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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (3) : 706-721    https://doi.org/10.1007/s11709-020-0612-9
RESEARCH ARTICLE
Semi-active fuzzy control of Lali Cable-Stayed Bridge using MR dampers under seismic excitation
Sajad JAVADINASAB HORMOZABAD, Amir K. GHORBANI-TANHA()
School of Civil Engineering, College of Engineering, University of Tehran, Tehran 11155-4563, Iran
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Abstract

Seismic control of cable-stayed bridges is of paramount importance due to their complex dynamic behavior, high flexibility, and low structural damping. In the present study, several semi-active Fuzzy Control Algorithms (FCAs) for vibration mitigation of Lali Cable-Stayed Bridge are devised. To demonstrate the efficiency of the algorithms, a comprehensive nonlinear 3-D model of the bridge is created using OpenSees. An efficient method for connecting MATLAB and OpenSees is devised for applying FCAs to the structural model of the bridge. Two innovative fuzzy rule-bases are introduced. A total of six different fuzzy rule-bases are utilized. The efficiency of the FCAs is evaluated in a comparative manner. The performance of fuzzy control systems is also compared with a sky-hook and a passive-on system. Moreover, the sensitivity of efficiency of control systems to the peak ground acceleration is evaluated qualitatively. In addition, the effect of time lag is also investigated. This study thoroughly examines the efficiency of the FCAs in different aspects. Therefore, the results can be regarded as a general guide to design semi-active fuzzy control systems for vibration mitigation of cable-stayed bridges.
Keywords semi-active control      Fuzzy Control Algorithm      cable-stayed bridge      MR damper      Lali Bridge     
Corresponding Author(s): Amir K. GHORBANI-TANHA   
Just Accepted Date: 07 May 2020   Online First Date: 16 June 2020    Issue Date: 13 July 2020
 Cite this article:   
Sajad JAVADINASAB HORMOZABAD,Amir K. GHORBANI-TANHA. Semi-active fuzzy control of Lali Cable-Stayed Bridge using MR dampers under seismic excitation[J]. Front. Struct. Civ. Eng., 2020, 14(3): 706-721.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0612-9
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I3/706
Fig.1  Overall layout of the Lali Bridge (dimensions in m).
Fig.2  Pier, pylon, and deck sections of the Lali Bridge.
Fig.3  Finite element model of the Lali Bridge: (a) overall view of the SAP2000 model; (b) mechanical behavior of tension-only material used for cables in OpenSees model.
parameter element value
yielding strength of steel deck beams 360 MPa (ST52)
elastic modulus of steel deck beams 2.1E5 MPa
yielding strength of steel cables 1000 MPa
elastic modulus of steel cables 1.95E5 MPa
compressive strength of concrete deck slabs 45 MPa
compressive strength of concrete piers 40 MPa
yielding strength of steel reinforcement piers 400 MPa (S400)
Tab.1  General characteristics of the finite element model of the bridge
parameter value
αa 1.0872×105 N/cm
αb 4.9616×105 N/cm/V
C0a 4.40 N s/cm
C0b 44.0 N s/cm/V
Am 1.2
n 1
β 3 cm−1
γ 3 cm−1
η 50 s−1
Tab.2  Parameters used for simulating the MR dampers
Fig.4  The (a) first, (b) second, (c) third, (d) fourth, (e) fifth, and (f) sixth mode shapes of the Lali Bridge.
Fig.5  Verification of the displacement response of the middle point of the deck subjected to (a) El Centro and (b) Northridge earthquake; (c) verification of the vertical displacements of the deck due to cable prestress forces.
record type Earthquake Station PGA
near-field Kobe, 1995 KJM 0.83g
Northridge, 1994 Sylmar-Olive 0.84g
Tabas, 1978 Tabas 0.85g
Chi Chi, 1999 TCU065 0.83g
far-field Imperial Valley, 1940 El Centro 0.35g
Tokachi_Oki, 1968 Hachinohe 0.23g
Tabas, 1978 Ferdows 0.11g
Loma Prieta, 1989 Richmond City Hall 0.12g
Tab.3  Characteristics of the ground motion records
Fig.6  (a) Schematic model of the MR damper; (b) hysteretic behavior of the MR damper for various values of input voltage.
Fig.7  Schematic arrangement of MR dampers and measurement sensors.
Fig.8  Membership functions for (a) input variables used in rule base 1, 3, 4, and 5; (b) input variables used in rule base 2 and 3; (c) input variables used in rule base 2 and 6; (d) output variables (units are in SI).
