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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
References:
[1]

A. K. AgrawalP. TanS. Nagarajaiah and J. Zhang, Benchmark structural control problem for a seismically excited highway bridge-Part Ⅰ: Phase Ⅰ Problem definition, Struct. Control Heal. Monit., 16 (2009), 509-529.   Google Scholar

[2]

S. Ali, Semi-active Control of Earthquake Induced Vibrations in Structures Using Mr Dampers : Algorithm Development, Experimental Verification and Benchmark Applications, Ph.D thesis, Indian Institute of Science, Bangalore, 560 012, 2008. Google Scholar

[3]

J. M. CaicedoS. J. DykeS. J. MoonL. A. BergmanG. Turan and S. Hague, Phase Ⅱ benchmark control problem for seismic response of cable-stayed bridges, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.   Google Scholar

[4]

M. DehghaniA. Seifi and H. Riahi-Madvar, Novel forecasting models for immediate-short-term to long-term influent flow prediction by combining ANFIS and grey wolf optimization, J. Hydrol., 576 (2019), 698-725.   Google Scholar

[5]

S. J. DykeJ. M. CaicedoG. TuranL. A. Bergman and S. Hague, Phase Ⅰ benchmark control system for seismic response of cable-stayed bridges, J. Struct. Eng., 129 (2003), 857-872.   Google Scholar

[6]

R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 12 (1995), 39-43. Google Scholar

[7]

O. K. Erol and I. Eksin, A new optimization method: Big BangBig Crunch, Adv. Eng. Softw., 37 (2006), 106-111.   Google Scholar

[8]

H. Ghaffarzadeh, Semi-active structural fuzzy control with MR dampers subjected to near-fault ground motions having forward directivity and fling step, Smart Struct. Syst., 12 (2013), 595-617.   Google Scholar

[9]

A. GoliH. Khademi ZarehR. Tavakkoli-Moghaddam and A. Sadeghieh, A comprehensive model of demand prediction based on hybrid artificial intelligence and metaheuristic algorithms: A case study in dairy industry, Int. J. Ind. Syst. Eng., 11 (2018), 190-203.   Google Scholar

[10]

M. S. Gonalves, R. H. Lopez and L. F. F. Miguel, Search group algorithm: A new metaheuristic method for the optimization of truss structures, Comput. Struct., 153 (2015), 165-184. Google Scholar

[11]

G. HeoC. KimS. JeonC. Lee and J. Jeon, A hybrid seismic response control to improve performance of a two-span bridge, Struct. Eng. Mech., 61 (2009), 675-684.   Google Scholar

[12]

R. S. Jangid and J. M. Kelly, Base isolation for near-fault motions, Earthq. Eng. Struct. Dyn., 35 (2001), 691-707.   Google Scholar

[13]

S. JaypuriaM. T. Ranjan and O. Jaypuria, Metaheuristic tuned ANFIS model for input-output modeling of friction stir welding, Materials Today: Proceedings, 18 (2019), 3922-3930.   Google Scholar

[14]

A. A. Kalteh and S. Babouei, Control chart patterns recognition using ANFIS with new training algorithm and intelligent utilization of shape and statistical features, ISA Transactions, 1 (2019). Google Scholar

[15]

A. Kaveh and N. Khayatazad, A new meta-heuristic method: ray optimization, Comput. Struct., 59 (2012), 283-294.   Google Scholar

[16]

A. KavehS. M. Motie and M. Moslehi, Magnetic charged system search: a new meta-heuristic algorithm for optimization, Acta Mech., 224 (2014), 85-107.   Google Scholar

[17]

A. Kaveh and N. Farhoudi, A new optimization method: dolphin echolocation, Adv. Eng. Softw., 59 (2013), 53-70.   Google Scholar

[18]

A. Kaveh and A. Zolghadr, Democratic PSO for truss layout and size optimization with frequency constraints, Comput. Struct., 130 (2014), 10-21.   Google Scholar

