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Main.lyx
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#LyX 2.2 created this file. For more info see http://www.lyx.org/
\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
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\textclass dlrreport
\begin_preamble
\usepackage{nomencl}
\makenomenclature
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\usepackage{lscape} %% supplies a landscape environment
% Tabellen
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\usepackage{rotating} %benoetigt fuer tabellen quer
\usepackage{booktabs} %Schoenere trennlinien in tabellen
\usepackage{colortbl}
\usepackage{transparent}
\usepackage{framed}
\usepackage{amsmath} %spezielle mathematikzeichen wie doppelintegral
\usepackage{amssymb}
\usepackage{fancyhdr}
\usepackage{capt-of}
\usepackage{wrapfig}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{bibgerm}
%\usepackage{harvard}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%% Definitionen %%%%%%%%%%%%%%%%%%%%%%%%%
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\ifthenelse{\equal{#1}{S}}{\item[\textbf{Strömungstechnische Bezeichnungen}]}{}}}}}
\makeatletter % @in Befehlen auf code 11 setzen
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% Einstellungen + Extras %%%%%%%%%%%%%%%
\sloppy % Silbentrennung - keine Trennung bevorzugt auch bei größeren Abständen zwischen den Worten
\makeglossary
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%% Titel, Autor, etc. %%%%%%%%%%%%%%%%%
\title{Multifidelity-Optimierungsverfahren für Turbomaschinen \vspace{0.5cm} \vspace{0.5cm} \bf}
\runningtitle{Rachete}
\trname{Dissertation}
\author{Andreas Schmitz}
\date{Oktober 2018}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%% Schalter %%%%%%%%%%%%%%%%%
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%\commentstrue % comment out to hide comments
%%%%%%%%%%%%% Seitenzahlen Header alternierend %%%%%%%%%%%%%%%
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\options AT, texfonts
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\begin_modules
algorithm2e
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\end_header
\begin_body
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status open
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\backslash
maketitle
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\begin_layout Standard
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\begin_layout Standard
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\series bold
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Multifidelity-Optimierungsverfahren für Turbomaschinen
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 50bp
\end_inset
\end_layout
\begin_layout Standard
\align center
Dissertation
\end_layout
\begin_layout Standard
\align center
zur
\end_layout
\begin_layout Standard
\align center
Erlangung des Grades
\end_layout
\begin_layout Standard
\align center
Doktor-Ingenieur
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 40bp
\end_inset
\end_layout
\begin_layout Standard
\align center
an der
\end_layout
\begin_layout Standard
\align center
Fakultät für Maschinenbau
\end_layout
\begin_layout Standard
\align center
der Ruhr-Universität Bochum
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 15bp
\end_inset
\end_layout
\begin_layout Standard
\align center
von
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 15bp
\end_inset
\end_layout
\begin_layout Standard
\align center
\series bold
Andreas Schmitz
\end_layout
\begin_layout Standard
\align center
geb.
in Waldbröl
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 15bp
\end_inset
\end_layout
\begin_layout Standard
\align center
Bochum 2019
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace 15bp
\end_inset
\end_layout
\begin_layout Standard
\align center
Erster Referent: Prof.
Dr.-Ing.
R.
Mönig (Ruhr-Universität Bochum)
\end_layout
\begin_layout Standard
\align center
Zweiter Referent: Prof.
Dr.
rer.
nat.
H.
Gottschalk (Bergische Universität Wuppertal)
\end_layout
\begin_layout Standard
\align center
\begin_inset Newpage newpage
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\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
thispagestyle{empty}
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\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
Abkürzungen:
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\series bold
\size largest
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "SSE"
description "Streaming SIMD Extensions, eine Befehlssatzerweiterung für Prozessoren."
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "AVX"
description "Advanced Vector Extensions, eine Befehlssatzerweiterung für Prozessoren. Nachfolger der SSE Architektur."
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "SIMD"
description "Single Instruction Multiple Data, eine Architektur welche es erlaubt dieselbe Operation parallel auf einen sich verändernden Datenstrom anzuwenden. "
\end_inset
\series default
\size default
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "Member"
description "Ein Satz freier Variablen mit dazugehörigen Funktionswerten. Beispielsweise ein Satz geometrischer Parameter mit berechneten mechanischen und aerodynamischen Größen."
