Scholarship Repository
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The Florida Tech Scholarship Repository system captures, stores, indexes, preserves, and distributes digital research material.2020-02-18T15:49:41ZOptimal Control of the Second Order Elliptic Equations with Biomedical Applications
http://hdl.handle.net/11141/3065
Optimal Control of the Second Order Elliptic Equations with Biomedical Applications
Seif, Saleheh
Dissertation analyzes optimal control of systems with distributed parameters described
by the general boundary value problems in a bounded Lipschitz domain for the linear
second order uniformly elliptic partial differential equations (PDE) with bounded measurable coefficients. Broad class of elliptic optimal control problems under Dirichlet or
Neumann boundary conditions are considered, where the control parameter is the density of sources, and the cost functional is the L2-norm difference of the weak solution
of the elliptic problem from measurement along the boundary or subdomain. The optimal control problems are fully discretized using the method of finite differences. Two
types of discretization of the elliptic boundary value problem depending on Dirichlet
or Neumann type boundary condition are introduced. Convergence of the sequence of
finite-dimensional discrete optimal control problems both with respect to the cost functional and the control is proved. The methods of the proof are based on energy estimates
in discrete Sobolev spaces, Lax-Milgram theory, weak compactness and convergence of
interpolations of solutions of discrete elliptic problems, and delicate estimation of the
cost functional along the sequence of interpolations of the minimizers for the discrete
optimal control problems. Dissertation pursues application of the optimal control theory
of elliptic systems with distributed parameters to biomedical problem on the identification of cancerous tumor. The Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the m electrodes for a given electrode current is
analyzed. A PDE constrained optimal control framework in Besov space is developed,
where the electrical conductivity tensor and boundary voltages are control parameters,
and the cost functional is the norm difference of the boundary electrode current from the
given current pattern and boundary electrode voltages from the measurements. The state
vector is a solution of the second order elliptic PDE in divergence form with bounded
measurable coefficients under mixed Neumann/Robin type boundary condition. The
novelty of the control theoretic model is its adaptation to clinical situation when additional "voltage-to-current" measurements can increase the size of the input data from
m up to m! while keeping the size of the unknown parameters fixed. Existence of
the optimal control is established. Fréchet differentiability in the Banach-Besov spaces
framework is proved and the formula for the Frechet gradient expressed in terms of the
adjoined state vector is derived. Optimality condition is formulated, and gradient type
iterative algorithm in Hilbert-Besov spaces setting is developed. EIT optimal control
problem is fully discretized using the method of finite differences. New Sobolev-Hilbert
space is introduced, and the convergence of the sequence of finite-dimensional optimal
control problems to EIT coefficient optimal control problem is proved both with respect
to functional and control in 2- and 3-dimensional domains.
Thesis (Ph.D.) - Florida Institute of Technology, 2020.
2020-05-01T00:00:00ZDevelopment of Plane Rotating Traction System: Based on the High-speed Rail (72+128+72) m Continuous Prestressed Concrete Beam Bridge
http://hdl.handle.net/11141/3064
Development of Plane Rotating Traction System: Based on the High-speed Rail (72+128+72) m Continuous Prestressed Concrete Beam Bridge
Wang, Weinan
With the advent of rotate construction techniques, it is easy to build a new bridge
crossing over existing structures, rivers and valleys quickly, easily and safely. Although the
general concept of the rotating method is similar for different engineering characteristics,
it is necessary to make some changes, which are more in line with the requirements of the
particular project.
Based on a 3-spans (72+128+72)m continuous concrete bridge, this paper presents a
new rotation method, the down-slide-way unbalanced rotation system, which can save time
and reduce cost compared to the up-slide-way rotation method. Through the improvements
of the traction system and the travel system, the rotation construction period and cost-effectively saved, yet the construction quality is still guaranteed. The construction
technology of this new method will also reduce construction risks and simplify the process.
Thesis (M.S.) - Florida Institute of Technology, 2020.
2020-05-01T00:00:00ZApplying Formal Methods for Integrating Advanced Algorithms in Safety Critical Systems
http://hdl.handle.net/11141/3063
Applying Formal Methods for Integrating Advanced Algorithms in Safety Critical Systems
Stafford, Milton
In software engineering it is essential that updates are deployed for continual improvement. While software updates bring new functionality, updates also may
introduce instability. This leads to failures of various kinds. This is especially
problematic in safety-critical systems where there is a potential for injury or loss
of life. However, newer and more sophisticated software carries potential advantages, including higher performance and reliability. Therefore, there are benefits
in adopting newer software if the integration process is assured. In this thesis, I
present a framework for assured integration; one that links requirements, design,
and implementation. The proposed framework includes a new design approach and
new software design tools. The approach calls for an embedded decision-making
architecture in an autonomous system which contains constrained variants of the
desired complex software. The modules are subject to an authoritative module
that observes their behavior. Constrained modules are developed by creating verified formal models from underlying component requirements. Those models are
used to generate runtime validation code that detects requirement failures.
Thesis (M.S.) - Florida Institute of Technology, 2019.
2019-12-01T00:00:00ZSemantic and Qualitative Physics-Based Formal Reasoning for Functional Decomposition in Mechanical Design
http://hdl.handle.net/11141/3062
Semantic and Qualitative Physics-Based Formal Reasoning for Functional Decomposition in Mechanical Design
Mao, Xiaoyang
Function modeling plays an essential role in academy design studies, yet a
lack of acceptance in industry. A possible reason is that the designer must have well
understand of the controlled vocabularies and grammars to utilize this method. The
research presented in this dissertation is to fill this gap so that designers can use
function-based design method without relevant knowledge. In graph-based function
models, the function verbs and flow nouns are usually chosen from predefined
vocabularies. The vocabulary class definitions, combined with function modeling
grammars defined at various levels of formalism, enable function-based reasoning.
However, the text written in plain English for the names of the functions and
flows is presently not exploited for formal reasoning. This dissertation presents
a formalism (representation and reasoning) to support semantic and physics-based
reasoning on the information hidden in the plain-English flow terms, esp. for automatically decomposing black-box function models and to generate multiple
design alternatives. First, semantic reasoning infers the changes of flow types, flow
attributes, and the direction of those changes between the input and output flows
attached to the black-box. Then, a representation of qualitative physics is used to
determine the material and energy exchanges between the flows and the function
features needed to achieve them. Finally, the topological layer provides reasonings
to infer multiple options of composing those function features into topologies and to
thus generate multiple alternative decompositions of the functional black-box. The
data representation formalizes flow phases, flow attributes, qualitative value scales
for the attributes, and qualitative physics laws. A three-layer algorithm manipulates
this data for reasoning. The dissertation shows four validation case studies to
demonstrate the workings of this formalism.
Thesis (Ph.D.) - Florida Institute of Technology, 2019.
2019-12-01T00:00:00Z