[19]

A. Kaveh and V. R. Mahdavi, Colliding bodies optimization: a novel meta-heuristic method, Comput. Struct., 139 (2014), 18-27.  doi: 10.1007/978-3-319-19659-6.  Google Scholar

[20]

A. Kaveh and A. Zolghadr, A novel meta-heuristic algorithm: TUG OF WAR optimization, Iran Univ. Sci. Technol., 6 (2014), 469-492.   Google Scholar

[21]

S. Khalilpourazari and S. Khalilpourazari, Optimization of time, cost and surface roughness in grinding process using a robust multi-objective dragonfly algorithm, Neural Comput. Appl., 1 (2018), 1-12.   Google Scholar

[22]

S. Khalilpourazari and H. R. Pasandideh, Modeling and optimization of multi-item multi-constrained EOQ model for growing items, Knowl-Based Syst., 164 (2019), 150-162.   Google Scholar

[23]

S. KhalilpourazariH. R. PasandidehH. R. Niaki and S. T. Akhavan, Optimizing a multi-item economic order quantity problem with imperfect items, inspection errors, and backorders, Soft Computing, 23 (2019), 11671-11698.   Google Scholar

[24]

S. Khalilpourazari and H. R. Pasandideh, Sinecosine crow search algorithm: theory and applications, Neural Comput. Appl., 1 (2019). Google Scholar

[25]

S. KhalilpourazariA. MirzazadehG. W. Weber and H. R. Pasandideh, A robust fuzzy approach for constrained multi-product economic production quantity with imperfect items and rework process, Optimization, 69 (2020), 63-90.  doi: 10.1080/02331934.2019.1630625.  Google Scholar

[26]

S. N. Madhekar and R. S. Jangid, Seismic performance of benchmark highway bridge installed with piezoelectric friction dampers, IES J. Part A Civ. Struct. Eng., 4 (2011), 191-212.   Google Scholar

[27]

M. J. MahmoodabadiF. Farhadi and S. Sampour, Firefly algorithm based optimum design of vehicle suspension systems, Int. J. Dyn. Control., 7 (2019), 134-146.   Google Scholar

[28]

G. P. MavroeidisG. Dong and A. S. Papageorgiou, Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom(SDOF) systems, Earthq. Eng. Struct. Dyn., 33 (2004), 1023-1049.   Google Scholar

[29]

S. Narasimhan, S. Nagarajaiah, H. Gavin and E. J. Johnson, Smart base-isolated benchmark building. Part Ⅰ: Problem definition, Struct. Control Heal. Monit., 13 (2006), 573-588. Google Scholar

[30]

S. NarasimhanS. Nagarajaiah and E. A.Johnson, Smart base-isolated benchmark building part Ⅳ: Phase Ⅱ sample controllers for nonlinear isolation systems, Struct. Control Heal. Monit., 15 (2008), 657-672.   Google Scholar

[31]

S. Narasimhan, Robust direct adaptive controller for the nonlinear highway bridge benchmark, Struct. Control Heal. Monit., 16 (2009), 599-612.   Google Scholar

[32]

S. NagarajaiahS. NarasimhanP. Tan and A. K. Agrawal, Benchmark structural control problem for a seismically excited highway bridge-Part Ⅲ: Phase Ⅱ Sample controller for the fully base-isolated case, Struct. Control Heal. Monit., 16 (2009), 549-563.   Google Scholar

[33]

X. L. NingP. TanD. Y. Huang and F. L. Zhou, Application of adaptive fuzzy sliding mode control to a seismically excited highway bridge, Struct. Control Heal. Monit., 16 (2009), 207-216.   Google Scholar

[34]

Y. OhtoriR. E. ChristensonB. F. Spencer and S. J. Dyke, Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 366-385.   Google Scholar

[35]

A. PreumontM. VoltanA. SangiovanniB. Mokrani and D. Alaluf, Active tendon control of suspension bridges, Smart Struct. Syst., 18 (2016), 31-52.   Google Scholar

