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Description
When solving analysis, estimation, and control problems for Partial Differential Equations (PDEs) via computational methods, one must resolve three main challenges: (a) the lack of a universal parametric representation of PDEs; (b) handling unbounded differential operators that appear as parameters; and (c), enforcing auxiliary constraints such as Boundary conditions and continuity conditions. To address these challenges, an alternative representation of PDEs called the `Partial Integral Equation' (PIE) representation is proposed in this work. Primarily, the PIE representation alleviates the problem of the lack of a universal parametrization of PDEs since PIEs have, at most, $12$ Partial Integral (PI) operators as parameters. Naturally, this also resolves the challenges in handling unbounded operators because PI operators are bounded linear operators. Furthermore, for admissible PDEs, the PIE representation is unique and has no auxiliary constraints --- resolving the last of the $3$ main challenges. The PIE representation for a PDE is obtained by finding a unique unitary map from the states of the PIE to the states of the PDE. This map shows a PDE and its associated PIE have equivalent system properties, including well-posedness, internal stability, and I/O behavior. Furthermore, this unique map also allows us to construct a well-defined dual representation that can be used to solve optimal control problems for a PDE. Using the equivalent PIE representation of a PDE, mathematical and computational tools are developed to solve standard problems in Control theory for PDEs. In particular, problems such as a test for internal stability, Input-to-Output (I/O) $L_2$-gain, $\hinf$-optimal state observer design, and $\hinf$-optimal full state-feedback controller design are solved using convex-optimization and Lyapunov methods for linear PDEs in one spatial dimension. Once the PIE associated with a PDE is obtained, Lyapunov functions (or storage functions) are parametrized by positive PI operators to obtain a solvable convex formulation of the above-stated control problems. Lastly, the methods proposed here are applied to various PDE systems to demonstrate the application.
ContributorsShivakumar, Sachin (Author) / Peet, Matthew (Thesis advisor) / Nedich, Angelia (Committee member) / Marvi, Hamidreza (Committee member) / Platte, Rodrigo (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2024
Description
Carbon nanotubes (CNTs) have emerged as compelling materials for enhancing both electrical and mechanical properties of aerospace structures. Buckypaper (BP), a porous
membrane consisting of a highly cross-linked network of CNTs, can be effectively
integrated with carbon fiber reinforced polymer (CFRP) composites to simultaneously
enhance their electromagnetic interference (EMI) shielding effectiveness (SE) and
mechanical properties. In existing literature, CNT based nanocomposites are shown to
improve the flexural strength and stiffness of CFRP laminates. However, a limited amount
of research has been reported in predicting the EMI SE of hybrid BP embedded CFRP
composites.
To characterize the EMI shielding response of hybrid BP/CFRP laminates, a novel
modeling approach based on equivalent electrical circuits is employed to estimate the
electrical conductivity of unidirectional CFRP plies. This approach uses Monte Carlo
simulations and accounts for the effects of quantum tunneling at the fiber-fiber contact
region. This study specifically examines a signal frequency range of 50 MHz to 12 GHz,
corresponding to the very high to X band spectrum. The results indicate that at a frequency
of 12 GHz, the longitudinal conductivity decreases to around ~3,300 S/m from an initial
DC value of 40,000 S/m, while the transverse conductivity concurrently increases from
negligible to approximately ~12.67 S/m. These results are then integrated into Ansys High
Frequency Structure Simulator (HFSS) to predict EMI SE by simulating the propagation
of electromagnetic waves through a semi-infinite composite shield representative volume
element. The numerical simulations illustrate that incorporating BP allows for significant
ii
improvements in SE of hybrid BP/CFRP composites. At 12 GHz signal frequency, for
example, the incorporation of a single BP interleave enhances the SE of a [90,0] laminate
by up to ~64%, while the incorporation of two BP interleaves in a [90,0,+45,-45,0,90]s
balanced symmetric laminate enhances its SE by ~20% . This enhancement is due to the
high conductivity of BP at high frequencies.
Additionally, to evaluate the flexural property enhancements due to BP, experimental
three-point bend tests were conducted on different configurations of hybrid BP/CFRP
laminates, and their strength and stiffness were compared with the non-BP samples.
Micrographs of failed samples are acquired using an optical microscope, which provides
insights into their underlying damage mechanisms. Fractography analysis confirms the role
of BP in preventing through-thickness crack propagation, attributed to the excellent crack
retardation properties of CNTs.
