* dong-hyawn kim: graduate student, kaist ju-won oh: professor, hannam university ju-won oh:...
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** Dong-Hyawn Kim: Graduate Student, KAIST Dong-Hyawn Kim: Graduate Student, KAIST Ju-Won Oh: Professor, Hannam UniversityJu-Won Oh: Professor, Hannam University In-Won Lee: Professor, KAISTIn-Won Lee: Professor, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST
STRUCTURAL CONTROL USING CMAC NEURAL NETWORK
Nha Trang 2000Nha Trang 2000Nha Trang, Vietnam, Aug. 14-18, 2000Nha Trang, Vietnam, Aug. 14-18, 2000
2 2Structural Dynamics & Vibration Control Lab., KAIST, Korea
1 INTRODUCTION
2 CMAC FOR VIBRATION CONTROL
3 NUMERICAL EXAMPLES
4 CONCLUSIONS
CONTENTS
3 3Structural Dynamics & Vibration Control Lab., KAIST, Korea
1 INTRODUCTION1 INTRODUCTION
- mathematical model is not required in
designing controller
• Features of neural network control• Features of neural network control Background
• Application areas• Application areas
- control of structures with uncertainty or nonlinearity
4 4Structural Dynamics & Vibration Control Lab., KAIST, Korea
structure
external load
neural networkneural
network
sensor
• Structural control using neural network• Structural control using neural network
5 5Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Multilayer neural network (MLNN)• Multilayer neural network (MLNN)
training is too slowtraining is too slow
control forcecontrol force
state ofstructurestate of
structure
weights to be adjustedweights to be adjusted
6 6Structural Dynamics & Vibration Control Lab., KAIST, Korea
1) H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng.
2) J. Ghaboussi et al. (1995). ASCE J. Eng. Mech.
3) K. Nikzad et al. (1996). ASCE J. Eng. Mech.
4) K. Bani-Hani et al. (1998). ASCE J. Eng. Mech.
5) J. T. Kim et al. (2000). ASCE J. Eng. Mech.
Previous studies
- All methods are based on multilayer neural network whose learning speed is too slow- A new neural network with fast learning speed is required
7 7Structural Dynamics & Vibration Control Lab., KAIST, Korea
Objective and Scope- apply CMAC* neural network to structural con
trol to reduce learning time.
- compare performance of CMAC with multilayer neural network.
*Cerebellar Model Articulation Controller
8 8Structural Dynamics & Vibration Control Lab., KAIST, Korea
Introduction
2 CMAC FOR VIBRATION CONTROL2 CMAC FOR VIBRATION CONTROL
- proposed by J. S. Albus(1975)- a neural network with fast learning speed- mainly used for manipulator control
• CMAC• CMAC
9 9Structural Dynamics & Vibration Control Lab., KAIST, Korea
input space output
space
x
memory space
W1
W2
W3
Wn-1
Wn
u
Procedure of CMAC
weight
displacementvelocity
control signal
10 10Structural Dynamics & Vibration Control Lab., KAIST, Korea
x2
x1
W13 W14 W15 W16
W9 W10 W11 W12
W5 W6 W7 W8
W1 W2 W3 W4
x1
x2
(quantization mesh)
• Block quantization of input space• Block quantization of input space
W37 W38 W39 W40 W41
W32 W33 W34 W35 W36
W27 W28 W29 W30 W31
W22 W23 W24 W25 W26
W17 W18 W19 W20 W21
(made by shifting left mesh)
block sizeblock size shiftingshifting
11 11Structural Dynamics & Vibration Control Lab., KAIST, Korea
x2
x1
W13 W14 W15 W16
W9 W10 W11 W12
W5 W6 W7 W8
W1 W2 W3 W4
x1
x2
1st mesh
• Activation of weights-(1)• Activation of weights-(1)
