Master of Science, Miami University, 2025, Mechanical and Manufacturing Engineering

Reduced order modeling (ROM) methods, such as those based upon Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), offer data-based turbulence modeling with potential applications for flow control. While these models are often cheaper than numerical approaches, their results require validation with source data. Within the literature, the metrics and standards used to validate these models are often inconsistent. Chabot (2014) produced a data-driven framework for validating these ROMs that used surrogate Markov models (SMMs) to compare how the system dynamics evolved rather than how any single metric evolved. These SMMs were constructed by clustering the flow data into different states of suitably similar flow fields, and the Markov model then mapped how likely each state was to transition into another. While this method was successful, there persisted an amount of uncertainty in how the outlier states within this clustering scheme were determined. Additionally, the study only examined the application of this procedure to POD-Galerkin ROMs. This study aims to tie the outlier state determination directly to the models' parent data. The study will also apply this procedure to ROMs generated from DMD to investigate how this framework's effectiveness carries over to different classes of ROMs.

Committee: Edgar Caraballo (Advisor); Andrew Sommers (Committee Member); Mehdi Zanjani (Committee Member) Subjects: Aerospace Engineering; Fluid Dynamics; Mathematics; Mechanical Engineering; Statistics

PhD, University of Cincinnati, 2019, Engineering and Applied Science: Mechanical Engineering

Efforts to develop a general framework to quantify nonlinearities have increased in the past few decades owing to a surge in the applicability of structures that exhibit nonlinearity. There are several excellent methods for system identification that can be used when the functional form of the nonlinearity is known or can be adequately guessed through analytical models. There is, however, a need for a black-box method that can detect, localize and characterize nonlinear behavior from experimental data obtained from multiple input multiple output systems, which can then complement any of the aforementioned identification algorithms. The methods that exist in the current state of the art require case-specific testing and, usually, significant excitation. A method that could circumvent both these issues would find widespread application in structural dynamics testing as an initial indicator for the presence of a nonlinearity. One such method based on the reverse path formulation has been presented in this dissertation. It makes use of the fact that the nonlinearities present can be modeled as internal restoring forces which are at least partially uncorrelated with the input force. The algorithm is shown to successfully find and localize the nonlinearity present on an array of numerical models and experimental setups when subjected to broadband input without assigning any parameters to the same. A means to isolate the uncorrelated spectrum resulting from leakage, which is a signal processing based nonlinearity, from the overall orthogonal projection spectrum has been presented and validated on experimental datasets.

Committee: Randall Allemang Ph.D. (Committee Chair); Allyn Phillips Ph.D. (Committee Member); S. Michael Spottswood Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member); Yongfeng Xu Ph.D. (Committee Member) Subjects: Mechanical Engineering

Master of Science in Electrical Engineering (MSEE), Wright State University, 2018, Electrical Engineering

In this thesis, we develop and evaluate change detection algorithms for longwave infrared (LWIR) hyperspectral imagery. Because measured radiance in the LWIR domain depends on unknown surface temperature, care must be taken to prevent false alarms resulting from in-scene temperature differences that appear as material changes. We consider four strategies to mitigate this effect. In the first, pre-processing via traditional temperatureemissivity separation yields approximately temperature-invariant emissivity vectors for use in change detection. In the second, we utilize alpha residuals to obtain robustness to temperature errors. Next, we adopt a minimax approach that minimizes the maximal spectral deviation between measurements. Finally, we reduce our minmax approach to solve with fewer variables. Examples using synthetic and measured data quantify the computational complexity of the proposed methods and demonstrate orders of magnitude reduction in false alarm rates relative to existing methods.

Committee: Joshua Ash Ph.D. (Advisor); Fred Garber Ph.D. (Committee Member); Arnab Shaw Ph.D. (Committee Member) Subjects: Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2016, Aero/Astro Engineering

Galerkin projection is a commonly used reduced order modeling approach; however, stability and accuracy of the resulting reduced order models are highly dependent on the modal decomposition technique used. In particular, deriving stable and accurate reduced order models from highly turbulent flow fields is challenging due to the presence of multi-scale phenomenon that cannot be ignored and are not well captured using the ubiquitous Proper Orthogonal Decomposition (POD). A truncated set of proper orthogonal modes is biased towards energy dominant, large-scale structures and results in over-prediction of kinetic energy from the corresponding reduced order model. The accumulation of energy during time-integration of a reduced order model may even cause instabilities. A modal decomposition technique that captures both the energy dominant structures and energy dissipating small scale structures is desired in order to achieve a power balance. The goal of this dissertation is to address the stability and accuracy issues by developing and examining alternative basis identification techniques. In particular, two modal decomposition methods are explored namely, sparse coding and Dynamic Mode Decomposition (DMD). Compared to Proper Orthogonal Decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that span all scales of the observed data. Dynamic mode decomposition seeks to identity bases that capture the underlying dynamics of a full order system. Each of the modal decomposition techniques (POD, Sparse, and DMD) are demonstrated for two canonical problems of an incompressible flow inside a two-dimensional lid-driven cavity and past a stationary cylinder. The constructed reduced order models are compared against the high-fidelity solutions. The sparse coding based reduced order models were found to outperform those developed using the dynamic mode and (open full item for complete abstract)

Committee: Jack McNamara (Advisor); Datta Gaitonde (Committee Member); Ryan Gosse (Committee Member); Joseph Hollkamp (Committee Member); Mohammad Samimy (Committee Member) Subjects: Aerospace Engineering

Master of Science, Miami University, 2014, Physics

Reduced order models that can capture and predict general flow characteristics are essential for closed-loop flow control around aerodynamic bodies. This research tests Galerkin based reduced order models using proper orthogonal decomposition modes derived experimentally to predict the flow over a NACA-0015 airfoil. Each of the models is tested on the airfoil at incident angles ranging from α=20° to α=10° for the baseline flow and a flow forced at 1250 Hz by nanosecond dielectric barrier discharge plasma actuators. It was found that both reduced order models were most successful in using 8 ≤n≤12 POD modes for their calculations.