ContributorsTripathi, Kartik (Author) / Chattopadhyay, Aditi (Thesis advisor) / Henry, Todd C. (Committee member) / Nian, Qiong (Committee member) / Arizona State University (Publisher)
Created2024
Description
Human thermoregulation is substantially based on sweat evaporation, yet little is known about this process at the microscopic level. Midwave infrared thermography (MWIR) and optical coherence tomography (OCT) can assess the sweat evaporation dynamics from the skin, from the onset of a sweat droplet emergence from the sweat pores to its filmwise stage. In physiological studies, the rate of sweat evaporation is frequently determined using ventilated capsules or using technical absorbent pads. The first part of this thesis compares flow fields and water film evaporation rates from a capsule with a sudden expansion transition section, from a round tube to a rectangular evaporation section and one with a transition consisting of a wind tunnel-like diffuser section. The comparative study shows that the ventilated capsule with the diffuser transition section is effective at minimizing the flow disturbances as compared to the chaotic flow occurring with the capsule with a sudden expansion transition section. The second part of this thesis focuses on optimization and implementation of the ventilated capsule with diffuser transition section in pilot human trials. The experimental setup and protocol for pilot human trials are also described. The capsule geometry is altered to increase the imaging field and include calibration or alignment marks on the skin to enable quantitative image analysis. Based on pilot human trials, several additional improvements to the ventilated capsule, including a soft gasket and alternative sapphire window, are proposed to further refine this sweat evaporation measurement and imaging technique.
ContributorsJose, Cibin Thomas (Author) / Rykaczewski, Konrad KR (Thesis advisor) / Pathikonda, Gokul GP (Committee member) / Kavouras, Stavros SK (Committee member) / Arizona State University (Publisher)
Created2024
Description
The increasing demands of air travel and the escalating complexity of air traffic management (ATM) necessitate advanced air traffic flow prediction and optimization methodologies. This dissertation delves into integrating physics-guided machine learning techniques to address these challenges. By encompassing four pivotal studies, it contributes to the ATM field, showcasing how data-driven insights and physical principles can revolutionize our understanding and management of air traffic density, state predictions, flight delays, and airspace sectorization. The first study investigates the Bayesian Ensemble Graph Attention Network (BEGAN), a novel machine learning framework designed for precise air traffic density prediction. BEGAN combines spatial-temporal analysis with domain knowledge, enabling the model to interpret complex air traffic patterns in a highly dynamic and regulated airspace environment. The second study introduces the Physics-Informed Graph Attention Transformer, a novel approach integrating graph-based spatial learning with temporal Transformers. This model excels in capturing dynamic spatial-temporal interdependencies and integrates partial differential equations from fluid mechanics, enhancing the predictive accuracy and interpretability in ATM. The third study shifts focus to predictive modeling of aircraft delays, employing Physics-Informed Neural Networks. By utilizing sparse regression for system identification, this approach adeptly deciphers the intricate partial differential equations that dictate near-terminal air traffic dynamics, providing a novel perspective in forecasting flight delays with enhanced precision. The final study focuses on dynamic airspace sectorization, deploying an attention-based deep learning model that adeptly navigates the complexities of workload dynamics. In conjunction with constrained K-means clustering and evolutionary algorithms, it facilitates a more efficient and adaptable approach to airspace management, ensuring optimal traffic flow and safety. The findings of these studies demonstrate the significant impact of physics-guided machine learning in advancing ATM's safety and efficiency. They mark a shift from traditional empirical methods to innovative, data-driven approaches for air traffic management. This research enhances current practices and charts new paths for future technological advancements in aviation, especially in autonomous systems and digital transformation.
ContributorsXu, Qihang (Author) / Liu, Yongming YL (Thesis advisor) / Yan, Hao HY (Committee member) / Zhou, Xuesong XZ (Committee member) / Huang, Huei-Ping HH (Committee member) / Zhuang, Houlong HZ (Committee member) / Arizona State University (Publisher)
Created2024
Description
This dissertation contributes to uncertainty-aware neural networks using multi-modality data, with a focus on industrial and aviation applications. Drawing from seminal works in recent years that have significantly advanced the field, this dissertation develops techniques for incorporating uncertainty estimation and leveraging multi-modality information into neural networks for tasks such as fault detection and environmental perception. The escalating complexity of data in engineering contexts demands models that predict accurately and quantify uncertainty in these predictions. The methods proposed in this document utilize various techniques, including Bayesian Deep Learning, multi-task regularization and feature fusion, and efficient use of unlabeled data. Popular methods of uncertainty quantification are analyzed empirically to derive important insights on their use in real world engineering problems. The primary objective is to develop and refine Bayesian neural network models for enhanced predictive accuracy and decision support in engineering. This involves exploring novel architectures, regularization methods, and data fusion techniques. Significant attention is given to data handling challenges in deep learning, particularly in the context of quality inspection systems. The research integrates deep learning with vision systems for engineering risk assessment and decision support tasks, and introduces two novel benchmark datasets designed for semantic segmentation and classification tasks. Additionally, the dissertation delves into RGB-Depth data fusion for pipeline defect detection and the use of semi-supervised learning algorithms for manufacturing inspection tasks with imaging data. The dissertation contributes to bridging the gap between advanced statistical methods and practical engineering applications.
ContributorsRathnakumar, Rahul (Author) / Liu, Yongming (Thesis advisor) / Yan, Hao (Committee member) / Jayasuriya, Suren (Committee member) / Zhuang, Houlong (Committee member) / Kwon, Beomjin (Committee member) / Arizona State University (Publisher)
Created2024
Description
Human-robot interactions can often be formulated as general-sum differential games where the equilibrial policies are governed by Hamilton-Jacobi-Isaacs (HJI) equations. Solving HJI PDEs faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) alleviate CoD in solving PDEs with smooth solutions, they fall short in learning discontinuous solutions due to their sampling nature. This causes PINNs to have poor safety performance when they are applied to approximate values that are discontinuous due to state constraints. This dissertation aims to improve the safety performance of PINN-based value and policy models. The first contribution of the dissertation is to develop learning methods to approximate discontinuous values. Specifically, three solutions are developed: (1) hybrid learning uses both supervisory and PDE losses, (2) value-hardening solves HJIs with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique lifts the value to a higher-dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance. The second contribution is a learning-theoretical analysis of PINN for value and policy approximation. Specifically, by extending the neural tangent kernel (NTK) framework, this dissertation explores why the choice of activation function significantly affects the PINN generalization performance, and why the inclusion of supervisory costate data improves the safety performance. The last contribution is a series of extensions of the hybrid PINN method to address real-time parameter estimation problems in incomplete-information games. Specifically, a Pontryagin-mode PINN is developed to avoid costly computation for supervisory data. The key idea is the introduction of a costate loss, which is cheap to compute yet effectively enables the learning of important value changes and policies in space-time. Building upon this, a Pontryagin-mode neural operator is developed to achieve state-of-the-art (SOTA) safety performance across a set of differential games with parametric state constraints. This dissertation demonstrates the utility of the resultant neural operator in estimating player constraint parameters during incomplete-information games.
ContributorsZhang, Lei (Author) / Ren, Yi (Thesis advisor) / Si, Jennie (Committee member) / Berman, Spring (Committee member) / Zhang, Wenlong (Committee member) / Xu, Zhe (Committee member) / Arizona State University (Publisher)
Created2024
Description
The microelectronics industry is actively focusing on advanced packaging technologies, notably on three-dimensional stacking of heterogeneous integrated (3D-HI) circuits for enhanced performance. Despite its computational performance benefits, this approach faces challenges in thermal management due to increased power density and heat generation. Conventional cooling methods struggle to address this issue effectively. This study investigates microfluidic intralayer cooling techniques using analytical correlation and computational fluid dynamics (CFD) principles to propose a method capable of managing thermal performance across varying load conditions. The proposed configuration achieved a dissipation of 40 W/cm2 with a volumetric flow rate of 200 mL/min, maintaining chip temperature at 315K. Additionally, extreme hotspot conditions generating 1kW/cm2, along with the presence of thermal resistance from redistribution layers (RDLs), are analyzed. This research aims to establish a model for understanding geometric property variations under different heat flux conditions in 3D heterogeneous integration of semiconductor packaging.
ContributorsGandhi, Rohit Mahavir (Author) / Wang, Robert Y (Thesis advisor) / Rykaczewski, Konrad (Committee member) / Kwon, Beomjin (Committee member) / Arizona State University (Publisher)
Created2024
Description
Additive manufacturing, also known as 3D printing, has revolutionized modern manufacturing in several key areas: complex geometry fabrication, rapid prototyping and iteration, customization and personalization, reduced material waste, supply chain flexibility, complex assemblies and consolidated parts, and material innovation. As the technology continues to evolve, its impact on manufacturing is expected to grow, driving further innovation and reshaping traditional production processes. Some innovation examples in this field are inspired by natural or bio-systems, such as honeycomb structures for internal morphological control to increase strength, bio-mimetic composites for scaffold structures, or shape memory materials in 4D printing for targeted drug delivery. However, the technology is limited by its ability to manipulate multiple materials, especially tuning their submicron characteristics when they show non-compatible chemical or physical features. For example, the deposition and patterning of nanoparticles with different dimensions have seen little success, except in highly precise and slow 3D printing processes like aerojet or electrohydrodynamic. Taking inspiration from the layered patterns and structures found in nature, this research aims to demonstrate the development and versatility of a newly developed ink-based composite 3D printing mechanism called multiphase direct ink writing (MDIW). The MDIW is a multi-materials extrusion system, with a unique nozzle design that can accommodate two immiscible and non-compatible polymer or nano-composite solutions as feedstock. The intricate internal structure of the nozzle enables the rearrangement of the feedstock in alternating layers (i.e., ABAB...) and multiplied within each printed line. This research will first highlight the design and development of the MDIW 3D printing mechanism, followed by laminate processing to establish the requirements of layer formation in the XY-axis and the effect of layer formation on its microstructural and mechanical properties. Next, the versatility of the mechanism is also shown through the one-step fabrication of shape memory polymers with dual stimuli responsiveness, highlighting the 4D printing capabilities. Moreover, the MDIW's capability of dual nanoparticle patterning for manufacturing multi-functional carbon-carbon composites will be highlighted. Comprehensive and in-depth studies are conducted to investigate the morphology-structure-property relationships, demonstrating potential applications in structural engineering, smart and intelligent devices, miniature robotics, and high-temperature systems.