VelRel
NVL NL NM NS NVS ZO PVS PS PM PL PVL
VL L M S VS ZO VS S M L VL
Tab.4  Fuzzy rule table for RB1
Disp
NVL NL NM NS NVS ZO PVS PS PM PL PVL
VelRel P ZO ZO ZO ZO ZO VL VL VL VL VL VL
N VL VL VL VL VL VL ZO ZO ZO ZO ZO
Tab.5  Fuzzy rule table for RB2
Disp
NVL NL NM NS NVS ZO PVS PS PM PL PVL
VelRel PVL L VL VL VL VL VL VL VL VL VL VL
PL M L VL VL VL VL VL VL VL VL VL
PM S M L VL VL VL VL VL VL VL VL
PS VS S M L VL VL VL VL VL VL VL
PVS ZO VS S M L VL VL VL VL VL VL
ZO VL VL VL VL VL VL VL VL VL VL VL
NVS VL VL VL VL VL VL L M S VS ZO
NS VL VL VL VL VL VL VL L M S VS
NM VL VL VL VL VL VL VL VL L M S
NL VL VL VL VL VL VL VL VL VL L M
NVL VL VL VL VL VL VL VL VL VL VL L
Tab.6  Fuzzy rule table for RB3
VelRel
NVL NL NM NS NVS ZO PVS PS PM PL PVL
ZO VS S M L VL L M S VS ZO
Tab.7  Fuzzy rule table for RB4
Vel
NVL NL NM NS NVS ZO PVS PS PM PL PVL
VelRel PVL ZO ZO ZO ZO ZO ZO VS S M L VL
PL ZO ZO ZO ZO ZO VS S M L VL VL
PM ZO ZO ZO ZO ZO S M L VL VL VL
PS ZO ZO ZO ZO ZO M L VL VL VL VL
PVS ZO ZO ZO ZO ZO L VL VL VL VL VL
ZO VL VL VL VL VL VL VL VL VL VL VL
NVS VL VL VL VL VL L ZO ZO ZO ZO ZO
NS VL VL VL VL L M ZO ZO ZO ZO ZO
NM VL VL VL L M S ZO ZO ZO ZO ZO
NL VL VL L M S VS ZO ZO ZO ZO ZO
NVL VL L M S VS ZO ZO ZO ZO ZO ZO
Tab.8  Fuzzy rule table for RB5
Vel
NVL NL NM NS NVS ZO PVS PS PM PL PVL
VelRel P ZO ZO ZO ZO ZO VL VL VL VL VL VL
N VL VL VL VL VL VL ZO ZO ZO ZO ZO
Tab.9  Fuzzy rule tables for RB6
control system J1 J2 J3 J4 J5 J6 J7 J8 J9 J10
FIS1 0.630 0.889 0.969 0.919 0.931 0.430 0.645 0.570 0.448 0.993
FIS2 0.739 1.072 1.057 1.166 0.992 0.538 0.779 0.897 0.714 0.999
FIS3 0.648 0.965 1.014 1.034 0.972 0.400 0.737 0.706 0.614 0.995
FIS4 0.698 0.981 1.002 1.065 0.967 0.506 0.749 0.734 0.576 0.995
FIS5 0.465 1.016 0.992 1.001 0.985 0.325 0.668 0.674 0.454 0.998
FIS6 0.433 1.011 0.998 1.006 1.000 0.290 0.726 0.734 0.495 0.999
sky-hook 0.420 1.048 1.020 1.028 1.016 0.233 0.956 0.906 0.751 0.999
passive 0.575 0.969 0.957 0.966 0.956 0.361 0.775 0.637 0.488 0.995
Tab.10  Average performance criteria for control systems subjected to scaled earthquake records
qualitative efficiency overall ranking
FIS1 F E E E E F E E E E 5
FIS2 P P P P F P G P P P 8
FIS3 F G G G G G VG G G VG 6
FIS4 P G G G G P VG G G VG 7
FIS5 E F VG VG F VG E VG E F 2
FIS6 E F G VG P E VG G E P 1
sky-hook E P F G P E P P P P 3
Passive G G E E VG G G E E VG 4
Tab.11  Overall Qualitative Evaluation of Efficiency of Control Systems
criterion J1 J2 J3 J4 J5 J6 J7 J8 J9 J10
relative importance 10.0 0.2 2.0 2.0 2.0 10.0 4.0 2.0 2.0 0.2
Tab.12  Relative importance of each criterion considered for the overall evaluation
?control system average slope sensitivity of efficiency to PGA
FIS1 0.128 very stable
FIS2 0.338 very sensitive
FIS3 0.319 very sensitive
FIS4 0.341 very sensitive
FIS5 0.256 sensitive
FIS6 0.325 very sensitive
sky-hook 0.346 very sensitive
passive 0.284 sensitive
Tab.13  Evaluation of sensitivity of control systems to PGA
criterion average slope variation of control systems efficiency due to increase in PGA
J1 0.403 very significant decrease
J2 −0.440??? very significant increase
J3 0.121 moderate decrease
J4 0.435 very significant decrease
J5 0.070 no meaningful change
J6 0.215 significant decrease
J7 −0.114??? moderate increase
J8 0.302 very significant decrease
J9 0.353 very significant decrease
J10 −0.002??? no meaningful change
Tab.14  Evaluation of sensitivity of performance criteria to PGA
control system relative error (%)
J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 average
FIS1 ?3.77 ??7.02 2.23 6.99 0.16 11.82 150.98 7.30 ?8.81 0.02 19.91
FIS2 18.91 148.06 1.42 −2.11?? 0.10 43.10 485.77 24.32? 43.63 0.11 76.33
FIS3 11.24 167.74 1.09 −0.76?? 0.45 36.32 642.47 7.32 10.55 0.04 87.65
FIS4 ?9.30 ?83.98 2.75 −1.32?? −1.56?? 35.74 321.68 6.36 ?9.68 −0.01?? 46.66
FIS5 25.63 142.16 7.17 1.86 3.99 39.54 598.95 6.96 11.05 0.03 83.74
FIS6 26.63 148.53 12.86? 0.23 0.92 46.46 656.11 5.17 ?8.68 0.05 90.57
average 15.91 116.25 4.59 0.82 0.68 35.50 475.99 9.57 15.40 0.04
Tab.15  The average percentage of relative errors due to a 0.1 sec time lag
Fig.9  Variation of J1 vs. PGA for El Centro earthquake.
Fig.10  Evaluation of failure and unseating of cables for (a) FIS1, (b) FIS6 subjected to Northridge record.
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