Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2012, Article ID 268938, 18 pages
doi:10.1155/2012/268938
Research Article
Application of Support Vector Machine-Based
Semiactive Control for Seismic Protection of
Structures with Magnetorheological Dampers
Chunxiang Li,1 Qing Liu,1 and Shengning Lan2
1
Department of Civil Engineering, Shanghai University, Shanghai 200072, China
2
School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
Correspondence should be addressed to Chunxiang Li,
Received 30 September 2011; Revised 4 March 2012; Accepted 21 March 2012
Academic Editor: J. Rodellar
Copyright q 2012 Chunxiang Li et al. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Based on recent research by Li and Liu in 2011, this paper proposes the application of support
vector machine- SVM- based semiactive control methodology for seismic protection of structures
with magnetorheological MR dampers. An important and challenging task of designing the MR
dampers is to develop an effective semiactive control strategy that can fully exploit the capabilities
of MR dampers. However, amplification of the local acceleration response of structures exists in the
widely used semiactive control strategies, namely “Switch” control strategies. Then the SVM-based
semiactive control strategy has been employed to design MR dampers. Firstly, the LQR controller
for the numerical model of a multistory structure formulated using the dynamic dense method is
constructed by using the classic LQR control theory. Secondly, an SVM model which comprises the
observers and controllers in the control system is designed and trained to emulate the performance
of the LQR controller. Finally, an online autofeedback semiactive control strategy is developed
by resorting to SVM and then used for designing MR dampers. Simulation results show that the
MR dampers utilizing the SVM-based semiactive control algorithm, which eliminates the local
acceleration amplification phenomenon, can remarkably reduce the displacement, velocity, and
acceleration responses of the structure.
1. Introduction
Reducing structural seismic responses, without doubt, can remarkably enhance the buildings’
security. Researches are attaching much more importance on resisting the disasters due to
earthquakes, after several latest big earthquakes in the world, especially the Wen-chuan great
earthquake in China. The application of protective systems to mitigate the effects of seismic
loads on civil engineering structures offers a promising alternative to traditional earthquake
resistant design approaches. Various types of passive, active, and semiactive devices have
been studied extensively by many researchers.
,2 Mathematical Problems in Engineering
x
c0
F − f0
Figure 1: Bingham model of MR damper.
x
c0
k0
F
Bouc-Wen
Figure 2: Bouc-Wen model of MR damper.
Passive supplemental damping strategies, including base isolation systems, viscoelas-
tic dampers, and tuned mass dampers, are well understood and widely accepted by
the engineering community as a means for mitigating the effects of dynamic loading on
structures. But, these passive devices are unable to adapt to structural changes and to varying
usage patterns and loading conditions 1. It is well known that active control has the
advantage of being adaptable to real-time external excitations. Nevertheless, there exist a
number of serious challenges before active control can gain general acceptance by both the
engineering and construction professions. If the active control system is taken into account,
then a large control force must be created and the power limitation of actuator prevents this
system from being implemented in actual buildings. Naturally, at current stage of structural
vibration control, the semiactive control with both low power and low cost seems to be the
most promising schemes for seismic protection of structures 2, 3. Studies have shown that
appropriately implemented semiactive damping systems significantly perform better than
passive devices and have the potential to achieve, or even surpass, the performance of fully
active systems, thus allowing for the possibility of effective response reduction during both
moderate and strong seismic activity.
Among all the semiactive control devices, the magnetorheological MR damper is
a kind of intelligent and effective semiactive control device for its attractive characteristics
in applications of civil engineering, including high strength, insensitivity to contamination,
and small power requirement, and can be viewed as fail-safe in that it becomes a passive
damper in the case of control hardware malfunction. This device overcomes many of the
expenses and technical difficulties associated with semiactive devices previously considered.
Another important and challenging task of the semiactive control system design is to develop
a semiactive control strategy that is implementable and can fully utilize the capability of the
, Mathematical Problems in Engineering 3
Earthquakes
x(t)
ẋ(t) Output Structure
Design
ẍ(t) Feedbacks
Optimal control forces
MR damper mechanic
parameters
MR damper
control forces
Figure 3: Flow diagram of semiactive control for structures with the MR dampers.
Observer
(sensor)
M3
U3 (t) K3
MR damper
M2
U2 (t) K2
M1
U1 (t) K1
System data
at time t − 1
Earthquake
SVM
Controller training
Figure 4: Structural semiactive control system with SVM control strategy.
MR damper. Nowadays, there has been growing trend toward both the application research
and utilization of the MR dampers, such as Hyung et al., 2009 4; Bitaraf et al., 2010 5;
K-Karamodin and H-Kazemi, 2010 6; Kori and Jangid, 2009 7.
