-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathFinalPaper.aux
382 lines (382 loc) · 31.4 KB
/
FinalPaper.aux
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
\relax
\providecommand\hyper@newdestlabel[2]{}
\providecommand\babel@aux[2]{}
\@nameuse{bbl@beforestart}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand \oddpage@label [2]{}
\babel@aux{english}{}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Project Aim}{1}{subsection.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Data pre-processing}{1}{subsubsection.1.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}Data preparation}{1}{subsubsection.1.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}MLP design}{2}{subsubsection.1.1.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.4}Mathematical models}{2}{subsubsection.1.1.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.5}Simulation models}{2}{subsubsection.1.1.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.6}Simulation results}{2}{subsubsection.1.1.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.7}Evaluation}{2}{subsubsection.1.1.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Background}{2}{subsection.1.2}\protected@file@percent }
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\@writefile{toc}{\contentsline {section}{\numberline {2}Theory and Methodology}{3}{section.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}System}{3}{subsection.2.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces System representation \cite {kaestner:basics}\relax }}{3}{figure.caption.1}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:SystemParts}{{1}{3}{System representation \cite {kaestner:basics}\relax }{figure.caption.1}{}}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Model}{4}{subsection.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.1}Linear or non-linear:}{4}{subsubsection.2.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.2}Static or dynamic:}{4}{subsubsection.2.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.3}Externally influenced or autonomous:}{4}{subsubsection.2.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.4}Location dependent or independent:}{4}{subsubsection.2.2.4}\protected@file@percent }
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.5}Deterministic or stochastic:}{5}{subsubsection.2.2.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.6}Time-invariant or time-variant:}{5}{subsubsection.2.2.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.7}Time continuous or discrete:}{5}{subsubsection.2.2.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.8}Model of behavior}{5}{subsubsection.2.2.8}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Real system vs. Model of behavior \cite {kaestner:basics}\relax }}{5}{figure.caption.2}\protected@file@percent }
\newlabel{fig:ModelOfBehavior}{{2}{5}{Real system vs. Model of behavior \cite {kaestner:basics}\relax }{figure.caption.2}{}}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:basics}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.9}System model}{6}{subsubsection.2.2.9}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Real system vs. System model \cite {kaestner:basics}\relax }}{6}{figure.caption.3}\protected@file@percent }
\newlabel{fig:SystemModel}{{3}{6}{Real system vs. System model \cite {kaestner:basics}\relax }{figure.caption.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Simulation}{6}{subsection.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Soft Computing}{6}{subsection.2.4}\protected@file@percent }
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Artificial Neural Network (ANN)}{7}{subsubsection.2.4.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Multi-Layer Perceptron (MLP)}{7}{subsubsection.2.4.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Multilayer perceptron \cite {kaestner:SCANN}\relax }}{7}{figure.caption.4}\protected@file@percent }
\newlabel{fig:ArtificialNeuron}{{4}{7}{Multilayer perceptron \cite {kaestner:SCANN}\relax }{figure.caption.4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Artificial neuron \cite {kaestner:SCANN}\relax }}{7}{figure.caption.5}\protected@file@percent }
\newlabel{fig:ArtificialNeuronProcess}{{5}{7}{Artificial neuron \cite {kaestner:SCANN}\relax }{figure.caption.5}{}}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\citation{kaestner:SCANN}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Artificial neural networks in a feed forward configuration \cite {kaestner:SCANN}\relax }}{8}{figure.caption.6}\protected@file@percent }
\newlabel{fig:FeedForward}{{6}{8}{Artificial neural networks in a feed forward configuration \cite {kaestner:SCANN}\relax }{figure.caption.6}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Artificial neural networks in a lateral configuration \cite {kaestner:SCANN}\relax }}{8}{figure.caption.7}\protected@file@percent }
\newlabel{fig:Lateral}{{7}{8}{Artificial neural networks in a lateral configuration \cite {kaestner:SCANN}\relax }{figure.caption.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Artificial neural networks in a recurrent configuration \cite {kaestner:SCANN}\relax }}{8}{figure.caption.8}\protected@file@percent }
\newlabel{fig:Recurrent}{{8}{8}{Artificial neural networks in a recurrent configuration \cite {kaestner:SCANN}\relax }{figure.caption.8}{}}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.3}Multi-Layer Perceptron (MLP) Design}{9}{subsubsection.2.4.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Markov Model}{9}{subsection.2.5}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Binary model system state \cite {kaestner:Mark}\relax }}{9}{figure.caption.9}\protected@file@percent }
\newlabel{fig:BinaryModel}{{9}{9}{Binary model system state \cite {kaestner:Mark}\relax }{figure.caption.9}{}}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Failure rate}{10}{subsubsection.2.5.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Failure rate curve \cite {kaestner:Mark}\relax }}{10}{figure.caption.10}\protected@file@percent }
\newlabel{fig:BathCurve}{{10}{10}{Failure rate curve \cite {kaestner:Mark}\relax }{figure.caption.10}{}}
\newlabel{eq:Rt1}{{1}{10}{Failure rate}{equation.2.1}{}}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\newlabel{eq:Ft1}{{2}{11}{Failure rate}{equation.2.2}{}}
\newlabel{eq:T1}{{3}{11}{Failure rate}{equation.2.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Failure vs survival rate on a single component w/without repair \cite {kaestner:Mark}\relax }}{11}{figure.caption.11}\protected@file@percent }
\newlabel{fig:FailurevSurvival}{{11}{11}{Failure vs survival rate on a single component w/without repair \cite {kaestner:Mark}\relax }{figure.caption.11}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.2}Redundancy}{11}{subsubsection.2.5.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Single component \cite {kaestner:Mark}\relax }}{11}{figure.caption.12}\protected@file@percent }
\newlabel{fig:SingleComponent}{{12}{11}{Single component \cite {kaestner:Mark}\relax }{figure.caption.12}{}}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Two components in parallel \cite {kaestner:Mark}\relax }}{12}{figure.caption.13}\protected@file@percent }
\newlabel{fig:TwoComponents}{{13}{12}{Two components in parallel \cite {kaestner:Mark}\relax }{figure.caption.13}{}}
\newlabel{eq:Rt2}{{5}{12}{Redundancy}{equation.2.5}{}}
\newlabel{eq:Ft2}{{6}{12}{Redundancy}{equation.2.6}{}}
\newlabel{eq:T2}{{7}{12}{Redundancy}{equation.2.7}{}}
\citation{kaestner:Mark}
\citation{kaestner:Mark}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Markov model: Evaluation of reliability}{13}{subsubsection.2.5.3}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Markov model \cite {kaestner:Mark}\relax }}{13}{figure.caption.14}\protected@file@percent }
\newlabel{fig:Markov}{{14}{13}{Markov model \cite {kaestner:Mark}\relax }{figure.caption.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Methodology}{13}{subsection.2.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {3}Data pre-processing}{14}{section.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Atypical values}{14}{subsection.3.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Raw data visualization\relax }}{14}{figure.caption.15}\protected@file@percent }
\newlabel{fig:RawData2}{{15}{14}{Raw data visualization\relax }{figure.caption.15}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Raw data on a mesh-grid\relax }}{15}{figure.caption.16}\protected@file@percent }
