-
Previous Article
An inexact alternating direction method of multipliers for a kind of nonlinear complementarity problems
- NACO Home
- This Issue
- Next Article
September
2021, 11(3): 333-351.
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 |
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:
Tug of war; Neural networks,
ANFIS,
Active control,
Nonlinear base-isolated structures,
Highway benchmark bridge.
Mathematics Subject Classification:
Primary: 93C42; Secondary: 47N10.
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 and Optimization,
2021, 11
(3)
: 333-351.
doi: 10.3934/naco.2020029
![]()
References:
| [1] |
A. K. Agrawal, P. Tan, S. 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.
|
| [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. |
| [3] |
J. M. Caicedo, S. J. Dyke, S. J. Moon, L. A. Bergman, G. Turan and S. Hague,
Phase Ⅱ benchmark control problem for seismic response of cable-stayed bridges, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.
|
| [4] |
M. Dehghani, A. 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.
|
| [5] |
S. J. Dyke, J. M. Caicedo, G. Turan, L. A. Bergman and S. Hague,
Phase Ⅰ benchmark control system for seismic response of cable-stayed bridges, J. Struct. Eng., 129 (2003), 857-872.
|
| [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. |
| [7] |
O. K. Erol and I. Eksin,
A new optimization method: Big BangBig Crunch, Adv. Eng. Softw., 37 (2006), 106-111.
|
| [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.
|
| [9] |
A. Goli, H. Khademi Zareh, R. 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.
|
| [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. |
| [11] |
G. Heo, C. Kim, S. Jeon, C. Lee and J. Jeon,
A hybrid seismic response control to improve performance of a two-span bridge, Struct. Eng. Mech., 61 (2009), 675-684.
|
| [12] |
R. S. Jangid and J. M. Kelly,
Base isolation for near-fault motions, Earthq. Eng. Struct. Dyn., 35 (2001), 691-707.
|
| [13] |
S. Jaypuria, M. T. Ranjan and O. Jaypuria,
Metaheuristic tuned ANFIS model for input-output modeling of friction stir welding, Materials Today: Proceedings, 18 (2019), 3922-3930.
|
| [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). |
| [15] |
A. Kaveh and N. Khayatazad,
A new meta-heuristic method: ray optimization, Comput. Struct., 59 (2012), 283-294.
|
| [16] |
A. Kaveh, S. M. Motie and M. Moslehi,
Magnetic charged system search: a new meta-heuristic algorithm for optimization, Acta Mech., 224 (2014), 85-107.
|
| [17] |
A. Kaveh and N. Farhoudi,
A new optimization method: dolphin echolocation, Adv. Eng. Softw., 59 (2013), 53-70.
|
| [18] |
A. Kaveh and A. Zolghadr,
Democratic PSO for truss layout and size optimization with frequency constraints, Comput. Struct., 130 (2014), 10-21.
|
| [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. |
| [20] |
A. Kaveh and A. Zolghadr,
A novel meta-heuristic algorithm: TUG OF WAR optimization, Iran Univ. Sci. Technol., 6 (2014), 469-492.
|
| [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.
|
| [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.
|
| [23] |
S. Khalilpourazari, H. R. Pasandideh, H. 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.
|
| [24] |
S. Khalilpourazari and H. R. Pasandideh, Sinecosine crow search algorithm: theory and applications, Neural Comput. Appl., 1 (2019). |
| [25] |
S. Khalilpourazari, A. Mirzazadeh, G. 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. |
| [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.
|
| [27] |
M. J. Mahmoodabadi, F. Farhadi and S. Sampour,
Firefly algorithm based optimum design of vehicle suspension systems, Int. J. Dyn. Control., 7 (2019), 134-146.
|
| [28] |
G. P. Mavroeidis, G. 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.
|
| [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. |
| [30] |
S. Narasimhan, S. 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.
|
| [31] |
S. Narasimhan,
Robust direct adaptive controller for the nonlinear highway bridge benchmark, Struct. Control Heal. Monit., 16 (2009), 599-612.
|
| [32] |
S. Nagarajaiah, S. Narasimhan, P. 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.
|
| [33] |
X. L. Ning, P. Tan, D. 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.
|
| [34] |
Y. Ohtori, R. E. Christenson, B. F. Spencer and S. J. Dyke,
Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 366-385.
|
| [35] |
A. Preumont, M. Voltan, A. Sangiovanni, B. Mokrani and D. Alaluf,
Active tendon control of suspension bridges, Smart Struct. Syst., 18 (2016), 31-52.
|
| [36] |
A. Sadollah, H. Eskandar, A. 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.
|
| [37] |
A. Saha, P. 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.
|
| [38] |
B. F. Spencer, S. 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.
|
| [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.
|
| [40] |
J. N. Yang, A. K. Agrawal, B. Samali and J. C. Wu,
Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 437-446.