[36]

A. SadollahH. EskandarA. Bahreininejad and J. H. Kim, Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures, Comput. Struct., 149 (2015), 1-16.   Google Scholar

[37]

A. SahaP. Saha and P. S. Kumar, Polynomial friction pendulum isolators (PFPIs) for seismic performance control of benchmark highway bridge, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.   Google Scholar

[38]

B. F. SpencerS. J. Dyke and H. S. Deoskar, Benchmark problems in structural control: Part Ⅰ Active Mass Driver system, Earthq. Eng. Struct. Dyn., 27 (1998), 1127-1139.   Google Scholar

[39]

P. Tan and A. K. Agrawal, Benchmark structural control problem for a seismically excited highway bridge, Part Ⅱ : Phase Ⅰ Sample control designs, Struct. Control Heal. Monit., 129 (2009), 857-872.   Google Scholar

[40]

J. N. YangA. K. AgrawalB. Samali and J. C. Wu, Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 437-446.   Google Scholar

show all references

References:
[1]

A. K. AgrawalP. TanS. Nagarajaiah and J. Zhang, Benchmark structural control problem for a seismically excited highway bridge-Part Ⅰ: Phase Ⅰ Problem definition, Struct. Control Heal. Monit., 16 (2009), 509-529.   Google Scholar

[2]

S. Ali, Semi-active Control of Earthquake Induced Vibrations in Structures Using Mr Dampers : Algorithm Development, Experimental Verification and Benchmark Applications, Ph.D thesis, Indian Institute of Science, Bangalore, 560 012, 2008. Google Scholar

[3]

J. M. CaicedoS. J. DykeS. J. MoonL. A. BergmanG. Turan and S. Hague, Phase Ⅱ benchmark control problem for seismic response of cable-stayed bridges, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.   Google Scholar

[4]

M. DehghaniA. Seifi and H. Riahi-Madvar, Novel forecasting models for immediate-short-term to long-term influent flow prediction by combining ANFIS and grey wolf optimization, J. Hydrol., 576 (2019), 698-725.   Google Scholar

[5]

S. J. DykeJ. M. CaicedoG. TuranL. A. Bergman and S. Hague, Phase Ⅰ benchmark control system for seismic response of cable-stayed bridges, J. Struct. Eng., 129 (2003), 857-872.   Google Scholar

[6]

R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 12 (1995), 39-43. Google Scholar

[7]

O. K. Erol and I. Eksin, A new optimization method: Big BangBig Crunch, Adv. Eng. Softw., 37 (2006), 106-111.   Google Scholar

[8]

H. Ghaffarzadeh, Semi-active structural fuzzy control with MR dampers subjected to near-fault ground motions having forward directivity and fling step, Smart Struct. Syst., 12 (2013), 595-617.   Google Scholar

[9]

A. GoliH. Khademi ZarehR. Tavakkoli-Moghaddam and A. Sadeghieh, A comprehensive model of demand prediction based on hybrid artificial intelligence and metaheuristic algorithms: A case study in dairy industry, Int. J. Ind. Syst. Eng., 11 (2018), 190-203.   Google Scholar

[10]

M. S. Gonalves, R. H. Lopez and L. F. F. Miguel, Search group algorithm: A new metaheuristic method for the optimization of truss structures, Comput. Struct., 153 (2015), 165-184. Google Scholar

[11]

G. HeoC. KimS. JeonC. Lee and J. Jeon, A hybrid seismic response control to improve performance of a two-span bridge, Struct. Eng. Mech., 61 (2009), 675-684.   Google Scholar

[12]

R. S. Jangid and J. M. Kelly, Base isolation for near-fault motions, Earthq. Eng. Struct. Dyn., 35 (2001), 691-707.   Google Scholar

[13]

S. JaypuriaM. T. Ranjan and O. Jaypuria, Metaheuristic tuned ANFIS model for input-output modeling of friction stir welding, Materials Today: Proceedings, 18 (2019), 3922-3930.   Google Scholar

