Ultrahigh-dimensional variable selection is of great importance in the statistical research. And independence screening is a powerful tool to select important variable when there are massive variables. Some commonly used independence screening procedures are based on single replicate data and are not applicable to longitudinal data. This motivates us to propose a new Sure Independence Screening (SIS) procedure to bring the dimension from ultra-high down to a relatively large scale which is similar to or smaller than the sample size. In chapter 2, we provide two types of SIS, and their iterative extensions (iterative SIS) to enhance the finite sample performance. An upper bound on the number of variables to be included is derived and assumptions are given under which sure screening is applicable. The proposed procedures are assessed by simulations and an application of them to a study on systemic lupus erythematosus illustrates the practical use of these procedures. After the variables screening process, we then explore the relationship among the variables. Graphical models are commonly used to explore the association network for a set of variables, which could be genes or other objects under study. However, graphical modes currently used are only designed for single replicate data, rather than longitudinal data. In chapter 3, we propose a penalized likelihood approach to identify the edges in a conditional independence graph for longitudinal data. We used pairwise coordinate descent combined with second order cone programming to optimize the penalized likelihood and estimate the parameters. Furthermore, we extended the nodewise regression method the for longitudinal data case. Simulation and real data analysis exhibit the competitive performance of the penalized likelihood method. / Doctor of Philosophy / Longitudinal data have received a considerable amount of attention in the fields of health science studies. The information from this type of data could be helpful with disease detection and control. Besides, a graph of factors related to the disease can also be built up to represent their relationships between each other. In this dissertation, we develop a framework to find out important factor(s) from thousands of factors in longitudinal data that is/are related to the disease. In addition, we develop a graphical method that can show the relationship among the important factors identified from the previous screening. In practice, combining these two methods together can identify important factors for a disease as well as the relationship among the factors, and thus provide us a deeper understanding about the disease.

The conventional power factor correction circuit has a fixed output voltage. However, in some applications, a PFC circuit with a wide output voltage range is needed. A single phase power factor correction circuit with wide output voltage range is developed in this work. After a comparison of two main power stage candidates (Buck+Boost and Sepic) in terms of efficiency, complexity, cost and device rating, the buck+boost converter is employed as the variable output PFC power stage. From the loss analysis, this topology has a high efficiency from light load to heavy load. The control system of the variable output PFC circuit is analyzed and designed. Charge average current sensing scheme has been adopted to sense the input current. The problem of high input harmonic currents at low output voltage is discussed. It is found that the current loop gain and cross over frequency will change greatly when the output voltage changes. To solve this problem, an automatic gain control scheme is proposed and a detailed circuit is designed and added to the current loop. A modified input current sensing scheme is presented to overcome the problem of an insufficient phase margin of the PFC circuit near the maximum output voltage. The charge average current sensing circuit will be bypassed automatically by a logical circuit when the output voltage is higher than the peak line voltage. Instead, a resistor is used to sense the input current at that condition. Therefore, the phase delay caused by the charge average current sensing circuit is avoided. The design and analysis are based on a novel air conditioner motor system application. Some detailed design issues are discussed. The experimental results show that the variable output PFC circuit has good performance in the wide output voltage range, under both the Boost mode when the output voltage is high and the Buck+Boost mode when the output voltage is low. / Master of Science

Previous applications have shown that a wingtip treatment on a commercial airliner will reduce drag and increase fuel efficiency and the most common types of treatment are blended winglets and raked wingtips. With Boeing currently investigating novel designs for its next generation of airliners, a variable geometry raked wingtip novel control effector (VGRWT/NCE) was studied to determine the aerodynamic performance benefits over an untreated wingtip. The Boeing SUGAR design employing a truss-braced wing was selected as the baseline. Vortex lattice method (VLM) and computational fluid dynamics (CFD) software was implemented to analyze the aerodynamic performance of such a configuration applied to a next-generation, transonic, mid-range transport aircraft. Several models were created to simulate various sweep positions for the VGRWT/NCE tip, as well as a baseline model with an untreated wingtip. The majority of investigation was conducted using the VLM software, with CFD used largely as a validation of the VLM analysis. The VGRWT/NCE tip was shown to increase the lift of the wing while also decreasing the drag. As expected, the unswept VGRWT/NCE tip increases the amount of lift available over the untreated wingtip, which will be very beneficial for take-off and landing. Similarly, the swept VGRWT/NCE tip reduced the drag of the wing during cruise compared to the unmodified tip, which will favorably impact the fuel efficiency of the aircraft. Also, the swept VGRWT/NCE tip showed an increase in moment compared to the unmodified wingtip, implying an increase in stability, as well providing an avenue for roll control and gust alleviation for flexible wings. CFD analysis validated VLM as a useful low fidelity tool that yielded quite accurate results. The main results of this study are tabulated "deltas" in the forces and moments on the VGRWT/NCE tip as a function of sweep angle and aileron deflection compared to the baseline wing. A side study of the effects of the joint between the main wing and the movable tip showed that the drag impact can be kept small by careful design. / Master of Science

