Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures


A developed comparative analysis of metaheuristic optimization algorithms has been used for optimal active control of structures. The linear quadratic regulator (LQR) has ignored the external excitation in solving the Riccati equation with no sufficient optimal results. To enhance the efficiency of LQR and overcome the non-optimality problem, six intelligent optimization methods including BAT, BEE, differential evolution, firefly, harmony search and imperialist competitive algorithm have been discretely added to wavelet-based LQR to seek the attained optimum feedback gains. The proposed approach has not required the solution of Riccati equation enabling the excitation effect in controlling process. Employing this advantage by each of six mentioned algorithms to three-story and eight-story structures under different earthquakes led to define (1) the best solution, (2) convergence rate and (3) computational effort of all methods. The purpose of this research is to study the aforementioned methods besides the superiority of ICA in finding the optimal responses for active control problem. Numerical simulations have confirmed that the proposed controller is enabling to significantly reduce the structural responses using less control energy compared to LQR.

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  1. 1.

    Ali Toghroli et al (2014) Prediction of shear capacity of channel shear connectors using the ANFIS model. Steel Compos Struct 17(5):623–639

    Google Scholar 

  2. 2.

    Safa M et al (2016) Potential of adaptive neuro fuzzy inference system for evaluating the factors affecting steel-concrete composite beam’s shear strength. Steel Compos Struct Int J 21(3):679–688

    Google Scholar 

  3. 3.

    Mohammadhassani M et al (2015) Fuzzy modelling approach for shear strength prediction of RC deep beams. Smart Struct Syst 16(3):497–519

    Google Scholar 

  4. 4.

    Mansouri I et al (2017) Analysis of influential factors for predicting the shear strength of a V-shaped angle shear connector in composite beams using an adaptive neuro-fuzzy technique. J Intell Manuf 1–11

  5. 5.

    Toghroli A (2015) Applications of the ANFIS and LR models in the prediction of shear connection in composite beams. Jabatan Kejuruteraan Awam, Fakulti Kejuruteraan, Universiti Malaya

  6. 6.

    Aghakhani M et al (2015) A simple modification of homotopy perturbation method for the solution of Blasius equation in semi-infinite domains. Math Prob Eng 2015:7

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Toghroli A et al (2016) Potential of soft computing approach for evaluating the factors affecting the capacity of steel–concrete composite beam. J Intell Manuf 29:1–9

    Google Scholar 

  8. 8.

    Sadeghipour Chahnasir E et al (2018) Application of support vector machine with firefly algorithm for investigation of the factors affecting the shear strength of angle shear connectors. Smart Struct Syst 22(4):413–424

    Google Scholar 

  9. 9.

    Safa M et al (2016) Potential of adaptive neuro fuzzy inference system for evaluating the factors affecting steel–concrete composite beam’s shear strength. Steel Compos Struct 21(3):679–688

    Google Scholar 

  10. 10.

    Mansouri I et al (2016) Strength prediction of rotary brace damper using MLR and MARS. Struct Eng Mech 60(3):471–488

    Google Scholar 

  11. 11.

    Toghroli A et al (2018) Evaluation of the parameters affecting the Schmidt rebound hammer reading using ANFIS method. Comput Concr 21(5):525–530

    Google Scholar 

  12. 12.

    Sari PA, et al (2018) An intelligent based-model role to simulate the factor of safe slope by support vector regression. Eng Comput

  13. 13.

    Sedghi Y et al (2018) Application of ANFIS technique on performance of C and L shaped angle shear connectors. Smart Struct Syst 22(3):335–340

    Google Scholar 

  14. 14.

    Shariat M, Shariati M (2018) Computational Lagrangian multiplier method by using for optimization and sensitivity analysis of rectangular reinforced concrete beams. Steel Compos Struct 29:243–256

    Google Scholar 

  15. 15.

    Grandhi RV (1990) Optimum design of space structures with active and passive damping. Eng Comput 6(3):177–183

    Google Scholar 

  16. 16.

    Hadi MN, Uz ME (2015) Investigating the optimal passive and active vibration controls of adjacent buildings based on performance indices using genetic algorithms. Eng Optim 47(2):265–286

    MathSciNet  Google Scholar 

  17. 17.

    Amini F, Tavassoli MR (2005) Optimal structural active control force, number and placement of controllers. Eng Struct 27(9):1306–1316

    Google Scholar 

  18. 18.

    Datta T (2003) A state-of-the-art review on active control of structures. ISET J Earthq Technol 40(1):1–17

    Google Scholar 

  19. 19.

    Elseaidy WM, Baugh JW, Cleaveland R (1996) Verification of an active control system using temporal process algebra. Eng Comput 12(1):46–61

    Google Scholar 

  20. 20.

    Liu J, Wang Y (2008) Design approach of weighting matrices for LQR based on multi-objective evolution algorithm. In: 2008 International conference on information and automation (ICIA). IEEE, Changsha, China, pp 1188–1192

  21. 21.

    Wang W et al (2012) Weight optimization for LQG controller based on the artificial bee colony algorithm. AASRI Procedia 3:686–693

    Google Scholar 

  22. 22.

    Wang H, et al (2013) Optimization of LQR controller for inverted pendulum system with artificial bee colony algorithm. In: Proceedings of the 2013 international conference on advanced mechatronic systems 2013. IEEE, Louyang, China, pp 158–162

  23. 23.

    Bottura CP, da Fonseca Neto J (1999) Parallel eigenstructure assignment via LQR design and genetic algorithms. In: Proceedings of the 1999 American control conference. IEEE, San Diego, CA, USA

  24. 24.

    Bottura CP, da Fonseca Neto JV (2000) Rule-based decision-making unit for eigenstructure assignment via parallel genetic algorithm and LQR designs. In: Proceedings of the 2000 American control conference. IEEE, Chicago, IL, USA

  25. 25.

    Shen P (2014) Application of genetic algorithm optimization LQR weighting matrices control inverted pendulum. Appl Mech Mater 543–547:1274–1277

    Google Scholar 

  26. 26.

    Joghataie A, Mohebbi M (2012) Optimal control of nonlinear frames by Newmark and distributed genetic algorithms. Structl Des Tall Spec Build 21(2):77–95

    Google Scholar 

  27. 27.

    Petković D, Ćojbašič Ž, Nikolić V (2013) Adaptive neuro-fuzzy approach for wind turbine power coefficient estimation. Renew Sustain Energy Rev 28:191–195

    Google Scholar 

  28. 28.

    Petković D et al (2014) Adaptive neuro-fuzzy maximal power extraction of wind turbine with continuously variable transmission. Energy 64:868–874

    Google Scholar 

  29. 29.

    Petković D et al (2014) Adapting project management method and ANFIS strategy for variables selection and analyzing wind turbine wake effect. Nat Hazards 74(2):463–475

    Google Scholar 

  30. 30.

    Nikoli V et al (2017) Wind speed parameters sensitivity analysis based on fractals and neuro-fuzzy selection technique. Knowl Inf Syst 52(1):255–265

    Google Scholar 

  31. 31.

    Petković D, Pavlović NT, Ćojbašić Ž (2016) Wind farm efficiency by adaptive neuro-fuzzy strategy. Int J Electr Power Energy Syst 81:215–221

    Google Scholar 

  32. 32.

    Bishop J, Striz A (2004) On using genetic algorithms for optimum damper placement in space trusses. Struct Multidiscip Optim 28(2–3):136–145

    Google Scholar 

  33. 33.

    Singh MP, Moreschi LM (2002) Optimal placement of dampers for passive response control. Earthq Eng Struct Dyn 31(4):955–976

    Google Scholar 

  34. 34.

    Cha Y-J et al (2012) Multi-objective genetic algorithms for cost-effective distributions of actuators and sensors in large structures. Expert Syst Appl 39(9):7822–7833

    Google Scholar 

  35. 35.

    Amini F, Hazaveh NK, Rad AA (2013) Wavelet PSO-based LQR algorithm for optimal structural control using active tuned mass dampers. Comput-Aid Civ Infrastruct Eng 28(7):542–557

    Google Scholar 

  36. 36.

    Aghajanian S et al (2014) Optimal control of steel structures by improved particle swarm. Int J Steel Struct 14(2):223–230

    Google Scholar 

  37. 37.

