From 378e961e0527ea453985eab507ca29fa46480bd2 Mon Sep 17 00:00:00 2001 From: rylon Date: Sat, 10 Aug 2013 04:00:29 +0200 Subject: [PATCH] thesis --- .../Bachelor Thesis/thesis_ug/TUDthesis.aux | 23 ++-- .../Bachelor Thesis/thesis_ug/TUDthesis.log | 84 ++++++------ .../Bachelor Thesis/thesis_ug/TUDthesis.pdf | Bin 1946097 -> 1947417 bytes .../thesis_ug/TUDthesis.synctex.gz | Bin 160187 -> 169329 bytes .../Bachelor Thesis/thesis_ug/TUDthesis.toc | 21 +-- .../thesis_ug/tex/berechnung.tex | 9 +- .../Bachelor Thesis/thesis_ug/tex/modell.tex | 128 +++++++++--------- .../thesis_ug/tex/validierung.tex | 14 +- 8 files changed, 151 insertions(+), 128 deletions(-) diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux index 55f7dd8d..99aeaac4 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.aux @@ -7,7 +7,7 @@ \@writefile{toc}{\contentsline {section}{\numberline {4}Related Work}{5}} \@writefile{toc}{\contentsline {section}{\numberline {5}Modell}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Modell der Ministadt}{6}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Kreuzungsübersicht 'Ministadt'in der Stadt Darmstadt}}{6}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Kreuzungs\active@dq \dq@prtct{u}bersicht 'Ministadt'in der Stadt Darmstadt}}{6}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Kreuzung A59}}{7}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Modell als Graph}{8}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}Kreuzungsgraph}{8}} @@ -32,21 +32,22 @@ \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.4.4}Geographischer Ausschnitt der Daten}{13}} \@writefile{toc}{\contentsline {section}{\numberline {7}Berechnung}{15}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Das Zeitproblem}{15}} -\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Ans\"atze}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.2.1}Markov-Ketten HMM}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.2.2}Neuronale Netze}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.2.3}Gleichungssystem}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.2.4}Wegfindungsalgorithmen}{15}} -\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Lineares Gleichungssystem}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.1}Lineares Gleichungssystem einer Kreuzung}{15}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.2}Gleichungen zwischen Kreuzungen}{15}} -\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Lineares Gleichungssystem als Graph}{16}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Das Abbiegeproblem}{15}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Ans\"atze}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.1}Markov-Ketten HMM}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.2}Neuronale Netze}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.3}Gleichungssystem}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.4}Wegfindungsalgorithmen}{15}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Lineares Gleichungssystem}{16}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.4.1}Lineares Gleichungssystem einer Kreuzung}{16}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.4.2}Gleichungen zwischen Kreuzungen}{16}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.5}Lineares Gleichungssystem als Graph}{16}} \@writefile{toc}{\contentsline {section}{\numberline {8}Visualisierung}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.1}Visualisierung des Graphen mit Geoinformationen}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.2}Visualisierung des JGraphT-Graphen}{17}} \@writefile{toc}{\contentsline {section}{\numberline {9}Validierung}{18}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.1}Testdatenmenge}{18}} -\@writefile{toc}{\contentsline {subsection}{\numberline {9.2}Verkehrszählung}{18}} +\@writefile{toc}{\contentsline {subsection}{\numberline {9.2}Verkehrsz\active@dq \dq@prtct{a}hlung}{18}} \@writefile{toc}{\contentsline {subsection}{\numberline {9.3}Validierung der Verkehrsaufkommensvorhersage}{18}} \@writefile{toc}{\contentsline {section}{\numberline {10}Ausblick}{19}} \bibstyle{plainnat} diff --git a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log index aef08639..b69f4820 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log +++ b/ss2013/Bachelor Thesis/thesis_ug/TUDthesis.log @@ -1,7 +1,7 @@ -This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.7.23) 9 AUG 2013 21:55 +This is pdfTeX, Version 3.1415926-1.40.11 (MiKTeX 2.9) (preloaded format=pdflatex 2013.7.23) 10 AUG 2013 03:57 entering extended mode **TUDthesis.tex -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.tex" +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\TUDthesis.tex" LaTeX2e <2009/09/24> Babel and hyphenation patterns for english, afrikaans, ancientgreek, ar abic, armenian, assamese, basque, bengali, bokmal, bulgarian, catalan, coptic, @@ -616,7 +616,7 @@ LaTeX Info: Redefining \] on input line 2667. LaTeX Warning: Unused global option(s): [article,colorback,accentcolor=tud9d]. -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux") +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\TUDthesis.aux") LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 15. LaTeX Font Info: ... okay on input line 15. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 15. @@ -841,7 +841,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 24--24 [0 -] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/danke.tex") +] ("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/danke.tex") [1 @@ -855,24 +855,24 @@ File: t15sf.fd 2008/06/23 Fontinst v1.927 font definitions for T1/5sf. ] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/uebersicht.tex") +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/uebersicht.tex") Underfull \hbox (badness 10000) in paragraph at lines 1--35 [] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/abstract.tex") +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/abstract.tex") Underfull \hbox (badness 10000) in paragraph at lines 1--36 [] [1 -] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.toc") +] ("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\TUDthesis.toc") \tf@toc=\write3 [2] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/einleitung.tex" +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/einleitung.tex" Underfull \hbox (badness 10000) in paragraph at lines 10--11 [] @@ -880,10 +880,10 @@ Underfull \hbox (badness 10000) in paragraph at lines 10--11 File: pic/overview.png Graphic file (type png) ) -[3 ] +[3 ] [4] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/relatedwork.tex" -) [5] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/modell.tex +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/relatedwork.tex" +) [5] ("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/modell.tex " Underfull \hbox (badness 10000) in paragraph at lines 1--3 @@ -893,23 +893,23 @@ Underfull \hbox (badness 10000) in paragraph at lines 1--3 File: ext/Kreuzungsuebersicht.pdf Graphic file (type pdf) -LaTeX Font Info: Try loading font information for TS1+5ch on input line 31. +LaTeX Font Info: Try loading font information for TS1+5ch on input line 33. ("C:\Program Files\tuddesign\texmf\tex\latex\tex-tudfonts\softmake\charter\ts15 ch.fd" File: ts15ch.fd 2008/06/23 Fontinst v1.927 font definitions for TS1/5ch. -) [6 ] File: ext/KreuzungA59.pdf Graphic file (type pdf) - [7 [7 ] [8] File: ext/KreuzungA23.pdf Graphic file (type pdf) -) [9 ] [10] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/daten.tex" + [9 ]) [10] +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/daten.tex" Underfull \hbox (badness 10000) in paragraph at lines 1--2 [] @@ -926,7 +926,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 9--10 File: pic/csv.png Graphic file (type png) - [11 [11 ] Overfull \hbox (2.61195pt too wide) in paragraph at lines 81--85 \T1/5ch/m/n/9.5 Abbiegewahrscheinlichkeiten von Mi-cha-el Scholz. Wur-den duch @@ -934,28 +934,28 @@ Lö-sung des Kreu-zungs-glei-chungs-sys-tem be-stimmt.Dabei [] [12]) [13] [14] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/berechnung.tex" -Underfull \hbox (badness 10000) in paragraph at lines 21--22 +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/berechnung.tex" +Underfull \hbox (badness 10000) in paragraph at lines 28--29 [] -) [15] [16] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/visualisierung.t +[15]) [16] +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/visualisierung.t ex") [17] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/validierung.tex" +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/validierung.tex" Underfull \hbox (badness 10000) in paragraph at lines 4--6 [] ) [18] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/ausblick.tex") -[19] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.bbl" +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/ausblick.tex") +[19] ("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\TUDthesis.bbl" LaTeX Warning: Empty `thebibliography' environment or \BreakBibliography before end of `thebibliography' environment on input line 8. -) [20] ("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\tex/anhang.te +) [20] ("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\tex/anhang.te x" File: ext/MessgruppentabelleNord-2013-01-08.pdf Graphic file (type pdf) @@ -1003,27 +1003,27 @@ File: ext/KreuzungA59.pdf Graphic file (type pdf) File: ext/KreuzungA104.pdf Graphic file (type pdf) -) [21] [22 ] [23 ] [24] [25 ] [26 ] [27 ] [28 ] [29] [30 ] [31 ] [32 ] [33] [34 ] -("C:\Daten\source\college\ss2013\Bachelor