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

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WR01

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2

WR13

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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)

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2

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N

����������

GPS�������

Control Stations of TWD97

M002

Height Variations at M002

1997 2000 2002

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2

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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

ccchang@ydu.edu.twccchang@ydu.edu.tw