|
show all references
References:
| [1] |
A. K. Agrawal, P. Tan, S. 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.
|
| [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. |
| [3] |
J. M. Caicedo, S. J. Dyke, S. J. Moon, L. A. Bergman, G. Turan and S. Hague,
Phase Ⅱ benchmark control problem for seismic response of cable-stayed bridges, Earthq. Eng. Eng. Vib., 16 (2017), 827-840.
|
| [4] |
M. Dehghani, A. 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.
|
| [5] |
S. J. Dyke, J. M. Caicedo, G. Turan, L. A. Bergman and S. Hague,
Phase Ⅰ benchmark control system for seismic response of cable-stayed bridges, J. Struct. Eng., 129 (2003), 857-872.
|
| [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. |
| [7] |
O. K. Erol and I. Eksin,
A new optimization method: Big BangBig Crunch, Adv. Eng. Softw., 37 (2006), 106-111.
|
| [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.
|
| [9] |
A. Goli, H. Khademi Zareh, R. 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.
|
| [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. |
| [11] |
G. Heo, C. Kim, S. Jeon, C. Lee and J. Jeon,
A hybrid seismic response control to improve performance of a two-span bridge, Struct. Eng. Mech., 61 (2009), 675-684.
|
| [12] |
R. S. Jangid and J. M. Kelly,
Base isolation for near-fault motions, Earthq. Eng. Struct. Dyn., 35 (2001), 691-707.
|
| [13] |
S. Jaypuria, M. T. Ranjan and O. Jaypuria,
Metaheuristic tuned ANFIS model for input-output modeling of friction stir welding, Materials Today: Proceedings, 18 (2019), 3922-3930.
|
| [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). |
| [15] |
A. Kaveh and N. Khayatazad,
A new meta-heuristic method: ray optimization, Comput. Struct., 59 (2012), 283-294.
|
| [16] |
A. Kaveh, S. M. Motie and M. Moslehi,
Magnetic charged system search: a new meta-heuristic algorithm for optimization, Acta Mech., 224 (2014), 85-107.
|
| [17] |
A. Kaveh and N. Farhoudi,
A new optimization method: dolphin echolocation, Adv. Eng. Softw., 59 (2013), 53-70.
|
| [18] |
A. Kaveh and A. Zolghadr,
Democratic PSO for truss layout and size optimization with frequency constraints, Comput. Struct., 130 (2014), 10-21.
|
| [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. |
| [20] |
A. Kaveh and A. Zolghadr,
A novel meta-heuristic algorithm: TUG OF WAR optimization, Iran Univ. Sci. Technol., 6 (2014), 469-492.
|
| [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.
|
| [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.
|
| [23] |
S. Khalilpourazari, H. R. Pasandideh, H. 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.
|
| [24] |
S. Khalilpourazari and H. R. Pasandideh, Sinecosine crow search algorithm: theory and applications, Neural Comput. Appl., 1 (2019). |
| [25] |
S. Khalilpourazari, A. Mirzazadeh, G. 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. |
| [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.
|
| [27] |
M. J. Mahmoodabadi, F. Farhadi and S. Sampour,
Firefly algorithm based optimum design of vehicle suspension systems, Int. J. Dyn. Control., 7 (2019), 134-146.
|
| [28] |
G. P. Mavroeidis, G. 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.
|
| [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. |
| [30] |
S. Narasimhan, S. 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.
|
| [31] |
S. Narasimhan,
Robust direct adaptive controller for the nonlinear highway bridge benchmark, Struct. Control Heal. Monit., 16 (2009), 599-612.
|
| [32] |
S. Nagarajaiah, S. Narasimhan, P. 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.
|
| [33] |
X. L. Ning, P. Tan, D. 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.
|
| [34] |
Y. Ohtori, R. E. Christenson, B. F. Spencer and S. J. Dyke,
Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 366-385.
|
| [35] |
A. Preumont, M. Voltan, A. Sangiovanni, B. Mokrani and D. Alaluf,
Active tendon control of suspension bridges, Smart Struct. Syst., 18 (2016), 31-52.
|
| [36] |
A. Sadollah, H. Eskandar, A. 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.
|
| [37] |
A. Saha, P. 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.
|
| [38] |
B. F. Spencer, S. 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.
|
| [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.
|
| [40] |
J. N. Yang, A. K. Agrawal, B. Samali and J. C. Wu,
Benchmark control problems for seismically excited nonlinear buildings, J. Eng. Mech., 130 (2004), 437-446.
|
Figure 2.
Finite element model of the bridge
Figure 3.