Thesis\thesis_ug\TUDthesis.aux") ) +) [21] [22 ] [23 ] [24] [25 ] [26 ] [27 ] [28 ] [29] [30 ] [31 ] [32 ] [33] [34 ] +("C:\daten\source\college\ss2013\bachelor thesis\thesis_ug\TUDthesis.aux") ) Here is how much of TeX's memory you used: 7954 strings out of 494019 122133 string characters out of 3145626 - 213804 words of memory out of 3000000 + 214804 words of memory out of 3000000 10968 multiletter control sequences out of 15000+200000 123302 words of font info for 77 fonts, out of 3000000 for 9000 714 hyphenation exceptions out of 8191 - 65i,13n,77p,728b,488s stack positions out of 5000i,500n,10000p,200000b,50000s + 65i,13n,77p,826b,488s stack positions out of 5000i,500n,10000p,200000b,50000s {C: /Program Files (x86)/MiKTeX/fonts/enc/dvips/fontname/texnansi.enc}{C:/Program F iles (x86)/MiKTeX/fonts/enc/dvips/fontname/8r.enc} -Output written on TUDthesis.pdf (38 pages, 1946097 bytes). +Output written on TUDthesis.pdf (38 pages, 1947417 bytes). 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{subsection}{\numberline {7.1}Das Zeitproblem}{15} -\contentsline {subsection}{\numberline {7.2}Ans\"atze}{15} -\contentsline {subsubsection}{\numberline {7.2.1}Markov-Ketten HMM}{15} -\contentsline {subsubsection}{\numberline {7.2.2}Neuronale Netze}{15} -\contentsline {subsubsection}{\numberline {7.2.3}Gleichungssystem}{15} -\contentsline {subsubsection}{\numberline {7.2.4}Wegfindungsalgorithmen}{15} -\contentsline {subsection}{\numberline {7.3}Lineares Gleichungssystem}{15} -\contentsline {subsubsection}{\numberline {7.3.1}Lineares Gleichungssystem einer Kreuzung}{15} -\contentsline {subsubsection}{\numberline {7.3.2}Gleichungen zwischen Kreuzungen}{15} -\contentsline {subsection}{\numberline {7.4}Lineares Gleichungssystem als Graph}{16} +\contentsline {subsection}{\numberline {7.2}Das Abbiegeproblem}{15} +\contentsline {subsection}{\numberline {7.3}Ans\"atze}{15} +\contentsline {subsubsection}{\numberline {7.3.1}Markov-Ketten HMM}{15} +\contentsline {subsubsection}{\numberline {7.3.2}Neuronale Netze}{15} +\contentsline {subsubsection}{\numberline {7.3.3}Gleichungssystem}{15} +\contentsline {subsubsection}{\numberline {7.3.4}Wegfindungsalgorithmen}{15} +\contentsline {subsection}{\numberline {7.4}Lineares Gleichungssystem}{16} +\contentsline {subsubsection}{\numberline {7.4.1}Lineares Gleichungssystem einer Kreuzung}{16} +\contentsline {subsubsection}{\numberline {7.4.2}Gleichungen zwischen Kreuzungen}{16} +\contentsline {subsection}{\numberline {7.5}Lineares Gleichungssystem als Graph}{16} \contentsline {section}{\numberline {8}Visualisierung}{17} \contentsline {subsection}{\numberline {8.1}Visualisierung des Graphen mit Geoinformationen}{17} \contentsline {subsection}{\numberline {8.2}Visualisierung des JGraphT-Graphen}{17} \contentsline {section}{\numberline {9}Validierung}{18} \contentsline {subsection}{\numberline {9.1}Testdatenmenge}{18} -\contentsline {subsection}{\numberline {9.2}Verkehrszählung}{18} +\contentsline {subsection}{\numberline {9.2}Verkehrsz\active@dq \dq@prtct {a}hlung}{18} \contentsline {subsection}{\numberline {9.3}Validierung der Verkehrsaufkommensvorhersage}{18} \contentsline {section}{\numberline {10}Ausblick}{19} \contentsline {section}{\numberline {11}Anhang}{21} diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex index f34b99ee..0750f31e 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/berechnung.tex @@ -1,11 +1,18 @@ In diesem Kapitel werden einige Berechnungsansätze beschrieben, sowie Probleme mit diesen Ansätzen. Außerdem werden Problemstellungen formuliert, welche sich teilweise als lösbar herausgestellt haben. \subsection{Das Zeitproblem}{ - Die Daten sind zeitdeterministisch(?). Außerdem zeigen sie eine Momentaufnahme des geschehens. Das Hauptproblem ist, dass zwischen Kreuzungen keine Sensoren verbaut sind. Eine 'Verfolgung' eines Autos ist somit nicht möglich, da nicht festgestellt werden kann, wie weit es bis zur nächsten Momentaufnahme gekommen ist. + Die Daten der Induktionsschleifen sind die Werte der Sensoren über die letzte Minute. Sie zeigen eine Art summierte Momentaufnahme des Verkehrs an den Messpunkten. Das macht es allerdings schwer zwei Messungen in eine Beziehung zu stellen. Bildlich gesprochen kann man nicht trivial bestimmen, wie lange ein Auto von der einen zur anderen Kreuzung benötigt. Da die Daten nur für bestimmte Zeitpunkte zur Verfügung stehen, kann nicht mehr festgetsllt werden wann ein Auto, welches an Kreuzung A über den Sensor gefahren ist, an Kreuzung B ankommt und dort über den Sensor fährt. + Eine 'Verfolgung' eines Autos ist somit nicht möglich, da nicht festgestellt werden kann, wie weit es bis zur nächsten Momentaufnahme gekommen ist. Ein Naiver Ansatz für viele Berechnungen ist es den Ausgangswerte einer Kreuzung an den Eingang der nächsten zu legen. Dieses