# Browsing by Author "Mann, Brian P"

###### Results Per Page

###### Sort Options

Item Open Access A Multi-Disciplinary Systems Approach for Modeling and Predicting Physiological Responses and Biomechanical Movement Patterns(2017) Mazzoleni, MichaelIt is currently an exciting time to be doing research at the intersection of sports and engineering. Advances in wearable sensor technology now enable large quantities of physiological and biomechanical data to be collected from athletes with minimal obstruction and cost. These technological advances, combined with an increased public awareness of the relationship between exercise, fitness, and health, has created an environment where engineering principles can be integrated with biomechanics, exercise physiology, and sports science to dramatically improve methods for physiological assessment, injury prevention, and athletic performance.

The first part of this dissertation develops a new method for analyzing heart rate (HR) and oxygen uptake (VO2) dynamics. A dynamical system model was derived based on the equilibria and stability of the HR and VO2 responses. The model accounts for nonlinear phenomena and person-specific physiological characteristics. A heuristic parameter estimation algorithm was developed to determine model parameters from experimental data. An artificial neural network (ANN) was developed to predict VO2 from HR and exercise intensity data. A series of experiments was performed to validate: 1) the ability of the dynamical system model to make accurate time series predictions for HR and VO2; 2) the ability of the dynamical system model to make accurate submaximal predictions for maximum heart rate (HRmax) and maximal oxygen uptake (VO2max); 3) the ability of the ANN to predict VO2 from HR and exercise intensity data; and 4) the ability of a system comprising an ANN, dynamical system model, and heuristic parameter estimation algorithm to make submaximal predictions for VO2max without requiring VO2 data collection. The dynamical system model was successfully validated through comparisons with experimental data. The model produced accurate time series predictions for HR and VO2 and, more importantly, the model was able to accurately predict HRmax and VO2max using data collected during submaximal exercise. The ANN was successfully able to predict VO2 responses using HR and exercise intensity as system inputs. The system comprising an ANN, dynamical system model, and heuristic parameter estimation algorithm was able to make accurate submaximal predictions for VO2max without requiring VO2 data collection.

The second part of this dissertation applies a support vector machine (SVM) to classify lower extremity movement patterns that are associated with increased lower extremity injury risk. Participants for this study each performed a jump-landing task, and experimental data was collected using two video cameras, two force plates and a chest-mounted single-axis accelerometer. The video data was evaluated to classify the lower extremity movement patterns of the participants as either excellent or poor using the Landing Error Scoring System (LESS) assessment method. Two separate linear SVM classifiers were trained using the accelerometer data and the force plate data, respectively, with the LESS assessment providing the classification labels during training and evaluation. The same participants from this study also performed several bouts of treadmill running, and an additional set of linear SVM classifiers were trained using accelerometer data and gyroscope data to classify movement patterns, with the LESS assessment again providing the classification labels during training and evaluation. Both sets of SVM's performed with a high level of accuracy, and the objective and autonomous nature of the SVM screening methodology eliminates the subjective limitations associated with many current clinical assessment tools.

Item Open Access Analysis of spherical, rolling magnet generator for passive energy harvesting(2021) Gong, ChengIn this thesis, a spherical, rolling magnet generator for passive energy harvesting is investigated. It was designed for gathering energy from human motion. This thesis focuses on the analysis of the dynamics of this device and gives its governing equations. Then under two expected applications, this thesis finds the parameters that greatly influence its efficiency and provide optimal parameter combinations.

Item Open Access Data-Driven Parameter Estimation of Time Delay Dynamical Systems for Stability Prediction(2021) Turner, James D.Subtractive machining operations such as milling, turning, and drilling are an essential part of many manufacturing processes. Unfortunately, under certain combinations of machine settings, the motion of the cutting tool can become unstable, due to feedback between consecutive passes of the tool. This phenomenon is known as chatter. Mathematical models, specifically delay differential equations (DDEs), can describe the motion of the cutting tool and predict this instability. While these models are useful, estimates of the models' parameters are necessary in order to apply them to real systems. Unfortunately, estimating the parameters directly can be time-consuming, expensive, and difficult. The objective of this research is to develop automated methods to estimate these parameters indirectly, from time series measurements of the tool's motion which can be collected in a few minutes with sensors attached to the machine. The estimated parameters can then be used to predict when chatter will occur so that the machine operator can select appropriate settings.

One way to estimate the parameters of a dynamics model is to match the characteristic multipliers (CMs) predicted by the model to CMs estimated from time series data. CMs describe the behavior, such as stability, of a dynamical system near a limit cycle. While existing CM estimation methods are available, practical challenges such as measurement noise, limited time series length, and repeated CMs can substantially reduce their accuracy. The first part of this dissertation presents improved methods for estimating CMs from time series. Numerical validation studies demonstrate that the improved methods consistently provide more accurate CM estimates than existing methods in a variety of scenarios.

The second part of this dissertation introduces improvements to CM matching and trajectory matching methods for estimating the parameters of DDEs from noisy time series data. For CM matching, it incorporates the empirical CM estimation improvements from the previous part, and it introduces a way to match multiple CM estimates for each time series. For trajectory matching, it describes how to handle multivariate observations and prior knowledge in a principled way; it uses the spectral element method to provide a convenient representation of the initial interval and reduce the computational cost of computing the objective function; and it fits multiple time series simultaneously. Simulation results demonstrate that these improved methods work well in practice, although CM matching has some limitations which are not a problem for the trajectory matching method.

The final part of this dissertation introduces a new approach to estimate the parameters of a DDE model for milling from noisy time series data, based on the trajectory matching approach described in the previous part. It extends models from the literature to more closely fit the time series data, and it describes a procedure to estimate the unknown parameters in stages, without having to solve a global optimization algorithm for all the parameters simultaneously. Additionally, it adapts the spectral element method to make predictions for this model. Experimental results using time series data collected on an instrumented milling machine demonstrate that the model and fitting procedure successfully estimate parameters for which the predicted stability boundaries approximate the true stability boundaries.

Item Open Access Dynamic Analysis of a Cantilever Beam with an Offset Mass(2019) Zhan, YuruiThis thesis investigates the dynamic characteristics of a cantilever beam with an offset mass. Starting with a linear system consisting of a cantilever beam with a tip mass, Hamilton's principle is utilized to derive the equation of motion for the system, then similar method is applied to a cantilever beam with an offset mass. The equation of motion and boundary conditions are nondimensionalized to simplify the situation. The theoretical trend of natural frequency is also derived to show the effects of mass ratio, offset ratio and moment of inertia. Experimental results are derived using a system consisting of a base, a 3D-printed beam and several attachments. After comparing with theoretical data, several factors including damping ratio, moment of inertia and Poisson's ratio are taken into consideration. Both damping ratio and moment of inertia have very little effect and Poisson's ratio has opposite influence on the results. Explanation for the deviation lies on the isotropy of 3D-printed beam, which also puts forward a question on the qualification of using 3D-printed structures for dynamical analysis.

Item Open Access Dynamics of an Ocean Energy Harvester(2013) McGehee, Clark ColemanOcean-based wireless sensor networks serve many important purposes ranging from tsunami early warning to anti-submarine warfare. Developing energy harvesting devices that make these networks self-sufficient allows for reduced maintenance cost and greater reliability. Many methods exist for powering these devices, including internal batteries, photovoltaic cells and thermoelectric generators, but the most reliable method, if realized, would be to power these devices with an internal kinetic energy harvester capable of reliably converting wave motion into electrical power. Designing such a device is a challenge, as the ocean excitation environment is characterized by shifting frequencies across a relatively wide bandwidth. As such, traditional linear kinetic energy harvesting designs are not capable of reliably generating power. Instead, a nonlinear device is better suited to the job, and the task of this dissertation is to investigate the behaviors of devices that could be employed to this end.

This dissertation is motivated by the design and analysis of an ocean energy harvester based on a horizontal pendulum system. In the course of investigating the dynamics of this system, several discoveries related to other energy harvesting systems were made and are also reported herein. It is found that the most reliable method of characterizing the behaviors of a nonlinear energy harvesting device in the characteristically random forcing environment of the ocean is to utilize statistical methods to inform the design of a functional device. It is discovered that a horizontal pendulum-like device could serve as an energy harvesting mechanism in small self-

sufficient wireless sensor buoys if properly designed and if the proper transduction mechanisms are designed and employed to convert the mechanical energy of the device into electrical power.

Item Open Access Dynamics of Electromagnetic Systems for Energy Harvesting and Filtering(2014) Owens, Benjamin Andrew MichaelThe focus of this dissertation is on the dynamics of electromagnetic systems for energy harvesting and filtering applications. The inclusion of magnets into systems generates nonlinearity due to the nature of electromagnetic interactions. In this work, magnetic nonlinearity manifests in tip interactions for cantilever beams, coupling effects for electromagnetic transduction, and bistable potential wells for a two beam system. These electromagnetic interactions are used to add non-contact coupling effects for the creation of bistable oscillators or arrays of coupled beams for energy filtering.

Nonlinearity at the tip of cantilever beams acts to change the dynamic and static behavior of the system. In this dissertation, these interactions are analyzed both with and without the nonlinear tip interactions. A linear analysis of the system without the tip interaction first provides insight into the shifting frequencies of the first four natural oscillation modes when considering a rigid body tip mass with rotational inertia and a center of mass that is offset from the tip of the beam. Then, the characterization of the nonlinearities in the beam stiffness and magnetic interaction provide insight into the static and dynamic behavior of the beam. The analytical and numerical investigations, using Rayleigh-Ritz methods and an assumed static deflection, are shown to be consistent with experimental tests. These methods provide a framework for theoretically establishing nonlinear static modes and small-amplitude linear modes that are consistent with physical behavior.

In electromagnetic coupling, the role of nonlinearity can have a detrimental or beneficial effect on energy harvesting. This work includes an investigation of the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. The system's response behavior with linear coupling or a physically motivated form of nonlinear coupling is compared with single and multi-frequency base excitation. This analysis is performed with combined theoretical and numerical studies.

The ability of magnets to add nonlinearity to a system allows for the expansion of the phenomenological behavior of said system and potential advantages and disadvantages for energy harvesting. This work studies a two beam system made up of carbon fiber cantilever beams and attached magnetic tip masses with a focus on energy harvesting potential. Numerical and experimental investigations reveal an array of phenomena from static bifurcations, chaotic oscillations, and sub-harmonic orbits. These features are used to highlight the harvesting prospects for a similarly coupled system.

Beyond nonlinearity, the non-contacting coupling effects of magnets allow for the hypothetical creation of energy filtering systems. In this work, the band structure of a two dimensional lattice of oscillating beams with magnetic tip masses is explored. The focus of the wave propagation analysis is primarily on regions in the band structure where propagation does not occur for the infinite construction of the system. These band gaps are created in this system of 2 x 2 repeating unit cells by periodically varying the mass properties and, for certain configurations, the frequency band gaps manifest in different size and band location. Uncertainty in these regions is analyzed using potential variations associated with specific physical parameters in order to elucidate their influence on the band gap regions. Boundary effects and damping are also investigated for a finite-dimensional array, revealing an erosion of band gaps that could limit the expected functionality.

Item Embargo Dynamics of Electrostatic Systems for Energy Conversion Applications(2023) Coonley, Kip D.The work presented here describes the electrostatic force, it’s nature, and it’s use in electromechanical systems. Energy transfer from both electrical-to-mechanical and mechanical-to-electrical are described. The electrostatic force is investigated in detail.Patterning of electrostatic rotary capacitive plates provides a novel strategy for up-converting low frequency mechanical excitation sources. The rotating plates allow for output waveform signal conditioning in both control of frequency and waveform shaping. An experimental set-up consisting of a 5.08 cm (2”) diameter rotary electrostatic capacitor harvester was designed and tested at mechanical rotation frequencies ranging from 1–35 Hz. Quarter plates were used to double the rate of change in area. Plates were spaced 3 mm apart with an applied voltage of 6.55 kV maintained by a 8.3 nF capacitor bank. Resistive loads between 10kΩ−10M Ω were used to verify current flow from the rotary capacitor. Simulation was carried out using a current source GTABLE model in PSPICE. Electrostatic theory demonstrates similar current magnitudes and the same upward trend with frequency. Further experimental analysis of a translating spring-mass system with a constant electrostatic force in the presence of viscous damping is presented and compared with simulation. A model for the linear translating electrostatic system not under the influence of viscous damping is first considered. An analytical equation is derived which provides a theoretical model for the behavior of the system and simulation in carried out and compared with the solution and theoretical model. Next, an approximate analytical solution to the electrostatic oscillator system in the presence of viscous damping is completed and a recursive relationship for the piecewise solution is presented. Conclusions and future work suggest several avenues for further investigation where the electrostatic force in electromechanical systems could be advanced including application areas.

Item Open Access Dynamics of Ocean Buoys and Athlete Motion for Energy Harvesting(2013) Ballard, ZachSmall scale energy harvesting has become a prevalent area of study over the last decade. These harvesters are used in a wide range of applications, including the powering of remote sensors for structural health in buildings or bridges, tsunami, submarine and wildlife detection in the ocean, as well as general motion analysis of systems. Though many designs have been created to harvest energy for these purposes, the nonlinear dynamics of both the harvester and, when applicable, its housing (i.e. buoy casing) are widely ignored. Because of this, a significant amount of available power is lost through the limitations of linear designs.

The first part of this dissertation gives an overview of commonly used linear energy harvesting designs and gives a brief explanation of the limitations of a linear design. Both a simple inertial and linearized magnet-coil model are analytically and numerically studied. This sets the stage for improvement of energy harvesters to operate at a wider range of frequencies by including the inherent nonlinearities of the harvester and/or its environment.

In the second part, the nonlinear dynamics of ocean buoys of standard, fundamental shapes (spherical and cylindrical) due to wave loading is studied. Experimental, as well as numerical and analytical analysis is performed on these designs. Also given is a description of common wave-loading devices that can be used in a laboratory setting (wavemakers), as well as for the specific device used to obtain experimental data. Additionally, a simple dynamical system is excited by the buoy motion, which is used to calculate the power available if the system was used as an energy harvester.

The last part of this dissertation looks at the nonlinear dynamics of human motion, with a focus on running events. Analysis is performed on running subjects in order to determine the amount of energy available, as well the frequencies where the most energy is available. This information is then used to recreate the motion numerically, which makes it possible to design a simple energy harvester that operates efficiently in such an environment. This harvester is used to power a timing mechanism that gives frequent and useful information about the athlete's position and speed.

Item Open Access Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation(2016) Wang, XuesheThis paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Item Open Access Intra-Operative Surgical Instrument Tracking with Radio-Frequency Identification(2021) Hill, IanAs data revolutionizes supply chains across diverse industries, healthcare lags. Sensor systems have struggled to automate the capture of actionable data without impeding clinical workflows. This work focuses on the development of a radio-frequency identification system to track surgical instruments in the operating room. The system was developed to integrate into existing infrastructure without impacting the delivery of care. In the background, it collects data that can be used to measure the presence of a surgical instrument, infer use, and predict location. This novel data was leveraged to eliminate unnecessary instrument supplies and begins to enable analytics describing how surgery is performed.

Item Open Access Machine Learning Applications for Objectively Assessing Surgical Skill and Instrument Dynamics(2019) Hutchins, Andrew RyanThe goals set forth in this dissertation are centered on advancing the current state-of-the-art literature for applying analytical approaches to determining surgical proficiency, testing new metrics for surgical movement efficacy, and understanding surgical instrument dynamics. Each of these three core research areas are focused on using modern, data-driven approaches to providing better patient care and improving the efficacy of surgical training programs. The amount of under-utilized data collected during surgical training and in live cases is astounding as simulation labs and operating rooms are equipped with countless types of sensors for monitoring patient data and spatio-temporal operating room dynamics, including surgical instrument motion.

Initially, a series of regression models are trained and tested using a feature vector derived from the kinematics of two laparoscopic instrument while participants complete the Fundamentals of Laparoscopic Surgery peg transfer and suture with intracorporeal knot assessments. Models were trained to predict objective (time and error) and subjective scores. A recursive information gain feature selection method was applied for choosing the number of features to represent in each model. Model performances are compared and a discussion on the use of instrument kinematics as a measure of surgical competency is given.

A second machine learning study is presented comparing deep neural network classification accuracies for determining performance at the peg transfer assessment. Two neural network architectures were tested: vanilla long short-term memory and convolutional neural network long short-term memory. The inputs to these models were the raw motion tracking points and the down-sampled video frames, respectively. Comparisons between the two neural network architectures were made and overall performances are discussed in the context of video-based surgical skill evaluation and conventional, objective metrics for assessing surgical proficiency.

Instrument movement smoothness has served as a heuristic for suggesting surgical competency in several prior studies; however, the conventional metrics that have been used to quantify movement smoothness are susceptible to several pitfalls when applied to real-world data. Such metrics also consider movement patterns at a single time-scale. A new method for quantifying movement smoothness is presented using multiscale entropy of the velocity time series to calculate the complexity index over varying downsampling intervals. Tests using this metric are conducted on simulated point-to-point movement profiles with and without random noise and is validated using laparoscopic instrument tip motion data from a point-to-point movement experiment.

Finally, a fundamental analysis of the dynamic response of a laparoscopic instrument under the presence of vibrotactile excitation and variable gripping pressures is presented. Conventional laparoscopic instruments lack the ability to transmit haptic feedback to surgeons’ hands, but future instrumentation could have this capability. To this end, it is essential that the impact of interfacial damping and stiffness, induced by contact forces exerted at the hand-handle interface, are understood. The connection between each of these studies is grounded in studying methods to improve inefficient training methods for laparoscopic surgery and improving laparoscopic instrument capabilities. The long-term vision for the foundational work in this dissertation is to develop a closed-loop system for intraoperative performance assessment and instrument feedback to recommend movements to surgeons in an effort to mitigate risk to patients and expedite learning for residents.

Item Open Access Micro-Fabrication Methods and Experimentation of Liquid-Solid Triboelectric Nanogenerators(2017) Hermiller, Brent D.This study is an exploration of the liquid-solid electrication phenomena in tribo-

electric nanogenerator devices, its fabrication and assembly, as well as notable results

and analysis on all aspects of the nanogenerator device. Energy harvesting in water-

based environments is ideal because the harvester can be shown to generate sucient

energy provided it is scaled for the application. As a renewable energy source, it is

desirable to incorporate for remote ocean-based sensors that demand on-site energy.

These devices are currently technically dicult to produce and require specialized

clean room and chemical altering equipment. Due to the complex nature of the cur-

rent fabrication method, this work also explores an alternate method for fabrication of

the triboelectric layers for use in water-based environments. Polymer nanowire mod-

ications to increase the contact area with liquid are shown to moderately improve

the overall performance using specic chemical gases during the etching process. Cir-

cuitry for optimizing these devices in building up and storing energy to power several

LEDs has merit, but failed in testing after successive attempts. With continued re-

search and design improvement, triboelectric nanogenerator energy harvesters could

prove useful in a wide variety of sensor applications.

Item Open Access Models To Derive the Resonant Frequency of a Liquid in a Rectangular Tank With a Curved Bottom(2021) Garcia, Alejandro DanielThis thesis investigates the resonant frequency of a partially-filled rectangular tank of water with a curved bottom that is subject to a horizontal harmonic excitation. The primary goal was to find a model that can accurately find the resonant frequency to study the change in the natural frequency when the parameters of the curved base and system were changed. The EOM model, the h ̅ model, and the ω ̅_n model were derived all from the same linear assumptions and approximation for the velocity potential. Frequency sweeps were done for several curved base systems and compared to each of the models’ predictions. It was found that the h ̅ and ω ̅_n models both agreed well with the data generally, while the EOM model did not. An additional investigation was done on this system to understand the presence of nonlinearities and damping and their significance to the problem. It was found that while several nonlinearities exist like additional harmonic frequency content and surface tension, they are not significant in determining the resonant frequency. Furthermore, the accuracy in the h ̅ and ω ̅_n models show that the linear assumptions and simplifications made for the velocity potential equation were feasible to a degree. Despite this, it is clear that this approximation of the velocity potential needs further work as the EOM model utilizes it fully and is inaccurate.

Item Open Access Nonlinear Dynamics of Energy Harvesting Ocean Buoys(2019) Sequeira, DaneThis dissertation looks to investigate different ways that the performance of ocean energy harvesting buoys can be improved by intentionally inserting nonlinearities into the system. The goal is to maximize the amount of energy that is extracted from ocean waves across a broad range of environmental conditions. First, the bifurcation and stability behavior of inhomogeneous floating bodies is studied. Bifurcation diagrams and basins of attraction that illustrate the stability of the equilibrium positions as a function of the vertical position of the center of mass within the body are generated. Static experiments in still water are conducted to validate these results and dynamic experiments in a wave flume are carried out to examine how potential well hopping behavior can be encouraged for various wave conditions.

Next, the gimballed horizontal pendulum is studied for use as an energy harvester that can be designed for threshold escape behavior rather than the conventional method of matching frequencies. A nonlinear electromechanical model is developed to study the system's equilibrium states as a function of tilt angle. A static bifurcation point is solved for analytically and the implications for an energy harvester, one that can be designed to jump across stable attractors based on forcing amplitudes, are discussed. Amplitude sweeps are conducted showing a dynamic bifurcation point that varies as a function of frequency and effective damping and experiments are run to validate computational results.

This system is examined further to study how it can be used specifically for harvesting energy from ocean waves. Threshold escape behavior for parametrically excited systems with a time dependent term in the potential energy function is discussed and a criterion is proposed for predicting escape events. Performance metrics are identified to quantify and compare different responses. Numerical and experimental studies are conducted showing how the system can be designed for enhanced performance by altering geometric parameters to suit various excitations. The system's response to both deterministic single harmonic and stochastic multiharmonic excitations are investigated. Design implications are discussed.

Then, variable area plate capacitors are studied to determine how topological optimization can be applied to identify nonintuitive capacitor plate patterning that maximize average power dissipated through an electrical circuit during energy harvesting. Coupled electromechanical equations of motion are derived that include both the instantaneous and change in overlapping conductive area as functions of plate rotation. A genetic algorithm is used to optimize these terms and then map them to physical plate configurations. The results obtained apply specifically to the case presented, however the methods are general and can be used to solve a broad range of electrostatic energy harvesting problems.