Tug of war tournament
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 | |
| 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 | |
| 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 |
EL-Ce |
N.P.Spr. |
N.P.Spr. |
| 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 |
EL-Ce |
N.P.Spr. |
N.P.Spr. |
| 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 |
EL-Ce |
N.P.Spr. |
N.P.Spr. |
| 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 |
EL-Ce |
N.P.Spr. |
N.P.Spr. |
| 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 |
Northridge |
| J1 | 0.7321 | 0.7125 |
| J3 | 0.3988 | 0.3846 |
| J5 | 0.3833 | 0.3644 |
| Optimization by minimizing criterion J4 | ||
| Earthquake | Northridge |
Northridge |
| J1 | 0.7466 | 0.7389 |
| J3 | 0.4038 | 0.6089 |
| J5 | 0.3957 | 0.4782 |
| Optimization by minimizing criterion J1 | ||
| Earthquake | Northridge |
Northridge |
| J1 | 0.7321 | 0.7125 |
| J3 | 0.3988 | 0.3846 |
| J5 | 0.3833 | 0.3644 |
| Optimization by minimizing criterion J4 | ||
| Earthquake | Northridge |
Northridge |
| 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 | ||||||
| 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 | ||||||
| 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 | |
| [1] |
Juan J. Manfredi, Julio D. Rossi, Stephanie J. Somersille. An obstacle problem for Tug-of-War games. Communications on Pure and Applied Analysis, 2015, 14 (1) : 217-228. doi: 10.3934/cpaa.2015.14.217 |
| [2] |
Ángel Arroyo, Joonas Heino, Mikko Parviainen. Tug-of-war games with varying probabilities and the normalized p(x)-laplacian. Communications on Pure and Applied Analysis, 2017, 16 (3) : 915-944. doi: 10.3934/cpaa.2017044 |
| [3] |
Ivana Gómez, Julio D. Rossi. Tug-of-war games and the infinity Laplacian with spatial dependence. Communications on Pure and Applied Analysis, 2013, 12 (5) : 1959-1983. doi: 10.3934/cpaa.2013.12.1959 |
| [4] |
Yong Zhao, Qishao Lu. Periodic oscillations in a class of fuzzy neural networks under impulsive control. Conference Publications, 2011, 2011 (Special) : 1457-1466. doi: 10.3934/proc.2011.2011.1457 |
| [5] |
Mauro Maggioni, James M. Murphy. Learning by active nonlinear diffusion. Foundations of Data Science, 2019, 1 (3) : 271-291. doi: 10.3934/fods.2019012 |
| [6] |
Ying Sue Huang. Resynchronization of delayed neural networks. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 397-401. doi: 10.3934/dcds.2001.7.397 |
| [7] |
Jianping Zhou, Yamin Liu, Ju H. Park, Qingkai Kong, Zhen Wang. Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1569-1589. doi: 10.3934/dcdss.2020357 |
| [8] |
Xilin Fu, Zhang Chen. New discrete analogue of neural networks with nonlinear amplification function and its periodic dynamic analysis. Conference Publications, 2007, 2007 (Special) : 391-398. doi: 10.3934/proc.2007.2007.391 |
| [9] |
Leong-Kwan Li, Sally Shao, K. F. Cedric Yiu. Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm. Journal of Industrial and Management Optimization, 2011, 7 (2) : 385-400. doi: 10.3934/jimo.2011.7.385 |
| [10] |
Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139-148. doi: 10.3934/mbe.2014.11.139 |
| [11] |
Paolo Rinaldi, Heinz Schättler. Minimization of the base transit time in semiconductor devices using optimal control. Conference Publications, 2003, 2003 (Special) : 742-751. doi: 10.3934/proc.2003.2003.742 |
| [12] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
| [13] |
Suoqin Jin, Fang-Xiang Wu, Xiufen Zou. Domain control of nonlinear networked systems and applications to complex disease networks. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2169-2206. doi: 10.3934/dcdsb.2017091 |
| [14] |
Wenjun Liu, Hefeng Zhuang. Global attractor for a suspension bridge problem with a nonlinear delay term in the internal feedback. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 907-942. doi: 10.3934/dcdsb.2020147 |
| [15] |
Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar. Partitioned integrators for thermodynamic parameterization of neural networks. Foundations of Data Science, 2019, 1 (4) : 457-489. doi: 10.3934/fods.2019019 |
| [16] |
Ricai Luo, Honglei Xu, Wu-Sheng Wang, Jie Sun, Wei Xu. A weak condition for global stability of delayed neural networks. Journal of Industrial and Management Optimization, 2016, 12 (2) : 505-514. doi: 10.3934/jimo.2016.12.505 |
| [17] |
Benedetta Lisena. Average criteria for periodic neural networks with delay. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 761-773. doi: 10.3934/dcdsb.2014.19.761 |
| [18] |
Larry Turyn. Cellular neural networks: asymmetric templates and spatial chaos. Conference Publications, 2003, 2003 (Special) : 864-871. doi: 10.3934/proc.2003.2003.864 |
| [19] |
Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2021, 8 (2) : 131-152. doi: 10.3934/jcd.2021006 |
| [20] |
Leslaw Skrzypek, Yuncheng You. Feedback synchronization of FHN cellular neural networks. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6047-6056. doi: 10.3934/dcdsb.2021001 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]