Verfahren ist allerdings problematisch, da die Sensorwerte im einem Regelmäßigen Abstand gemessen werden, ein Auto sich allerdings nicht daran halten muss. Es könnte also zwei kreuzungen oder 1,5 in einer Zeiteinheit hinter sich lassen. } +\subsection{Das Abbiegeproblem}{ + Das 'Abbiegeproblem' ist auf zu wenige Sensorwerte zurückzuführen. In den Kreuzungen von Darmstadt sind die Induktionsschleifen am Kreuzungseingang verbaut, allerdings nicht am Kreuzungs Ausgang(bis auf wenige Ausnahmen). Es kann für Mischspursensoren folglich nicht live bestimmt werden, wie viele Autos in die eine und wie viele in die andere gefahren sind. + + [Beispiel Kreuzung, mit validierung, und ohne] +} + \subsection{Ans\"atze}{ \subsubsection{Markov-Ketten HMM}{ Problem, nicht zyklischer Graph. Ein Verkehrsnetz hat viele Kreise und ein solches Modell ist aus diesen Gründen nicht sinnvoll. diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex index f6e3f1ec..47461a3b 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/modell.tex @@ -1,44 +1,46 @@ -In diesem Kapitel werden verschiedene Modellierungen der Ministadt vorgestellt und erklärt. Die beiden diskutierten Modelle sind die Darstellung als Matrix und die als Graph. Diese beiden Darstellungen sind untereinander kompatibel, können deshalb ineinander überführt werden. -Dabei ist der Graph ein nützliches Werkzeug der Visualisierung während die Matrixdarstellung der Berechnung dient.\\ +In diesem Kapitel werden verschiedene Modellierungen der Ministadt vorgestellt und erkl"art. Die beiden diskutierten Modelle sind die Darstellung als Matrix und die als Graph. Diese beiden Darstellungen sind untereinander kompatibel, k"onnen deshalb ineinander "uberf"uhrt werden. +Dabei ist der Graph ein n"utzliches Werkzeug der Visualisierung w"ahrend die Matrixdarstellung der Berechnung dient.\\ -In der Industrie eingesetzte Software zur Berechnung und Modellierung von Verkehrsflüssen, verwenden meistens ein sog. Micro Modell(ZITAT). Ein solches Micro Modell modelliert jedes einzelne Auto, um eine hohe Genauigkeit der Berechnung zu gewährleisten. Allerdings erfordert das neben sehr vielen Messwerten auch einen erheblichen Mehraufwand zur Modellierung. +In der Industrie eingesetzte Software zur Berechnung und Modellierung von Verkehrsfl"ussen, verwenden meistens ein sog. Micro Modell(ZITAT). Ein solches Micro Modell modelliert jedes einzelne Auto, um eine hohe Genauigkeit der Berechnung zu gew"ahrleisten. Allerdings erfordert das neben sehr vielen Messwerten auch einen erheblichen Mehraufwand zur Modellierung. -In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches für Kreuzungen eine genauere Modellierung zulässt, während es für zwischen den Kreuzungen ein ungenauere Modellierung vornimmt. Dies ist sinnvoll, da nur im Kreuzungsbereich Sensoren zur Verfügung stehen, während kleinere Kreuzungen nicht mit Sensoren bestückt sind und aus diesem Grund keine qualifiziert Aussage über diese gemacht werden kann. +In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches f"ur Kreuzungen eine genauere Modellierung zul"asst, w"ahrend es f"ur zwischen den Kreuzungen ein ungenauere Modellierung vornimmt. Dies ist sinnvoll, da nur im Kreuzungsbereich Sensoren zur Verf"ugung stehen, w"ahrend kleinere Kreuzungen nicht mit Sensoren best"uckt sind und aus diesem Grund keine qualifiziert Aussage "uber diese gemacht werden kann. \subsection{Modell der Ministadt}{ - Um ein Modell zu erstellen, muss man sich der Realität bewusst werden und diese (partiell) im Computer abbilden (ZITAT). - Für das hier entwickelte Straßenmodell wurden folgende Objekte modelliert: + Die 'Ministadt' enth"alt folgende mit Sensoren best"uckte Kreuzungen: A3, A4, A5, A12, A23, A28, A29, A46, A59, A104. + Um ein Modell zu erstellen, muss man sich der Realit"at bewusst werden und diese (partiell) im Computer abbilden (ZITAT). + F"ur das hier entwickelte Stra"senmodell wurden folgende Objekte definiert und modelliert: \begin{enumerate} - \item{Straße: Eine Straße, auf der Autos fahren dürfen. Sie ist nicht mit Sensoren bestückt.} - \item{Kreuzung: Eine Kreuzung ist das Zusammentreffen von Straßen. Sie kann mit Sensoren bestückt sein, welche den Verkehr messen.} + \item{Stra"se: Eine Stra"se, auf der Autos fahren d"urfen. Sie ist nicht mit Sensoren best"uckt.} + \item{Kreuzung: Eine Kreuzung ist das Zusammentreffen von Stra"sen. Sie kann mit Sensoren best"uckt sein, welche den Verkehr messen.} \item{Sensoren: Sensoren messen den Verkehr an dem Punkt des Verkehrsnetzes, an dem sie Verbaut sind.} - \item{Virtuelle Sensoren: Punkte welche das Straßennetz aufspannen, für welche allerdings keine Messwerte vorliegen.} + \item{Virtuelle Sensoren: Punkte welche das Stra"sennetz aufspannen, f"ur welche allerdings keine Messwerte vorliegen.