<p dir="ltr">To ensure safety, traditional industrial robots must operate within cages to separate them from human workers. This requirement has led to the rapid development of collaborative robots (cobots) designed to work closely to humans. However, existing cobots often prioritize <a href="" target="_blank">performance </a>aspects, such as precision, speed, and payload capacity, or prioritize safety, leading to a challenging balance between them. To address this issue, this dissertation introduces innovative concepts and methodologies for variable stiffness mechanisms. These mechanisms are applied to create easily fabricated cobot components to allow for controllable trade-offs between safety and performance in human-robot collaboration intrinsically. Additionally, the end-effectors developed based on these mechanisms enable the flexible and adaptive gripping of objects, enhancing the utility and efficiency of cobots in various applications.</p><p dir="ltr">This article-based dissertation comprises five peer-reviewed articles. The first essay introduces a reconfigurable variable stiffness parallel-guided beam (VSPB), whose stiffness can be adjusted discretely. An accurate stiffness model is also established, capable of leveraging a simple and reliable mechanical structure to achieve broad stiffness variation. The second essay discusses several discrete variable stiffness actuators (DVSAs) suitable for robotic joints. These DVSAs offer high stiffness ratios, rapid shifting speeds, low energy consumption, and compact structures compared to most existing variable stiffness actuators. The third essay introduces a discrete variable stiffness link (DVSL), applied to the robotic arm of a collaborative robot. Comprising three serially connected VSPBs, it offers eight different stiffness modes to accommodate diverse application scenarios, representing the first DVSL in the world. The fourth essay presents a variable stiffness gripper (VSG) with two fingers, each capable of continuous stiffness adjustment. The VSG is a low-cost, customizable universal robotic hand capable of successfully grasping objects of different types, shapes, weights, fragility, and hardness. The fifth essay introduces another robotic hand, the world's first discrete variable stiffness gripper (DVSG). It features four different stiffness modes for discrete stiffness adjustment in various gripper positions by on or off the ribs. Therefore, unlike the VSG, the DVSG focuses more on adaptability to object shapes during grasping.</p><p dir="ltr">These research achievements have the potential to facilitate the construction and popularize of next-generation collaborative robots, thereby enhancing productivity in industry and possibly leading to the integration of personal robotic assistants into countless households.</p>

Variable Frequency Drives (VFDs) are utilized in commercial and industrial facilities to improve motor efficiency and provide process flexibility. VFDs are nonlinear loads that inject harmonic currents into the power system, and result in harmonic voltages across the system impedance. This harmonic distortion can negatively impact the performance of other sensitive loads in the system. If a VFD serves a critical function, it may be necessary to supply the VFD from a Diesel Generator or Uninterruptible Power Supply (UPS). These sources have relatively high impedance when compared to a standard utility source, and will result in greater harmonic voltage distortion. This increases the likelihood of equipment failure due to harmonics. The full extent of the impact, however, is typically unknown until an extensive harmonic analysis is performed or the system is installed and tested. This thesis evaluates the impact that source impedance has on the harmonic voltage distortion that is produced by nonlinear loads such as VFDs. An ideal system of varying source types (Utility, Generator and UPS) and varying VFD rectifier technologies (6-Pulse, 12-Pulse and 18-Pulse) is created to perform this analysis and plot the results. The main output of this thesis is a simplified methodology for harmonic analysis that can be implemented when designing a power system with a VFD serving a critical function and a high impedance source like a generator or UPS. Performing this analysis will help to ensure that other sensitive loads will operate properly in the system. / Master of Science