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "HPC"
description "High-Performance-Computing"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "MO"
description "Multi-Objective"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "ROI"
description "Region of Interest. Ein für die Zielfunktionen festgelegtes Gültigkeitsintervall. "
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "CFD"
description "Computational Fluid Dynamics"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "CSM"
description "Computational Structure Mechanics"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "EVG"
description "Erwarteter Volumenzugewinn, auch Expected Volume Gain oder Expected Hypervolume Improvement"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "EGO"
description "Efficient Global Optimization. Ein Optimierungsverfahren, welches die Unsicherheiten in einer Ersatzmodellvorhersage miteinbezieht"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "GPU"
description "Abkürzung für Graphics Processing Unit. Grafikbeschleuniger, in der Regel als Zusatzkarte in einem Rechner"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "A"
symbol "GPGPU"
description "General Purpose Computation on Graphics Processing Unit. Beschreibt die Verwendung von GPUs über den ursprünglichen Einsatz hinaus. Meist für die Verwendung von massiv parallelen und rechenintensiven Algorithmen."
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
Formelzeichen:
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{\\beta}$"
description "Beta Vektor, beinhaltet alle Erwartungswerte des Modells."
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\sigma^{2}$"
description "Varianz"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{r}$"
description "Korrelationsvektor"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{y}_{s}$"
description "Vektor, welcher alle bekannten Stützstellen enthält"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{\\theta}$"
description "Hyperparameter einer Korrelationsfunktion, ohne Varianzen oder Regularisierungsterme"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\textrm{var}(X)$"
description "Varianz der Zufallsvariable X"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\textrm{cov}(X,Y)$"
description "Kovarianzfunktion zwischen den Zufallsvariablen X und Y"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\textrm{cov}(\\vec{x},\\vec{y})$"
description "Ortsabhängige Kovarianzfunktion zwischen den Ortsvektoren x und y"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\mathbf{R}$"
description "Korrelationsmatrix"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$c(X,Y)$"
description "Korrelationsfunktion zwischen den Zufallsvariablen X und Y"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$y^{*}\\left(\\vec{x}\\right)$"
description "Geschätzter Funktionswert an der Stelle $\\vec{x}$"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$y\\left(\\vec{x}\\right)$"
description "Bekannter Funktionswert oder Stützstelle an der Stelle $\\vec{x}$"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$F\\left(\\vec{x}\\right)$"
description "Fehlerfunktion an der Stelle $\\vec{x}$"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\mathbf{Cov}$"
description "Kovarianzmatrix"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\kappa$"
description "Konditionszahl"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\omega$"
description "Druckverlustbeiwert"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\Xi$"
description "Eigenwert einer Matrix"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\delta$"
description "Kronecker Delta"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\lambda$"
description "Diagonalaufschlag"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$E[X]$"
description "Erwartungswert der Zufallsvariable X"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$f_{dec}(...)$"
description "Entscheidungsfunktion"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{c}$"
description "Kovarianzvektor"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{x}$"
description "Ortsvektor"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$\\vec{w}$"
description "Gewichte eines Kriging Modells"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$P_{t}$"
description "Totaldruck"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "$T_{t}$"
description "Totaltemperatur"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "L"
description "Likelihood Funktion"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "N"
description "Multivariate Normalverteilung"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "a"
description "Skalierungsfaktor für das CO-Kriging Kovarianzmodel"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "t"
description "Zeit"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "P"
description "Wahrscheinlichkeit"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "k"
description "Anzahl der freien Variablen eines Members"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "z"
description "Anzahl der Zielfunktionen einer Optimierung"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "c"
description "Anzahl der Nebenbedingungen"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "s"
description "Anzahl der verschiedenen Gütestufen bei einem Multifidelty Modell"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "I"
description "Informationsgehalt"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "n"
description "Anzahl der beprobten Stützstellen, auch Member oder Samples genannt"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "o"
description "Anzahl der Hyperparameter"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "m"
description "Anzahl der gegebenen partiellen Ableitungen"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "h"
description "Allgemeiner Hyperparameter "
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "q"
description "Anzahl der verwendeten Ersatzmodelle innerhalb einer Optimierung"
\end_inset
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
prefix "L"
symbol "w"
description "Anzahl der Flowparameter"
\end_inset
\end_layout
\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
thispagestyle{empty}
\end_layout
\end_inset
\end_layout
\begin_layout Chapter*
\size normal
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
addcontentsline{toc}{chapter}{Kurzfassung}
\end_layout