} \end{enumerate} - Bevor die Modellierung im Computer beginnen kann, ist es hilfreich manuell Zeichnungen von den Kreuzungen anzufertigen. Die gewählte intuitive Modellierung entspricht in etwa der, welche später im Computer entsteht. Die Grundlage für diese Modellierung sind die CAD-Zeichnungen der Stadt Darmstadt. Sie werden im Kapitel [Daten] genauer beschrieben. + Bevor die Modellierung im Computer beginnen kann, ist es hilfreich manuell Zeichnungen von den Kreuzungen anzufertigen. Die gew"ahlte intuitive Modellierung entspricht in etwa der, welche sp"ater im Computer entsteht. Die Grundlage f"ur diese Modellierung sind die CAD-Zeichnungen der Kreuzungen der Stadt Darmstadt. Sie werden im Kapitel [Daten] genauer beschrieben. - Um eine Übersicht über das zu betrachtende Gebiet der 'Ministadt' zu erhalten wurde - eine Übersicht über alle Kreuzungen in dem gesamten betrachteten Gebiet erstellt. In dieser Modellierung entfallen alle Seitenstraßen und Zwischenkreuzungen ohne Sensoren. + Um eine "Ubersicht "uber das zu betrachtende Gebiet der 'Ministadt' zu erhalten wurde + eine Übersicht "uber alle Kreuzungen in dem gesamten betrachteten Gebiet erstellt. In dieser Modellierung entfallen alle Seitenstra"sen und Zwischenkreuzungen ohne Sensoren. + Die Zwischenkreuzungen entfallen, da keinerlei Messdaten f"ur diese Kreuzungen vorhanden sind. \begin{figure}[htbp!] \centering \fbox{\includegraphics[width=0.50\textwidth-2\fboxsep-2\fboxrule]{ext/Kreuzungsuebersicht}} - \caption{Kreuzungsübersicht 'Ministadt'in der Stadt Darmstadt} + \caption{Kreuzungs"ubersicht 'Ministadt'in der Stadt Darmstadt} \end{figure} Die einzelnen Kreuzungen lassen sich dagegen sehr gut auf Sensorebene darstellen. Sensoren sind dabei in zwei Klassen zu unterteilen: \begin{itemize} - \item{Einspursensor: Ein Auto auf dieser Spur kann die Kreuzung nur in eine Richtung verlassen.} + \item{Einspursensor: Ein Auto auf dieser Spur kann die Kreuzung nur in genau eine Richtung verlassen.} \item{Mischspursensor: Ein Auto auf dieser Spur kann die Kreuzung in mehr als eine Richtung verlassen.} \end{itemize} - Die Zuordnung der Sonoren zu ihren Klassen erfolgte mithilfe der CAD-Zeichnungen der Kreuzungen, welche die Stadt Darmstadt zur Verfügung stellte. Die beiden Sensortypen können jeweils nochmal unterschieden werden. Einspursensoren unterteilen sich nochmals in: + Die Zuordnung der Sensoren zu ihren Klassen erfolgte mithilfe der CAD-Zeichnungen der Kreuzungen, welche die Stadt Darmstadt zur Verf"ugung stellte. Die beiden Sensortypen k"onnen jeweils nochmal unterschieden werden. Einspursensoren unterteilen sich nochmals in drei Subklassen: \begin{itemize} \item{Geradeaus} \item{Links} \item{Rechts} \end{itemize} - Mischspursensoren dagegen bieten mehr Möglichkeiten: + Mischspursensoren dagegen lassen sich in vier Subklassen unterteilen: \begin{itemize} \item{Geradeaus + Rechts} \item{Geradeaus + Links} @@ -52,87 +54,89 @@ In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches für Kreu \caption{Kreuzung A59} \end{figure} + Diese intuitive Modellierung auf zwei Ebenen hat sich sowohl aus "Ubersichtsgr"unden, als auch f"ur die Berechnung als sinnvoll erwiesen. W"ahrend ein Kreuzungsbild eine wesentlich genauere Abbildung der Realit"at ist, so ist im Vergleich die Kreuzungs"ubersicht relativ ungenau, da Seitenstra"sen nicht modelliert werden und alle Kreuzungen als gleich weit voneinander entfernt betrachtet werden. Die gew"ahlte Modellierung hat folglich zwei Genauigkeitsstufen. Die "Ubersicht "uber die Kreuzungen gew"ahrt einen Blick auf die Gesammtverkehrssituation. Sie dient wie der Name schon sagt der "Ubersicht. Ein wesentliches Ziel ist es Verkehrsdaten f"ur dieses Modell zu errechnen, da wir keine Informationen "uber die einzelnen Kreuzungen zur Verf"ugung haben + \begin{itemize} - \item{Eine Übersicht über die Kreuzungen (Macro Modell).} - \item{Eine Übersicht über eine Kreuzung (Micro Modell). Hier sind uns einige Daten bekannt, die Sensorwerte. Ziel ist es unbekannte Werte zu berechnen und diese auf das Macro Modell zu übertragen.} + \item{Eine "Ubersicht "uber die Kreuzungen (Macro Modell).} + \item{Eine "Ubersicht "uber eine Kreuzung (Micro Modell).} \end{itemize} - Bereits hier ist eine Zweischichtenmodellierung zu erkennen, welche sich aus Übersichtsgründen als sinnvoll erwiesen hat. Während ein Kreuzungsbild eine wesentlich genauere Abbildung der Realität ist, so ist im Vergleich die Kreuzungsübersicht relativ ungenau, da Seitenstraßen nicht modelliert werden und alle Kreuzungen als gleich weit voneinander entfernt betrachtet werden. Die gewählte Modellierung hat folglich zwei Genauigkeitsstufen. - - Die Übersicht über die Kreuzungen gewährt einen Blick auf die Gesammtverkehrssituation. Sie dient wie der Name schon sagt der Übersicht. Ein wesentliches Ziel ist es Verkehrsdaten für dieses Modell zu errechnen, da wir keine Informationen über die einzelnen Kreuzungen zur Verfügung haben. + Innerhalb von den Kreuzungen sind die Induktionsschleifenwerte bekannt. Als Zielsetzung wurde festgelegt + \begin{itemize} + \item{unbekannte Werte innerhalb von Kreuzungen zu berechnen.} + \item{und diese in einem zweiten Schritt auf die Kreuzungs"ubersicht zu "ubertragen, um eine "Ubersicht "uber die Verkehrssituation aller Kreuzungen zu erhalten.} + \end{itemize} + . - Dagene sind für Kreuzungen mehr Daten vorhanden und man kann eine genauere Modellierung vornehmen. - Der Zwischenkreuzungsgraph modelliert nun den Zusammenhang zwischen den Kreuzungen reduziert auf 'in welche Richtung kann das Auto von Kreuzung x fahren'. Dies entspricht auch der Sensorverteilung, die ausschließlich auf Kreuzungen auftreten und nicht auf Straßen zu finden sind.\\ - Die schwäche des Modells ist die Annahme, dass ein Auto in Luftlinie von eingangssensor zum Ausgangssensor fährt und keine geoinformationen über die Kante zur Verfügung stehen. + Dagene sind f"ur Kreuzungen mehr Daten vorhanden und man kann eine genauere Modellierung vornehmen. + Der Zwischenkreuzungsgraph modelliert nun den Zusammenhang zwischen den Kreuzungen reduziert auf 'in welche Richtung kann das Auto von Kreuzung x fahren'. Dies entspricht auch der Sensorverteilung, die ausschlie"slich auf Kreuzungen auftreten und nicht auf Stra"sen zu finden sind.\\ + Die schw"ache des Modells ist die Annahme, dass ein Auto in Luftlinie von eingangssensor zum Ausgangssensor f"ahrt und keine Geoinformationen "uber die Kante zur Verf"ugung stehen. } \subsection{Modell als Graph}{ - Ein naheliegender Modellierungsansatz ist es, das Straßennetz als Graph zu modellieren. Dies eignet sich nicht nur, da Graphen sehr gut erforscht und viele Algorithmen auf ihnen zur Verfügung stehen, sonder auch, weil die intuitiv gewählte manuelle Modellierung sich als Graph darstellen lässt. Aus diesem Grund wurden Graphen als Basis der Modellierung gewählt. Insbesondere die Möglichkeit Graphen in Matrizen zu überführen, oder Matrizen-Rechnungen an Graphen zu vollführen erweist sich als äußerst nützlich. Graphen bieten dabei zwei Modellierungseinheiten, Knoten und Kanten, welche Knoten verbinden. + Ein naheliegender Modellierungsansatz ist es, das Stra"sennetz als Graph zu modellieren. Dies eignet sich nicht nur, da Graphen sehr gut erforscht und viele Algorithmen auf ihnen zur Verf"ugung stehen, sonder auch, weil die intuitiv gew"ahlte manuelle Modellierung sich als Graph darstellen l"asst. Aus diesem Grund wurden Graphen als Basis der computergest"utzten Modellierung gew"ahlt. Insbesondere die M"oglichkeit Graphen in Matrizen zu "uberf"uhren, oder Matrizen-Rechnungen an Graphen zu vollf"uhren erweist sich als n"utzlich. Graphen bieten dabei zwei Modellierungseinheiten, Knoten und Kanten. Kanten verbinden dabei zwei Knoten. Da Einbahnstra"sen oder sogar einzelne Spuren modelliert werden m"ussen, w"ahlt man einen gerichteten Graphen. - Die gewählte Zweistufenmodellierung hat sich als nützlich erwiesen, weshalb auch diese als Graph abgebildet werden soll. Um das zu gewährleisten müssen zwei verschiedene Graphen generiert werden: - \begin{itemize} - \item{eine Kreuzungsübersicht} - \item{viele Einzelkreuzungen} - \end{itemize} + Da sich die Zweistufenmodellierung als n"utzlich erwiesen hat, wird auch diese als Graph abgebildet. Daf"ur m"ussen zwei verschiedenen Graphen aufgebaut werden. Der einer Kreuzung, mit Sensoren und virtuellen Sensoren als Knoten, sowie Stra"sen als Kanten. Der Graph der Kreuzungs"ubersicht dagegen hat Kreuzungen als Knoten und Stra"sen als Kanten. - Es erschien an dieser Stelle sinnvoll, die Graphen im Computer zu modellieren. Dafür wird auf die Java Graphen-Bibliothek JGraphT zurückgegriffen. Diese erlaubt es nicht nur Graphen aufzubauen und auf diesen zu rechnen, sondern auch die Visualisierung dieser mithilfe der JGraph-Bibliothek. Die Bibliothek erlaubt es dank sog. Templates in Java, Knoten von beliebigem Typ zu definieren. Diese Freiheit gilt eingeschränkt auch für Kanten(allerdings können diese keine Konstruktoren beinhalten). + Zur modellierung am Computer wird auf die Java Bibliothek JGraphT zur"uckgegriffen. Sie erlaubt es, dank moderner 'Templatisierung', Graphen mit belieben Klassen als Knoten aufzubauen. Das selbe gilt f"ur Kanten mit wenigen Einschr"ankungen. Desweiteren erlaubt JGraphT eine Konvertierung zu der weit verbreiteten Bibliothek JGraph, welche eine Visualisierungschnittstelle mitbringt. + + Es soll dabei die Knoten des Kreuzungs"ubersichtsgraphen die Graphen der einzelnen Kreuzungen enthalten um den Zusmmenhalt des Modells zu gew"ahrleisten. \subsubsection{Kreuzungsgraph}{ - Da der Kreuzungsübersichtsgraph die Kreuzungsgraphen beinhalten soll, wird zuerst die Kreuzung modelliert. Dabei gilt es folgende Elemente abzubilden und entweder als Knoten oder Kante zu definieren. + Da der Kreuzungs"ubersichtsgraph die Kreuzungsgraphen beinhalten soll, wird zuerst der Kreuzungsgraph modelliert. Dabei gilt es folgende Elemente abzubilden und entweder als Knoten oder Kante zu definieren. \begin{itemize} - \item{Straße} - \item{Sensor} - \item{Virtueller Sensor} + \item{Stra"se: Ein nicht mit Sensoren best"uckte Stra"se, auf der Autos fahren d"urfen.