PhD, University of Cincinnati, 2009, Engineering : Electrical Engineering

Advances in material and construction technology has resulted in long span bridges being built with increasing regularity. Because of their aesthetic value and reduced construction requirements, among many other factors, cable-stayed bridges have become the design of choice for medium to long spans. As confidence grows in bridges of this type, their span lengths are being pushed to new boundaries. This has had the unavoidable consequence of creating a more lively structure. The collection of cables on a given stay bridge possess a wide range of closely spaced natural frequencies and any arbitrary source of excitation, i.e., wind, traffic, superstructure motion, is likely to provide energy at an arbitrary resonant cable(s) frequency.Cable-stayed bridge designs have continuously evolved in response to experiences encountered with previous designs. A study put forth by the Federal Highway Administration (FHWA) provided a collective discussion for what types of modifications have been applied and the degree of their success and put forth a consistent set of guidelines for reducing cable vibrations in future bridge designs. As mentioned in the study, many early bridge designs did not incorporate measures to reduce cable vibrations, but those that did have reported few cable concerns.Two cable-stayed bridges recently constructed by the Ohio Department of Transportation (ODOT) incorporate measures put forth by the FHWA study to mitigate stay motion. Also, following recent design trends, the stays at this bridge were constructed without the use of grout for the purpose of inspection and, if necessary, strand replacement. A common approach for objective condition assessment of the stays involves experimentally estimating cable force. The predominant method for estimating cable force uses an indirect approach where an accelerometer is mounted on the cable sheath, or a non-contact laser vibrometer is aimed at the sheath from a distance, to measure cable resonant frequencies an (open full item for complete abstract)

Committee: Arthur Helmicki PhD (Committee Chair); James Swanson PhD (Committee Member); Ali Minai PhD (Committee Member); Victor Hunt PhD (Committee Member); Randall Allemang PhD (Committee Member) Subjects: Civil Engineering; Electrical Engineering; Mechanical Engineering

MS, Kent State University, 2010, College of Arts and Sciences / Department of Mathematical Sciences

This thesis examines solution methods for large linear systems of equations with a matrix of ill-determined rank and an error-contaminated right-hand side. The numerical solution is delicate, because the matrix is very ill-conditioned and may be singular. To solve such systems, one replaces the system with one that is less sensitive to error a process known as regularization. This thesis focuses on the regularization method known as truncated iteration. A new algorithm is presented and compared to other existing methods.

Committee: Lothar Reichel PhD (Advisor); M. Kazim Khan PhD (Committee Member); Jing Li PhD (Committee Member) Subjects: Mathematics

PHD, Kent State University, 2021, College of Arts and Sciences / Department of Mathematical Sciences

To solve an ill-posed linear discrete inverse problem, we usually solve a nearby penalized (or regularized) problem instead, and when such regularized problem has a large scale, a iterative method based on Krylov subspace is usually the first choice. But these Krylov methods generate solution subspace sequentially and only one new solution subspace basis vector is computed at a time. Therefore it can be difficult to take advantage of multiprocessor or parallel computing. In this thesis we look into the potential of a certain type of non-iterative non-krylov methods which update its solution subspace with a “block”. First, in Chapter 2 we compare the performance of a classic Krylov method based on Golub-Kahan bidiagonalization with a randomized method on a Tikhonov regularized problem and discusses characteristics of linear discrete ill-posed problems that suited for solution by a randomized method. Then in Chapter 3 with the help of a randomized singular value decomposition(RSVD) method to approximate the singular value decomposition(SVD) of a large matrix A, we can therefore apply truncated singular value decomposition(TSVD) regularization method or modified TSVD method, where it is usually not feasible due to efficiency consideration. We also discussed possible remedy for situations when a linear discrete ill-posed problem doesn't present a randomized method favoring characteristics. And at last, in Chapter 4 we propose another non-iterative non-Krylov method based on discretized Chebyshev polynomials, which is competitive in experiments compared to a Krylov method and a randomized method.

Committee: Lothar Reichel (Committee Chair); Alessandro Buccini (Committee Co-Chair); Jing Li (Committee Member); Jun Li (Committee Member); Hassan Peyravi (Committee Member); Mikhail Nesterenko (Committee Member) Subjects: Applied Mathematics

Doctor of Philosophy (PhD), Ohio University, 2020, Mathematics (Arts and Sciences)

In regression analysis, sufficient dimension reduction (SDR) models have gained significant popularity in the past three decades. While many methods have been proposed in the literature regarding the analysis of SDR models, the vast majority are of the type called inverse regression methods, pioneered by the sliced inverse regression method (Li \cite{Li91}). Most of these inverse regression methods rely on a matrix, commonly known as the central matrix. One of the main goals of the analysis of SDR models is the estimation of the central space. An influence function (IF) is a tool that analyzes the performance of a statistical estimator. In this dissertation, we focus on the application of IF on the analysis of SDR models. There are various inverse regression methods in existence. But none of them stands out in all cases, and it is not clear which central matrix one should use out of numerous options existing in the literature. We propose an IF-based approach for selection of a best performing central matrix from a class of inverse regression methods, and we extend this approach to the situation where the data are partially contaminated. Asymptotic results are established, and an extensive simulation study is conducted to examine the performance of the proposed algorithm. Another issue in an SDR model is the estimation of the dimension of its central space. Based on the IF, we propose a measure that combines the eigenvalues of the central matrix and an IF measure to estimate the dimension of the central space. In addition, we analyze the IF of the functional of Benasseni's measure for a specific inverse regression method, the $k{\text-th}$ moment method.

Committee: Wei Lin (Advisor); Rida Benhaddou (Committee Member); Feng Yaqin (Committee Member); Justin Holub (Committee Member) Subjects: Mathematics; Statistics

Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering

Distributed sensor networks are growing in popularity for a large number of sensing applications ranging from environmental monitoring to military target classification and tracking. However, knowledge of the individual sensor positions is a prerequisite to obtaining meaningful information from measurements made by the sensors. With the scale of sensor networks rapidly increasing due to advances in communications and MEMS technology, an automatic localization service based on inter-sensor measurements is becoming an essential element in modern networks. This dissertation studies fundamental aspects of localization performance while deriving general results for singular estimation problems. Because inter-sensor measurements, such as distances or angles-of-arrival (AOA), are invariant to absolute positioning of the sensor scene, localizing sensors with an absolute reference, e.g., latitude and longitude, is inherently a singular estimation problem suffering from non-identifiability of the absolute location parameters. This results in a corresponding singular Fisher information matrix. We consider means of regularizing the absolute localization problem and devise novel performance characterizations by showing that the location parameters have a natural decomposition into relative configuration and centroid transformation components based on the singularity of the problem. A linear representation of the transformation manifold, which includes representations of rotation, translation, and scaling, is used for decomposition of general localization error covariance matrices. The unified statistical framework presented – which naturally generalizes to non-localization problems – allows us to quantify and bound performance in the relative and transformation domains. These tools facilitate analysis of relative-only algorithms while enabling new algorithm development to finely tune performance in each subdomain. The analysis is applied to a novel closed-form AOA-based localiza (open full item for complete abstract)

Committee: Randolph Moses (Advisor) Subjects: