Ranking of design scenarios of TMD for seismically excited structures using TOPSIS

doi:10.1007/s11709-020-0671-y

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (6) : 1372-1386 https://doi.org/10.1007/s11709-020-0671-y

RESEARCH ARTICLE

Ranking of design scenarios of TMD for seismically excited structures using TOPSIS

Sadegh ETEDALI(

)

Department of Civil Engineering, Birjand University of Technology, Birjand 97175-569, Iran

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Abstract

In this paper, design scenarios of a tuned mass damper (TMD) for seismically excited structures are ranked. Accordingly, 10 design scenarios in two cases, namely unconstrained and constrained for the maximum TMD, are considered in this study. A free search of the TMD parameters is performed using a particle swarm optimization (PSO) algorithm for optimum tuning of TMD parameters. Furthermore, nine criteria are adopted with respect to functional, operational, and economic views. A technique for order performance by similarity to ideal solution (TOPSIS) is utilized for ranking the adopted design scenarios of TMD. Numerical studies are conducted on a 10-story building equipped with TMD. Simulation results indicate that the minimization of the maximum story displacement is the optimum design scenario of TMD for the seismic-excited structure in the unconstrained case for the maximum TMD stroke. Furthermore, H₂ of the displacement vector of the structure exhibited optimum ranking among the adopted design scenarios in the constrained case for the maximum TMD stroke. The findings of this study can be useful and important in the optimum design of TMD parameters with respect to functional, operational, and economic perspectives.

Keywords seismic-excited building TMD optimum design PSO design scenario TOPSIS

Corresponding Author(s): Sadegh ETEDALI

Just Accepted Date: 30 October 2020 Online First Date: 21 December 2020 Issue Date: 12 January 2021

Cite this article:

Sadegh ETEDALI. Ranking of design scenarios of TMD for seismically excited structures using TOPSIS[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1372-1386.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0671-y
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I6/1372

scenario	objective function
A₁	$m i n i m i z e : 1 2 π ∫ − ∞ ∞ T r a c e [G D i s p (j ω) T G D i s p (j ω)] d ω 1 2 π ∫ − ∞ ∞ T r a c e [G D i s p (j ω) T G D i s p (j ω)] d ω$
A₂	$m i n i m i z e : 1 2 π ∫ − ∞ ∞ T r a c e [G D r i f t (j ω) T G D r i f t (j ω)] d ω 1 2 π ∫ − ∞ ∞ T r a c e [G D r i f t (j ω) T G D r i f t (j ω)] d ω$
A₃	$m i n i m i z e : s u p ω σ max ? [G D i s p (j ω)] * s u p ω σ max ? [G D i s p (j ω)]$
A₄	$m i n i m i z e : s u p ω σ max ? [G D r i f t (j ω)] s u p ω σ max ? [G D r i f t (j ω)]$
A₅	$m i n i m i z e : max ? t ‖ x ¨ i (t) ‖ max ? t ‖ x ¨ ¯ ? (t) ‖, ? i = 1, ..., N$
A₆	$m i n i m i z e : max ? t ‖ ∑ i m i x ¨ i (t) ‖ max ? t ‖ ∑ i m i x ¨ ¯ i (t) ‖, ? i = 1, ..., N$
A₇	$m i n i m i z e :$ $max ? t ‖ ∫ 0 t f (X T K X + X T M X) d t ‖ max ? t ‖ ∫ 0 t f (X T K X + X T M X) d t ‖$
A₈	$m i n i m i z e : max ? t ‖ x i (t) ‖ max ? t ‖ x ¯ i (t) ‖, ? i = 1, ..., N$
A₉	$m i n i m i z e : max ? t ‖ d i (t) ‖ max ? t ‖ d ¯ i (t) ‖, ? i = 1, ..., N$
A₁₀	$m i n i m i z e :$ $max ? t ‖ ∫ 0 t f X T M r x ˙ g d t ‖ max ? t ‖ ∫ 0 t f X T M r x g d t ‖$

Tab.1 The design scenarios of TMD for the unconstrained case

criteria	definition
C1	$(m T M D ?) O p t ? (m T M D ?) max ? × 100$
C₂	$(c T M D ?) O p t ? (c T M D ?) max ? × 100$
C₃	$(k T M D ?) O p t ? (k T M D ?) max ? × 100$
C₄	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ x i (t) ‖ max ? t ‖ x ¯ i (t) ‖) × 100], i = 1, …, N$
C₅	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ x i (t) ‖ max ? t ‖ x ¯ i (t) ‖) × 100], i = 1, …, N$
C₆	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ x ¨ i (t) ‖ max ? t ‖ x ¨ ¯ i (t) ‖) × 100], i = 1, …, N$
C₇	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ ∑ i m i x ¨ i (t) ‖ max ? t ‖ ∑ i m i x ¨ ¯ i (t) ‖) × 100], i = 1, …, N$
C₈	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ ∫ 0 t f X ˙ T M r x ¨ g d t ‖ max ? t ‖ ∫ 0 t f X ˙^T M r x ¨ g d t ‖) × 100], i = 1, …, N$
C₉	$A v e r a g e F o r j = 1 : 44 [(1 − max ? t ‖ ∫ 0 t f X ˙ T K X ˙ + X ˙ M X ¨ d t ‖ max ? t ‖ ∫ 0 t f (X ˙^T K X ˙^+ X ˙^M X ¨^) d t ‖) × 100], i = 1, …, N$