    Amini F, Ghaderi P (2012) Optimal locations for MR dampers in civil structures using improved Ant Colony algorithm. Opt Control Appl Methods 33(2):232–248

    MathSciNet  MATH  Google Scholar 

  38. 38.

    Bekdaş G, Nigdeli SM (2011) Estimating optimum parameters of tuned mass dampers using harmony search. Eng Struct 33(9):2716–2723

    Google Scholar 

  39. 39.

    Amini F, Ghaderi P (2013) Hybridization of harmony search and ant colony optimization for optimal locating of structural dampers. Appl Soft Comput 13(5):2272–2280

    Google Scholar 

  40. 40.

    Aydin E (2012) Optimal damper placement based on base moment in steel building frames. J Constr Steel Res 79:216–225

    Google Scholar 

  41. 41.

    Mohebbi M, Joghataie A (2012) Designing optimal tuned mass dampers for nonlinear frames by distributed genetic algorithms. Struct Des Tall Spec Build 21(1):57–76

    Google Scholar 

  42. 42.

    Zarbaf SEHAM et al (2017) Stay cable tension estimation of cable-stayed bridges using genetic algorithm and particle swarm optimization. J Bridge Eng 22(10):05017008

    Google Scholar 

  43. 43.

    Chen X et al (2018) Prediction of shear strength for squat RC walls using a hybrid ANN–PSO model. Eng Comput 34(2):367–383

    Google Scholar 

  44. 44.

    Tian H, Shu J, Han L (2018) The effect of ICA and PSO on ANN results in approximating elasticity modulus of rock material. Eng Comput 35:1–10

    Google Scholar 

  45. 45.

    Sierra MR, Coello CAC (2005) Improving PSO-based multi-objective optimization using crowding, mutation and ∈-dominance. In: International conference on evolutionary multi-criterion optimization. Springer, New York

  46. 46.

    Leung A, Zhang H (2009) Particle swarm optimization of tuned mass dampers. Eng Struct 31(3):715–728

    Google Scholar 

  47. 47.

    Özsarıyıldız ŞS, Bozer A (2015) Finding optimal parameters of tuned mass dampers. Struct Des Tall Spec Build 24(6):461–475

    Google Scholar 

  48. 48.

    Bagheri A, Amini F (2013) Control of structures under uniform hazard earthquake excitation via wavelet analysis and pattern search method. Struct Control Health Monit 20(5):671–685

    Google Scholar 

  49. 49.

    Amini F, Bagheri A (2014) Optimal control of structures under earthquake excitation based on the colonial competitive algorithm. Struct Des Tall Spec Build 23(7):500–511

    Google Scholar 

  50. 50.

    Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Google Scholar 

  51. 51.

    Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, New York, pp 65–74

  52. 52.

    Varaee H, Ghasemi MR (2017) Engineering optimization based on ideal gas molecular movement algorithm. Eng Comput 33(1):71–93

    Google Scholar 

  53. 53.

    Ghasemi MR, Varaee H (2017) A fast multi-objective optimization using an efficient ideal gas molecular moment algorithm. Eng Comput 33(3):477–496

    Google Scholar 

  54. 54.

    Gendreau M, Potvin J-Y (2010) Handbook of metaheuristics, vol 2. Springer, New York

    Google Scholar 

  55. 55.

    Yang X-S (2013) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29(2):175–184

    Google Scholar 

  56. 56.

    Ohtori Y et al (2004) Benchmark control problems for seismically excited nonlinear buildings. J Eng Mech 130(4):366–385

    Google Scholar 

  57. 57.

    Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE Congress on evolutionary computation (CEC). IEEE, Singapore, pp 4661–4667

  58. 58.

    Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  59. 59.

    Pham D, et al (2005) The bees algorithm. Technical note. Manufacturing Engineering Centre, Cardiff University, UK, pp 1–57

  60. 60.

    Yang X-S (2008) Firefly algorithm. In: Nature-inspired metaheuristic algorithms. Luniver Press, pp 79–90

  61. 61.

    Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Google Scholar 

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Katebi, J., Shoaei-parchin, M., Shariati, M. et al. Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures. Engineering with Computers 36, 1539–1558 (2020).

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  • Active control
  • Metaheuristic optimization algorithm
  • Linear quadratic regulator (LQR)
  • Discrete wavelet transform (DWT)