ContributorsRavichandran, Dharneedar (Author) / Nian, Qiong (Thesis advisor) / Song, Kenan (Committee member) / Green, Matthew (Committee member) / Jin, Kailong (Committee member) / Bhate, Dhruv (Committee member) / Arizona State University (Publisher)
Created2024
Description
This study investigates the energy saving potential of high albedo roof coatings which are designed to reflect a large proportion of solar radiation compared to traditional roofing materials. Using EnergyPlus simulations, the efficacy of silicone, acrylic, and aluminum roof coatings is assessed across two prototype commercial buildings—a standalone retail (2,294 m2 or 24,692 ft2) and a strip-mall (2,090 m2 or 22,500 ft2)—located in four cities: Phoenix, Houston, Los Angeles, and Miami. The performance of reflective coatings was compared with respect to a black roof having a solar reflectance of 5% and a thermal emittance of 90%. A sensitivity analysis was done to assess the impact of solar reflectance and thermal emittance on the ability of roof coatings to reduce surface temperatures, a key factor behind energy savings. This factor plays a crucial role in all three heat transfer mechanisms: conduction, convection, and radiation. The rooftop surface temperature exhibits considerable variation depending on the solar reflectance and thermal emittance attributes of the roof. A contour plot between these properties reveals that high values of both result in reduced cooling needs and a heating penalty which is insignificant when compared with cooling savings for cooling-dominant climates like Phoenix where the cooling demand significantly outweighs the heating demand, yielding significant energy savings. Furthermore, the study also investigates the effects of reflective coatings on buildings that have photovoltaic solar panels installed on them. This includes exploring their impact on building HVAC loads, as well as the performance improvement due to the reduced temperatures beneath them.
ContributorsSharma, Ajay Kumar (Author) / Phelan, Patrick (Thesis advisor) / Neithalath, Narayanan (Committee member) / Milcarek, Ryan (Committee member) / Arizona State University (Publisher)
Created2024
Description
Energetic materials with granular microstructures find wide applications in military and civilian sectors. A comprehensive understanding of their shock response is crucial for the development of safer explosives and predictive models. Initiation of the explosive reaction, a critical safety concern, is believed to be triggered by the formation of hotspots, i.e., localized high-temperature regions. Although direct observation of hotspots remains elusive, computational simulations offer a window into their behavior. This work investigates effect of porosity on reactivity of hotspots in Pentaerythritol Tetranitrate (PETN) and potential shock surrogate Meso-Erythritol (ME). Building upon findings that link hotspot size and temperature to material heterogeneity, this research integrates experimental characterization of ME and mesoscale simulations of both ME and PETN to quantify how the pore distribution influences hotspots. Results showed that shock impedance of ME is within 10% of PETN up to 1 GPa, highlighting its potential as a shock surrogate for weak shocks. Gas gun tests with ME validated Hugoniot parameters in literature, which were used in a P-α compaction model, validating that mesoscale simulations of shock loaded ME agree with experiments within measured uncertainty. This mesoscale approach was then applied to PETN by using synthetically generated microstructures, which demonstrates that enlarging pore size in PETN results in more individually reactive hotspots and greater variability in thermodynamic states over time than increasing pore count or starting with a lower porosity. A higher pore count produces a more right-skewed temperature distribution, indicating a greater total number of hotspots compared to other conditions. Simulations also show that air in individual pores lowers the peak hotspot temperatures due to work done compressing the air and affects secondary hotspot formation. Hotspots within 0.15 μm can react at temperatures below 800 K, their proximity enabling them to bypass thermal quenching via local heat transfer.
ContributorsWilde, Zakary Robert (Author) / Peralta, Pedro (Thesis advisor) / Arizona State University (Publisher)
Created2024