W37 W38 W39 W40 W41
W32 W33 W34 W35 W36
W27 W28 W29 W30 W31
W22 W23 W24 W25 W26
W17 W18 W19 W20 W21x1*
x2*
x1*
x2*
2nd mesh
input: [x1*, x2
*]T output:[W11 + W34]
12 12Structural Dynamics & Vibration Control Lab., KAIST, Korea
x2
x1
W13 W14 W15 W16
W9 W10 W11 W12
W5 W6 W7 W8
W1 W2 W3 W4
x1
x2
• Activation of weights-(2)• Activation of weights-(2)
W37 W38 W39 W40 W41
W32 W33 W34 W35 W36
W27 W28 W29 W30 W31
W22 W23 W24 W25 W26
W17 W18 W19 W20 W21x1^
x2^
x1^
x2^
input: [ , ]Tx1^ x2
^ output:[W11 + W30]
x2*
x1*x1
*
x2*
1st mesh 2nd mesh
13 13Structural Dynamics & Vibration Control Lab., KAIST, Korea
Weights [W11, W34] [W11, W30] Weights [W11, W34] [W11, W30]
no. of meshes: 2 no. of meshes: 2
3411 WW Output Output
• Summary• Summary
no. of weights: 41 no. of weights: 41
no. of division: 4, 5/variable no. of division: 4, 5/variable
Input [x1*, x2
*]T Input [x1*, x2
*]T x1^ x2
^[ , ]T[ , ]T
3011 WW
14 14Structural Dynamics & Vibration Control Lab., KAIST, Korea
CMAC MLNN
memory size Large Small
learning speed Fast Slow
computing mode Local Global
• CMAC vs. MLNN• CMAC vs. MLNN
items
real-time application Feasible Impossible
15 15Structural Dynamics & Vibration Control Lab., KAIST, Korea
Vibration Control using CMAC
structure
external load
CMACCMAC
learning rule
sensor
16 16Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Control criterion: cost function• Control criterion: cost function
1
0112
1 fN
kk
Tkk
TkJ RuuQzz (1)
fNk
RQuz,, : state, control vector
: relative weighting matrix: time step: final time step
: state, control vector: relative weighting matrix: time step: final time step
17 17Structural Dynamics & Vibration Control Lab., KAIST, Korea
kTkk
TkkJ RuuQzz 112
1
: learning rate: learning rate
kikiki WWW ,,1,
(2)
(3)
(5)
Ru
u
zQz T
kk
kTkkiW
11,
• Learning rule• Learning rule
i
kki W
JW
, (4)
18 18Structural Dynamics & Vibration Control Lab., KAIST, Korea
3. NUMERICAL EXAMPLES3. NUMERICAL EXAMPLES
Model structure
Three-story building with Active Mass DriverThree-story building with Active Mass Driver
19 19Structural Dynamics & Vibration Control Lab., KAIST, Korea
: Mass matrix: Damping matrix: Restoring force : Location vector
: displacement vector: ground acceleration: control force
(6) gxLf 1M)xK(x,xCxM
L
K
C
M
f
xgx
• Equation of motion• Equation of motion
20 20Structural Dynamics & Vibration Control Lab., KAIST, Korea
dykxkxk 00 )1()(
)(1 1 pp
yxyyxxd
y
0k : linear stiffness
: contribution of k0
• Nonlinear restoring force (Bouc-Wen, 1981)• Nonlinear restoring force (Bouc-Wen, 1981)
(7)
(8)
21 21Structural Dynamics & Vibration Control Lab., KAIST, Korea
mass
pump
• Active Mass Driver (AMD)• Active Mass Driver (AMD)
piston
22 22Structural Dynamics & Vibration Control Lab., KAIST, Korea
mass : 200kg (story)stiffness : 2.25105 N/m(inter-story)damping : 0.6, 0.7, 0.3% (modal)
mass : 18kg (3% of building mass)stiffness : 3.71103 N/mdamper : 8.65%
Structure
AMD
• Parameters• Parameters
23 23Structural Dynamics & Vibration Control Lab., KAIST, Korea
CMAC structure
input: 2 (disp., vel. of 3rd floor)
output: 1 (control signal)
no. of division: 3/variable
no. of meshes: 200
no. of weights: 1800
input: 2 (disp., vel. of 3rd floor)
output: 1 (control signal)
no. of division: 3/variable
no. of meshes: 200
no. of weights: 1800
