Reliability-based multi-objective optimal design of spatial trusses using NSGA-II

Document Type : Research

Authors

1 Ph.D. Candidate, Civil Engineering Department, Shahrood University of Technology, Shahrood, Iran.

2 Associate professor, Civil Engineering Department, Shahrood University of Technology, Shahrood, Iran.

Abstract

This paper addresses a reliability-based multi-objective desgin method for spatial truss structures.The uncertainties of the applied load and the resistance of the truss members have been taken into account by generating a set of 50 random numbers. The failure probability of each truss member have been evaluated and consequently the failure probability of the entire truss system have been calculated considering as a series system. A multi-objective optimization problem has been defined with objective functions of truss weight and failure probability of the entire truss structure. The cross sectional area of the truss members have been considered as the design variables. The limitations of nodal displacements and allowable stress of the members have been defined as constraints. A 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the non-dominated sorting genetic algorithm II (NSGA-II). The results show effectivness and simlicity of the proposed method which can provide a wide range of optimal solutions through Pareto fronts. These optimal solutions can provide both safety and reliability for the truss structure. Also, the results indicate that the failure probability of the truss structure reduces by increasing the uncertainty level of load and resistance. 

Keywords

References

1. Schutte, JJ., & Groenwold, AA. "Sizing design of truss structures using particle swarms". Struct Multidisc Optim, vol. 25, 2003, p. 261-269.
https://doi.org/10.1007/s00158-003-0316-5
 
2. Lee, KS., & Geem, ZW. "A new structural optimization method based on the harmony search algorithm". Comput Struct, vol. 82, 2004, p. 781-798.
https://doi.org/10.1016/j.compstruc.2004.01.002
 
3. Camp, CV. "Design of space trusses using Big Bang-Big Crunch optimization". J Struct Eng, ASCE, vol. 133, 2007, p. 999-1008.
https://doi.org/10.1061/(ASCE)0733-9445(2007)133:7(999)
 
4. Kaveh, A., Farahmand Azar, B., & Talatahari, S. "Ant colony optimization for design of space trusses". Int J Space Struct, vol. 23, 2008, p. 167-181.
https://doi.org/10.1260/026635108786260956
 
5. Kaveh, A. & Talatahari, S. "A hybrid particle swarm and ant colony optimization for design of truss structures". Asian J Civil Eng, vol. 9, 2008, p. 329-348.
 
6. Kaveh, A. & Talatahari, S. "Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures". Comput Struct, vol. 87, 2009, p. 267-283.
https://doi.org/10.1016/j.compstruc.2009.01.003
 
7. Kaveh, A. & Talatahari, S. "Size optimization of space trusses Big Bang-Big Crunch algorithm". Comput Struct, vol. 87, 2009, p. 1129-1140.
https://doi.org/10.1016/j.compstruc.2009.04.011
 
8. Assimi, H., Jamali, A. & Nariman-zadeh, N. Sizing and topology optimization of truss structures using genetic programming. Swarm Evolut Comput, vol. 37, 2017, p. 90-103.
https://doi.org/10.1016/j.swevo.2017.05.009
 
9. Charan, PRS., Hui, NB. & Davim, JP. "Analysis and optimization of truss structures, constrained handling using genetic algorithm". J Appl Comput Mech, vol. 7, 2021, p. 1324-1333.
 
10. Millan-Paramo, C. & Filho, JEA. "Size and shape optimization of truss structures with natural frequency constraints using modified simulated annealing algorithm". Arabian J Sci Eng, vol. 45, 2020, p. 3511-3525.
https://doi.org/10.1007/s13369-019-04138-5
 
11. Papadrakakis, M., Lagaros, ND. & Plevris, V. "Design optimization of steel structures considering uncertainties". Eng Struct, vol. 27, 2005, p. 1408-1418.
https://doi.org/10.1016/j.engstruct.2005.04.002
 
12. Yadav, R. & Ganguli, R. "Reliability based and robust design optimization of truss and composite plate using particle swarm optimization". Mech Adv Mater Struct, 2020, p. 1-11.
 
13. Doltsinis, I. & Kang, Z. "Robust design of structures using optimization methods". Comp Methods Appl Mech Eng, vol. 193, 2004, p. 2221-2237.
https://doi.org/10.1016/j.cma.2003.12.055
 
14. Lee, KH. & Park, GJ. "Robust optimization considering tolerances of design variables". Comput Struct, vol. 79, 2001, p. 77-86.
https://doi.org/10.1016/S0045-7949(00)00117-6
 
15. Sandgren, E. & Cameron, TM. "Robust design optimization of structures through consideration of variation". Comput Struct, vol. 80, 2002, p. 1605-1613.
https://doi.org/10.1016/S0045-7949(02)00160-8
 
16. Babaei Semriomi, R. & Keyhani, A. "Reliability-based multi-objective design of spatial trusses using game theory and GA". Int J Optim Civil Eng, vol. 12, 2022, p. 185-199.
 
