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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.
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
2
. 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.
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
3
Dam location and
Reference control net
work
• Location & Controls
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
4
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:
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
5
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).
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
6
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:
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
7
Velocity and Acceleration
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
8
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.
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
9
RESULTS
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
10
• 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
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
11
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
12
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
13
Prediction
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
14
Prediction and Correlation
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
15
Graph of correlation for year 2008
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
16
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.
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
17
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
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
18
XXV International Federation of Surveyors
Congress, Kuala Lumpur, Malaysia, 16 – 21
June 2014
19
THANKS FOR YOUR
ATTENTION