[14]

A. A. Kalteh and S. Babouei, Control chart patterns recognition using ANFIS with new training algorithm and intelligent utilization of shape and statistical features, ISA Transactions, 1 (2019). Google Scholar

[15]

A. Kaveh and N. Khayatazad, A new meta-heuristic method: ray optimization, Comput. Struct., 59 (2012), 283-294.   Google Scholar

[16]

A. KavehS. M. Motie and M. Moslehi, Magnetic charged system search: a new meta-heuristic algorithm for optimization, Acta Mech., 224 (2014), 85-107.   Google Scholar

[17]

A. Kaveh and N. Farhoudi, A new optimization method: dolphin echolocation, Adv. Eng. Softw., 59 (2013), 53-70.   Google Scholar

[18]

A. Kaveh and A. Zolghadr, Democratic PSO for truss layout and size optimization with frequency constraints, Comput. Struct., 130 (2014), 10-21.   Google Scholar

[19]

A. Kaveh and V. R. Mahdavi, Colliding bodies optimization: a novel meta-heuristic method, Comput. Struct., 139 (2014), 18-27.  doi: 10.1007/978-3-319-19659-6.  Google Scholar

[20]

A. Kaveh and A. Zolghadr, A novel meta-heuristic algorithm: TUG OF WAR optimization, Iran Univ. Sci. Technol., 6 (2014), 469-492.   Google Scholar

[21]

S. Khalilpourazari and S. Khalilpourazari, Optimization of time, cost and surface roughness in grinding process using a robust multi-objective dragonfly algorithm, Neural Comput. Appl., 1 (2018), 1-12.   Google Scholar

[22]

S. Khalilpourazari and H. R. Pasandideh, Modeling and optimization of multi-item multi-constrained EOQ model for growing items, Knowl-Based Syst., 164 (2019), 150-162.   Google Scholar

[23]

S. KhalilpourazariH. R. PasandidehH. R. Niaki and S. T. Akhavan, Optimizing a multi-item economic order quantity problem with imperfect items, inspection errors, and backorders, Soft Computing, 23 (2019), 11671-11698.   Google Scholar

[24]

S. Khalilpourazari and H. R. Pasandideh, Sinecosine crow search algorithm: theory and applications, Neural Comput. Appl., 1 (2019). Google Scholar

[25]

S. KhalilpourazariA. MirzazadehG. W. Weber and H. R. Pasandideh, A robust fuzzy approach for constrained multi-product economic production quantity with imperfect items and rework process, Optimization, 69 (2020), 63-90.  doi: 10.1080/02331934.2019.1630625.  Google Scholar

[26]

S. N. Madhekar and R. S. Jangid, Seismic performance of benchmark highway bridge installed with piezoelectric friction dampers, IES J. Part A Civ. Struct. Eng., 4 (2011), 191-212.   Google Scholar

[27]

M. J. MahmoodabadiF. Farhadi and S. Sampour, Firefly algorithm based optimum design of vehicle suspension systems, Int. J. Dyn. Control., 7 (2019), 134-146.   Google Scholar

[28]

G. P. MavroeidisG. Dong and A. S. Papageorgiou, Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom(SDOF) systems, Earthq. Eng. Struct. Dyn., 33 (2004), 1023-1049.   Google Scholar

[29]

S. Narasimhan, S. Nagarajaiah, H. Gavin and E. J. Johnson, Smart base-isolated benchmark building. Part Ⅰ: Problem definition, Struct. Control Heal. Monit., 13 (2006), 573-588. Google Scholar

[30]

S. NarasimhanS. Nagarajaiah and E. A.Johnson, Smart base-isolated benchmark building part Ⅳ: Phase Ⅱ sample controllers for nonlinear isolation systems, Struct. Control Heal. Monit., 15 (2008), 657-672.   Google Scholar

[31]