However, amplification of the local acceleration response of structures exists in the
widely used semiactive control strategies, namely, “Switch” control strategies. To solve these
problems, in this paper, a support vector machine SVM technique is introduced into the
semiactive control of structure with MR dampers. SVM is a promising statistical learning
theory developed by Vapnik 8. As far as the neural network NN is concerned, the local
minimum point, over learning, and the excessive dependence on experience in the choice
of architectures and types are its inevitable limitations 9. Whereas SVM gets rid of these
Mathematical Problems in Engineering
Volume 2012, Article ID 268938, 18 pages
doi:10.1155/2012/268938
Research Article
Application of Support Vector Machine-Based
Semiactive Control for Seismic Protection of
Structures with Magnetorheological Dampers
Chunxiang Li,1 Qing Liu,1 and Shengning Lan2
1
Department of Civil Engineering, Shanghai University, Shanghai 200072, China
2
School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
Correspondence should be addressed to Chunxiang Li,
Received 30 September 2011; Revised 4 March 2012; Accepted 21 March 2012
Academic Editor: J. Rodellar
Copyright q 2012 Chunxiang Li et al. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Based on recent research by Li and Liu in 2011, this paper proposes the application of support
vector machine- SVM- based semiactive control methodology for seismic protection of structures
with magnetorheological MR dampers. An important and challenging task of designing the MR
dampers is to develop an effective semiactive control strategy that can fully exploit the capabilities
of MR dampers. However, amplification of the local acceleration response of structures exists in the
widely used semiactive control strategies, namely “Switch” control strategies. Then the SVM-based
semiactive control strategy has been employed to design MR dampers. Firstly, the LQR controller
for the numerical model of a multistory structure formulated using the dynamic dense method is
constructed by using the classic LQR control theory. Secondly, an SVM model which comprises the
observers and controllers in the control system is designed and trained to emulate the performance
of the LQR controller. Finally, an online autofeedback semiactive control strategy is developed
by resorting to SVM and then used for designing MR dampers. Simulation results show that the
MR dampers utilizing the SVM-based semiactive control algorithm, which eliminates the local
acceleration amplification phenomenon, can remarkably reduce the displacement, velocity, and
acceleration responses of the structure.
1. Introduction
Reducing structural seismic responses, without doubt, can remarkably enhance the buildings’
security. Researches are attaching much more importance on resisting the disasters due to
earthquakes, after several latest big earthquakes in the world, especially the Wen-chuan great
earthquake in China. The application of protective systems to mitigate the effects of seismic
loads on civil engineering structures offers a promising alternative to traditional earthquake
resistant design approaches. Various types of passive, active, and semiactive devices have
been studied extensively by many researchers.
,2 Mathematical Problems in Engineering
x
c0
F − f0
Figure 1: Bingham model of MR damper.
x
c0
k0
F
Bouc-Wen
Figure 2: Bouc-Wen model of MR damper.
Passive supplemental damping strategies, including base isolation systems, viscoelas-
tic dampers, and tuned mass dampers, are well understood and widely accepted by
the engineering community as a means for mitigating the effects of dynamic loading on
structures. But, these passive devices are unable to adapt to structural changes and to varying
usage patterns and loading conditions 1. It is well known that active control has the
advantage of being adaptable to real-time external excitations. Nevertheless, there exist a
number of serious challenges before active control can gain general acceptance by both the
engineering and construction professions. If the active control system is taken into account,
then a large control force must be created and the power limitation of actuator prevents this
system from being implemented in actual buildings. Naturally, at current stage of structural
vibration control, the semiactive control with both low power and low cost seems to be the
most promising schemes for seismic protection of structures 2, 3. Studies have shown that
appropriately implemented semiactive damping systems significantly perform better than
passive devices and have the potential to achieve, or even surpass, the performance of fully
active systems, thus allowing for the possibility of effective response reduction during both
moderate and strong seismic activity.
Among all the semiactive control devices, the magnetorheological MR damper is
a kind of intelligent and effective semiactive control device for its attractive characteristics
in applications of civil engineering, including high strength, insensitivity to contamination,
and small power requirement, and can be viewed as fail-safe in that it becomes a passive
damper in the case of control hardware malfunction. This device overcomes many of the
expenses and technical difficulties associated with semiactive devices previously considered.
Another important and challenging task of the semiactive control system design is to develop
a semiactive control strategy that is implementable and can fully utilize the capability of the
, Mathematical Problems in Engineering 3
Earthquakes
x(t)
ẋ(t) Output Structure
Design
ẍ(t) Feedbacks
Optimal control forces
MR damper mechanic
parameters
MR damper
control forces
Figure 3: Flow diagram of semiactive control for structures with the MR dampers.
Observer
(sensor)
M3
U3 (t) K3
MR damper
M2
U2 (t) K2
M1
U1 (t) K1
System data
at time t − 1
Earthquake
SVM
Controller training
Figure 4: Structural semiactive control system with SVM control strategy.
MR damper. Nowadays, there has been growing trend toward both the application research
and utilization of the MR dampers, such as Hyung et al., 2009 4; Bitaraf et al., 2010 5;
K-Karamodin and H-Kazemi, 2010 6; Kori and Jangid, 2009 7.
However, amplification of the local acceleration response of structures exists in the
widely used semiactive control strategies, namely, “Switch” control strategies. To solve these
problems, in this paper, a support vector machine SVM technique is introduced into the
semiactive control of structure with MR dampers. SVM is a promising statistical learning
theory developed by Vapnik 8. As far as the neural network NN is concerned, the local
minimum point, over learning, and the excessive dependence on experience in the choice
of architectures and types are its inevitable limitations 9. Whereas SVM gets rid of these