Committee: Edgar Caraballo PhD (Advisor); Michael Pechan PhD (Committee Member); T. William Houk PhD (Committee Member); Andrew Sommers PhD (Committee Member) Subjects: Mechanical Engineering; Physics

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2013, Mathematics

If X is a topological vector space and T : X → X is a continuous linear operator, then T is said to be hypercyclic when there is a vector x in X such that the set {Tnx : n = 0, 1, 2, … } is dense in X. If a hypercyclic operator has a dense set of periodic points it is said to be chaotic. This paper is divided into five chapters. In the first chapter we introduce the hypercyclicity phenomenon. In the second chapter we study the range of a hypercyclic operator and we find hypercyclic vectors outside the range. We also study arithmetic means of hypercyclic operators and their convergence. The main result of this chapter is that for a chaotic operator it is possible to approximate its periodic points by a sequence of arithmetic means of the first iterates of the orbit of a hypercyclic vector. More precisely, if z is a periodic point of multiplicity p, that is Tpz = z then there exists a hypercyclic vector of T such that An,px =(1/n)(z + Tpz +
...
+Tp(n-1)z) converges to the periodic point z. In the third chapter we show that for any given operator T : M → M on a closed subspace M of a Hilbert space H with finnite codimension it has an extension A : H → H that is chaotic. We conclude the chapter by observing that the traditional Rota model for operator theory can be put in the hypercyclicity setting. In the fourth chapter, we show that if T is an operator on a closed subspace M of a Hilbert space H, and P : H → M is the orthogonal projection onto M, then there is an operator A : H → H such that PAP = T, PA*P = T* and both A, A* are hypercyclic.

Committee: Kit Chan (Advisor); Ron Lancaster (Committee Member); Juan Bes (Committee Member); Craig Zirbel (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2011, Mechanical Engineering

Localized arc filament plasma actuators have demonstrated significant potential in controlling high-speed and high Reynolds number jets in open-loop. The two primary goals of jet control are either noise reduction or bulk mixing enhancement. This research develops the tools for implementing feedback for this flow control system. The particular jet considered is a Mach 0.9 axisymmetric configuration with Reynolds number 670,000. The jet near-field pressure is well-suited for real-time non-intrusive observation of the flow state. Its response to forcing is similar to that of the far acoustic field. Forcing near the jet column mode results in amplification; forcing close to the shear layer mode yields attenuation. As a preliminary effort, two model-free feedback control algorithms are developed and implemented for online optimization of the forcing frequency to extremize the near-field pressure fluctuations. The steady-state behavior of the jet under closed-loop control matches the optimal open-loop results. However, the responsiveness of the controllers is poor since the dynamics of the jet are neglected. The first step in model-based feedback control is the development of a reduced-order model for the unforced jet. A cylindrical domain spanning the end of the jet potential core is chosen for the significance of its dynamics to the applications at hand. A combination of proper orthogonal decomposition and Galerkin projection is used to reduce the Navier-Stokes equations into a small set of ordinary differential equations employing empirical data. Extensive validation is performed on two existing numerical simulation databases of jets spanning low and high Reynolds numbers, and subsonic and supersonic speeds. Subsequently, a 35-dimensional model is derived from experimental data and shown to capture the most important dynamical aspects. The short-term prediction accuracy is found to be acceptable for the purpose of feedback control. The statistics from intermediate-ter (open full item for complete abstract)

Committee: Mo Samimy PhD (Advisor); Andrea Serrani PhD (Committee Co-Chair); Datta Gaitonde PhD (Committee Member); Jeffrey Bons PhD (Committee Member) Subjects: Acoustics; Aerospace Engineering; Applied Mathematics; Fluid Dynamics; Mechanical Engineering

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

Flow control refers to the ability to manipulate fluid flow so as to achieve a desired change in its behavior, which offers many potential technological benefits, such as reducing fuel costs for vehicles and improving effectiveness of industrial processes. An interesting case of flow control is cavity flow control, which has been the motivation of this study: When air flow passes over a shallow cavity a strong resonance is produced by a natural feedback mechanism, scattering acoustic waves that propagate upstream and reach the shear layer, and developing flow structures. These cause many practical problems including damage and fatigue in landing gears and weapons bays in aircrafts. Presently there is a lack of sufficient mathematical analysis and control design tools for flow control problems. This includes mathematical models that are amenable to control design. Recently reduced-order modeling techniques, such as those based on proper orthogonal decomposition (POD) and Galerkin projection (GP), have come to interest. However, a main issue with these models is that the effect of boundary conditions, which is where the control input is, gets embedded into system coefficients. This results in a form quite different from what one deals with in standard control systems framework, which is a set of ordinary differential equations (ODE) where the input appears as an explicit term. Another issue with the standard POD/GP models is that they do not yield to systems that have any apparent structure in their coefficients. This leaves one with little choice other than to neglect the nonlinearities of the models and employ standard linear control theory based designs. The research presented in this thesis makes an effort at closing the gaps mentioned above by 1) presenting a reduced-order modeling method utilizing a novel technique for input separation on POD/GP models, 2) introducing a technique based on averaging theory and center manifold theory so as to reveal certain struct (open full item for complete abstract)

Committee: Andrea Serrani (Advisor) Subjects: