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- Title
- KERNEL FREE BOUNDARY INTEGRAL METHOD AND ITS APPLICATIONS
- Creator
- Cao, Yue
- Date
- 2022
- Description
-
We developed a kernel-free boundary integral method (KFBIM) for solving variable coefficients partial differential equations (PDEs) in a...
Show moreWe developed a kernel-free boundary integral method (KFBIM) for solving variable coefficients partial differential equations (PDEs) in a doubly-connected domain. We focus our study on boundary value problems (BVP) and interface problems. A unique feature of the KFBIM is that the method does not require an analytical form of the Green’s function for designing quadratures, but rather computes boundary or volume integrals by solving an equivalent interface problem on Cartesian mesh. We decompose the problem defined in a doubly-connected domain into two separate interface problems. Then we evaluate integrals using a Krylov subspace iterative method in a finite difference framework. The method has second-order accuracy in space, and its complexity is linearly proportional to the number of mesh points. Numerical examples demonstrate that the method is robust for variable coefficients PDEs, even for cases when diffusion coefficients ratio is large and when two interfaces are close. We also develop two methods to compute moving interface problems whose coefficients in governing equations are spatial functions. Variable coefficients could be a non-homogeneous viscosity in Hele-Shaw problem or an uptake rate in tumor growth problems. We apply the KFBIM to compute velocity of the interface which allows more flexible boundary condition in a restricted domain instead of free space domain. A semi-implicit and an implicit methods were developed to evolve the interface. Both methods have few restrictions on the time step regardless of numerical stiffness. Theyalso could be extended to multi-phase problem, e.g., annulus domain. The methods have second-order accuracy in both space and time. Machine learning techniques have achieved magnificent success in the past decade. We couple the KFBIM with supervised learning algorithms to improve efficiency. In the KFBIM, we apply a finite difference scheme to find dipole density of the boundary integral iteratively, which is quite costly. We train a linear model to replace the finite difference solver in GMRES iterations. The cost, measured in CPU time, is significantly reduced. We also developed an efficient data generator for training and derived an empirical rule for data set size. In the future work, the model could be expanded to moving interface problems. The linear model will be replaced by neural network models, e.g., physics-informed neural networks (PINNs).
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- Title
- PROGRAM SURVIVABILITY THROUGH K-VARIANT ARCHITECTURE
- Creator
- BEKIROGLU, BERK
- Date
- 2021
- Description
-
Numerous software systems, particularly mission and safety-critical systems, require a high level of security during their execution....
Show moreNumerous software systems, particularly mission and safety-critical systems, require a high level of security during their execution. Enhancing software security through architecture is a highly effective method of defending against cyberattacks. The N-version is a software architecture that was developed to increase the security of software systems. In the N-version architecture, functionally equivalent versions of a program run concurrently to complete a mission or task. Each version is developed independently by a different team using only the software specifications in common. As a result, each version is expected to contain unique vulnerabilities. Due to the high cost of developing and maintaining an N-version system, this architecture is typically used only in high-budget projects requiring a high-security level. The K-variant, an alternative architecture for enhancing system security, is explained and analyzed in this thesis. In contrast to the N-version architecture, each variant is automatically generated using source-to-source program transformation techniques. Automation significantly reduces the cost of developing variants in the K-variant architecture. The K-variant architecture can help protect systems from memory exploitation attacks. Various attack strategies can be used against K-variant systems in order to increase the likelihood of a successful attack. Various attack strategies are proposed and investigated in this thesis. Furthermore, experimental studies are being conducted to investigate various defense mechanisms against proposed attack strategies. The effectiveness of each defense mechanism against various attack strategies is evaluated by using a metric of the probability of an unsuccessful attack. Additionally, various source code program transformation techniques for generating new variants in the K-variant architecture have been proposed and investigated experimentally. This thesis also describes a machine learning technique for estimating the survivability of K-variant systems under various attack types and defense strategies. To make the design of K-variant systems easier, a neural network model is proposed. With the developed tool that utilizes the neural network model, fast and accurate predictions about the survivability of K-variant systems can be obtained.
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- Title
- Assessing the Impact of Understanding Nature of Scientific Knowledge and Understanding Nature of Scientific Inquiry on Learning about Evolution in High School Students
- Creator
- Jimenez Pavez, Juan Paulo
- Date
- 2022
- Description
-
Nature of Scientific Knowledge (NOSK) and Nature of Scientific Inquiry (NOSI) are important components of scientific literacy and important...
Show moreNature of Scientific Knowledge (NOSK) and Nature of Scientific Inquiry (NOSI) are important components of scientific literacy and important educational objectives in science education. Recent literature theorizes that understanding both NOSK and NOSI increases students' understanding of science content knowledge. However, this assumption has yet to be tested empirically. Much research has been done on developing informed views of NOSK and NOSI for students in kindergarten through twelfth grade, but research on the effect of understanding NOSK and NOSI on facilitating science learning in high school appears limited.The main purpose of this study was to empirically test the assumption that understanding NOSK and NOSI improves science student content learning, in particular learning about evolution. This study also aimed to determine which NOSK and NOSI aspects are most useful in such an endeavor. Using a quasi-experimental, nonequivalent control group design, a sample of 453 9th grade high school students from 12 classes in a large Chilean city were randomly assigned to intervention and control groups via classroom clusters (Intervention groups = 6, Control groups = 6). Students in the intervention groups were given a special online explicit and reflective five-week NOSK/NOSI Unit, followed by an online five-week Evolution Content Unit, as a treatment. Those in the control groups received only the online five-week Evolution Content Unit. To measure understanding of NOSK, understanding of NOSI, and understanding about evolution, students answered three valid and reliable instruments: The Views of Nature of Science (VNOS D+), the Views about Scientific Inquiry (VASI), and a multiple-choice Evolution Content Test. The students' answers to the VNOS D+ and VASI questionnaires were scored as naive, mixed, or informed according to the level of understanding for each aspect, and the answers to the evolution content test were scored as correct or incorrect. The results of this study showed that the NOSK/NOSI Unit was effective in improving understanding of NOSK and NOSI aspects in the intervention groups. The results also showed that the Evolution Content Unit was effective in improving understanding about evolution in both groups. However, students in the intervention groups outperformed their peers in the control groups by scoring higher on the Evolution Content Test. Further analysis revealed that students with informed views of NOSK and NOSI achieved better scores on the Evolution Content Test than students with naive views, supporting the argument that understanding NOSK and NOSI facilitates learning about evolution. In addition, all aspects except for the difference between Theories and Laws (NOSK) had a significant positive impact on learning about evolution. Taken together, the findings of this dissertation support the assumption that understanding NOSK and NOSI improves learning about evolution. Furthermore, most NOSK and NOSI aspects seem to foster understanding about evolution. These are new insights, especially about the importance of understanding NOSI for learning about evolution. Some limitations for this study include the remote context in which the study took place and the potential bias in the qualitative analysis of the VNOS D+ and VASI questionnaires.
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- Title
- Efficiency of Carbon Fiber Composite Structural Systems for Tall Buildings: A Parametric Simulation Based Framework for Finite Element Analysis
- Creator
- Khairnar, Piyush Rajendra
- Date
- 2022
- Description
-
The rate of global urban migration has increased drastically over the last century. With increasing population, the need for dense urban...
Show moreThe rate of global urban migration has increased drastically over the last century. With increasing population, the need for dense urban habitats is growing. Tall buildings are at the forefront of this growth and changing skyline of different cities around the globe is evident. The Structural system is an important and critical component of any tall building. Structural material can significantly impact the performance of a structural system as well as the way it is constructed. Carbon composite is known for its high strength and stiffness, also it is a lightweight structural material. Current industrial techniques allow for manufacturing of structural components made of carbon composite to be used in building structures. Carbon composite as a structural material shows potential to be used in tall buildings where strength and stiffness requirements are a key parameter.This research focuses on applications of Carbon Composite, also known as Carbon Fiber Reinforced Polymer (CFRP), as a structural material for tall buildings. The research aims to study the properties of carbon composite as a structural material and to explore its application in the structural system for tall buildings. Mechanical properties of CFRP such as strength, stiffness, etc. are studied with available literature to assess the potential of the material to be used in the design of structural system for tall buildings. Manufacturing processes along with fabrication methods are also studied to investigate the constructability using CFRP. The research draws attention on the issues of connectivity within CFRP structural components as well as performance of CFRP as a structural material in tall building structural systems. Computer based simulations are utilized to develop digital models and analyze the performance of the material in structural systems of tall buildings. Current applications of the material in building and construction sector are addressed in the literature review. This research evaluates the performance of the structural systems for tall buildings using carbon composite as the primary structural material. Connection level simulations presented in this research provide insights on the significance of fiber orientation in the fabrication of structures. Other challenges in the widespread use of CFRP material in tall buildings are addressed in the research but focus of the research is on the structural applications of the material in tall buildings. The research provides information about the use of CFRP as a structural material in tall buildings. The results of this study offer significant insights about the issues of connectivity and constructability related to use of CFRP in tall buildings. This research also provides a parametric framework for architects and designers to evaluate and study the performance of a structural materials to be used in tall building structural systems using finite element analysis.
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- Title
- Evaluating the Impact of Residential Indoor Air Quality and Ventilation and Filtration Interventions on Adult Asthma-Related Health Outcomes in Chicago, IL
- Creator
- Kang, Insung
- Date
- 2022
- Description
-
Human exposure to a variety of airborne pollutants is associated with various adverse health effects, ranging from respiratory symptoms to...
Show moreHuman exposure to a variety of airborne pollutants is associated with various adverse health effects, ranging from respiratory symptoms to exacerbation of chronic diseases to cardiovascular disease and cancer. While most of our knowledge of the adverse impacts of air pollution comes from studies utilizing outdoor air pollutants as surrogates for exposure, people spend most of their time indoors, especially at home, where pollutant concentrations are often higher than outdoors. And within homes, mechanical ventilation systems and filtration are increasingly recommended to provide fresh air for ventilation and dilute indoor pollutant sources. There are a variety of ventilation system types that can be used for home retrofits; however, there is limited information on how they affect indoor air quality (IAQ) from both indoor and outdoor sources and how they influence occupant health and well-being. Therefore, to fill some of these knowledge gaps, this research aims to evaluate the effects of indoor air quality broadly, as well as interventions with three common types of residential mechanical ventilation system retrofits (i.e., continuous exhaust-only, intermittent fan-integrated supply, and continuous balanced systems with energy recovery ventilators), on asthma-related health outcomes in a cohort of adults in Chicago, IL. The key findings of this dissertation indicate that exposures to indoor NO2 and PM, higher indoor temperature, and mold/dampness were associated with poorer asthma control. The home ventilation and air filtration interventions, regardless of ventilation system type, significantly improved asthma control of the study population (~4% increase in ACT score; p < 0.001), and led to reductions in indoor concentrations of formaldehyde (HCHO) (-19.5 ppb; -63%; p < 0.001), carbon dioxide (CO2) (-120 ppm; -15%; p < 0.001), nitrogen dioxide (NO2) (-1.8 ppb; -3%; p = 0.035), and particulate matter (PM), including PM1 (-4.9 µg/m3; -43%; p = 0.001), PM2.5 (-4.9 µg/m3; -39%; p = 0.003), and PM10 (-6.2 µg/m3; -41%; p = 0.003). Additionally, asthma control was significantly improved in all subgroups: participants who received both ventilation and filtration interventions (~6% increase in ACT score; p < 0.001); continuous exhaust-only systems (~3% increase in ACT score; p = 0.033); intermittent central-fan-integrated-supply (CFIS) systems (~3% increase in ACT score; p = 0.018); and continuous balanced systems with an energy recovery ventilator (ERV) (~7% increase in ACT score; p < 0.001). Indoor CO2 concentrations were significantly reduced in homes with continuous ventilation systems, including exhaust-only (-165 ppm, -20%; p = 0.005) and balanced ERV systems (-186 ppm, -23%; p = 0.004), while indoor particulate matter (PM1, PM2.5, and PM10) concentrations were significantly reduced in homes with ventilation systems with filtration upgrades, including CFIS (PM1: -5.3 µg/m3, -46%; PM2.5: -5.0 µg/m3, -39%; and PM10: -6.2 µg/m3, -41%; all p < 0.05) and balanced ERV systems (PM1: -7.5 µg/m3, -59%; PM2.5: -8.3 µg/m3, -58%; and PM10: -10.4 µg/m3, -61%; all p < 0.05). Last, results of a cost-benefit analysis (CBA) of the three types of mechanical ventilation systems over an assumed 10-year life span, which predicted impacts on mortality and asthma outcomes based on measured impacts on two indoor pollutants – PM2.5 and NO2 – relative to initial and operational costs, as well as filtration upgrade costs, suggest that the intermittent CFIS system with improved MERV 10 filtration was the most beneficial approach, with the central benefit-cost ratio (BCR) of 6.0, followed by the continuous balanced ERV system (central BCR = 3.7) and exhaust-only system (central BCR = 3.2). This dissertation provides the first known empirical data in the U.S. on asthma outcomes associated with different types of mechanical ventilation systems that have highly varying impacts on indoor pollutant concentrations of both indoor and outdoor origin and environmental conditions. Results are also expected to provide much-needed guidance to homeowners, contractors, builders, and agencies on the advantages and disadvantages of different types of residential mechanical ventilation systems.
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- Title
- Self-Reconfigurable Soft Robots Based on Boundary-Constrained Granular Swarms
- Creator
- Karimi, Mohammad Amin
- Date
- 2022
- Description
-
Unlike conventional robots, which consist of rigid bodies and linkages, soft robots are composed of compliant and flexible components and...
Show moreUnlike conventional robots, which consist of rigid bodies and linkages, soft robots are composed of compliant and flexible components and actuators. This distinction enables adaptive behaviors in response to unpredictable environments, like manipulating objects with a variety of shapes. As such, soft robots afford greater potential over traditional robots for safe human interaction.Despite these advantages, there remain obstacles due to the challenges in modeling, controlling, and fabricating soft materials. For example, soft robots that rely on thermal or electrical actuation are typically slow to respond and unable to apply large forces as compared to traditional robots. Pneumatically actuated soft robots, while more responsive and capable of applying larger forces, generally need to be tethered to external control mechanisms, which becomes limiting in tasks that require lightweight, autonomous functionality.In contrast, this thesis describes a new type of robot that exhibits those same characteristics, but achieves them via a boundary-constrained swarm.The robotic structure consists of passive granular material surrounded by an active membrane that is composed of a swarm of interconnected robotic sub-units. The internal components are important for overall function, but their relative configuration is not. This allows for an effectively random, unstructured placement of the internal components, which in turn creates excellent morphability. Collectively, the subunits determine the overall shape of the robot and enable locomotion through interaction with external surfaces.The constrained swarm embodies the continuum, compliant, and configurable properties found in soft robots, but in this state the robot is limited in its ability to manipulate objects due to the relatively low force it can apply to external objects.To address this issue, the unique ability to execute a jamming phase transition is added to the robot. Importantly, jamming is controlled by the degree by which the passive particles are spatially confined by the membrane, and this in turn is controlled by the active sub-unit robots using different jamming mechanisms. The robot exploits its ability to transition between soft (unjammed) and rigid (jammed) states to induce fluid-like flexibility or solid-like rigidity in response to objects and features in the environment.In order to investigate this design concept, I have studied different prototype designs for the robot that varied in terms of the locomotion and jamming mechanisms. I also present a simulation framework in which I model the design and study the scalability of this class of robots. The simulation framework uses the Project Chrono platform, which is a multi-body dynamics library that allows for physics-driven collision and contact modeling.
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- Title
- Workload Interference Analysis and Mitigation on Dragonfly Class Networks
- Creator
- Kang, Yao
- Date
- 2022
- Description
-
Dragonfly class of networks are promising interconnect topologies that support current and next-generation high-performance computing (HPC)...
Show moreDragonfly class of networks are promising interconnect topologies that support current and next-generation high-performance computing (HPC) systems. Serving as the "central nervous system", Dragonfly tightly couples tens of thousands of compute nodes together by providing high-bandwidth, low-latency data exchange for exascale computing capability. Dragonfly can support unprecedented system scale at a reasonable cost thanks to its hierarchical architecture. In Dragonfly systems, network resources such as routers and links are arranged into identical groups.Groups are all-to-all connected through global links, and routers within groups are connected via local links. In contrast to the fully connected inter-group topology, connections for the routers within groups are designed according to the system requirement. For example, the one-dimensional all-to-all connection is favored for higher network bandwidth, a two-dimensional grid arrangement can be constructed to support larger system size, and a tree structure router connection is built for the extreme system scale. The hierarchical design with groups enables the topology to support unprecedented system size while maintaining a low-diameter network. Packets can be minimally delivered by simply traversing the network hierarchy between groups through global links and reaching their destinations through local links. In case of network congestion, packets can be non-minimally forwarded through any intermediate group to increase the system throughput. As a result, all network resources are shared such that links and routers are not dedicated to any node pair. While link utilization is increased, shared network resources lead to inevitable network contention among different traffic flows, especially for the systems that hold multiple workloads at the same time. This network contention is observed as the workload interference that causes degraded system performance with delayed workload execution time. In this thesis, we first model and analyze the workload interference effect on Dragonfly+ topology through extensive system simulation.Based on the comprehensive interference study, we propose Q-adaptive routing, a multi-agent reinforcement learning based solution for Dragonfly systems. Compared with the existing routing solutions, the proposed Q-adaptive routing can learn to forward packets more efficiently with smaller packet latency and higher system throughput. Next, we demonstrate that intelligent routing algorithms such as Q-adaptive routing can greatly mitigate workload interference and optimize the overall system performance. Subsequently, we propose a dynamic job placement strategy for workload interference prevention. When combined with Q-adaptive routing, dynamic job placement gives users the flexibility to either reduce workload interference from communication intensive applications or protect target applications for higher performance stability.
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- Title
- Intelligent Battery Switching Module for Hybrid Electric Aircraft
- Creator
- Kamal, Ahmad
- Date
- 2022
- Description
-
The growth in world economics, tourism and international cooperation has resulted in significant growth of civil aviation industry. This...
Show moreThe growth in world economics, tourism and international cooperation has resulted in significant growth of civil aviation industry. This growing number of fossil fuel reliant aircrafts will significantly increase waste gas emissions with detrimental impact on the environment. The system efficiency of the aircraft must be substantially improved to reduce the fuel burn and thus waste gas emissions. Therefore, the aircraft industry is pushing towards higher electrification of future aircrafts to increase system efficiency, reduce fuel burn and to lower emissions as well as operational costs. The more electric aircraft (MEA) design concept, commercially realized by Boeing 787 and Airbus A380, increases system efficiency by replacing the mechanical, pneumatic, and hydraulic systems with electrical systems. However, global regulation authorities demand further reduction in waste gas emissions and fuel burn. To meet these stringent demands, the aircraft industry is exploring hybrid electric aircrafts which can significantly reduce fuel burn by electrifying the propulsion train of the aircraft. This higher penetration of electrical energy in the aircraft warrants smart short-circuit protection with ultrafast response time. However, current hybrid aircrafts still use outdated mechanical and thermal short-circuit protection which have historically proven to cause numerous tragedies. Solid-state power controller (SSPC) is an alternate solution which uses semiconductor devices to offer faster response. However, the main drawbacks of SSPCs are their need for active cooling due to higher conduction loss and the use of foldback current limiting approach to limit the inrush current of DC-link capacitor of the powertrain. The foldback current limiting approach degrades the power semiconductor devices used due to excessive heat loss by driving the device near the safe operating area (SOA) limits of the device. This thesis presents a 750V/250A intelligent Li-ion battery switching module (BSM) for hybrid electric aircraft propulsion application. The BSM uses commercially available 1200 V SiC JFET power modules with ultra-low RDSON in parallel to achieve sub-mΩ total on-resistance, comparable to the incumbent mechanical contactor solution. This allows the total nominal conduction power loss of the BSM to be less than merely 23 W, permitting maintenance-free passive cooling. In contrast to the incumbent contactor solution, the BSM has ultrafast response (µs-level) to a fault condition. Which, in conjunction with the reduced fault current stress, significantly improves the operation lifetime of the entire system. The BSM incorporates various intelligent features by implementing a tri-mode operation concept, which allows to pre-charge the DC-link capacitor with a limited charging current in PWM mode. To mitigate single-point failures, several design redundancy measures are implemented to ensure reliability and safety for the aircraft. Design considerations of the circuit and physical design of the BSM are discussed in detail including the design of the custom laminated busbar and thermal analysis. Furthermore, the inherent uncontrolled oscillation phenomenon of the JFET cascode structure is explored and addressed. Finally, the experimental results obtained from the built and tested prototype of the BSM are reported.
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- Title
- Advanced methods for storage ring nonlinear beam dynamics design and implementation
- Creator
- Song, Minghao
- Date
- 2022
- Description
-
To meet the increasing demands of scientific researchers for brighter photonbeams, storage ring beam emittance is continually pushed down to a...
Show moreTo meet the increasing demands of scientific researchers for brighter photonbeams, storage ring beam emittance is continually pushed down to a new ultra-low level. It, therefore, becomes correspondingly more challenging to ensure such storage rings have good nonlinear beam dynamics performance. This thesis work is focused on developing advanced methods for low emittance storage ring nonlinear beam dynamics design and implementation.Nonlinear beam dynamics optimization is essential to low emittance storagering design. A highly efficient multi-objective optimization algorithm is needed to simultaneously achieve a large dynamic aperture and a large local momentum aperture. Work was done to improve and test a machine learning-based algorithm called multi-generation Gaussian process optimizer (MG-GPO). This advanced method uses constructed GP models to pre-select solutions, and benchmarking of results on toy problems shows that MG-GPO converges significantly faster than traditional algorithms. The MG-GPO algorithm was successfully applied to nonlinear lattice design optimization, for example, to the SPEAR3 upgrade 7-nm lattice, and it was demonstrated to converge faster than NSGA-II and MOPSO. This was due to its capability of selecting candidates that tend to have better performance. This algorithm will help accelerate nonlinear lattice studies.Correction of nonlinear beam dynamics is also important for low emittancestorage ring commissioning and operation. In order to measure and correct features relevant to the nonlinear beam dynamics, an effective method is needed to excite sustained beam oscillations to large amplitude. A method based on the concept of autoresonance was proposed. This advanced technique excites nonlinear transverse beam motion in storage rings by sweeping the drive frequency. The theory for the autoresonance threshold was derived for the nonlinear optics systems in storage rings, both with and without damping effects, using Hamiltonian dynamics. The theoretical predictions for the drive amplitude threshold were found to agree well with simulations for a simple storage ring model, as well as for simulations with the actual SPEAR3 and APS lattices. The theory was also compared favorably to historical data from experiments on SPEAR3. Simulations verified that an oscillation driven by autoresonant excitation matches the character of a free oscillation, so that beam oscillation data taken during the ramping process can confidently be used to characterize the nonlinear beam dynamics performance. The precision of measurements can be improved by using autoresonant excitation since large amplitude beam oscillations are sustained significantly longer. Simulations of autoresonant excitation demonstrated the measurements of the detuning coefficients and resonance driving terms. The use of autoresonant excitation for the detection of faulty magnets and correction of resonance driving terms was also demonstrated.Online optimization is an alternative way to effectively improve nonlinear beamdynamics performance in a real storage ring. The greater efficiency of an advanced optimization algorithm is also needed to find globally optimal solutions in the limited experimental time that is typically available. The MG-GPO algorithm was implemented for SPEAR3 vertical emittance minimization and injection efficiency optimization. Again, the optimized solutions demonstrate that MG-GPO is more efficient than the commonly used PSO algorithm. SPEAR3 performance was successfully improved during the online optimization runs with MG-GPO.
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- Title
- Predictive Energy Management of Connected Hybrid Electric Vehicles in the Presence of Uncertainty
- Creator
- Sotoudeh, Seyedeh Mahsa
- Date
- 2022
- Description
-
Energy efficiency improvements brought by electrification of the powertrain in Hybrid Electric Vehicles (HEVs) highly depend on their...
Show moreEnergy efficiency improvements brought by electrification of the powertrain in Hybrid Electric Vehicles (HEVs) highly depend on their powertrain Energy Management Strategy (EMS) that determines optimal power allocation between powertrain components.Eco-driving based EMS seeks further energy efficiency improvements through optimizing vehicle's driving cycle (velocity and hence torque demand), in addition to the powertrain's EMS. A novel hierarchical EMS is developed in this thesis for connected human-driven HEVs and then extended to automated HEVs that effectively addresses some of the major challenges of the energy management problem. At its high-level, a computationally-tractable Pseudospectral Optimal Controller (PSOC) with discounted cost is employed to approximately solve the powertrain's energy management problem over driving cycle previews of the entire trip. The high-level's approximate solution is then used as a reference by the low-level tube-based Model Predictive Controller (MPC) that solves the problem over higher-quality, short-horizon driving cycles in a real-time applicable fashion. For human-driven HEVs, a Long Short-Term Memory (LSTM) neural network predicts the human driver's velocity profile over low-level's short horizons. A velocity optimizer is added to the low-level for automated HEVs that optimizes the vehicle's driving cycle by effectively utilizing regenerative braking capability of the HEV. At the low-level, the tube-based MPC controller solves the powertrain's energy management problem over either predicted (human-driven HEV) or optimized (automated HEV) driving cycles by accounting for driving cycle's uncertainty, due to uncertain future information, and hence ensures robust constraints satisfaction. A novel cost-to-go approximation method is developed that uses the optimal costate trajectories obtained from the high-level PSOC controller to generate terminal costs for the low-level controller. This improves suboptimality of the short-horizon solutions and ensures charge balance constraint satisfaction at the end of the trip without having to impose conservative constraints. A novel learning-based framework is also proposed to jointly optimize the automated HEV's driving cycle and its powertrain's power split. A Deep Neural Network (DNN)-based MPC controller is developed for the low-level that jointly optimizes the HEV's driving cycle and powertrain energy management in a real-time applicable manner. To ensure constraints satisfaction, a novel Quadratic Programming (QP)-based projection of the DNN-based approximate control laws is proposed that can be efficiently solved in real-time. Simulation results over standard and real-world driving cycles demonstrate efficacy of the proposed control frameworks in terms of suboptimality (fuel efficiency) improvement, potential real-time applicability, and constraints (especially charge balance constraint) satisfaction in the presence of driving cycle uncertainty.
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- Title
- Thermal Effects in Fluid Dynamics
- Creator
- Sulzbach, Jan-Eric
- Date
- 2021
- Description
-
In this thesis we propose a mathematical framework modeling non-isothermal fluids.The framework is based on a coupling between non-equilibrium...
Show moreIn this thesis we propose a mathematical framework modeling non-isothermal fluids.The framework is based on a coupling between non-equilibrium thermodynamics and an energetic variational approach for the mechanical parts of the system. From this general model we derive and analyze three separate systems.The first application is the Brinkman-Fourier model. This is related to the ideal gas system, where the pressure and internal energy depend linearly on the product of density and temperature. This is a subsystem to the general Navier-Stokes-Fourier system. We prove the existence of local-in-time weak solutions via compensated compactness arguments.The next model we study is a non-isothermal diffusion system involving chemical reactions. For a system close to chemical equilibrium we show the well-posedness of classical solution using a fixed-point argument involving theory of homogeneous Besov spaces.The third application of the general theory is for another general diffusion system with a Cahn-Hilliard energy. In this framework, we study in detail how the temperature can affect the system on different scales, leading to different models. For the analysis, we focus on one case and show the well-posedness of classical solutions. The proof relies on methods from the theory of Besov spaces and paradifferential calculus.
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- Title
- Technological Consciousness in Midwestern American Farming: From Party Lines to Autonomous Tractors
- Creator
- Sziron, Mónika
- Date
- 2022
- Description
-
This dissertation is primarily concerned with understanding the current conceptions, perceptions, and ethical concerns of artificial...
Show moreThis dissertation is primarily concerned with understanding the current conceptions, perceptions, and ethical concerns of artificial intelligence in Midwestern agriculture. Using the theory of technological consciousness as a backdrop for understanding the relationship between Midwestern agriculture and technology, in chapter two this dissertation first provides a narrative review of major technological developments throughout history in Midwestern farming and how the human experience in farming is influenced by technology throughout history. This history provides context for the current state of Midwestern agriculture, which is now increasingly entangled with artificial intelligence. The theory behind artificial intelligence ethics and general trends in artificial intelligence are discussed in chapter three. To understand present conceptions, perceptions, and ethical concerns of artificial intelligence for Midwestern farmers, a pilot survey was dispersed to farmers and pilot media content analysis was conducted on Midwestern agriculture publications. The results from this pilot survey and pilot media content analysis are discussed in chapter four. Chapter five delves into theory and how the human experience with technology has evolved over time and its effects on the human experience today. This chapter also provides theoretical insights for the future of farming with artificial intelligence. The dissertation concludes with reviewing the ethical concerns relating to artificial intelligence in agriculture for Midwestern farmers, provides recommendations for developers of agriculture technology, and highlights the new partnership between farmers and computer scientists and how this partnership will lead the way in the future of Midwestern farming.
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- Title
- DO ACT CONSTRUCTS MODERATE ASSOCIATIONS BETWEEN SOCIAL MEDIA AND EATING PATHOLOGY?
- Creator
- Badillo Regan , Krystal E
- Date
- 2022
- Description
-
Limited research has assessed individuals with disordered eating and their social media use. Additionally, there has been limited...
Show moreLimited research has assessed individuals with disordered eating and their social media use. Additionally, there has been limited investigation into psychotherapy constructs that could be used when addressing social media use in those with eating pathology. This study aims to improve the existing literature on social media and eating pathology by recruiting a sample of probable eating disorders and assessing if Acceptance and Commitment Therapy (ACT) constructs moderate the relation between social media and eating pathology. It is anticipated that 1) eating disorder pathology severity will be positively correlated with photo-based social media behavior; 2) eating disorder symptom severity will be positively associated with importance of social media; and 3) those who score higher in mindful eating, body image flexibility, and body image acceptance will have a weaker positive association between ED pathology and importance of social media and those who score lower in body image cognitive fusion will have a weaker positive association between ED pathology and importance of social media mindful eating, body image flexibility, body image acceptance, and body image cognitive fusion will moderate the relation between eating disorder symptom severity and social media use. To test the hypotheses women with a probable eating disorder (N=121) completed online questionnaires via prolific. The majority of participants identified as non-Hispanic (81%) and White (45.5%). Results suggest that there are associations between ED pathology, ACT constructs, Importance of Twitter and Instagram, and photo-based behaviors but not Importance of Facebook. Additionally, the moderation models examined were not statistically significant. Implications of these findings are discussed as well as future direction for research and clinical work.
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- Title
- OPTIMUM WEIGHT STIFFNESS STRUCTURAL DESIGN
- Creator
- Barnett, Ralph L.
- Date
- 2021
- Description
-
My adventures with flexible structures began on the IIT campus with an extracurricular undergraduate project to design an “Open House Exhibit”...
Show moreMy adventures with flexible structures began on the IIT campus with an extracurricular undergraduate project to design an “Open House Exhibit” for the Civil Engineering Department. I chose to display a reinforced concrete diving board together with a prestressed concrete diving board. Visitors enthusiastically pounced on the reinforced concrete structure whose rigid response disappointed one and all. Their indignation was transferred to the prestressed cantilever which thrust them upward from six to ten feet into the air. This unexpected response from a diving board became so dangerous that the Exhibit was unceremoniously closed. I still have the display sign, “More Bounce to the Ounce.”While still an undergraduate, I secured a part-time job at Armour Research Foundation where I responded to a bid request from Rock Island Arsenal to design the 26 foot Honest John Rocket Launcher Rail at minimum weight. This tactical weapon was transported by helicopter. I basked in the fantasy that I was Leonardo da Vinci without his artistic proclivity. Rocket launchers that droop during operation are similar in concept to a circular firing squad. So began my research into minimum weight beams based on deflection rather than strength. I searched for the shoulders of Giants. I found them in the form of mathematicians not structural engineers. I achieved a 26.5% weight savings in the 1126 pound rail by optimizing the geometry. When I developed an optimum prestressed and segmented Kentanium cermet rail, the weight savings became 89%. The right material provides a bigger bang for the buck. When my journey into optimum design began, I was armed only with analysis tools: strength, stability, and stiffness. This thesis begins with an outline of my present toolbox which contains eight design concepts: 1. Establish the Geometry, 2. Select a material from a finite number of candidates, 3. Prestress and Prestrain, 4. Statistical Screening (Proof Testing), 5. Manipulation of Boundary Conditions, 6. Energized Systems, 7. Counterweights, 8. Self-Healing and Self-Reinforcing. Four of these are used through this review which focuses on stiffness. Beginning with beams, deflection control examples are described where prestraining and prestressing techniques are used to produce both a zero-deflection beam and a method for pushing with a chain. The calculus of variations made it possible to establish optimum tapers for the flanges and webs of I-beams that minimize beam weight for a specified deflection or, because of reciprocity, minimize beam deflection for a specified beam weight. An anomaly is encountered that enables one to achieve an upward, downward, or zero deflection with a set of beams of vanishing weight. In addition, special circumstances are defined where a uniform strength design is identical to the minimum weight design based on a specific deflection. Closed form solutions are obtained for a variety of loading scenarios. One problem is presented for self-weight that leads to a nonlinear integral equation. The optimum stiffness-weight design of trusses is undertaken where the area distribution of the truss members is optimized using Lagrange’s method of undetermined multipliers. Once again, we obtain a degenerate case where upward, downward, and zero deflection conditions can be met with an infinite set of trusses of vanishing weight. We photograph a simply supported truss under a downward load that leads to an upward deflection at one of the joints. Special loading conditions are identified that lead to uniform stress designs that are identical to the minimum weight designs based on deflections. This study provides a Segway into the world of minimum weight strength design of trusses. The resulting Maxwell and Michell trusses sometimes display the optimum distribution of bar areas from the point of view of stiffness. Many practitioners are under the mistaken impression that Michell structures, when they exist, provide the optimum truss profile for stiffness. Unfortunately, the optimum array of truss joints based on deflection does not exist. For both trusses and beams the optimum distribution of mass is shown to be necessary and sufficient; the sufficiency is established using well-known inequalities. The role of stiffness in the design of columns is explored in our final chapter. This cringe-worthy history of column analysis begins our study as a warning to practitioners who use analysis as their basis for design and especially optimum design. Conventional elastic and inelastic buckling theories provide little insight into the design of columns. The fundamentals of minimum weight column design are presented to show the power of design theory in contrast to analysis. Both prismatic and tapered columns are studied with one surprise result; the optimum taper gives rise to a uniform bending stress (without axial stresses). It was fun to see that in 1733 Lagrange made a mistake in calculus of variations that led to the incorrect solution for the optimum tapered column. It took 78 years before Clausen obtained the correct solution. The problem has been revisited by William Prager and again by the author who used dynamic programming. Of course, we all got the same result which is a dreadful solid circular tapered column that is heavier than any ordinary waterpipe. The best of a class is not necessarily the best possible design. Under the heading, “Intuition is a good servant but a bad master,” we introduce the notions of tension members that buckle, columns constructed from spherical beads, optimum rigging of crane booms, and deflection reversal of beam-columns. In several places we observe that the weight of optimum columns is proportional to P^α where P is the axial load and α is less than unity. We fail to tell the reader that this implies that minimum weight columns require putting all your eggs in one basket; one column under load P is lighter than two columns each under load P/2. On the other hand, we expose the solid circular column as the least efficient shape among all regular polygons, the equilateral triangle is the best. Indeed, there is a family of rectangles that are superior to the circular cross-section. Finally, the author’s prestressed tubular column is introduced that is pressurized to eliminate local buckling. Euler’s buckling can always be eliminated with a thin-wall section of sufficient width without a weight penalty. The weight of the balloon-like member is proportional to (PL) which implies that at last we have a compressive member that meets the requirement of a Michell structure. Bundling of pressurized gas columns are possible without a weight penalty. Further, the column is insensitive to most imperfections. It is the lightest known column for small structural indices (P/L^2 ). When coupled with circulating cryogenic liquid as a prestressing system, a limiting column has a vanishing weight.
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- Title
- A Network Analysis of the Six Core Processes Associated with Acceptance and Commitment Therapy
- Creator
- Bailey, Jennifer Rose
- Date
- 2022
- Description
-
According to the theoretical model of Acceptance and Commitment Therapy, six core processes comprise a latent factor of psychological...
Show moreAccording to the theoretical model of Acceptance and Commitment Therapy, six core processes comprise a latent factor of psychological flexibility: present moment, chosen values, committed action, self as context, cognitive defusion, and acceptance. Little research has directly examined the unique relations among the processes. The present study extended our knowledge of the structure and relations between these processes by examining the relative importance and influence of a single process to the system of processes as a whole utilizing network analysis with a sample of 277 adult, non-clinical participants. Committed action was the most central of all the processes, demonstrating the highest strength centrality and most number of edges. Cognitive defusion and present moment also showed high strength centrality, suggesting that these processes exert the greatest influence on other processes in the network based on partial correlations controlling for all other constructs. Results provided support for the conceptualization of the three response styles (i.e., open, centered, and engaged). The addition of neuroticism to the core processes network showed little effect on the number of edges present between the six core processes. Neuroticism was strongly related to cognitive defusion and more weakly related to committed action. Results not only increased our understanding of the relations between processes and provided knowledge that may be useful to our understanding of the ACT theoretical model, but it also may have potential clinical implications, such as aiding in the identification of treatment targets to enhance psychological flexibility.
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- Title
- Sharpen Quality Investing: A PLS-based Approach
- Creator
- Jiao, Zixuan
- Date
- 2022
- Description
-
I apply a disciplined dimension reduction technique called Partial Least Square (PLS) to construct a new quality factor by aggregating...
Show moreI apply a disciplined dimension reduction technique called Partial Least Square (PLS) to construct a new quality factor by aggregating information from 16 individual signals. It earns significant risk-adjusted returns and outperforms quality factors constructed by alternative techniques, namely, PCA, Fama-Macbeth regression, a combination of PCA and Fama-Mabeth regression and a Rank-based approach. I show that my quality factor performs even better during rough economic patches and thus appears to hedge periods of market distress. I further show adding our quality factor to an opportunity set consisting of the other classical factors increases the maximum Sharpe ratio.
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- Title
- MICROSTRUCTURE AND MECHANICAL PROPERTIES OF DISCONTINUOUSLY PRECIPITATED NI-CO-AL ALLOYS
- Creator
- Ho, Kathy
- Date
- 2022
- Description
-
The study of high temperature structural materials has been one of great interest and immense focus in recent years of research and...
Show moreThe study of high temperature structural materials has been one of great interest and immense focus in recent years of research and development. With the capability of catering to specific needs and applications while being commercially cost-effective, these materials can be synthesized using various types of methods and materials for a large range of applications. In order to implement the advantageous properties of these materials for practical use in service, empirical data relating to the material and mechanical properties of these high temperature structural alloys must first be obtained. This can be achieved through numerous processing methods. One particular method involves precipitation strengthening. Two types of transformation modes include discontinuous and continuous precipitation. Discontinuous precipitation (DP) nucleates at high angle, incoherent grain boundary, grows through grain boundary diffusion, and produces a lamellar structure consisting of alternating layers of γ and γˡ (Ephler, 2004). Continuous precipitation (CP) nucleates within the grain, is controlled through volume diffusion producing, and results in a homogeneous distribution of equilibrium composition precipitates with a spherical/cuboidal morphology. Since both modes of transformation possess a chemical driving force, resulting from the supersaturation of solute, the coexistence of both DP and CP transformation in a material is possible. However, as demonstrated from past studies, the presence of a partial DP transformation in structural alloys is undesirable as detrimental effects on mechanical properties are observed. As a result, numerous studies have focused on suppressing DP all together. In 1972 Erhard Hornbogen hypothesized that a fully DP transformed material would yield superior mechanical properties, similar to pearlite formation in steel, since the lamellar structure would increase barriers to dislocation movement (Hornbogen, 1972). As a result, recent studies have redirected their focus in an effort to encourage DP transformation to completion for improved mechanical properties. Therefore, the purpose of this work was to 1) determine the aging conditions under which a complete, 100% DP transformation would be achieved in select alloys, 2) determine the conditions where optimal precipitate size via CP transformation is obtained to effectively use precipitation strengthening without the concern of over-aging, 3) experimentally compare the material and mechanical properties between 100% DP aged samples and CP aged samples consisting of the optimal precipitate size, 4) compare the mechanical properties between alloys that have undergone a complete DP transformation to commercial alloys currently used in service, and 5) provide empirical data to verify Hornbogen’s claim. The results from this work indicated that 1) a lower aging temperature promote DP transformation while a higher temperature promotes CP transformation, 2) a smaller grain size prior to aging was more favorable for DP transformation while larger grains were favorable for CP transformation, 3) a complete DP transformation was observed for Alloy 9 and Alloy 10 after aging at 500°C for 4 hours and 550°C for 4 hours, 4) Alloy 1, Alloy 3, and Alloy 5 were potentially undergoing a different type of transformation at lower DP aging temperatures, where β phase was present, 5) optimal precipitate size for effective use of precipitation strengthening (CP transformation) was achieved under CP aging conditions 700°C-1HR for Alloy 10 and 750°C-1HR for Alloy 9 and the forged stock bar, 6) a small fraction of DP consistently formed at the grain boundaries of the CP aged samples for all alloy samples, indicating that the nucleation of DP was quick, but growth was limited, 7) mechanical properties of the DP aged samples for Alloy 9, Alloy 10 and the forged bar were superior to their corresponding CP aged samples in terms of the hardness, UTS, and yield stress, but were less ductile than the CP aged samples, and 8) the mechanical properties of DP aged samples for Alloy 9, Alloy 10, and the forged bar were comparable, and at times superior, to the commercially available alloys. Due to limited prior research conducted on the mechanical properties of DP alloys, this investigation serves as a pioneering effort experimentally determine if the mechanical properties of completely DP transformed material are superior to that of CP transformed material, aged to optimal precipitate size, while collecting empirical data to verify Hornbogen’s claim.
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- Title
- EMAT DESIGN CONFIGURATIONS AND SOFTWARE-DEFINED ULTRASONIC COMMUNICATIONS THROUGH METALLIC CHANNELS IN NUCLEAR FACILITIES
- Creator
- Huang, Xin
- Date
- 2022
- Description
-
Nuclear facilities are partitioned into different blocks, and all equipment therein is well-packed for isolation purposes. The primary...
Show moreNuclear facilities are partitioned into different blocks, and all equipment therein is well-packed for isolation purposes. The primary barriers of each block include a thick, reinforced, high-strength concrete wall. The presence of physical boundaries introduces a major challenge to implementing wired or radio frequency (RF) wireless communication. Achieving data communication through the solids channel, especially considering the complex environment in nuclear power plants, is very challenging. Ultrasonic communication is a desirable method for information transfer through solid mediums such as metallic bars or pipes. This thesis is methodologically innovative in the way it seeks the best solution for ultrasonic communications through metallic channels. Therefore, we address the following research areas: 1. The advantages of using electrical-magnetic acoustic transducers (EMATs) as transmitter and receiver; 2. The fundamentals of the EMAT structure and wave generation mechanism for ultrasonic communications; 3. The channel model and behavior of ultrasonic wave propagation in a different structure of solid channels; 4. How to minimize the adverse impact of wave dispersion and reverberation; 5. How to increase the bitrate and decrease the bit error rate (BER) of an ultrasonic communication system; 6. How to utilize the software-defined system-on-chip (SoC) platform for ultrasonic communications; and 7. How to implement secure ultrasonic video transmission through solid channels. In this thesis, we have investigated the feasibility of using Periodic-permanent-magnet electromagnetic acoustic transducers (PPM-EMATs) transmitter and receiver as the information-bearing of ultrasonic waves across the plate channels (shear horizontal waves) and pipe channels (torsional waves). Methods such as time-reversal (TR), pulse shaping, and adaptive equalizer techniques are studied for improving the signal-to-noise ratio (SNR) of ultrasonic communication systems. We also investigated a novel software-defined ultrasonic communication system (SDUC) for real-time video transmission through a highly reverberant and dispersive metallic bar channel. Furthermore, we investigated the feasibility of combining orthogonal frequency-division multiplexing (OFDM) with quadrature amplitude modulations (QAM) for bitrate peak performance. Strategies and guidelines were established for the best solutions to combat intersymbol interference (ISI) caused by the severe reverberation inherent in metallic channels. A practical solution for video transmission, adhering to the Digital Video Broadcasting Terrestrial (DVB-T) standard, was also examined for video streaming transmission of 240p, 480p, and 720p resolutions at 20 frames per second (FPS) across a rectangular aluminum bar (ARB) channel. Through ultrasonic experimental studies for channel analysis, we achieved a peak video transmission rate of 1074 kbps with 3.3×10-4 BER despite reverberation, the multipath effect, and signal fading within the ARB channel.
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- Title
- Numerical Analysis and Deep Learning Solver of the Non-local Fokker-Planck Equations
- Creator
- Jiang, Senbao
- Date
- 2022
- Description
-
This thesis is divided into three mutually connected parts. ...
Show moreThis thesis is divided into three mutually connected parts. In the first part, we introduce and analyze arbitrarily high-order quadrature rules for evaluating the two-dimensional singular integrals of the forms \begin{align*} I_{i,j} = \int_{\mathbb{R}^2}\phi(x)\frac{x_ix_j}{|x|^{2+\alpha}} \d x, \quad 0< \alpha < 2 \end{align*} where $i,j\in\{1,2\}$ and $\phi\in C_c^N$ for $N\geq 2$. This type of singular integrals and its quadrature rule appear in the numerical discretization of fractional Laplacian in non-local Fokker-Planck Equations in 2D. The quadrature rules are trapezoidal rules equipped with correction weights for points around singularity. We prove the order of convergence is $2p+4-\alpha$, where $p\in\mathbb{N}_{0}$ is associated with total number of correction weights. We present numerical experiments to validate the order of convergence of the proposed modified quadrature rules. In the second part, we propose and analyze a general arbitrarily high-order modified trapezoidal rule for a class of weakly singular integrals of the forms $I = \int_{\R^n}\phi(x)s(x)\d x$ in $n$ dimensions, where $\phi$ and $s$ is the regular and singular part respectively. The admissible class requires $s$ satisfies three hypotheses and is large enough to contain singular kernel of the form $P(x)/|x|^r,\ r > 0$ where $P(x)$ is any monomial with degree strictly less than $r$. The modified trapezoidal rule is the singularity-punctured trapezoidal rule plus correction terms involving the correction weights for grid points around singularity. Correction weights are determined by enforcing the quadrature rule to exactly evaluate some monomials and solving corresponding linear systems. A long-standing difficulty of these types of methods is establishing the non-singularity of the linear system, despite strong numerical evidence. By using an algebraic-combinatorial argument, we show the non-singularity always holds and prove the general order of convergence of the modified quadrature rule. We present numerical experiments to validate the order of convergence. In the final part, we propose \emph{trapz-PiNN}, a physics-informed neural network incorporated with a modified trapezoidal rule and solve the space-fractional Fokker-Planck equations in 2D and 3D. We verify the modified trapezoidal rule has the second-order accuracy for evaluating the fractional laplacian. We demonstrate trapz-PiNNs have high expressive power through predicting solutions with low $\mathcal{L}^2$ relative error on a variety of numerical examples. We also use local metrics such as point-wise absolute and relative errors to analyze where could be further improved. We present an effective method for improving performance of trapz-PiNN on local metrics, provided that physical observations of high-fidelity simulation of the true solution are available. Besides the usual advantages of the deep learning solvers such as adaptivity and mesh-independence, the trapz-PiNN is able to solve PDEs with fractional laplacian with arbitrary $\alpha\in (0,2)$ and specializes on rectangular domains. It also has potential to be generalized into higher dimensions.
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- Title
- FACTORS INFLUENCING INDIVIDUALS’ PROVISION OF AUTONOMY SUPPORT TO THEIR PARTNERS WITH CHRONIC PAIN: A PATH ANALYSIS MODEL BASED ON SELF-DETERMINATION THEORY
- Creator
- Ivins-Lukse, Melissa N.
- Date
- 2021
- Description
-
Receiving autonomy support from a relationship partner has been associated with increased physical activity among individuals with chronic...
Show moreReceiving autonomy support from a relationship partner has been associated with increased physical activity among individuals with chronic pain (ICP), but no studies have explored what factors may influence partners’ use of an autonomy supportive interpersonal style with an ICP. Self-determination theory (SDT) posits that contextual, perceptual, and individual factors influence how much individuals use an autonomy supportive interpersonal style through the mediators of basic psychological need satisfaction and autonomous motivation. The present study used path analysis to test a SDT model of the relationships between a contextual factor (autonomy support from health care provider), a perceptual factor (partner’s perception of ICP motivation for physical activity), an individual factor (partner catastrophizing about ICP’s pain), and the sequential mediators of relationship need satisfaction and autonomous motivation with respect to the dependent variable of partners’ use of an autonomy supportive interpersonal style. 176 partners of ICPs completed a cross-sectional survey including the Health Care Climate Questionnaire, partner-report revised Behavioral Regulation in Exercise Questionnaire, Pain Catastrophizing Scale – Significant Other version, Need Satisfaction Scale, Motivation to Help, and Interpersonal Behaviours Questionnaire-Self. The proposed model demonstrated poor fit to the data: χ2 (10) = 31.949, p < 0.001), RMSEA = 0.11 (90% CI = .07 to .16, p = 0.01), CFI = 0.81, and SRMR = .10. While the overall model was not supported, most individual pathways in the model were significant. Alternative analyses were conducted to identify a model with acceptable fit.
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