24 24Structural Dynamics & Vibration Control Lab., KAIST, Korea
integration time: 0.25msec
sampling time: 5.0msec
delay time: 0.5msec
Simulation
25 25Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Learning during El Centro earthquake (linear case)• Learning during El Centro earthquake (linear case)
※1 Epoch = 0.005sec × 2000 steps ※1 Epoch = 0.005sec × 2000 steps
CMAC
MLNN
0 100 200 300 400 500Epoch
0.0
0.1
0.2
0.3
Cos
t fun
ctio
n
26 26Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Minimum costs • Minimum costs
neural network Jmin (ratio) neural network Jmin (ratio)
MLNN 1.77 10-2 (1.00) MLNN 1.77 10-2 (1.00)
CMAC 1.94 10-2 (1.09) CMAC 1.94 10-2 (1.09)
• Epochs• Epochs
neural network epoch (ratio)neural network epoch (ratio)
MLNN 478 (1.00) MLNN 478 (1.00)
CMAC 65 (0.14) CMAC 65 (0.14)
27 27Structural Dynamics & Vibration Control Lab., KAIST, Korea
Dis
plac
emen
t (m
)
w/o controlw/ control
0 5 10 15 20-0.10-0.050.000.050.10
Time (sec)
• Northridge earthquake (3rd floor)• Northridge earthquake (3rd floor)
0 5 10 15 20-1.00-0.500.000.501.00
Vel
ocity
(m/s
ec)
28 28Structural Dynamics & Vibration Control Lab., KAIST, Korea
0 5 10 15 20-20.0-10.0
0.010.020.0
Acc
eler
atio
n (
m/s
ec2 )
w/o controlw/ control
Time (sec)
• Northridge earthquake (3rd floor) - continued• Northridge earthquake (3rd floor) - continued
29 29Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Kern County earthquake (3rd floor)• Kern County earthquake (3rd floor)
Time (sec)
0 5 10 15 20-0.10-0.050.000.050.10
Dis
plac
emen
t (m
)
0 5 10 15 20-1.00-0.500.000.501.00
w/o controlw/ control
Vel
ocity
(m/s
ec)
30 30Structural Dynamics & Vibration Control Lab., KAIST, Korea
0 5 10 15 20-20.0-10.0
0.010.020.0
Acc
eler
atio
n (
m/s
ec2 )
w/o controlw/ control
Time (sec)
• Kern County earthquake (3rd floor) - continued• Kern County earthquake (3rd floor) - continued
31 31Structural Dynamics & Vibration Control Lab., KAIST, Korea
5.0
0 100 200 300 400 500Epoch
0.0
0.1
0.2
0.3
Cos
t fun
ctio
n
• Learning during El Centro earthquake (nonlinear case, )• Learning during El Centro earthquake (nonlinear case, )
CMAC
MLNN
32 32Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Minimum costs• Minimum costs
neural network Jmin (ratio) neural network Jmin (ratio)
MLNN 1.91 10-2 (1.00) MLNN 1.91 10-2 (1.00)
CMAC 2.02 10-2 (1.06) CMAC 2.02 10-2 (1.06)
• Epochs• Epochs
neural network epoch (ratio)neural network epoch (ratio)
MLNN 484 (1.00) MLNN 484 (1.00)
CMAC 34 (0.07) CMAC 34 (0.07)
33 33Structural Dynamics & Vibration Control Lab., KAIST, Korea
w/o control
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
w/ control
• Northridge earthquake (1st floor)• Northridge earthquake (1st floor)
34 34Structural Dynamics & Vibration Control Lab., KAIST, Korea
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
• Kern County earthquake (1st floor)• Kern County earthquake (1st floor)
w/o control w/ control
35 35Structural Dynamics & Vibration Control Lab., KAIST, Korea
• Performance comparison (El Centro, 3rd floor)• Performance comparison (El Centro, 3rd floor)
0 5 10 15 20-0.04-0.020.000.020.04
CMAC
MLNN
Dis
plac
emen
t (m
)
Time (sec)
36 36Structural Dynamics & Vibration Control Lab., KAIST, Korea
4. CONCLUSIONS4. CONCLUSIONS
• Response controlled by CMAC is almost
same as that by MLNN.