Tab.2 The criteria adopted for utilization in TOPSIS

Tab.3 The detailed information of 44 far-field ground records [⁴⁷]

Fig.1 The convergence histories of the PSO for different alternative design scenarios in the unconstrained case for different design scenarios. (a) Scenario A1; (b) scenario A2; (c) scenario A3; (d) scenario A4; (e) scenario A5; (f) scenario A6; (g) scenario A7; (h) scenario A8; (i) scenario A9; (j) scenario A10.

Fig.2 The convergence histories of the PSO for different alternative design scenarios in the constrained case for different design scenarios. (a) Scenario A1; (b) scenario A2; (c) scenario A3; (d) scenario A4; (e) scenario A5; (f) scenario A6; (g) scenario A7; (h) scenario A8; (i) scenario A9; (j) scenario A10.

Fig.3 The cost function for different design scenarios of the TMD parameters.

Fig.4 The optimum damping coefficient of the TMD for different design scenarios.

Fig.5 The optimum stiffness coefficient of the TMD for different design scenarios.

Fig.6 The ranking of the design scenarios of TMD parameters for the unconstrained cases.

Fig.7 The ranking of the design scenarios of TMD parameters for the constrained cases.

Tab.4 The decision matrix for the unconstrained case

Tab.5 The decision matrix for the constrained case

Tab.6 Criteria weighting by Entropy method

scenario	unconstrained			constrained
scenario	$d i +$	$d i −$	$C C i +$	$d i +$	$d i −$	$C C i +$
A₁	0.119	0.142	0.546	0.005	0.056	0.916
A₂	0.120	0.141	0.541	0.005	0.055	0.915
A₃	0.159	0.112	0.414	0.031	0.034	0.523
A₄	0.161	0.110	0.405	0.031	0.035	0.531
A₅	0.083	0.205	0.712	0.051	0.017	0.249
A₆	0.094	0.159	0.628	0.051	0.015	0.228
A₇	0.097	0.161	0.625	0.048	0.023	0.324
A₈	0.036	0.224	0.862	0.049	0.020	0.294
A₉	0.083	0.199	0.705	0.049	0.019	0.282
A₁₀	0.055	0.243	0.816	0.055	0.005	0.091
A₁₁	0.083	0.172	0.674	–	–	–
A₁₂	0.242	0.063	0.207	–	–	–
A₁₃	0.112	0.148	0.569	–	–	–

Tab.7 The distance from ideal and nadir ideal solution and the closeness coefficient of each alternative for both unconstrained and constrained cases

Fig.8 Time histories of the top floor displacement during the Northridge earthquake.

Fig.9 Time histories of the first floor drift during the Northridge earthquake.

Fig.10 Time histories of the top floor acceleration during the Northridge earthquake.

Fig.11 Time histories of the base shear during the Northridge earthquake.