Rubber V-belt Continuously Variable Transmissions (CVT's) are commonplace in the Baja SAE collegiate design competition, and are also used widely in the power sports industry. These transmissions offer benefits of simplicity in mechanical design, consisting of only two pulleys, and are easy to use. While most teams in the competition use commercially available designs, custom designs are becoming more common, and the Baja team at Virginia Tech has used custom CVT's since the 2014 season. The design of these CVT's has relied heavily on trial and error, requiring significant adjustments to be made during the testing phase. In addition, only qualitative information is known for the relationship between efficiency and design parameters, such as sheave angle. The goal of this thesis is to create an improved V-belt model that may be used as a design tool. This model provides quantitative information about efficiency that can be used to make more informed design decisions. The belt model also provides insight into the magnitude and relationship between the axial forces in the pulleys. This can be used to create an initial design that is more accurate, and possibly reduce the time required for tuning. A CVT dynamometer was constructed to validate the analytical results for efficiency, and this will also serve as a tuning tool for future Baja teams at Virginia Tech. This thesis will advance the state of the custom CVT design and testing process at Virginia Tech, and hopefully lead to improved results at competition in the future. / Master of Science / Baja SAE is an annual collegiate competition where students design and build an off-road vehicle. Many teams choose to use Continuously Variable Transmissions (CVT’s) in order to maximize the efficiency of the vehicle’s transmission. By continually shifting ratios, CVT’s allow internal combustion engines to always run at peak performance. There are several types of CVT’s, but the most common one used in Baja SAE and the power sports industry is a rubber V-belt design that is controlled mechanically with springs and flyweights. While these devices are used extensively, the underlying dynamics are not well-documented in literature. The Baja team at Virginia Tech builds a custom CVT every year for the vehicle, but the success of the design relies heavily on tuning through trial and error. A better understanding of the dynamics of the belt will result in better initial designs, and will help to reduce the amount of tuning required for the success of the design. This thesis offers an improved dynamic model for a CVT belt, and validates the results of this model through testing on a custom-built dynamometer. This model is also able to predict the efficiency of the transmission, and these results may be used to influence design decisions by predicting their effects on performance. The results of this research will improve the design process for a rubber V-belt CVT and hopefully lead to improved results at competition for the Baja team at Virginia Tech.

The adjustable-pitch setting on an axial-flow fan is the most common method of controlling airflow for primary coal mine ventilation. With this method, the fan operates at a constant speed dictated by its motor design. The angles of the blades are adjusted to change the amount of airflow and pressure to meet ventilation requirements. Typically, the fan does not operate at its optimum efficiency, which only occurs in a narrow band of air pressures and quantities. The use of variable frequency drives (VFDs), which control fan speed, provides a solution to this problem. VFDs are already used in various similar applications such as pumping and building ventilation. New technology now enables efficient VFD operation in medium voltage (2,300 – 6,900 V) fan applications. The primary benefit of a variable frequency drive is that it allows motors to operate at reduced speeds, and thus at a lower power, without a loss of torque. VFDs also allow for efficient operation over the entire life of the fan. The technical considerations of using a VFD are presented in this work, along with a method for choosing and modeling a variable speed fan to achieve maximum energy savings. As a part of this research, a spreadsheet program was developed that will calculate the optimum fan operating speed based on given fan data and specified operating conditions. A representative room and pillar coal mine is modeled to illustrate the selection and modeling process and as an example of the economic implications of using a VFD. The use of VFDs is shown to potentially yield large energy savings by increasing the fan efficiency over the life of the mine. Although there are definite power savings while using variable speed fans, the magnitude of these savings is specific to an individual mine and the operating conditions encountered. The determination of whether the use of VFDs is economically feasible requires analysis for the specific mine and its operating conditions. This work provides the background and a method for such an evaluation. / Master of Science

Yes / Fluid Catalytic Cracking (FCC) unit is an important unit of modern refineries and any improvement in the unit’s operations and design to increase yield and meet the ever increasing demand for fuel brings about the overall profitability of the FCC. In this work, simulation of an FCC riser of varied diameter was carried out to improve the unit’s operations and design, and the results are compared with risers of different diameters. The riser with varied diameter produces 53.4 wt%, a 3.18% increased yield of gasoline at low catalyst to oil (C/O) ratio of 1.27 compared to 51.7 wt% from a 1 m diameter riser. At increased C/O ratio, more gases and coke are produced in the varied diameter riser. Larger diameter demands more catalyst but yields more gases. Process variables can be directly correlated with yield of gasoline, which can aid process design.