\newlabel{fig:RawData1}{{16}{15}{Raw data on a mesh-grid\relax }{figure.caption.16}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Sensor defect}{15}{subsubsection.3.1.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Data after first filter\relax }}{15}{figure.caption.17}\protected@file@percent }
\newlabel{fig:FirstFilter1}{{17}{15}{Data after first filter\relax }{figure.caption.17}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Redundant data}{16}{subsubsection.3.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}Measuring errors}{16}{subsubsection.3.1.3}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Final processed data graph\relax }}{16}{figure.caption.18}\protected@file@percent }
\newlabel{fig:Processed2}{{18}{16}{Final processed data graph\relax }{figure.caption.18}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Final processed data mesh-grid\relax }}{17}{figure.caption.19}\protected@file@percent }
\newlabel{fig:Processed1}{{19}{17}{Final processed data mesh-grid\relax }{figure.caption.19}{}}
\gdef \LT@i {\LT@entry
{3}{30.57782pt}\LT@entry
{3}{30.17783pt}\LT@entry
{2}{141.27945pt}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Data preparation}{18}{section.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Considerations}{18}{subsection.4.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Data}{18}{subsection.4.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.1}Training data}{18}{subsubsection.4.2.1}\protected@file@percent }
\gdef \LT@ii {\LT@entry
{3}{30.57782pt}\LT@entry
{3}{30.17783pt}\LT@entry
{2}{141.27945pt}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Training data set\relax }}{20}{table.1}\protected@file@percent }
\newlabel{table:TrainingData}{{1}{20}{Training data set\relax }{table.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.2.2}Test data}{20}{subsubsection.4.2.2}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Test data set\relax }}{21}{table.2}\protected@file@percent }
\newlabel{table:TestData}{{2}{21}{Test data set\relax }{table.2}{}}
\gdef \LT@iii {\LT@entry
{3}{80.5913pt}\LT@entry
{1}{102.48424pt}\LT@entry
{1}{113.6078pt}\LT@entry
{1}{77.2052pt}}
\gdef \LT@iv {\LT@entry
{3}{76.09822pt}\LT@entry
{2}{125.93687pt}}
\@writefile{toc}{\contentsline {section}{\numberline {5}MLP design}{22}{section.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Parameters}{22}{subsection.5.1}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Learning parameters\relax }}{22}{table.3}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Weights initialization\relax }}{22}{table.4}\protected@file@percent }
\gdef \LT@v {\LT@entry
{3}{188.73376pt}\LT@entry
{3}{152.7058pt}}
\gdef \LT@vi {\LT@entry
{3}{117.20222pt}\LT@entry
{1}{110.15784pt}\LT@entry
{1}{99.25508pt}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Stop conditions\relax }}{23}{table.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.1.1}Before pruning}{23}{subsubsection.5.1.1}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Architecture with pruning\relax }}{23}{table.6}\protected@file@percent }
\gdef \LT@vii {\LT@entry
{3}{124.55217pt}\LT@entry
{3}{92.4557pt}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces Graph of artificial neural network \relax }}{24}{figure.caption.20}\protected@file@percent }
\newlabel{fig:GraphWP}{{20}{24}{Graph of artificial neural network \relax }{figure.caption.20}{}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Learning process with pruning\relax }}{24}{table.7}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces Error development for network with pruning\relax }}{25}{figure.caption.21}\protected@file@percent }
\newlabel{fig:ErrorWP}{{21}{25}{Error development for network with pruning\relax }{figure.caption.21}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces Results before optimization\relax }}{25}{figure.caption.22}\protected@file@percent }
\newlabel{fig:BeforePruning1}{{22}{25}{Results before optimization\relax }{figure.caption.22}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Error scope before optimization\relax }}{26}{figure.caption.23}\protected@file@percent }
\newlabel{fig:BeforePruning2}{{23}{26}{Error scope before optimization\relax }{figure.caption.23}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces Weights values with pruning\relax }}{26}{figure.caption.24}\protected@file@percent }
\newlabel{fig:WVWP}{{24}{26}{Weights values with pruning\relax }{figure.caption.24}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.1.2}After pruning}{26}{subsubsection.5.1.2}\protected@file@percent }