• Learning speed of CMAC is much faster
than that of MLNN.
• Response controlled by CMAC is almost
same as that by MLNN.
• Learning speed of CMAC is much faster
than that of MLNN.
37 37Structural Dynamics & Vibration Control Lab., KAIST, Korea
Thank you for your attention.Thank you for your attention.
38 38Structural Dynamics & Vibration Control Lab., KAIST, Korea
utqgg
tqgg
)(1
)(2121
21, gg
u
q
: oil flow rate: control signal: time constant: valve gains
• Pump dynamics• Pump dynamics
(9)
39 39Structural Dynamics & Vibration Control Lab., KAIST, Korea
qfa
Vf
a
cxa
rr
lrr
2
: displacement of ram
: area of ram
: compression coefficient
: volume of cylinder
: leakage coefficientl
r
r
c
V
a
x
• Piston dynamics• Piston dynamics
(10)
40 40Structural Dynamics & Vibration Control Lab., KAIST, Korea
BuAzz
B
A
u
z : state vector
: control force vector
: system matrix
: control matrix
: state vector
: control force vector
: system matrix
: control matrix)(
)(
)1(
)1(
mn
nn
m
n
(s-1)
• Sensitivity Evaluation• Sensitivity Evaluation
• State equation• State equation
41 41Structural Dynamics & Vibration Control Lab., KAIST, Korea
kkk HuGzz 1
sTeAG
(s-2)
(s-3)
(s-4)
sT : sampling time: sampling time
BAH A 1 Ie sT
Hu
z
k
k 1 (s-5)
• Discretized equation using ZOH• Discretized equation using ZOH
• Sensitivity matrix• Sensitivity matrix
42 42Structural Dynamics & Vibration Control Lab., KAIST, Korea
kkk HuGzz 1
][0z k
mjijif
ijifkj ~1
)(0
)(1,
u
ik hz 1
initial condition:initial condition:
loading condition:loading condition:
measurement: measurement:
(s-6)
(s-7)
(s-8)
(s-9)
• Computation of H• Computation of H
43 43Structural Dynamics & Vibration Control Lab., KAIST, Korea
Method Time Method Time
Emulator minutes ~ hours Emulator minutes ~ hours
Proposed m sampling time Proposed m sampling time
Evaluation timeEvaluation time
mi hhhhH 21 (s-10)
44 44Structural Dynamics & Vibration Control Lab., KAIST, Korea
1
1
2
1
1n
i
n
j
eji
ji
ee WW
JJJ
1
0,
fN
k
ekji
eji WW
(c-1)
(c-2)
(c-3)
1
0
fN
kkJJ
1
0
fN
k ji
k
ji W
J
W
J
ji
kekji
W
JW
,
(c-4)
(c-5)
• Convergence of learning rule• Convergence of learning rule
45 45Structural Dynamics & Vibration Control Lab., KAIST, Korea
(c-6)
(c-7)
(c-8)
1
1
2
1
21
1
1n
i
n
j
N
k ji
keef
W
JJJ
eee JJJ 1
)0(1
1
2
1
21
1
n
i
n
j
N
k ji
kef
W
JJ
minlim JJ ee
(c-9)
Inserting (3), (4) into (2)
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