S. Narasimhan, Robust direct adaptive controller for the nonlinear highway bridge benchmark, Struct. Control Heal. Monit., 16 (2009), 599-612.   Google Scholar

[32]

S. NagarajaiahS. NarasimhanP. Tan and A. K. Agrawal, Benchmark structural control problem for a seismically excited highway bridge-Part Ⅲ: Phase Ⅱ Sample controller for the fully base-isolated case, Struct. Control Heal. Monit., 16 (2009), 549-563.   Google Scholar

[33]

X. L. NingP. TanD. Y. Huang and F. L. Zhou, Application of adaptive fuzzy sliding mode control to a seismically excited highway bridge, Struct. Control Heal. Monit., 16 (2009), 207-216.   Google Scholar

[34]

Y. OhtoriR. E. ChristensonB. F. Spencer and S. J. Dyke, Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 366-385.   Google Scholar

[35]

A. PreumontM. VoltanA. SangiovanniB. Mokrani and D. Alaluf, Active tendon control of suspension bridges, Smart Struct. Syst., 18 (2016), 31-52.   Google Scholar

[36]

A. SadollahH. EskandarA. Bahreininejad and J. H. Kim, Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures, Comput. Struct., 149 (2015), 1-16.   Google Scholar

[37]

A. SahaP. Saha and P. S. Kumar, Polynomial friction pendulum isolators (PFPIs) for seismic performance control of benchmark highway bridge, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.   Google Scholar

[38]

B. F. SpencerS. J. Dyke and H. S. Deoskar, Benchmark problems in structural control: Part Ⅰ Active Mass Driver system, Earthq. Eng. Struct. Dyn., 27 (1998), 1127-1139.   Google Scholar

[39]

P. Tan and A. K. Agrawal, Benchmark structural control problem for a seismically excited highway bridge, Part Ⅱ : Phase Ⅰ Sample control designs, Struct. Control Heal. Monit., 129 (2009), 857-872.   Google Scholar

[40]

J. N. YangA. K. AgrawalB. Samali and J. C. Wu, Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 437-446.   Google Scholar

Figure 1.  Elevation and plan views of $ 91/5 $ over-crossing[1]
Figure 2.  Finite element model of the bridge
Figure 3.  Tug of war tournament
Figure 4.  An idealized framework of tug of war [20]
Figure 5.  Membership functions of earthquake observer
Figure 6.  Input membership functions in ANFIS controller (Normalized displacement or Normalized acceleration)
Figure 7.  ANFIS configuration of the proposed controller
Figure 8.  The applied methodology to design a nero-fuzzy optimized controller
Figure 9.  F-ANFIS controller optimization under N.P.Spr. earthquake with a factor of 1.5 and J1 index
Figure 10.  N-ANFIS controller optimization under Northridge earthquake with a factor of 1.5 and J1 index
Figure 11.  The J1 index comparison among the different control methods
Figure 12.  The J3 index comparison among the different control methods
Figure 13.  The J4 index comparison among the different control methods
Figure 14.  A view of the results of the Friedman's test
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
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
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 $1.5
J1 1.1336 1.1295 0.8895 0.9459
J3 0.5983 0.5467 0.8763 0.8543
J5 0.3347 0.2733 0.5826 0.6372
Optimization by minimizing criterion J1
Earthquake EL-Ce$ \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 $1.5
J1 1.1336 1.1295 0.8895 0.9459
J3 0.5983 0.5467 0.8763 0.8543
J5 0.3347 0.2733 0.5826 0.6372
Table 3.  The mean of criteria J1, J3 and J5 in a Near-field earthquake, for different optimization scenarios of ANFIS controller (N-ANFIS).
Optimization by minimizing criterion J1
Earthquake Northridge$ \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 $1.5
J1 0.7466 0.7389
J3 0.4038 0.6089
J5 0.3957 0.4782
Optimization by minimizing criterion J1
Earthquake Northridge$ \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
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
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
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
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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