17. Nowak, AS. & Collins, KR. "Reliability of Structures, 2nd Edition". McGraw-Hill 2000.
 
18. Hasofer, AM. & Lind, N. "An exact and invariant first-order reliability format". J Eng Mech, vol. 100, 1974, p. 111-121.
https://doi.org/10.1061/JMCEA3.0001848
 
19. Mohebbi, M. & Bakhshinezhad, S. "Seismic risk-based optimal design og fluid viscous dampers for seismically excited nonlinear structures". J Num Meth Civ Eng, vol. 6, 2021, p. 14-24.
https://doi.org/10.52547/nmce.6.2.14
 
20. Mohebbi, M. & Bakhshinezhad, S. "Multiple performance criteria-based risk assessment for structures equipped with MR dampers". Earthg Struct, vol. 20, 2021, p. 495-512.
https://doi.org/10.1007/s11803-021-2032-9
 
21. Bakhshinezhad, S. & Mohebbi, M. "Multiple failure function based fragility curves for structures equipped with TMD".
 
22. Earthq Eng Eng Vib, vol. 20, 2021, p. 471-482.
https://doi.org/10.1007/s11803-021-2032-9
 
23. Rao, SS. "Optimization: Theory and Applications". Wiley: New York. 1984.
 
24. Irani H R, Kalatjari V R, Dibaei Bonab M. "Reliability based optimization of 3D steel moment frames considering axial force and biaxial bending moments interaction". Int J Optim Civil Eng, vol. 10, 2020, p. 137-155.
 
25. Gharebaghi, SA., Kaveh, A., M. A. Asl, " A new metaheuristic optimization algorithm using star graph ". J Comput Robot, vol. 12, 2019, p. 39-48.
 
26. Shabani, A., Asgarian, B. & Salido, M. "Search and rescue optimization algorithm for size optimization of truss structures with discrete variables". Int J Num Method Civil Eng, vol. 3, 2019, p. 28-39.
https://doi.org/10.29252/nmce.3.3.28
 
27. Shabani, A., Asgarian, B., Salido, M. & Gharebaghi, SA. "Search and rescue optimization algorithm: A new optimization method for solving constrained engineering optimization problems". Expert Systems Applications vol. 161, 2020, p. 113698.
https://doi.org/10.1016/j.eswa.2020.113698
 
28. Shabani, A., Asgarian, B., Gharebaghi, SA., Salido, M. & Giret, A. "A new optimization algorithm based on search and rescue operations." Math Prob Eng vol. 2019, 2019, p. 2482543.
https://doi.org/10.1155/2019/2482543
 
29. Holland, JH. "Adaptation in natural and artificial systems. Ann Arbor". The University of Michigan Press; 1975.
 
30. Bakhshinezhad, S. & Mohebbi, M. "Fragility curves for structures equipped with optimal SATMDs". Intern J Optimiz Civ Eng, vol. 9, 2019, p. 437-455.
 
31. Goldberg, DE. "Genetic algorithms in search, optimization and machine learning". Reading MA: Addison-Wesley; 1989.
 
32. Haimes, YY., Lasdon, LS. & Wismer, DA. "On a bi-criterion formulation of the problems of integrated system identification and system optimization". IEEE Trans Syst Man Cy, vol. 1, 1971, p. 296-297.
https://doi.org/10.1109/TSMC.1971.4308298
 
33. Srinivas, N. & Deb, K. "Multi-objective optimization using non-dominated sorting in genetic algorithms". Evol Comput, vol. 2, 1994, p. 221-248.
https://doi.org/10.1162/evco.1994.2.3.221
 
34. Deb, K., Pratap, A., Agarwal, S. & Meyarivan, T. "A fast and elitist multiobjective genetic algorithm: NSGA-II". IEEE T Evolut Comput, vol. 6, 2002, p. 182-197.
https://doi.org/10.1109/4235.996017
 
35. Deb, K. & Jain, H. "An evolutionary many-objective optimization algorithm using reference point-based non-dominated sorting approach, Part I: Solving problems with box constraints". IEEE T Evolut Comput, vol. 18, 2014, p. 577-601.
https://doi.org/10.1109/TEVC.2013.2281535
Numerical Methods in Civil Engineering
Volume 7, Issue 2
December 2022
Pages 68-76

Files

History

  • Receive Date: 12 January 2022
  • Revise Date: 29 May 2022
  • Accept Date: 20 June 2022

Share

How to cite

Statistics