33 research outputs found
Assessment of Linear Inverse Problems in Magnetocardiography and Lorentz Force Eddy Current Testing
Lineare inverse Probleme tauchen in vielen Bereichen von Wissenschaft und
Technik auf. Effiziente Lösungsstrategien für diese inversen Probleme
erfordern Informationen darüber, ob das Problem schlecht-gestellt und in
welchem Ausmaß dies der Fall ist. In der vorliegenden Dissertation wird
eine umfassende theoretische Analyse existierender Bewertungsmaße
durchgeführt. Aus diesen Untersuchungen werden schließlich zwei neue
Bewertungsmaße abgeleitet. Beide können bei einer Vielzahl linearer
inverser Probleme angewendet werden, einschließlich biomedizinische
Anwendungen oder der zerstörungsfreien Materialprüfung. Die theoretischen
Betrachtungen zur Behandlung linearer inverser Probleme werden auf zwei
Beispiele angewendet. Das erste ist die Magnetkardiographie, wo die
Optimierung magnetischer Sensoren in einem westenähnlichen Sensorfeld
untersucht wird. Für die Messungen der magnetischen Flussdichte werden
üblicherweise monoaxiale Sensoren in einem Feld perfekt parallel
angeordnet. Eine zufällige Variation ihrer Ausrichtungen kann die Kondition
des entsprechenden linearen inversen Problems verbessern. Eine theoretische
Definition des Falls, in dem zufällige Variationen monoaxialer Sensoren den
Zustand der Kernmatrix mit einer Wahrscheinlichkeit gleich Eins verbessern
wird ebenfalls in der Dissertation vorgestellt. Diese theoretische
Beobachtung ist allgemein gültig.Positionen und Orientierungen der
Magnetsensoren rund um den Oberkörper wurden mit drei aus der Literatur
bekannten Bewertungsmaßen und einem neu in dieser Arbeit vorgeschlagenen
Maß optimiert. Die besten Ergebnisse ergeben sich bei einer unregelmäßigen
Verteilung der Sensoren auf der Oberfläche des Brustkorbes. Im Vergleich zu
früheren Untersuchungsergebnissen kann daraus geschlussfolgert werden, dass
mit geringfügig abweichenden Sensoranordnungen ebenso gute Ergebnisse
erzielt werden können. Ein zweites Anwendungsbeispiel ist ein Verfahren der
zerstörungsfreien Materialprüfung, das auch als
Lorentzkraft-Wirbelstromprüfung bekannt geworden ist. In dieser Arbeit wird
eine neue Methode für die kontaktlose, zerstörungsfreie Untersuchung
leitfähiger Materialien vorgestellt. Dabei wird die Lorentzkraft gemessen,
die auf einen Dauermagneten wirkt, der relativ zu einem Testkörper bewegt.
Es wird eine neue Approximationsmethode für die Berechnung der magnetischen
Felder und der Lorentzkräfte vorgeschlagen.Linear inverse problems arise throughout a variety of branches of science
and engineering. Efficient solution strategies for these inverse problems
need to know whether a problem is ill-conditioned as well as its degree of
ill-conditioning. In this thesis, a comprehensive theoretical analysis of
known figures of merit has been done and finally two new figures of merit
have been developed. Both can be applied in a large variety of linear
inverse problems, including biomedical applications and nondestructive
testing of materials. Theoretical considerations of the conditioning of
linear inverse problems are applied to two examples. The first one is
magnetocardiography, where the optimization of magnetic sensors in a
vest-like sensor array has been considered. When measuring magnetic flux
density, usually mono-axial magnetic sensors are arranged in an array,
perfectly in parallel. It has been shown that a random variation of their
orientations can improve the condition of the corresponding linear inverse
problem. Thus, in this thesis a theoretical definition of the case when
random variations of mono-axial sensors orientations improve the condition
of the kernel matrix with a probability equal to one is presented. This
theoretical observation is valid in general. Positions and orientations of
magnetic sensors around the torso have been optimized minimizing three
figures of merit given in the literature and a novel one presented in the
thesis. Best results have been found for non-uniform sensors distribution
on the whole torso surface. In comparison to previous findings can be
concluded that quite different sensor sets can perform equally well.The
second application example is nondestructive testing of materials named
Lorentz force eddy current testing, where the Lorentz force exerting on a
permanent magnet, which is moving relative to the specimen, is determined.
A novel approximation method for the calculation of the magnetic fields and
Lorentz forces is proposed. Based on the new approximation method, a new
inverse procedure for defect reconstruction is proposed. A successful
reconstruction using data from finite elements method analysis and
measurements is obtained
Introduction to Linear Algebra: Models, Methods, and Theory
This book develops linear algebra around matrices. Vector spaces in the abstract are not considered, only vector spaces associated with matrices. This book puts problem solving and an intuitive treatment of theory first, with a proof-oriented approach intended to come in a second course, the same way that calculus is taught. The book\u27s organization is straightforward: Chapter 1 has introductory linear models; Chapter 2 has the basics of matrix algebra; Chapter 3 develops different ways to solve a system of equations; Chapter 4 has applications, and Chapter 5 has vector-space theory associated with matrices and related topics such as pseudoinverses and orthogonalization. Many linear algebra textbooks start immediately with Gaussian elimination, before any matrix algebra. Here we first pose problems in Chapter 1, then develop a mathematical language for representing and recasting the problems in Chapter 2, and then look at ways to solve the problems in Chapter 3-four different solution methods are presented with an analysis of strengths and weaknesses of each.https://commons.library.stonybrook.edu/ams-books/1000/thumbnail.jp
Development and Biomechanical Analysis toward a Mechanically Passive Wearable Shoulder Exoskeleton
Shoulder disability is a prevalent health issue associated with various orthopedic and neurological conditions, like rotator cuff tear and peripheral nerve injury. Many individuals with shoulder disability experience mild to moderate impairment and struggle with elevating the shoulder or holding the arm against gravity. To address this clinical need, I have focused my research on developing wearable passive exoskeletons that provide continuous at-home movement assistance. Through a combination of experiments and computational tools, I aim to optimize the design of these exoskeletons.
In pursuit of this goal, I have designed, fabricated, and preliminarily evaluated a wearable, passive, cam-driven shoulder exoskeleton prototype. Notably, the exoskeleton features a modular spring-cam-wheel module, allowing customizable assistive force to compensate for different proportions of the shoulder elevation moment due to gravity. The results of my research demonstrated that this exoskeleton, providing modest one-fourth gravity moment compensation at the shoulder, can effectively reduce muscle activity, including deltoid and rotator cuff muscles.
One crucial aspect of passive shoulder exoskeleton design is determining the optimal anti-gravity assistance level. I have addressed this challenge using computational tools and found that an assistance level within the range of 20-30% of the maximum gravity torque at the shoulder joint yields superior performance for specific shoulder functional tasks.
When facing a new task dynamic, such as wearing a passive shoulder exoskeleton, the human neuro-musculoskeletal system adapts and modulates limb impedance at the end-limb (i.e., hand) to enhance task stability. I have presented development and validation of a realistic neuromusculoskeletal model of the upper limb that can predict stiffness modulation and motor adaptation in response to newly introduced environments and force fields. Future studies will explore the model\u27s applicability in predicting stiffness modulation for 3D movements in novel environments, such as passive assistive devices\u27 force fields