Finally, an analytical method is developed to determine the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. The simplest case of a linear frequency sweep is first considered before generalizing to include more complex functions with nonlinear sweep rates and arbitrary phase shifts. This method improves the accuracy of various simulation results throughout this dissertation but can be extended to aid the analysis of any generic dynamical system.

Item Open Access Nonlinear Electroelastic Dynamical Systems for Inertial Power Generation(2011) Stanton, SamuelWithin the past decade, advances in small-scale electronics have reduced power consumption requirements such that mechanisms for harnessing ambient kinetic energy for self-sustenance are a viable technology. Such devices, known as energy harvesters, may enable self-sustaining wireless sensor networks for applications ranging from Tsunami warning detection to environmental monitoring to cost-effective structural health diagnostics in bridges and buildings. In particular, flexible electroelastic materials such as lead-zirconate-titanate (PZT) are sought after in designing such devices due to their superior efficiency in transforming mechanical energy into the electrical domain in comparison to induction methods. To date, however, material and dynamic nonlinearities within the most popular type of energy harvester, an electroelastically laminated cantilever beam, has received minimal attention in the literature despite being readily observed in laboratory experiments.

In the first part of this dissertation, an experimentally validated first-principles based modeling framework for quantitatively characterizing the intrinsic nonlinearities and moderately large amplitude response of a cantilevered electroelastic generator is developed. Nonlinear parameter identification is facilitated by an analytic solution for the generator's dynamic response alongside experimental data. The model is shown to accurately describe amplitude dependent frequency responses in both the mechanical and electrical domains and implications concerning the conventional approach to resonant generator design are discussed. Higher order elasticity and nonlinear damping are found to be critical for correctly modeling the harvester response while inclusion of a proof mass is shown to invigorate nonlinearities a much lower driving amplitudes in comparison to electroelastic harvesters without a tuning mass.

The second part of the dissertation concerns dynamical systems design to purposefully engage nonlinear phenomena in the mechanical domain. In particular, two devices, one exploiting hysteretic nonlinearities and the second featuring homoclinic bifurcation are investigated. Both devices exploit nonlinear magnet interactions with piezoelectric cantilever beams and a first principles modeling approach is applied throughout. The first device is designed such that both softening and hardening nonlinear resonance curves produces a broader response in comparison to the linear equivalent oscillator. The second device makes use of a supercritical pitchfork bifurcation wrought by nonlinear magnetic repelling forces to achieve a bistable electroelastic dynamical system. This system is also analytically modeled, numerically simulated, and experimentally realized to demonstrate enhanced capabilities and new challenges. In addition, a bifurcation parameter within the design is examined as a either a fixed or adaptable tuning mechanism for enhanced sensitivity to ambient excitation. Analytical methodologies to include the method of Harmonic Balance and Melnikov Theory are shown to provide superior insight into the complex dynamics of the bistable system in response to deterministic and stochastic excitation.

Item Open Access Nonlinear Energy Harvesting With Tools From Machine Learning(2020) Wang, XuesheEnergy harvesting is a process where self-powered electronic devices scavenge ambient energy and convert it to electrical power. Traditional linear energy harvesters which operate based on linear resonance work well only when excitation frequency is close to its natural frequency. While various control methods applied to an energy harvester realize resonant frequency tuning, they are either energy-consuming or exhibit low efficiency when operating under multi-frequency excitations. In order to overcome these limitations in a linear energy harvester, researchers recently suggested using "nonlinearity" for broad-band frequency response.

Based on existing investigations of nonlinear energy harvesting, this dissertation introduced a novel type of energy harvester designs for space efficiency and intentional nonlinearity: translational-to-rotational conversion. Two dynamical systems were presented: 1) vertically forced rocking elliptical disks, and 2) non-contact magnetic transmission. Both systems realize the translational-to-rotational conversion and exhibit nonlinear behaviors which are beneficial to broad-band energy harvesting.

This dissertation also explores novel methods to overcome the limitation of nonlinear energy harvesting -- the presence of coexisting attractors. A control method was proposed to render a nonlinear harvesting system operating on the desired attractor. This method is based on reinforcement learning and proved to work with various control constraints and optimized energy consumption.

Apart from investigations of energy harvesting, several techniques were presented to improve the efficiency for analyzing generic linear/nonlinear dynamical systems: 1) an analytical method for stroboscopically sampling general periodic functions with arbitrary frequency sweep rates, and 2) a model-free sampling method for estimating basins of attraction using hybrid active learning.

Item Open Access Novel Computational Approaches for the Objective Analysis of Surgical Activities(2021) Aubert, Miles ClintonThe primary goal of this dissertation is to advance the state-of-the-art in the objective analysis of surgical activities and to create novel metrics that can robustly and accurately compute the proficiency of surgical personnel. Toward these goals this work develops a range of computational approaches that takes advantage of a range of underused data available across surgical tasks both in an educational setting and in the operating room.

Initially a novel approach to the analysis of surgical activities is presented that utilizes the inherent gesture-based structure of surgical activities and applies multiple kinematic-based metrics to the motion of surgical instruments. This novel granular approach is compared to traditional analyses over three different surgical tasks using regressions to evaluate the ability of the technique to classify subjective measures of proficiency. Overall this work presents significant evidence that a granular approach to the analysis of surgical activities is far better than traditional approaches.

This dissertation also analyzes bimanual interaction, a component of surgical proficiency often discussed in literature that has yet to be addressed objectively in surgical activities. First, a general perspective is taken on the problem of evaluating the dependency between two or more systems by extending the non-linear systems concept of information transfer. Two novel extensions are presented in this chapter, first a multivariate extension that facilitates an evaluation of dependence between two or more multivariate systems, secondly a windowed extension is presented that facilitates the analysis of two or more multivariate systems whose dependency varies with time. These two extensions are evaluated on three unique simulated systems with results demonstrating their ability to accurately and robustly track dependence. Second, the non-linear systems concept of information transfer and the accompanying extensions presented in this dissertation is investigated as a metric in the analysis of proficiency in surgical activities. Multiple variants of information transfer are evaluated in both a traditional global formulation as well as in a granular analysis scheme like those discussed earlier in this dissertation. Regressions were used to evaluate the ability of information transfer in classifying subjective measures of proficiency. Results from these analyses showed strong evidence that such an approach is more discriminative than multiple existing state-of-the-art metrics and can offer unique insights in to the proficiency of surgical personnel.

In summary, this dissertation presented multiple validated extensions to the state-of-the-art in the analysis of proficiency in surgical activities. The long-term goal of this work is to develop a closed system capable of robustly and accurately tracking intraoperative surgical proficiency and contributing to the education of surgeons by offering enhanced feedback, thereby optimizing the operating room and improving outcomes for patients.

Item Open Access Numerical and Experimental Investigation of Multistable Systems(2013) Tweten, Dennis JeremyThe focus of this dissertation is on phenomena exhibited by multistable systems. Two phenomena of particular importance are chaos control and stochastic resonance. In this work, both models that can predict ordered responses and experiments in which ordered responses occur are explored. In addition, parameter identification methods are presented and improved.

Chaos control, when implemented with delays, can be an effective way to stabilize unstable periodic orbits within a multistable system experiencing a chaotic response. Delayed control is easy to implement physically but greatly increases the complexity of analyzing such systems. In this work, the spectral element method was adapted to evaluate unstable periodic orbits stabilized by feedback control implemented with delays. Examples are presented for Duffing systems in which the delay is equal to the forcing period. The spectral approach is also extended to analyze the control of chaos with arbitrary delays. Control with arbitrary delays can also be used to stabilize equilibria within the chaotic response. These methods for arbitrary delays are explored in self-excited, chaotic systems.

Stochastic resonance occurs in multistable systems when an increase in noise results in an ordered response. It is well known that noise excitation of multistable systems results in the system escaping from potential wells or switching between wells. In stochastic resonance, a small external signal is amplified due to these switching events. Methods for modeling stochastic resonance in both underdamped and overdamped systems are presented. In addition, stochastic resonance in a bistable, composite beam excited by colored noise is investigated experimentally. The experimental results are compared with analytical models, and the effect of modal masses on the analytical expressions is explored. Finally, an alternative approach for calculating the effect of colored noise excitation is proposed.

In order to implement analysis methods related to delay differential equations or stochastic resonance, the parameters of the system must be known in advance or determined experimentally. Parameter identification methods provide a natural connection between experiment and theory. In this work, the harmonic balance parameter identification method was applied to beam energy harvesters and is improved using weighting matrices. The method has been applied to a nonlinear, bistable, piezoelectric beam with a tip mass. Then, an experimental method of determining the number of restoring force coefficients necessary to accurately model the systems was demonstrated. The harmonic balance method was also applied to a bistable, beam system undergoing stochastic resonance. Finally, a new weighting strategy is presented based on the signal to noise ratio of each harmonic.

