Multi-objective Optimization of Steel Frames with Added Viscous Dampers using Imperialist Competitive Algorithm

Document Type : Original Article

Authors

Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

Abstract

Optimization is a big challenging task for engineers and designers. In practice, almost all of the engineering problems have more than one objective function, criterion to be optimized, therefore, multi-objective optimization procedure is necessary for many optimization problems. In this study, we presented the development of the Imperialistic Competitive Algorithm (ICA) to multi-objective optimal design of steel frames with dampers. Semi-active liquid viscous dampers are added to the steel frames to reduce the seismic response of structures subjected to earthquake loadings. The number and position of the dampers are considered as the design variables and the structural responses such as the acceleration of each floors, the maximum displacement of the top roof and the maximum relative displacement of the floors are the objective functions to be minimized simultaneously. A seven-story and a twelve-story 3D buildings are selected as the numerical examples to test the developed algorithm. The resultant Pareto-front sets are reported and discussed for the numerical examples. The obtained trade-offs demonstrate very smooth and reliable sets for all case studies. Meanwhile, the results indicate that the position of the dampers directly influences their effectiveness in decreasing the seismic response of structures. The maximum top floor displacement, the maximum story drifts and the maximum acceleration of each story have reduced in comparison to the uncontrolled condition, by respective values of 44.9%, 43.2% and 11.8%, for seven-story case study.

Highlights

  • Imperialistic Competitive Algorithm (ICA) developed to multi-objective optimal design of steel frames with dampers.
  • Trade-off between objective functions (displacement-acceleration and drift-acceleration) are illustrated for case studies.
  • The optimal number and location of the dampers are obtained for the numerical examples.

Keywords

Main Subjects


[1]      Holland JH. Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press; 1992.
[2]      Atashpaz-Gargari E, Lucas C. Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. 2007 IEEE Congr. Evol. Comput., IEEE; 2007, p. 4661–7. https://doi.org/10.1109/CEC.2007.4425083.
[3]      Kaveh A. Imperialist Competitive Algorithm. Adv. Metaheuristic Algorithms Optim. Des. Struct., Cham: Springer International Publishing; 2017, p. 353–73. https://doi.org/10.1007/978-3-319-46173-1_11.
[4]      Babaei M, Mollayi M. An improved constrained differential evolution for optimal design of steel frames with discrete variables. Mech Based Des Struct Mach 2020;48:697–723. https://doi.org/10.1080/15397734.2019.1657890.
[5]      Deb K, Agrawal S, Pratap A, Meyarivan T. Parallel Problem Solving from Nature PPSN VI. chapter A Fast Elit. Non-dominated Sorting Genet. Algorithm Multi-objectiveOptimization NSGA-II, Springer; 2000, p. 849–58.
[6]      Babaei M, Mollayi M. Multi-objective optimization of reinforced concrete frames using NSGA-II algorithm. Eng Struct Technol 2016;8:157–64. https://doi.org/10.3846/2029882X.2016.1250230.
[7]      Babaei M, Mollayi M. Multiobjective optimal design of reinforced concrete frames using two metaheuristic algorithms. J Eng Res 2021;9. https://doi.org/10.36909/jer.9973.
[8]      K. D. Multi-objective optimization using evolutionary algorithms. John-Wiley & Sons; 2001.
[9]      Babaei M, Sanaei E. Multi-objective optimal design of braced frames using hybrid genetic and ant colony optimization. Front Struct Civ Eng 2016;10:472–80. https://doi.org/10.1007/s11709-016-0368-4.
[10]     Babaei M. Multi-objective optimal number and location for steel outrigger-belt truss system. J Eng Sci Technol 2017;12:2599–612.
[11]     Kamgar R, Samea P, Khatibinia M. Optimizing parameters of tuned mass damper subjected to critical earthquake. Struct Des Tall Spec Build 2018;27:e1460. https://doi.org/10.1002/tal.1460.
[12]     Dadkhah M, Kamgar R, Heidarzadeh H, Jakubczyk-Gałczyńska A, Jankowski R. Improvement of Performance Level of Steel Moment-Resisting Frames Using Tuned Mass Damper System. Appl Sci 2020;10:3403. https://doi.org/10.3390/app10103403.
[13]     Khatibinia M, Gholami H, Kamgar R. Optimal design of tuned mass dampers subjected to continuous stationary critical excitation. Int J Dyn Control 2018;6:1094–104. https://doi.org/10.1007/s40435-017-0386-7.
[14]     Salimi M, Kamgar R, Heidarzadeh H. An evaluation of the advantages of friction TMD over conventional TMD. Innov Infrastruct Solut 2021;6:95. https://doi.org/10.1007/s41062-021-00473-5.
[15]     Kamgar R, Gholami F, Zarif Sanayei HR, Heidarzadeh H. Modified Tuned Liquid Dampers for Seismic Protection of Buildings Considering Soil–Structure Interaction Effects. Iran J Sci Technol Trans Civ Eng 2020;44:339–54. https://doi.org/10.1007/s40996-019-00302-x.
[16]     Symans MD, Constantinou MC. Semi-active control systems for seismic protection of structures: a state-of-the-art review. Eng Struct 1999;21:469–87. https://doi.org/10.1016/S0141-0296(97)00225-3.
[17]     Shames IH. Elastic and inelastic stress analysis. CRC Press; 1997.
[18]     Mathew L, Prabha C. Effect of fluid viscous dampers in multi-storeyed buildings. Impact Int J Res Eng Technol(IMPACT IJRET) 2014;2:59–64.
[19]     Lee D-G, Hong S, Kim J. Efficient siesmic analysis of building structures with added viscoelastic dampers. Eng Struct 2002;24:1217–27. https://doi.org/10.1016/S0141-0296(02)00058-5.
[20]     Liu J, Xia K, Zhu C. Intelligent Control Method of Structural Vibration Based on MR Damper. 2009 Second Int. Conf. Futur. Inf. Technol. Manag. Eng., IEEE; 2009, p. 320–2. https://doi.org/10.1109/FITME.2009.85.
[21]     Kurata N, Kobori T, Takahashi M, Niwa N, Midorikawa H. Actual seismic response controlled building with semi‐active damper system. Earthq Eng Struct Dyn 1999;28:1427–47.
[22]     Cu VH, Han B, Nguyen TN. Optimal parameters of viscous damper for hanged cables in arch bridges. KSCE J Civ Eng 2016;20:847–54. https://doi.org/10.1007/s12205-015-0771-8.
[23]     Sonmez M, Aydin E, Karabork T. Using an artificial bee colony algorithm for the optimal placement of viscous dampers in planar building frames. Struct Multidiscip Optim 2013;48:395–409. https://doi.org/10.1007/s00158-013-0892-y.
[24]     Amini F, Bagheri A. Optimal control of structures under earthquake excitation based on the colonial competitive algorithm. Struct Des Tall Spec Build 2014;23:500–11. https://doi.org/10.1002/tal.1055.