\gdef \LT@viii {\LT@entry
{3}{117.20222pt}\LT@entry
{1}{110.15784pt}\LT@entry
{1}{99.25508pt}}
\gdef \LT@ix {\LT@entry
{3}{124.55217pt}\LT@entry
{3}{92.4557pt}}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Architecture after pruning\relax }}{27}{table.8}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces Graph of artificial neural network without pruning\relax }}{27}{figure.caption.25}\protected@file@percent }
\newlabel{fig:GraphOP}{{25}{27}{Graph of artificial neural network without pruning\relax }{figure.caption.25}{}}
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Learning process without pruning\relax }}{27}{table.9}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces Error progression without pruning\relax }}{28}{figure.caption.26}\protected@file@percent }
\newlabel{fig:ErrorOP}{{26}{28}{Error progression without pruning\relax }{figure.caption.26}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {27}{\ignorespaces Results after optimization\relax }}{28}{figure.caption.27}\protected@file@percent }
\newlabel{fig:AfterPruning1}{{27}{28}{Results after optimization\relax }{figure.caption.27}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {28}{\ignorespaces Error scope after optimization\relax }}{29}{figure.caption.28}\protected@file@percent }
\newlabel{fig:AfterPruning2}{{28}{29}{Error scope after optimization\relax }{figure.caption.28}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {29}{\ignorespaces Error progression without pruning for test\relax }}{29}{figure.caption.29}\protected@file@percent }
\newlabel{fig:ErrorOP2}{{29}{29}{Error progression without pruning for test\relax }{figure.caption.29}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {30}{\ignorespaces Results test\relax }}{30}{figure.caption.30}\protected@file@percent }
\newlabel{fig:ResultsTest}{{30}{30}{Results test\relax }{figure.caption.30}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Mathematical models}{31}{section.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Calculations}{31}{subsection.6.1}\protected@file@percent }
\newlabel{eq:Lambda}{{11}{31}{Calculations}{equation.6.11}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {31}{\ignorespaces Model diagram\relax }}{32}{figure.caption.31}\protected@file@percent }
\newlabel{fig:ModelDiagram}{{31}{32}{Model diagram\relax }{figure.caption.31}{}}
\newlabel{eq: StateProbability}{{15}{34}{Calculations}{equation.6.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Expected results}{34}{subsection.6.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {32}{\ignorespaces Ideal model diagram\relax }}{34}{figure.caption.32}\protected@file@percent }
\newlabel{fig:IdealDiagram}{{32}{34}{Ideal model diagram\relax }{figure.caption.32}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {33}{\ignorespaces Ideal time life\relax }}{35}{figure.caption.33}\protected@file@percent }
\newlabel{fig:IdealT}{{33}{35}{Ideal time life\relax }{figure.caption.33}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {34}{\ignorespaces Ideal rates\relax }}{35}{figure.caption.34}\protected@file@percent }
\newlabel{fig:IdealRates}{{34}{35}{Ideal rates\relax }{figure.caption.34}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {35}{\ignorespaces Intersection between failure and survival rates \relax }}{36}{figure.caption.35}\protected@file@percent }
\newlabel{fig:IDIN}{{35}{36}{Intersection between failure and survival rates \relax }{figure.caption.35}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {36}{\ignorespaces Failure probability at the obtained lifetime\relax }}{36}{figure.caption.36}\protected@file@percent }
\newlabel{fig:IDTL}{{36}{36}{Failure probability at the obtained lifetime\relax }{figure.caption.36}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Simulation models}{38}{section.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Simulation parameters}{38}{subsection.7.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {37}{\ignorespaces Input graph\relax }}{38}{figure.caption.37}\protected@file@percent }
\newlabel{fig:InputGraph}{{37}{38}{Input graph\relax }{figure.caption.37}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {38}{\ignorespaces Input table\relax }}{39}{figure.caption.38}\protected@file@percent }
