DIMENSION REDUCTION FOR POWER SYSTEM MODELING USING PCA METHODS CONSIDERING INCOMPLETE DATA READINGS

Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental results show that EM-PCA method is more effective and more accurate for dimension reduction of power system measurement data than traditional PCA method when dealing with large portion of missing data set.

In-situ electrical, mechanical and electrochemical characterizations of one-dimensional nanostructures

One-dimensional nanostructures initiated new aspects to the materials applications due to their superior properties compared to the bulk materials. Properties of nanostructures have been characterized by many techniques and used for various device applications. However, simultaneous correlation between the physical and structural properties of these nanomaterials has not been widely investigated. Therefore, it is necessary to perform in-situ study on the physical and structural properties of nanomaterials to understand their relation. In this work, we will use a unique instrument to perform real time atomic force microscopy (AFM) and scanning tunneling microscopy (STM) of nanomaterials inside a transmission electron microscopy (TEM) system. This AFM/STM-TEM system is used to investigate the mechanical, electrical, and electrochemical properties of boron nitride nanotubes (BNNTs) and Silicon nanorods (SiNRs). BNNTs are one of the subjects of this PhD research due to their comparable, and in some cases superior, properties compared to carbon nanotubes. Therefore, to further develop their applications, it is required to investigate these characteristics in atomic level. In this research, the mechanical properties of multi-walled BNNTs were first studied. Several tests were designed to study and characterize their real-time deformation behavior to the applied force. Observations revealed that BNNTs possess highly flexible structures under applied force. Detailed studies were then conducted to understand the bending mechanism of the BNNTs. Formations of reversible ripples were observed and described in terms of thermodynamic energy of the system. Fracture failure of BNNTs were initiated at the outermost walls and characterized to be brittle. Second, the electrical properties of individual BNNTs were studied. Results showed that the bandgap and electronic properties of BNNTs can be engineered by means of applied strain. It was found that the conductivity, electron concentration and carrier mobility of BNNTs can be tuned as a function of applied stress. Although, BNNTs are considered to be candidate for field emission applications, observations revealed that their properties degrade upon cycles of emissions. Results showed that due to the high emission current density, the temperature of the sample was increased and reached to the decomposition temperature at which the B-N bonds start to break. In addition to BNNTs, we have also performed in-situ study on the electrochemical properties of silicon nanorods (SiNRs). Specifically, lithiation and delithiation of SiNRs were studied by our STM-TEM system. Our observations showed the direct formation of Li22Si5 phases as a result of lithium intercalation. Radial expansion of the anode materials were observed and characterized in terms of size-scale. Later, the formation and growth of the lithium fibers on the surface of the anode materials were observed and studied. Results revealed the formation of lithium islands inside the ionic liquid electrolyte which then grew as Li dendrite toward the cathode material.

Optical hysteresis of ridge waveguide magnetic garnet films and cavities in two-dimensional magneto-photonic crystal slabs

Magnetic iron garnets as well as magnetic photonic crystals are of great interests in magneto-optic applications such as isolators, current captors, circulators, TE-TM mode conversion, wavelength accordable filters, optical sensors and switches, all of which provide a promising platform for future integrated optical circuits. In the present work, two topics are studied based on magnetic iron garnet films. In the first part, the characteristics of the magnetization are investigated for ridge waveguides fabricated on (100) oriented iron garnet thin films. The magnetic response in magneto-optic waveguides patterned on epitaxial magnetic garnet films depends on the crystallographic orientation of the waveguides and the magnetic anisotropy of the material. These can be studied by polarization rotation hysteresis loops, which are related to the component of magnetization parallel to the light propagation direction and the linear birefringence. Polarization rotation hysteresis loops for low birefringence waveguides with different orientations are experimentally investigated. Asymmetric stepped curves are obtained from waveguides along, due to the large magnetocrystalline anisotropy in the plane. A model based on the free energy density is developed to demonstrate the motion of the magnetization and can be used in the design of magneto-optic devices. The second part of this thesis focuses on the design and fabrication of high-Q cavities in two-dimensional magneto-photonic crystal slabs. The device consists of a layer of silicon and a layer of iron garnet thin film. Triangular lattice elliptical air holes are patterned in the slab. The fundamental TM band gap overlaps with the first-order TE band gap from 0374~0.431(a/λ) showing that both TE and TM polarization light can be confined in the photonic crystals. A nanocavity is designed to obtain both TE and TM defect modes in the band gaps. Additional work is needed to overlap the TE and TM defect modes and obtain a high-Q cavity so as to develop miniaturized Faraday rotators.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.