# American Institute of Mathematical Sciences

doi: 10.3934/naco.2020029

## Neuro-fuzzy active control optimized by Tug of war optimization method for seismically excited benchmark highway bridge

 1 Department of Civil Engineering, Noshirvani University of Technology, Babol, Iran 2 Department of Civil Engineering, Ferdowsi University of Technology, Mashhad, Iran

* Corresponding author: Mostafa Ghelichi

Received  October 2019 Revised  January 2020 Published  May 2020

Fund Project: The authors are supported by Babol Noshirvani university grant BNUT/370680/97

Control algorithms can affect the performance and cost-effectiveness of the control system of a structure. This study presents an active neuro-fuzzy optimized control algorithm based on a new optimization method taken from Tug of War competition, which is highly efficient for civil structures. The performance of the proposed control method has been evaluated on the finite element model of a nonlinear highway benchmark bridge; which is consisted of nonlinear structural elements and isolation bearings and equipped with hydraulic actuators. The nonlinear control rules are approximated with a five-layer optimized neural network which transmits instructions to the actuators installed between the deck and abutments. The stability of control laws are obtained based on Lyapunov theory. The performance of the proposed algorithm in controlling bridge structural responses is investigated in six different earthquakes. The results are presented in terms of a well-defined set of performance indices that are comparable to previous methods. The results show that despite the simple description of nonlinearities and non-detailed structural information, the proposed control method can effectively reduce the performance indices of the structure. The application of artificial neural networks is a privilege, which in so far as which, despite their simplicity, they have significant effects even on complex structures such as nonlinear highway bridges.

Citation: Mostafa Ghelichi, A. M. Goltabar, H. R. Tavakoli, A. Karamodin. Neuro-fuzzy active control optimized by Tug of war optimization method for seismically excited benchmark highway bridge. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2020029
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##### References:
Elevation and plan views of $91/5$ over-crossing[1]
Finite element model of the bridge
Tug of war tournament
An idealized framework of tug of war [20]
Membership functions of earthquake observer
Input membership functions in ANFIS controller (Normalized displacement or Normalized acceleration)
ANFIS configuration of the proposed controller
The applied methodology to design a nero-fuzzy optimized controller
F-ANFIS controller optimization under N.P.Spr. earthquake with a factor of 1.5 and J1 index
N-ANFIS controller optimization under Northridge earthquake with a factor of 1.5 and J1 index
The J1 index comparison among the different control methods
The J3 index comparison among the different control methods
The J4 index comparison among the different control methods
A view of the results of the Friedman's test
Input membership functions parameters in ANFIS controller
 N1 N2 N3 P1 P2 P3 $\sigma$ 0.15 0.15 0.15 0.15 0.15 0.15 C -1.0 -0.6 -0.2 0.2 0.6 1.0
 N1 N2 N3 P1 P2 P3 $\sigma$ 0.15 0.15 0.15 0.15 0.15 0.15 C -1.0 -0.6 -0.2 0.2 0.6 1.0
The mean of criteria J1, J3 and J5 in a far-field earthquake, for different optimization scenarios of ANFIS controller (F-ANFIS)
 Optimization by minimizing criterion J1 Earthquake EL-Ce$\times$1 EL-Ce$\times$1.5 N.P.Spr.$\times$1 N.P.Spr.$\times$1.5 J1 1.1198 1.1153 0.8942 0.8867 J3 0.6153 0.5235 0.8856 0.8171 J5 0.3586 0.2684 0.6125 0.5928 Optimization by minimizing criterion J4 Earthquake EL-Ce$\times$1 EL-Ce$\times$1.5 N.P.Spr.$\times$1 N.P.Spr.$\times$1.5 J1 1.1336 1.1295 0.8895 0.9459 J3 0.5983 0.5467 0.8763 0.8543 J5 0.3347 0.2733 0.5826 0.6372
 Optimization by minimizing criterion J1 Earthquake EL-Ce$\times$1 EL-Ce$\times$1.5 N.P.Spr.$\times$1 N.P.Spr.$\times$1.5 J1 1.1198 1.1153 0.8942 0.8867 J3 0.6153 0.5235 0.8856 0.8171 J5 0.3586 0.2684 0.6125 0.5928 Optimization by minimizing criterion J4 Earthquake EL-Ce$\times$1 EL-Ce$\times$1.5 N.P.Spr.$\times$1 N.P.Spr.$\times$1.5 J1 1.1336 1.1295 0.8895 0.9459 J3 0.5983 0.5467 0.8763 0.8543 J5 0.3347 0.2733 0.5826 0.6372
The mean of criteria J1, J3 and J5 in a Near-field earthquake, for different optimization scenarios of ANFIS controller (N-ANFIS).
 Optimization by minimizing criterion J1 Earthquake Northridge$\times$1 Northridge$\times$1.5 J1 0.7321 0.7125 J3 0.3988 0.3846 J5 0.3833 0.3644 Optimization by minimizing criterion J4 Earthquake Northridge$\times$1 Northridge$\times$1.5 J1 0.7466 0.7389 J3 0.4038 0.6089 J5 0.3957 0.4782
 Optimization by minimizing criterion J1 Earthquake Northridge$\times$1 Northridge$\times$1.5 J1 0.7321 0.7125 J3 0.3988 0.3846 J5 0.3833 0.3644 Optimization by minimizing criterion J4 Earthquake Northridge$\times$1 Northridge$\times$1.5 J1 0.7466 0.7389 J3 0.4038 0.6089 J5 0.3957 0.4782
The results of the proposed controller