} + \item{Sensor: Eine Induktionsschleife} + \item{Virtueller Sensor: F"ur jede Richtung der Kreuzung jeweils einen virtuellen Aus- und Eingang.} \end{itemize} - Es liegt nahe Straßen als Kanten und Senoren, sowie virtuelle Sensoren als Knoten zu modellieren. + Es liegt nahe Stra"sen als Kanten und Senoren, sowie virtuelle Sensoren als Knoten zu modellieren. - Um eine Kreuzung zu modellieren wurden folgende zwei Klassen definiert: + Um eine Kreuzung mit JGraphT zu modellieren wurden folgende zwei Klassen definiert: \begin{itemize} \item{SE: Sensoren, virtuelle und real.} - \item{ST: Straße} + \item{ST: Stra"se} \end{itemize} Ein Sensor kann dabei folgende Werte halten: [CLASS] - Eine Straße hält dagegen nur die Information der Abbiegewahrscheinlichkeit. + Eine Stra"se h"alt dagegen nur die Information der Abbiegewahrscheinlichkeit. [CLASS] } \subsubsection{Kreuzungs"ubersicht}{ - Da Graphen nur Knoten und Kanten haben müssen alle zu modellierenden Elemente entweder Knoten oder Kante sein. Folgende festlegungen wurden für diese Arbeit dabei getroffen: + Da Graphen nur Knoten und Kanten haben m"ussen alle zu modellierenden Elemente entweder Knoten oder Kante sein. Folgende festlegungen wurden f"ur diese Arbeit dabei getroffen: \begin{itemize} - \item{Straße sei eine Kante} + \item{Stra"se sei eine Kante} \item{Kreuzung sei ein Knoten} - \end{itemize} Graph unter benutzung von JGraphT \\ - Graph für kreuzungsübersicht (zwischen Kreuzung) \\ - Graph für innerhalb der Kreuzung \\ + Graph f"ur kreuzungs"ubersicht (zwischen Kreuzung) \\ + Graph f"ur innerhalb der Kreuzung \\ Micro / Macro Modell - Es gilt das Straßennetz und die Sensoren in einen Graph zu überführen. Dabei sind Straßen Kanten und Kreuzungen Knoten. + Es gilt das Stra"sennetz und die Sensoren in einen Graph zu "uberf"uhren. Dabei sind Stra"sen Kanten und Kreuzungen Knoten. Innerhalb von Kreuzungen nehme ich eine Modellierung der Sensoren vor und bilde wieder einen Graphen, diesmal mit Verbindungen zwischen Sensoren als Kanten und Sensoren als Knoten. - Um die Kreuzungsübersicht im Computer abzubilden wurden folgende zwei Klassen definiert: + Um die Kreuzungs"ubersicht im Computer abzubilden wurden folgende zwei Klassen definiert: \begin{itemize} \item{XR: Kreuzung} - \item{ST: Straße} + \item{ST: Stra"se} \end{itemize} - 'XR' entspricht dabei dem oben beschrieben Graphen der Kreuzung, ST ist eine Straße, wie oben beschrieben. + 'XR' entspricht dabei dem oben beschrieben Graphen der Kreuzung, ST ist eine Stra"se, wie oben beschrieben. } } \subsection{Modell als Matrix}{ - Als Grundlage für die Berechnung wurde eine Matrixdarstellung für Kreuzungen entwickelt. Der oben entwickelte Graph lässt sich dabei einfach in Matrixform überführen. + Als Grundlage f"ur die Berechnung wurde eine Matrixdarstellung f"ur Kreuzungen entwickelt. Der oben entwickelte Graph l"asst sich dabei einfach in Matrixform "uberf"uhren. \subsubsection{Verbindungsmatrizen}{ - Um eine Kreuzung zu beschreiben ist es nötig die Verbindungen von Sensoren zu deren möglichen Ausgängen zu modellieren. - Dies lässt sich mit einer Verbindungsmatrix bewerkstelligen. Hierfür werden alle Ausgänge einer Kreuzung auf der X-Achse + Um eine Kreuzung zu beschreiben ist es n"otig die Verbindungen von Sensoren zu deren m"oglichen Ausg"angen zu modellieren. + Dies l"asst sich mit einer Verbindungsmatrix bewerkstelligen. Hierf"ur werden alle Ausg"ange einer Kreuzung auf der X-Achse der Matrix verzeichnet, alle Sensoren dieser Kreuzung auf der Y-Achse. Am Beispiel der Kreuzung A23 sei das hier demonstriert. @@ -159,8 +163,8 @@ In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches für Kreu Diese Matrix wird als Ausgangsmatrix bezeichnet. - Um nicht nur die Virtuellen Ausgänge zu modellieren, sondern auch die Eingänge ist eine zweite Matrix nötig, die - die Eingänge mit den Sensoren verbindet. Die Virtuellen Eingänge werden hierfür auf der X-Achse aufgetragen, alle + Um nicht nur die Virtuellen Ausg"ange zu modellieren, sondern auch die Eing"ange ist eine zweite Matrix n"otig, die + die Eing"ange mit den Sensoren verbindet. Die Virtuellen Eing"ange werden hierf"ur auf der X-Achse aufgetragen, alle Sensoren werden auf der Y-Achse der Matrix eingezeichnet. Hier im Beispiel die Eingangsmatrix von Kreuzung A23, der zentralen Kreuzung des