\newlabel{fig:InputTable}{{38}{39}{Input table\relax }{figure.caption.38}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Connections}{39}{subsection.7.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {39}{\ignorespaces Simulation of the $\lambda $ equation: scheme\relax }}{39}{figure.caption.39}\protected@file@percent }
\newlabel{fig:SimulationEquation}{{39}{39}{Simulation of the $\lambda $ equation: scheme\relax }{figure.caption.39}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {40}{\ignorespaces Simulation of the state model: scheme\relax }}{40}{figure.caption.40}\protected@file@percent }
\newlabel{fig:SimulationModel}{{40}{40}{Simulation of the state model: scheme\relax }{figure.caption.40}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Comparison}{40}{subsection.7.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.1}Classical Markov model}{40}{subsubsection.7.3.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {41}{\ignorespaces Classical Markov model: scheme\relax }}{40}{figure.caption.41}\protected@file@percent }
\newlabel{fig:ClassicalModel}{{41}{40}{Classical Markov model: scheme\relax }{figure.caption.41}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {7.3.2}Hybrid Markov model}{41}{subsubsection.7.3.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {42}{\ignorespaces Hybrid Markov model: scheme\relax }}{41}{figure.caption.42}\protected@file@percent }
\newlabel{fig:HybridModel}{{42}{41}{Hybrid Markov model: scheme\relax }{figure.caption.42}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Simulation results}{42}{section.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1}Raw results}{42}{subsection.8.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {43}{\ignorespaces Stress conditions and MLP output graph\relax }}{42}{figure.caption.43}\protected@file@percent }
\newlabel{fig:MLPOutput}{{43}{42}{Stress conditions and MLP output graph\relax }{figure.caption.43}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {44}{\ignorespaces $\tilde {\lambda }$ calculation\relax }}{43}{figure.caption.44}\protected@file@percent }
\newlabel{fig:LambdaCalculation}{{44}{43}{$\tilde {\lambda }$ calculation\relax }{figure.caption.44}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2}Comparison}{43}{subsection.8.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {8.2.1}Classical Markov model}{43}{subsubsection.8.2.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {45}{\ignorespaces Classical Markov model: states probabilities\relax }}{43}{figure.caption.45}\protected@file@percent }
\newlabel{fig:HybridStatesC}{{45}{43}{Classical Markov model: states probabilities\relax }{figure.caption.45}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {46}{\ignorespaces Classical Markov model: lifetime \relax }}{44}{figure.caption.46}\protected@file@percent }
\newlabel{fig:HybridTimeLifeC}{{46}{44}{Classical Markov model: lifetime \relax }{figure.caption.46}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {47}{\ignorespaces Classical Markov model: failure and survival rates\relax }}{44}{figure.caption.47}\protected@file@percent }
\newlabel{fig:FSCIn}{{47}{44}{Classical Markov model: failure and survival rates\relax }{figure.caption.47}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {48}{\ignorespaces Classical Markov model:Failure rate at obtained lifetime\relax }}{44}{figure.caption.48}\protected@file@percent }
\newlabel{fig:FSCLT}{{48}{44}{Classical Markov model:Failure rate at obtained lifetime\relax }{figure.caption.48}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {8.2.2}Hybrid Markov model}{45}{subsubsection.8.2.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {49}{\ignorespaces Hybrid Markov model: states probabilities\relax }}{45}{figure.caption.49}\protected@file@percent }
\newlabel{fig:HybridStatesH}{{49}{45}{Hybrid Markov model: states probabilities\relax }{figure.caption.49}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {50}{\ignorespaces Hybrid Markov model: lifetime\relax }}{45}{figure.caption.50}\protected@file@percent }
\newlabel{fig:HybridTimeLifeH}{{50}{45}{Hybrid Markov model: lifetime\relax }{figure.caption.50}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {51}{\ignorespaces Hybrid Markov model: lifetime failure and survival rates\relax }}{46}{figure.caption.51}\protected@file@percent }
