1
FIG Working Week 2007
Fitness Analysis of Height Variation for GPS Monitoring Site
CC--C Chang*C Chang*, P, P--S Hung** and HS Hung** and H--Z Chen***Z Chen***
* Department of Information Management, Yu* Department of Information Management, Yu--Da University, TaiwanDa University, Taiwan** Department of Land Management, Feng** Department of Land Management, Feng--Chia University, TaiwanChia University, Taiwan***Land Survey Bureau, Taiwan***Land Survey Bureau, Taiwan
Hong Kong 13-17 May 2007
Motivations
Accompanied with heavy withdrawal of under-ground water in the coastal regions
Subsidence area is enlarged towards inland andpotentially damages the engineering structure ofthe Taiwan High Speed Rail (THSR)
A long-term subsidence occurred in the middle-south of Taiwan
Taipei
Taichung
Yunlin
Kaohsiung
Background
Study Area
Track Bridge
Taiwan High Speed Rail (THSR)Significant Subsidence Area
THSR
Yunlin County
Monitoring by Spirit Leveling
Land Subsidence at Yunlin(1994-1995)
WR02WR03
WR04
WR05WR06
WR07
WR08
WR09
WR10
WR01
WR11WR1
2
WR13
WR14
WR15
WR16
WR17
WR18WR19
WR20
WR21
WR22
WR23
WR24
WR25
WR26
WR27
WR28
WR29
WR30WR31
WR32
WR33
WR34
WR35
WR36
WR37WR39
WR38
WR40
WR41
WR42
WR43
WR44
WR45
WR46
WR47
WR48
WR49
WR50
WR51
WR52
N
����������
GPS�������
GPS Set-up for Monitoring
2
Subsidence Rate (1998)
120.00 120.10 120.20 120.30 120.40 120.50 120.60 120.70
23.50
23.60
23.70
23.80
4.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.0020.0021.0022.0023.00
Subsidence (Jan-Nov 2000)
WR02WR03
WR04
WR05WR06
WR07
WR08
WR09
WR10
WR01
WR11WR1
2
WR13
WR14
WR15
WR16
WR17
WR18WR19
WR20
WR21
WR22
WR23
WR24
WR25
WR26
WR27
WR28
WR29
WR30WR31
WR32
WR33
WR34
WR35
WR36
WR37WR39
WR38
WR40
WR41
WR42
WR43
WR44
WR45
WR46
WR47
WR48
WR49
WR50
WR51
WR52
N
����������
GPS�������
Control Stations of TWD97
M002
Height Variations at M002
1997 2000 2002
WR02WR03
WR04
WR05WR06
WR07
WR08
WR09
WR10
WR01
WR11WR1
2
WR13
WR14
WR15
WR16
WR17
WR18WR19
WR20
WR21
WR22
WR23
WR24
WR25
WR26
WR27
WR28
WR29
WR30WR31
WR32
WR33
WR34
WR35
WR36
WR37WR39
WR38
WR40
WR41
WR42
WR43
WR44
WR45
WR46
WR47
WR48
WR49
WR50
WR51
WR52
N
����������
GPS�������
GPS Tracking Station
PKGM
THSRHeight (m)
42.400
42.500
42.600
42.700
42.800
42.900
43.000
43.100
43.200
43.300
1 33 65 97 129
161
193
225
257
289
321
353
385
417
449
481
hei ght
week
Weekly GPS Solutions at PKGM(1995-2004)
Vh= -3 cm/year
1999 Mw=7.6 Earthquake
3
Correlated to Seasonal Descending ?
Weekly GPS Heighting in 1997 Seasonal Subsidence Rates
- 3.1All-Span
(1995-2001)
- 9.0- 1.5Average- 9.8- 4.12001- 4.42.42000-12.2- 3.61999- 9.51.41998- 4.41.31997- 8.8- 1.41996-13.8- 6.61995
WinterSummerAnnual Rate (cm/year)Year
Objectives of this Study
Estimating the up-coming level of subsidence to further prevent any possible damage
Testing the fitness of the estimation modelswith a continuous GPS data set
Establishing a forecast technique by using a relatively short term of GPS monitoring data
Artificial Neural Network
Imitating the pattern of human thought and inducing an operation rule through learning process to build up its recognition and fore-cast capability
input layer hidden layer output layer
X1 (t) ��� Y1
X�(t) ��� Y2
Xn(t) ��� Yn
ANN Transfer Function
It transfers a set of input/output samples into a non-linear optimisation process by finding rules from massive data
1
( )n
j ij i ji
Y f W X θ=
= −∑
Wij is the weight connecting layer node i and jθj is the threshold of node j
Three-layer BP network’s training process is composed of a forward and back propagation
Grey Forecast Theory A common GM(1,1) model is approximate to a differential model
Modelling with very less data to estimate the variables for system’s future behavior
(1) (0)
(0) (1) (1)
,
ˆ ( 1) (1)
ˆ ˆ( ) ( 1) ( )
ak
dx ax bdt
b bx k x ea a
x k x k x k
−
+ =
+ = − + = + −%
(1) (0)
1
(1) (1) (1)
(1) (0) (0) (1) (1) 2
1 1 1 1
2 2
( ) ( )
( ) 0.5 ( ) 0.5 ( 1)
( ), ( ), ( )* ( ), [ ( )]
* 4* * *,
4* 4*
k
m
k k k k
m m m m
x k x m
z k x k x k
C z m D x m E x m x m F z m
C D E D F C Ea b
F C F C
=
= = = =
=
= + −
= = = =
− −= =
− −
∑
∑ ∑ ∑ ∑
4
Regression Analysis
Variable hi can be predicted using independentvariables of ti
hi=ati+b
a, b coefficients represent the slope and interceptti is defined as time variable hi is the height measurement
Data Sets & Test Models
Long Term DataNeural Network
Short Term DataRegression Analysis
Grey Theory
Regression Analysis(Pre 50-52 weekly solutions)
(Pre 5 weekly solutions)
ANN Sample Data
ANN Samples & Hidden Layers
ANN Hidden Layers
• Using Alyuda Neuro Intelligence Version 2.1 software• Training, testing and verifying samples are randomly made• Optimum hidden layers are automatically determined
ANN Training Algorithm & Testing Network
Default option of quick propagation algorithm is appliedwith the coefficient of 1.75 and learning rate of 0.1
Height Estimations & Errors
Estimation Models
Short Term DataLong Term Data(Pre 52 weekly solutions)
(ANN / RA)
Estimation Models(RA / GFT)
Height Estimates(for next epoch)
Height Estimates(for next epoch)
Average RMS Errors(check with measured heights
for one year)
(Pre 5 weekly solutions)
….….
…. 0.90.5Standard Deviation
1.41.1Average
1.81.32004
1.70.82003
3.72.22002
0.80.72001
1.21.12000
0.80.71999
1.01.21998
0.81.51997
1.00.81996
RA model (cm)ANN model (cm)Year of Data
Height estimation error based on long-term data
Fitness Analysis
5
0
0.5
1
1.5
2
2.5
3
3.5
4
1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
RMS(cm)
ANN
RA
ANN model provided a better performance of 27% than that of using RA model
Fitness Errors based on Long Term Data
0.40.5Standard Deviation
1.11.2Average
1.11.12004
1.61.82003
1.62.02002
0.60.62001
1.00.92000
0.90.91999
1.51.71998
0.80.91997
0.71.01996
RA model (cm)GFT model (cm)Year of Data
Height estimation error based on short-term data
Fitness Analysis
0
0.5
1
1.5
2
2.5
1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
RMS(cm) GFT
RA
Fitness Errors based on Short Term Data
Fitness based on RA or GFT model with short-term data is equivalent to the ANN model using long-term data measured at the significant land subsidence area
Future Study
Artificial IntelligenceAnalysis Models
GPS-based 3D Terrestrial & other Auxiliary Data
Determination & Predictionfor Land Movement
Information System
Visualised Land Movement Analysis Tool
Thanks for your attentionThanks for your attention
[email protected]@ydu.edu.tw