TS09E ehigiator - irughe ehiorobo et al 6848 ppt · DESCRIPTION OF STUDY AREA • The Ikpoba River Dam is located in Benin City, the capital of Edo State of Nigeria. The Dam together

PREDICTION OF DAM DEFORMATION

USING KALMAN FILTER TECHNIQUE

By

DR. R. EHIGIATOR IRUGHE,

DR. Jacob Odeh EHIOROBO

AND

DR. (MRS) M.O. EHIGIATOR

XXV International Federation of Surveyors

Congress, Kuala Lumpur, Malaysia, 16 – 21

June 2014

1

INTRODUCTION

• In this study Kalman filtering technique wasused in predicting current estimates of Damdeformation using two previous GPSmeasurements carried out in 2007 and 2008respectively. The Kalman filter equation wasthen used to compute the velocity andacceleration of the Damobject.



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. DESCRIPTION OF STUDY AREA• The Ikpoba River Damis located in Benin

City, the capital of Edo State of Nigeria. TheDam together with its head works is locatedabout 6kmfrom the city centre (see fig 1)

• The Ikpoba Dam water supply scheme wasdesigned to supply 160,000,000 litres of water perday at ultimate capacity. This account for about60% of the water supply requirement for BeninCity with a population of about 1.5 million.



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Dam location and

Reference control net

work

• Location & Controls



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The network for

Deformation

monitoring consist

of eleven control

points located at the

upstream and

downstream. Nine

monitoring points

was also established

on the Dam

KINEMATIC DEFORMATION MODEL:

THE KALMAN FILTER

�Kinematic deformation model determines

displacements, velocity and acceleration and

is time dependent. A time dependent 3-D

Kinematic model that contain position,

velocity and acceleration can be expressed

using the following equations:



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KINEMATIC DEFORMATION MODEL:

THE KALMAN FILTER

(1.0)

Where 111 ,, +++ KJ

KJ

KJ ZYX - Coordinates of point J at time tk+1 (predicted values),

KZ

KY

KX JJJ

vvv ,, – velocities of X, Y,Z coordinates of point J at time tk; KZ

KY

KX JJJ

aaa ,, –

accelerations of X, Y,Z coordinates of point J at time tk. k=1, 2, . . . , m (m: measurement period number( number of epochs)). j =1, 2, n (n: number of points).



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Kalman Filter

�In the dynamic model of the filtering, three

states with nine variables and three linear

degrees of freedom (position vector), the

corresponding velocity variables (velocity

Vector) and the acceleration variables

(acceleration vector) are considered. The state

velocity and acceleration models can be

written as:



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Velocity and Acceleration



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11

1

11

1

11

1

J

J

J

K KK J JX

k , k

K KK J J

Yk , k

K KK J JZ

k , k

X Xv ;

t

Y Yv ;

t

Z Zv .

t

∆

∆

∆

++

++

+

++

+

+

−= − = − =

11

21

11

21

11

21

J

J

J

K KK J JX

k ,k

K KK J JY

k ,k

K KK J JZ

k ,k

X Xa ;

t

Y Ya ;

t

Z Za .

t

∆

∆

∆

++

++

+

++

+

+

−=

− = − =

2 1 21

1

21

1

J

J

K ! K K Kk J J J Jxyz

(K ),K

K ! Kk J Jxyz

(K ),K

(X X ) (Y Y )v

t

(Z Z )a

t

∆

∆

+ ++

+

++

+

− + −=−

=

2 1 21

21

21

21

J

J

K ! K K Kk J J J Jxyz

(K ),K

K ! Kk J Jxyz

(K ),K

(X X ) (Y Y )a

t

(Z Z )a

t

∆

∆

+ ++

+

++

+

− + −=−

=

NUMERICAL APPLICATION OF THE

KALMAN FILTER

� In the first instance, static deformation analysis was carried out by evaluating the post adjustment coordinates together with the variance – covariance matrix. Next Kinematic deformation analysis based on Kalman filter technique was implemented on a MATALB software.

� The solution obtained from the Kinematic model using Kalman filter were compared with those obtained from the initial static deformation measurement results. Finally, the velocity and acceleration of the movement for each point in the network was plotted.



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RESULTS



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• The computed coordinates from the static GPS

measurement results along with the velocity and

acceleration of motion for each of the points is

shown below.

• The velocity and acceleration of motion for each

points in the network in X, Y, Z directions, the

predicted coordinates using the Kinematic model for

each of the points for are presented. A comparison

of the measured and predicted coordinates for 2008

are also presented.

GPS measurement Results for 2007 and 2008 measurement

period with velocity and acceleration.XXV International Federation of Surveyors


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Prediction



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Prediction and Correlation



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Graph of correlation for year 2008



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DISCUSSIONS

• Analysis of the results between the

measurement update and predicted

deformation results for 2008 indicate

a correlation between the two,

except in the case of 6SI and RF 7

where the correlation was weak.



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CONCLUSION� In this study, the Kalman filter technique based on Kinematic

Deformation analysis was applied to measurement data

collection by static GNSS at the Ikpoba River Dam in Benin City,

Nigeria.

� By comparing the predicted and measured displacements, the

efficiency of the Kinematic deformation model using Kalman

filter was demonstrated. A major advantage in the method is the

ability to carry out step wise computation of structural

movement parameters which projects forward the expected

deformation at any later time.

� The graph of correlation reveals the accuracy of the predicted

deformation values which compared quite well with the

measured deformation for 2008. Further research is on going in

order to determine the behavior for longer prediction period

based on measured displacement. XXV International Federation of Surveyors


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THANKS FOR YOUR

ATTENTION

Documents

TS09E ehigiator - irughe ehiorobo et al 6848 ppt · DESCRIPTION OF STUDY AREA • The Ikpoba River Dam is located in Benin City, the capital of Edo State of Nigeria. The Dam together