\newlabel{fig:FSHIn}{{51}{46}{Hybrid Markov model: lifetime failure and survival rates\relax }{figure.caption.51}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {52}{\ignorespaces Hybrid Markov model: Failure rate at obtained lifetime\relax }}{46}{figure.caption.52}\protected@file@percent }
\newlabel{fig:FSHLT}{{52}{46}{Hybrid Markov model: Failure rate at obtained lifetime\relax }{figure.caption.52}{}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Evaluation}{47}{section.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1}Comparison}{47}{subsection.9.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {53}{\ignorespaces Comparison between the states probabilities\relax }}{47}{figure.caption.53}\protected@file@percent }
\newlabel{fig:CSP}{{53}{47}{Comparison between the states probabilities\relax }{figure.caption.53}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {54}{\ignorespaces Life-time comparison\relax }}{48}{figure.caption.54}\protected@file@percent }
\newlabel{fig:CLT}{{54}{48}{Life-time comparison\relax }{figure.caption.54}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {55}{\ignorespaces Failure and survival rates comparison\relax }}{48}{figure.caption.55}\protected@file@percent }
\newlabel{fig:CFS}{{55}{48}{Failure and survival rates comparison\relax }{figure.caption.55}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {9.1.1}Dynamics: Classical Markov model}{48}{subsubsection.9.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {9.1.2}Dynamics: Hybrid Markov model}{49}{subsubsection.9.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {10}Conclusion}{51}{section.10}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {56}{\ignorespaces Failure rate at suggested maintenance of 27 units of time \relax }}{51}{figure.caption.56}\protected@file@percent }
\newlabel{fig:Main27}{{56}{51}{Failure rate at suggested maintenance of 27 units of time \relax }{figure.caption.56}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {57}{\ignorespaces Failure rate at suggested maintenance of 25 units of time \relax }}{52}{figure.caption.57}\protected@file@percent }
\newlabel{fig:Main25}{{57}{52}{Failure rate at suggested maintenance of 25 units of time \relax }{figure.caption.57}{}}
\@writefile{toc}{\contentsline {section}{Appendices}{53}{section*.58}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {A}Appendix of codes}{53}{appendix.a.A}\protected@file@percent }
\newlabel{appendix:codes}{{A}{53}{Appendix of codes}{appendix.a.A}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Matlab code for data preparation and pre-processing}{53}{subsection.a.A.1}\protected@file@percent }
\@writefile{lol}{\contentsline {lstlisting}{Codes/DataPreparatorA.m}{53}{lstlisting.-1}\protected@file@percent }
\newlabel{code:MatLab}{{A.1}{57}{Matlab code for data preparation and pre-processing}{lstnumber.-1.137}{}}
\@writefile{toc}{\contentsline {section}{\numberline {B}Appendix of MLP design}{58}{appendix.a.B}\protected@file@percent }
\newlabel{appendix:steps}{{B}{58}{Appendix of MLP design}{appendix.a.B}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B.1}Before pruning}{58}{subsection.a.B.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {B.2}After pruning}{61}{subsection.a.B.2}\protected@file@percent }
\gdef \LT@x {\LT@entry
{3}{67.8279pt}\LT@entry
{1}{45.23338pt}\LT@entry
{1}{38.78894pt}\LT@entry
{3}{38.51117pt}\LT@entry
{1}{12.4pt}\LT@entry
{3}{67.4279pt}\LT@entry
{1}{45.23338pt}\LT@entry
{1}{38.78894pt}\LT@entry
{3}{38.51117pt}}
\@writefile{toc}{\contentsline {section}{\numberline {C}Appendix of tables}{64}{appendix.a.C}\protected@file@percent }
\newlabel{appendix:tables}{{C}{64}{Appendix of tables}{appendix.a.C}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C.1}Initial set of data}{64}{subsection.a.C.1}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Initial set of data\relax }}{66}{table.10}\protected@file@percent }
\newlabel{table:InitialData}{{10}{66}{Initial set of data\relax }{table.10}{}}
\bibstyle{IEEEtran}
\bibdata{bibliography.bib}
\bibcite{kaestner:basics}{1}
\bibcite{kaestner:SCANN}{2}
\bibcite{kaestner:Mark}{3}
\@writefile{toc}{\contentsline {section}{References}{67}{table.10}\protected@file@percent }
\global\@namedef{scr@dte@section@lastmaxnumwidth}{16.09984pt}
\gdef \@abspage@last{74}