Matching Items (6)
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- All Subjects: Modeling
- Creators: Armbruster, Dieter
- Creators: Sugar, Thomas
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
The Kuramoto model is an archetypal model for studying synchronization in groups
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
ContributorsGilg, Brady (Author) / Armbruster, Dieter (Thesis advisor) / Mittelmann, Hans (Committee member) / Scaglione, Anna (Committee member) / Strogatz, Steven (Committee member) / Welfert, Bruno (Committee member) / Arizona State University (Publisher)
Created2018
Description
This thesis worked towards the development of a parameterized 3D model off a cover that could go over any specific prosthesis depending on the parameters that had been entered. It also focused on gathering user inputs, which was done with the aid of the Amputee Coalition, that could be used to create an aesthetic design on this cover. The Amputee Coalition helped to recruit participants through its website and social media platforms. Finally, multiple methods of creating a design were developed to increase the amount of customization that a user could have for their cover.
ContributorsRiley, Nicholas (Co-author) / Fusaro, Gerard (Co-author) / Sugar, Thomas (Thesis director) / Redkar, Sangram (Committee member) / Engineering Programs (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This thesis worked towards the development of a parameterized 3D model off a cover that could go over any specific prosthesis depending on the parameters that had been entered. It also focused on gathering user inputs, which was done with the aid of the Amputee Coalition, that could be used to create an aesthetic design on this cover. The Amputee Coalition helped to recruit participants through its website and social media platforms. Finally, multiple methods of creating a design were developed to increase the amount of customization that a user could have for their cover.
ContributorsFusaro, Gerard Anthony (Co-author) / Riley, Nicholas (Co-author) / Sugar, Thomas (Thesis director) / Redkar, Sangram (Committee member) / College of Integrative Sciences and Arts (Contributor) / Engineering Programs (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The main objective of mathematical modeling is to connect mathematics with other scientific fields. Developing predictable models help to understand the behavior of biological systems. By testing models, one can relate mathematics and real-world experiments. To validate predictions numerically, one has to compare them with experimental data sets. Mathematical modeling can be split into two groups: microscopic and macroscopic models. Microscopic models described the motion of so-called agents (e.g. cells, ants) that interact with their surrounding neighbors. The interactions among these agents form at a large scale some special structures such as flocking and swarming. One of the key questions is to relate the particular interactions among agents with the overall emerging structures. Macroscopic models are precisely designed to describe the evolution of such large structures. They are usually given as partial differential equations describing the time evolution of a density distribution (instead of tracking each individual agent). For instance, reaction-diffusion equations are used to model glioma cells and are being used to predict tumor growth. This dissertation aims at developing such a framework to better understand the complex behavior of foraging ants and glioma cells.
ContributorsJamous, Sara Sami (Author) / Motsch, Sebastien (Thesis advisor) / Armbruster, Dieter (Committee member) / Camacho, Erika (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2019
Description
The human ankle is a vital joint in the lower limb of the human body. As the point of interaction between the human neuromuscular system and the physical world, the ankle plays important role in lower extremity functions including postural balance and locomotion . Accurate characterization of ankle mechanics in lower extremity function is essential not just to advance the design and control of robots physically interacting with the human lower extremities but also in rehabilitation of humans suffering from neurodegenerative disorders.
In order to characterize the ankle mechanics and understand the underlying mechanisms that influence the neuromuscular properties of the ankle, a novel multi-axial robotic platform was developed. The robotic platform is capable of simulating various haptic environments and transiently perturbing the ankle to analyze the neuromechanics of the ankle, specifically the ankle impedance. Humans modulate ankle impedance to perform various tasks of the lower limb. The robotic platform is used to analyze the modulation of ankle impedance during postural balance and locomotion on various haptic environments. Further, various factors that influence modulation of ankle impedance were identified. Using the factors identified during environment dependent impedance modulation studies, the quantitative relationship between these factors, namely the muscle activation of major ankle muscles, the weight loading on ankle and the torque generation at the ankle was analyzed during postural balance and locomotion. A universal neuromuscular model of the ankle that quantitatively relates ankle stiffness, the major component of ankle impedance, to these factors was developed.
This neuromuscular model is then used as a basis to study the alterations caused in ankle behavior due to neurodegenerative disorders such as Multiple Sclerosis and Stroke. Pilot studies to validate the analysis of altered ankle behavior and demonstrate the effectiveness of robotic rehabilitation protocols in addressing the altered ankle behavior were performed. The pilot studies demonstrate that the altered ankle mechanics can be quantified in the affected populations and correlate with the observed adverse effects of the disability. Further, robotic rehabilitation protocols improve ankle control in affected populations as seen through functional improvements in postural balance and locomotion, validating the neuromuscular approach for rehabilitation.
In order to characterize the ankle mechanics and understand the underlying mechanisms that influence the neuromuscular properties of the ankle, a novel multi-axial robotic platform was developed. The robotic platform is capable of simulating various haptic environments and transiently perturbing the ankle to analyze the neuromechanics of the ankle, specifically the ankle impedance. Humans modulate ankle impedance to perform various tasks of the lower limb. The robotic platform is used to analyze the modulation of ankle impedance during postural balance and locomotion on various haptic environments. Further, various factors that influence modulation of ankle impedance were identified. Using the factors identified during environment dependent impedance modulation studies, the quantitative relationship between these factors, namely the muscle activation of major ankle muscles, the weight loading on ankle and the torque generation at the ankle was analyzed during postural balance and locomotion. A universal neuromuscular model of the ankle that quantitatively relates ankle stiffness, the major component of ankle impedance, to these factors was developed.
This neuromuscular model is then used as a basis to study the alterations caused in ankle behavior due to neurodegenerative disorders such as Multiple Sclerosis and Stroke. Pilot studies to validate the analysis of altered ankle behavior and demonstrate the effectiveness of robotic rehabilitation protocols in addressing the altered ankle behavior were performed. The pilot studies demonstrate that the altered ankle mechanics can be quantified in the affected populations and correlate with the observed adverse effects of the disability. Further, robotic rehabilitation protocols improve ankle control in affected populations as seen through functional improvements in postural balance and locomotion, validating the neuromuscular approach for rehabilitation.
ContributorsNalam, Varun (Author) / Lee, Hyunglae (Thesis advisor) / Artemiadis, Panagiotis (Committee member) / Santello, Marco (Committee member) / Sugar, Thomas (Committee member) / Lockhart, Thurmon (Committee member) / Arizona State University (Publisher)
Created2020