Item Open Access Parametric Identification of Delay Systems from Empirical Stability Information(2019) Little, Jared AndrewThe work presented in this document alleviates challenges associated with applying academically proven analysis techniques to real-world dynamical systems. Specifically, by providing improved parameter identification methods, the contributions of this work help bridge the gap between theoretical predictions and experimentally-observed behavior. This work is primarily motivated by the existence of powerful predictive methods in the literature of manufacturing research, specifically pertaining to the stability of subtractive manufacturing methods like milling and turning, which are not currently implemented in industry due to the prohibitive effort required by available methods for identifying system properties covering the range of cutting conditions that may be encountered. The motivating technique, temporal finite element analysis (TFEA), is first detailed and demonstrated to be sensitive to system parameters. The remainder of this document, subsequently, focuses on improving or developing approaches for identifying parameters influencing or quantifying the level of stability of dynamical systems, offering a connection between theory and experiment.

First, an improvement to the fundamental technique of logarithmic decrement damping estimation is provided. Specifically, an analytical expression for the optimal number of periods between samples is derived. This expression, obtained from an uncertainty analysis of the method's principal equation, is shown to be a function of only one system parameter: the damping ratio. This suggests that for linear systems with viscous damping there is a unique, damping-dependent period choice corresponding to minimum uncertainty in the estimated damping ratio. This result led to the discovery of a constant optimal amplitude ratio offering a straightforward guideline that can be applied by the experimenter to obtain damping ratio estimates with minimum uncertainty. The derived expressions are applied to a series of numerical and experimental systems to confirm their validity.

Next, focus is placed on systems with periodic steady-state behavior. This work applies empirical Floquet theory to extract characteristic multipliers from time series data and builds upon prior works by significantly reducing the influence of experimental noise. Characteristic multipliers (CMs), which are the eigenvalues of the transition matrix governing the evolution of transient solutions over one period of motion, quantify the local stability of periodic orbits and can be estimated experimentally without knowledge of the system model. Traditionally, empirical CM estimates were obtained from the transient dynamics observed by subtracting measured steady-state behavior from a recorded perturbed response. The subtraction of two experimentally measured quantities amplifies noise, producing inaccurate CM estimates. By applying a moving integral to isolate the transient dynamics, this work provides an approach to reduce, rather than amplify, the influence of noise on empirical CM results. This approach is applied to the reconstructed phase space of a numerical example and an experimental system to demonstrate the improvements.

This work culminates in a study identifying parameters of milling operations. In this work, a heuristic optimization routine is developed which, given information gleaned from vibration data collected during cutting, identifies modal parameters and cutting coefficients of the model governing interrupted cutting. Characteristic multipliers estimated from the transient induced by the onset of cutting forces provide information regarding the true stability characteristics of the system. Model parameters are fit to the collected empirical CMs with a genetic algorithm, which is well-suited to navigate the numerous local minima of the objective function. New insight is provided into how control parameters and modal properties affect stability, demonstrating that results can be influenced through careful selection of cutting tests. The approach is applied to single-degree-of-freedom and two-degree-of-freedom milling systems, where accurate estimates of parameters are achieved.

Item Open Access Single-track Vehicle Dynamics and Stability(2014) Lipp, Genevieve MarieThis work is concerned with the dynamics and stability of nonlinear systems that roll in a single track, including holonomic and nonholonomic systems. First the classic case of Euler's disk is introduced as an example of a nonholnomic system in three dimensions, and the methodology for deriving equations of motion that is used throughout this work is demonstrated, including use of Lagrange's equations, accommodating constraints with both Lagrange multipliers and with Gauss's Principle.

Next, a disk in two dimensions with an eccentric center of mass is explored. The disk is assumed to roll on a cubic curve, creating the possibility of well-escape behavior, which is examined analytically and numerically, showing regions of multi-periodicity and chaos. This theoretical system is compared to an experiment designed

to demonstrate the same behavior.

The remainder of the present document is concerned with the stability of a bicycle, both on flat ground, and on a type of trainer known as "rollers." The equations of motion are derived using Lagrange's equations with nonholonomic constraints, then the equations are linearized about a constant forward velocity, and a straight path, yielding a two degree of freedom system for the roll and steer angles. Stability is then determined for a variety of different parameters, exploring the roll of bicycle geometry and rider position, along with the effect of adding a steering torque, taking the form of different control laws.

Finally, the system is adapted to that of a bicycle on rollers, and the related equations of motion are derived and linearized. Notable differences with the classic bicycle case are detailed, a new eigenvalue behavior is presented, and configurations for optimal drum spacing are recommended.