1	J P Den Hartog. Mechanical Vibrations. New York: Courier Corporation, 1985
2	A G Thompson. Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system. Journal of Sound and Vibration, 1981, 77(3): 403–415 https://doi.org/10.1016/S0022-460X(81)80176-9
3	G B Warburton. Optimum absorber parameters for various combinations of response and excitation parameters. Earthquake Engineering & Structural Dynamics, 1982, 10(3): 381–401 https://doi.org/10.1002/eqe.4290100304
4	S V Bakre, R S Jangid. Optimum parameters of tuned mass damper for damped main system. Structural Control and Health Monitoring, 2007, 14(3): 448–470 https://doi.org/10.1002/stc.166
5	A Y T Leung, H Zhang. Particle swarm optimization of tuned mass dampers. Engineering Structures, 2009, 31(3): 715–728 https://doi.org/10.1016/j.engstruct.2008.11.017
6	J Salvi, E Rizzi. A numerical approach towards best tuning of Tuned Mass Dampers. In: The 25th International Conference on Noise and Vibration Engineering. Leuven, 2010, 17–19: 2419–2434
7	S Etedali, N Mollayi. Cuckoo search-based least squares support vector machine models for optimum tuning of tuned mass dampers. International Journal of Structural Stability and Dynamics, 2018, 18(2): 1850028 https://doi.org/10.1142/S0219455418500281
8	K Narmashiri, S M T Hosseini-Tabatabai. An energy dissipation device for earthquake/wind resistant buildings. LAP Lambert Academic Publishing, 2013
9	F Giuliano. Note on the paper “Optimum parameters of tuned liquid column-gas damper for mitigation of seismic-induced vibrations of offshore jacket platforms” by Seyed Amin Mousavi, Khosrow Bargi, and Seyed Mehdi Zahrai. Structural Control and Health Monitoring, 2013, 20(5): 852 https://doi.org/10.1002/stc.1499
10	A Farshidianfar, S Soheili. Ant colony optimization of tuned mass dampers for earthquake oscillations of high-rise structures including soil-structure interaction. Soil Dynamics and Earthquake Engineering, 2013, 51: 14–22 https://doi.org/10.1016/j.soildyn.2013.04.002
11	A Kaveh, S Mohammadi, O K Hosseini, A Keyhani, V R Kalatjari. Optimum parameters of tuned mass dampers for seismic applications using charged system search. Civil Engineering (Shiraz), 2015, 39(C1): 21–40
12	H Y Zhang, L J Zhang. Tuned mass damper system of high-rise intake towers optimized by improved harmony search algorithm. Engineering Structures, 2017, 138: 270–282 https://doi.org/10.1016/j.engstruct.2017.02.011
13	S M Nigdeli, G Bekdaş, X S Yang. Optimum tuning of mass dampers by using a hybrid method using harmony search and flower pollination algorithm. In: International Conference on Harmony Search Algorithm. Singapore: Springer, 2017, 222–231
14	G Bekdaş, S M Nigdeli, X S Yang. A novel bat algorithm based optimum tuning of mass dampers for improving the seismic safety of structures. Engineering Structures, 2018, 159: 89–98 https://doi.org/10.1016/j.engstruct.2017.12.037
15	M Yucel, G Bekdaş, S M Nigdeli, S Sevgen. Estimation of optimum tuned mass damper parameters via machine learning. Journal of Building Engineering, 2019, 26: 100847 https://doi.org/10.1016/j.jobe.2019.100847
16	S M Nigdeli, G Bekdas. Optimum tuned mass damper approaches for adjacent structures. Earthquakes and Structures, 2014, 7(6): 1071–1091 https://doi.org/10.12989/eas.2014.7.6.1071
17	S M Nigdeli, G Bekdas. Optimum design of multiple positioned tuned mass dampers for structures constrained with axial force capacity. Structural Design of Tall and Special Buildings, 2019, 28(5): e1593 https://doi.org/10.1002/tal.1593
18	Z Lu, K Li, Y Ouyang, J Shan. Performance-based optimal design of tuned impact damper for seismically excited nonlinear building. Engineering Structures, 2018, 160: 314–327 https://doi.org/10.1016/j.engstruct.2018.01.042
19	G Bekdaş, S M Nigdeli. Metaheuristic based optimization of tuned mass dampers under earthquake excitation by considering soil-structure interaction. Soil Dynamics and Earthquake Engineering, 2017, 92: 443–461 https://doi.org/10.1016/j.soildyn.2016.10.019
20	R N Jabary, S P G Madabhushi. Structure-soil-structure interaction effects on structures retrofitted with tuned mass dampers. Soil Dynamics and Earthquake Engineering, 2017, 100: 301–315 https://doi.org/10.1016/j.soildyn.2017.05.017
21	S Etedali, M Seifi, M Akbari. A numerical study on optimal FTMD parameters considering soil-structure interaction effects. Geomechanics and Engineering, 2018, 16(5): 527–538
22	J Salvi, F Pioldi, E Rizzi. Optimum tuned mass dampers under seismic soil-structure interaction. Soil Dynamics and Earthquake Engineering, 2018, 114: 576–597 https://doi.org/10.1016/j.soildyn.2018.07.014
23	M Shahi, M R Sohrabi, S Etedali. Seismic control of high-rise buildings equipped with ATMD including soil-structure interaction effects. Journal of Earthquake and Tsunami, 2018, 12(3): 1850010 https://doi.org/10.1142/S1793431118500100
24	E Nazarimofrad, S M Zahrai. Fuzzy control of asymmetric plan buildings with active tuned mass damper considering soil-structure interaction. Soil Dynamics and Earthquake Engineering, 2018, 115: 838–852 https://doi.org/10.1016/j.soildyn.2017.09.020