An application of binary state latch device with proper real-time control algorithm for energy redistribution application is introduced in this thesis. Unlike traditional tuned vibration absorber, the latch device can be viewed as variable semi-active dampers such as magnetorheological (MR) and piezoelectric friction dampers. The distinct difference between other semi-active dampers and our latch device is that other semi-active dampers can provide continuous resistance according to the amount of input current, however, the binary latch device can only provide two different values of resistance - either the maximum or no resistance at all. This property brings the latch possibly having higher maximum and minimum ratio of resistance than MR dampers. As for the operating structure, the mechanism of latch element is nearly the same as the piezoelectric friction dampers which the resistance force is provided according to the normal force acting on two rough plates. Nonetheless, because of the characteristic of the binary states output of the latch element, this make it very different from the ordinary variable dampers. Since it is either being turned on or turned off, a novel control law is required for shifting energy. Also, because of the simplicity of the binary states output, it is very accessible to implement the controller on Field Programmable Gate Array (FPGA). With this accessibility, it is promising to apply plenty of latch elements in the same time for large scale application, such as multi-agent networks. In this thesis, an energy-based analytic solution is proposed to illustrate the universal latch-off condition. And a latch-on condition under ideal situations is discussed. At the end, a control law under nonideal condition is being suggested for real-time periodically excited system. We found that energy redistribution is achievable by using the proper control law under fairly broad conditions. / Master of Science / A simple dynamic structure with a latch element device is introduced in this thesis. We found that energy redistribution is achievable by using a particular control law under specific condition. A energy-based analytic solution is introduced to illustrate the strategy of the energy transfer process under ideal condition. At the end of the thesis, we proposed non-single switch algorithm for real-time application. In this thesis, we found that energy redistribution is possible for this one dimentional structure. The latch devices can be implemented into two dimensional networks. If enery redistrbution is also possible for two dimentional multi-agent networks, it is promising to use it to do not only energy redirection to protect target from vibration but we can also accumulate the energy for energy harvesting.

Genome-wide associated study (GWAS) aims to identify associated single nucleotide polymorphisms (SNP) for phenotypes. SNP has the characteristic that the number of SNPs is from hundred of thousands to millions. If p is the number of SNPs and n is the sample size, it is a p>>n variable selection problem. To solve this p>>n problem, the common method for GWAS is single marker analysis (SMA). However, since SNPs are highly correlated, SMA identifies true causal SNPs with high false discovery rate. In addition, SMA does not consider interaction between SNPs. In this dissertation, we propose novel Bayesian variable selection methods BG2 and IBG3 for non-Gaussian GWAS data. To solve ultra-high dimension problem and highly correlated SNPs problem, BG2 and IBG3 have two steps: screening step and fine-mapping step. In the screening step, BG2 and IBG3, like SMA method, only have one SNP in one model and screen to obtain a subset of most associated SNPs. In the fine-mapping step, BG2 and IBG3 consider all possible combinations of screened candidate SNPs to find the best model. Fine-mapping step helps to reduce false positives. In addition, IBG3 iterates these two steps to detect more SNPs with small effect size. In simulation studies, we compare our methods with SMA methods and fine-mapping methods. We also compare our methods with different priors for variables, including nonlocal prior, unit information prior, Zellner-g prior, and Zellner-Siow prior. Our methods are applied to substance use disorder (alcohol comsumption and cocaine dependence), human health (breast cancer), and plant science (the number of root-like structure). / Doctor of Philosophy / Genome-wide associated study (GWAS) aims to identify genomics variants for targeted phenotype, such as disease and trait. The genomics variants which we are interested in are single nucleotide polymorphisms (SNP). SNP is a substitution mutation in the DNA sequence. GWAS solves the problem that which SNP is associated with the phenotype. However, the number of possible SNPs is from hundred of thousands to millions. The common method for GWAS is called single marker analysis (SMA). SMA only considers one SNP's association with the phenotype each time. In this way, SMA does not have the problem which comes from the large number of SNPs and small sample size. However, SMA does not consider the interaction between SNPs. In addition, SNPs that are close to each other in the DNA sequance may highly correlated SNPs causing SMA to have high false discovery rate. To solve these problems, this dissertation proposes two variable selection methods (BG2 and IBG3) for non-Gaussian GWAS data. Compared with SMA methods, BG2 and IBG3 methods detect true causal SNPs with low false discovery rate. In addition, IBG3 can detect SNPs with small effect sizes. Our methods are applied to substance use disorder (alcohol comsumption and cocaine dependence), human health (breast cancer), and plant science (the number of root-like structure).