betrachten Ausschnitts: @@ -175,16 +179,18 @@ In dieser Arbeit wird eine Zweistufenmodellierung vorgestellt, welches für Kreu } \subsubsection{Berechnungsmatrizen}{ - Während oben Verbindungsmatrizen beschrieben werden, welche ausschließlich modellieren, ob ein Knoten(virtuell oder Sensor) mit einem anderen verbunden ist, - so kann man bei bekannten Abbiegewahrscheinlichkeiten für die Kreuzung diese direkt in der Ausgangsmatrix verzeichnen: + W"ahrend oben Verbindungsmatrizen beschrieben werden, welche ausschlie"slich modellieren, ob ein Knoten(virtuell oder Sensor) mit einem anderen verbunden ist, + so kann man bei bekannten Abbiegewahrscheinlichkeiten f"ur die Kreuzung diese direkt in der Ausgangsmatrix verzeichnen: - A1 A2 A3 A4 - S1 0.3 0.7 - S2 1 - S3 0.5 0.5 - S4 0.1 0.9 + $\begin{Bmatrix} + & E1 & E2 & E3 & E4 \\ + S1 & 0.3 & 0.7 & 0 & 0 \\ + S2 & 0 & 0.2 & 0.8 & 0 \\ + S3 & 0 & 0 & 0 & 0 \\ + S4 & 0.9 & 0 & 0 & 0.1 + \end{Bmatrix}$ - Diese Darstellung erwies sich als hilfreich zur Berechnung von Ausgangswerten für eine Kreuzung. Siehe hierzu das Kapitel [Berechnung] + Diese Darstellung erwies sich als hilfreich zur Berechnung von Ausgangswerten f"ur eine Kreuzung. Siehe hierzu das Kapitel [Berechnung] } } diff --git a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex index 990ecdea..89bd740b 100644 --- a/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex +++ b/ss2013/Bachelor Thesis/thesis_ug/tex/validierung.tex @@ -1,4 +1,4 @@ -In diesem Kapitel wird die Validierung der berechneten Verkehrswerte beschrieben. Dabei wird zunächst ein angestrebtes Verfahren beschrieben, darauf eingegangen warum dieses Verfahren sich nicht eignet. Aus diesem Grund wurde eine Verkehrszählung im Rahmen dieser Arbeit vorgenommen, um die berechneten Werte zu validieren. +In diesem Kapitel wird die Validierung der berechneten Verkehrswerte beschrieben. Dabei wird zunächst ein angestrebtes Verfahren beschrieben und darauf eingegangen warum dieses Verfahren sich nicht eignet. Um die berechneten Werte dennoch validieren zu können, wurde eine Verkehrszählung im Rahmen dieser Arbeit vorgenommen. \subsection{Testdatenmenge}{ Ein übliches Testverfahren ist es ein Teil seiner Datenmenge aus der Berechnung außenvorzulassen[zitat] und durch die verwendete Berechnung diese fehlenden Daten zu reproduzieren. @@ -11,8 +11,16 @@ Dieses Verfahren eignet sich hier allerdings nicht, da bei den vorliegenden Sens Um das Modell zu validieren kann man aus seiner bekannten Menge an Daten, in diesem Fall die Sensordaten, ein Teil auswählen, welcher nicht zur Berechnung verwendet wird. Dieser Teil wird nach der Berechnung mit den Ergebnissen der entsprechenden Sensoren verglichen. Ist die Abweichung groß, ist das berechnete Ergebniss(für diesen Sensor/Bereich) ein schlechtes. bestätigt sich dagegen der Sensorwert, kann von einem guten Ergebniss für diesen Bereich gerechnet werden. Diese Vorgehen ist nicht möglich, da alle Sensorwerte zur Berechnung benötigt werden. Um die Daten zu validieren ist eine manuelle Verkehrszählung nötig.} -\subsection{Verkehrszählung}{ -Alternativ kann man ich auf die Straße stellen und Sensorwerte manuell zählen, bzw. Ausgangsknoten. Problem dieser Methode ist zum einen der Aufwand(das muss ein Mensch machen und kann nicht von einer Maschine übernommen werden) zum anderen, dass ich davon ausgehe, das ein Verkehrsverhalten sehr stark von der Uhrzeit und dem Tag der Messung abhängig ist. Deshalb ist es nicht sicher ob eine solche Messung überhaupt Aufschluss auf Daten aus der Vergangenheit bietet. +\subsection{Verkehrsz"ahlung}{ +Da kein anderes passendes Testverfahren gefunden wurde, wurde im Rahmen dieser Arbeit eine Verkehrszählung durchgeführt. Diese Verkehrszählung wurde mithilfe von Michael Scholz erhoben, welcher diese Daten ebenfalls für seine Bachelor Arbeit benötigt. +Gezählt wurde dabei mit Strichliste and den Kreuzungen [], [] und []. Dabei wurden in der einen Messreihe die Autos an den Ausgängen gezählt, um die berechneten Werte der virtuellen Kreuzungsausgänge in dem Graphenmodell validieren zu können. +Desweiteren wurden die Autos gezählt welche über einen speziellen Sensor gefahren sind. +Hierfür wurden die Sensoren [] und [] gezählt. In einer weiten Zählung wurde nur der Sensore [] betrachtet. +Die Ausgänge und Sensoren wurden dabei über 15 Minuten gezählt, da eine genaue Synkronisation mit dem Zeitgeber der Sensoren nicht genau möglich ist. Für die genauere Untersuchung des Sensors [] wurde eine Minutenweise Zählung vorgenommen, beginnend vom Minutenanfang. +In der ersten Messung wurden dabei alle Fahrzeuge gezählt, außer Fahrräder. + +Im anschließenden Vergleich von Sensorwerten mit den gezählten Sensorwerten wurde ein deutlicher unterschied sichtbar. +[statistik hier] 1. Zählen der Ausgänge 2. Zählen einzelner Sensoren