25	S Etedali, M Akbari, M Seifi. MOCS-based optimum design of TMD and FTMD for tall buildings under near-field earthquakes including SSI effects. Soil Dynamics and Earthquake Engineering, 2019, 119: 36–50 https://doi.org/10.1016/j.soildyn.2018.12.027
26	S Etedali. A new modified independent modal space control approach toward control of seismic-excited structures. Bulletin of Earthquake Engineering, 2017, 15(10): 4215–4243 https://doi.org/10.1007/s10518-017-0134-6
27	S Etedali, H Rakhshani. Optimum design of tuned mass dampers using multi-objective cuckoo search for buildings under seismic excitations. Alexandria Engineering Journal, 2018, 57(4): 3205–3218
28	F Sadek, B Mohraz, A W Taylor, R M Chung. A method of estimating the parameters of tuned mass dampers for seismic applications. Earthquake Engineering & Structural Dynamics, 1997, 26(6): 617–635 https://doi.org/10.1002/(SICI)1096-9845(199706)26:6<617::AID-EQE664>3.0.CO;2-Z
29	M N Hadi, Y Arfiadi. Optimum design of absorber for MDOF structures. Journal of Structural Engineering, 1998, 124(11): 1272–1280 https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1272)
30	C L Lee, Y T Chen, L L Chung, Y P Wang. Optimal design theories and applications of tuned mass dampers. Engineering Structures, 2006, 28(1): 43–53 https://doi.org/10.1016/j.engstruct.2005.06.023
31	S M Nigdeli, G Bekdaş. Optimum tuned mass damper design in frequency domain for structures. KSCE Journal of Civil Engineering, 2017, 21(3): 912–922
32	G Bekdaş, A E Kayabekir, S M Nigdeli, Y C Toklu. Transfer function amplitude minimization for structures with tuned mass dampers considering soil-structure interaction. Soil Dynamics and Earthquake Engineering, 2019, 116: 552–562 https://doi.org/10.1016/j.soildyn.2018.10.035
33	A H Heidari, S Etedali, M R Javaheri-Tafti. A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD. Frontiers of Structural and Civil Engineering, 2018, 12(1): 44–57 https://doi.org/10.1007/s11709-016-0382-6
34	E K Zavadskas, S Suūinskas, A Daniūnas, Z Turskis, H Sivilevičius. Multiple criteria selection of pile-column construction technology. Journal of Civil Engineering and Management, 2012, 18(6): 834–842 https://doi.org/10.3846/13923730.2012.744537
35	N Caterino, I Iervolino, G Manfredi, E Cosenza. Multi-criteria decision making for seismic retrofitting of RC structures. Journal of Earthquake Engineering, 2008, 12(4): 555–583 https://doi.org/10.1080/13632460701572872
36	N Caterino, I Iervolino, G Manfredi, E Cosenza. Comparative analysis of multi-criteria decision-making methods for seismic structural retrofitting. Computer-Aided Civil and Infrastructure Engineering, 2009, 24(6): 432–445 https://doi.org/10.1111/j.1467-8667.2009.00599.x
37	A M Billah, M S Alam. Performance-based prioritisation for seismic retrofitting of reinforced concrete bridge bent. Structure and Infrastructure Engineering, 2014, 10(8): 929–949 https://doi.org/10.1080/15732479.2013.772641
38	A Formisano, F M Mazzolani. On the selection by MCDM methods of the optimal system for seismic retrofitting and vertical addition of existing buildings. Computers & Structures, 2015, 159: 1–13 https://doi.org/10.1016/j.compstruc.2015.06.016
39	G Terracciano, G Di Lorenzo, A Formisano, R Landolfo. Cold-formed thin-walled steel structures as vertical addition and energetic retrofitting systems of existing masonry buildings. European Journal of Environmental and Civil Engineering, 2015, 19(7): 850–866 https://doi.org/10.1080/19648189.2014.974832
40	J Kennedy. Particle swarm optimization. Encyclopedia of Machine Learning. New York: Springer, 2010, 760–766
41	Y Shi. Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation. Seoul, 2001, 1: 81–86
42	Y Shi, R Eberhart. A modified particle swarm optimizer. In: International Conference on Evolutionary Computation Proceedings. IEEE, 1998, 69–73
43	C L Hwang, K Yoon. Multiple Attribute Decision Making. New York: Springer, 2012
44	O A Sianaki. Intelligent decision support system for energy management in demand response programs and residential and industrial sectors of the smart grid. Dissertation for the Doctoral Degree. Perth: Curtin University, 2015
45	C E Shannon. A mathematical theory of communication. Bell System Technical Journal, 1948, 27(3): 379–423 https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
46	M Behzadian, S Khanmohammadi Otaghsara, M Yazdani, J Ignatius. A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 2012, 39(17): 13051–13069 https://doi.org/10.1016/j.eswa.2012.05.056
47	FEMA P-695. Quantification of Building Seismic Performance Factors. Washington D.C.: Federal Emergency Management Agency, 2009
48	B Keshtegar, S Etedali. Nonlinear mathematical modeling and optimum design of tuned mass dampers using adaptive dynamic harmony search algorithm. Structural Control and Health Monitoring, 2018, 25(7): e2163 https://doi.org/10.1002/stc.2163

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