 NPalmspr ChiChi El Centro Northridge TurkBolu Kobe-NIS Avg J1:Pk. base Shear 0.925 0.652 0.678 0.729 0.697 0.892 0.762 J2:Pk. Over.Mom. 0.693 0.878 0.595 0.786 0.587 0.547 0.681 J3:Pk. Mid. Disp. 0.684 0.701 0.667 0.572 0.661 0.607 0.648 J4: Pk. Mid. Acc. 0.997 0.912 0.788 0.783 0.812 0.822 0.852 J5: Pk. Bear. Def. 0.546 0.554 0.563 0.514 0.605 0.451 0.538 J6: Pk. Ductility 0.647 0.517 0.576 0.547 0.186 0.585 0.509 J7: Dis. Energy 0.000 0.087 0.000 0.120 0.05 0.000 0.042 J8: Plas. Connect. 0.000 0.500 0.000 0.500 0.000 0.000 0.166 J9:Nor.Base shear 0.839 0.567 0.610 0.594 0.743 0.718 0.678 J10:Nor.Over. Mom. 0.561 0.597 0.642 0.686 0.459 0.745 0.615 J11: Nor. Mid. Disp. 0.611 0.487 0.504 0.473 0.514 0.639 0.538 J12: Nor. Mid. Acc. 0.798 0.694 0.568 0.681 0.842 0.765 0.724 J13: Nor. Bear. Def. 0.397 0.456 0.415 0.616 0.214 0.324 0.404 J14: Nor. Ductility 0.615 0.623 0.561 0.802 0.123 0.683 0.567 J15: Pk. Con. Force 0.010 0.024 0.007 0.025 0.018 0.012 0.016 J16: Pk. Stroke 0.509 0.517 0.518 0.452 0.580 0.451 0.504 J17: Pk. Power 0.037 0.110 0.024 0.098 0.077 0.029 0.063 J18: Total Power 0.010 0.014 0.005 0.017 0.015 0.015 0.012 J19:No.Con. Devices 16 16 16 16 16 16 16 J20: No. Sensors 12 12 12 12 12 12 12 J21:Comp. Resources 16 16 16 16 16 16 16
 NPalmspr ChiChi El Centro Northridge TurkBolu Kobe-NIS Avg J1:Pk. base Shear 0.925 0.652 0.678 0.729 0.697 0.892 0.762 J2:Pk. Over.Mom. 0.693 0.878 0.595 0.786 0.587 0.547 0.681 J3:Pk. Mid. Disp. 0.684 0.701 0.667 0.572 0.661 0.607 0.648 J4: Pk. Mid. Acc. 0.997 0.912 0.788 0.783 0.812 0.822 0.852 J5: Pk. Bear. Def. 0.546 0.554 0.563 0.514 0.605 0.451 0.538 J6: Pk. Ductility 0.647 0.517 0.576 0.547 0.186 0.585 0.509 J7: Dis. Energy 0.000 0.087 0.000 0.120 0.05 0.000 0.042 J8: Plas. Connect. 0.000 0.500 0.000 0.500 0.000 0.000 0.166 J9:Nor.Base shear 0.839 0.567 0.610 0.594 0.743 0.718 0.678 J10:Nor.Over. Mom. 0.561 0.597 0.642 0.686 0.459 0.745 0.615 J11: Nor. Mid. Disp. 0.611 0.487 0.504 0.473 0.514 0.639 0.538 J12: Nor. Mid. Acc. 0.798 0.694 0.568 0.681 0.842 0.765 0.724 J13: Nor. Bear. Def. 0.397 0.456 0.415 0.616 0.214 0.324 0.404 J14: Nor. Ductility 0.615 0.623 0.561 0.802 0.123 0.683 0.567 J15: Pk. Con. Force 0.010 0.024 0.007 0.025 0.018 0.012 0.016 J16: Pk. Stroke 0.509 0.517 0.518 0.452 0.580 0.451 0.504 J17: Pk. Power 0.037 0.110 0.024 0.098 0.077 0.029 0.063 J18: Total Power 0.010 0.014 0.005 0.017 0.015 0.015 0.012 J19:No.Con. Devices 16 16 16 16 16 16 16 J20: No. Sensors 12 12 12 12 12 12 12 J21:Comp. Resources 16 16 16 16 16 16 16
Results of the Friedman's test
 Responce indices Friedman's mean rank $P$ value ATF P-SAMP A-SAMP A-ANF SA-CLOP SA-AFSMC J1 1.6 5.2 5.6 1.8 4 2.8 8.95E-04 J2 1.2 1.8 4.6 5.4 4.4 3.6 1.10E-03 J3 1.4 1.6 5 4.7 4.7 3.6 2.00E-03 J4 3.8 5.9 1.4 1.7 3.2 5 3.34E-04 J5 2 1.8 5.5 5.5 4 2.2 2.16E-04 J6 1.2 1.8 5.5 3.9 5.3 3.3 4.07E-04 J7 1.4 1.6 4.9 5.6 4.5 3 3.80E-04 J8 1.2 1.8 4.1 4.8 3.5 5.6 4.95E-04 J9 2.9 1.9 4.3 4.6 4.1 3.2 1.67E-01 J10 2 2 5 6 4 2 3.78E-04 J11 1.4 1.6 5.5 3.9 5 3.6 7.31E-04 J12 1.4 5.7 2.1 2.5 4 5.3 3.87E-04 J13 2.6 1 5 6 4 2.4 1.89E-04 J14 3.3 2.9 6 2.8 5 1 4.02E-04 J15 5.3 5 1.5 2 2.7 4.5 4.02E-04 J16 2.2 1 5 6 4 2.8 4.02E-04 Average 2.18 2.66 4.43 4.20 4.15 3.38 SD 1.15 1.72 1.46 1.58 0.67 1.25
 Responce indices Friedman's mean rank $P$ value ATF P-SAMP A-SAMP A-ANF SA-CLOP SA-AFSMC J1 1.6 5.2 5.6 1.8 4 2.8 8.95E-04 J2 1.2 1.8 4.6 5.4 4.4 3.6 1.10E-03 J3 1.4 1.6 5 4.7 4.7 3.6 2.00E-03 J4 3.8 5.9 1.4 1.7 3.2 5 3.34E-04 J5 2 1.8 5.5 5.5 4 2.2 2.16E-04 J6 1.2 1.8 5.5 3.9 5.3 3.3 4.07E-04 J7 1.4 1.6 4.9 5.6 4.5 3 3.80E-04 J8 1.2 1.8 4.1 4.8 3.5 5.6 4.95E-04 J9 2.9 1.9 4.3 4.6 4.1 3.2 1.67E-01 J10 2 2 5 6 4 2 3.78E-04 J11 1.4 1.6 5.5 3.9 5 3.6 7.31E-04 J12 1.4 5.7 2.1 2.5 4 5.3 3.87E-04 J13 2.6 1 5 6 4 2.4 1.89E-04 J14 3.3 2.9 6 2.8 5 1 4.02E-04 J15 5.3 5 1.5 2 2.7 4.5 4.02E-04 J16 2.2 1 5 6 4 2.8 4.02E-04 Average 2.18 2.66 4.43 4.20 4.15 3.38 SD 1.15 1.72 1.46 1.58 0.67 1.25
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