prototype validate large signal model for standard and modified SVM, with and without duty-cycle compensation scheme. / Ph. D.

The performance of a mobile satellite communications link is conditioned by the characteristics of the propagation path between a satellite and mobile users. The most important propagation effect in land mobile satellite system is roadside attenuation of the signals due to vegetation or urban structures. System designers should have the most reliable information about the statistics of the propagation channel to build reliable systems that can compensate for bad propagation conditions. In 1998, the Virginia Tech Antenna Group developed a simulator, PROSIM, to simulate a propagation channel in the case of roadside tree attenuation in land mobile satellite systems. This thesis describes some improvements to PROSIM, and the adaptation and validation of PROSIM for Digital Audio Radio Satellite systems operating at S-band frequencies. The performance of the simulator for S-band frequencies was evaluated through a measurement campaign conducted with the XM Radio signals at 2.33 GHz in various propagation environments. Finally, additional results on dual satellite systems and fade correlation are described. / Master of Science