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

Mostafa Ghelichi; A. M. Goltabar; H. R. Tavakoli; A. Karamodin

doi:10.3934/naco.2020029

Article Contents

2021, Volume 11, Issue 3: 333-351. Doi: 10.3934/naco.2020029

This issue Previous Article Next Article An inexact alternating direction method of multipliers for a kind of nonlinear complementarity problems

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
^* Corresponding author: Mostafa Ghelichi

Received: October 2019

Revised: January 2020

Early access: May 2020

Published: September 2021

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

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 93C42; Secondary: 47N10.

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Figure 1. Elevation and plan views of $ 91/5 $ over-crossing[1]

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Figure 2. Finite element model of the bridge

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Figure 3. Tug of war tournament

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Figure 4. An idealized framework of tug of war [20]

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Figure 5. Membership functions of earthquake observer

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Figure 6. Input membership functions in ANFIS controller (Normalized displacement or Normalized acceleration)

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Figure 7. ANFIS configuration of the proposed controller

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Figure 8. The applied methodology to design a nero-fuzzy optimized controller

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Figure 9. F-ANFIS controller optimization under N.P.Spr. earthquake with a factor of 1.5 and J1 index

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Figure 10. N-ANFIS controller optimization under Northridge earthquake with a factor of 1.5 and J1 index

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Figure 11. The J1 index comparison among the different control methods

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Figure 12. The J3 index comparison among the different control methods

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Figure 13. The J4 index comparison among the different control methods

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Figure 14. A view of the results of the Friedman's test

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Table 1. 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

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Table 2. 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

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Table 3. 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

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Table 4. 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

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Table 5. 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

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