Reliability-Based Optimum Design of Dome Truss Structures through Enhanced Vibration Particle System

Document Type : Regular Paper


1 Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran

2 Department of Civil Engineering, Faculty of Engineering, University of Qom, Qom, Iran


Recent years have seen a significant increase in structural engineers' interest in the assessment of reliability and structural safety. The Reliability-Based Design Optimization (RBDO) method has been utilized to create the most efficient and safe design of structures. Although there have been several theoretical advances in reliability analysis, computational barriers still occur in realistic problems. The purpose of this paper is to provide a process for the optimization of dome truss structures based on reliability. For this purpose, a flowchart including the process of Deterministic Design Optimization (DDO) and RBDO was presented. An evaluation of the reliability of the structure is made by using random variables to represent uncertain parameters. Throughout this study, random variables such as the module of elasticity, material density, and the cross-sectional area of the elements are considered. The deterministic constraints for DDO are the vertical displacement of free nodes and the demand-capacity ratio of all members. Also, reliability index 3 is set as the minimum target reliability index. Meta-heuristic algorithms can be used to achieve optimal design and appropriate safety since mathematical calculations are time-consuming. As part of this study, the Enhanced Vibration Particle System (EVPS) and Vibration Particle System (VPS) have been applied to DDO (incorporating reliability assessment) and RBDO of three dome trusses. The results were obtained using the processes of RBDO and DDO without any deviation in the acceptable space. The solution of RBDO will increase the weight and safety of structures.


Main Subjects

[1] Cornell, C.A., (1969).  "A probability-based structural code."  Journal Proceedings, Vol. 66, Issue. 12, pp. 974_985.
[2] Hasofer, A.M., Lind, N. C (1974). "Exact and invariant second-moment code format. " Journal of the Engineering Mechanics, Vol. 100, Issue. 1, pp. 111–121.
[3] Keshtegar, B., Meng D., Seghier M., Xiao M., Trung N., Bui D. (2021).  "A hybrid sufficient performance measure approach to improve robustness and efficiency of reliability-based design optimization." Engineering with Computers, Vol. 37, Issue. 3, pp. 1695–1708.
[4] Abid, F., Hami, A., Merzouki, T., Walha, L. Haddar, M. (2021).  "An approach for the reliability-based design optimization of shape memory alloy structure." Mechanics Based Design of Structures and Machines, Vol. 49, Issue. 2, pp. 155_171.
[5] Zhu, S., Keshtgar, B., Trung, N., Yaseen, Z., Bui, D. (2021).  "Reliability-based structural design optimization: hybridized conjugate mean value approach." Engineering with Computers, Vol. 37, Issue. 1,  pp. 381–394.
[6] Hao, P., Yang, H., Wang, Y., Liu, X., Wang, B., Li, G. (2021).  "Efficient reliability-based design optimization of composite structures via isogeometric analysis." Reliability Engineering & System Safety, Vol. 209, pp. 107465.
[7] Duy, T., Duong, D., Huu, V., Thoi, N. (2020).  "An Effective Couple Method for Reliability-Based Multi-Objective Optimization of Truss Structures with Static and Dynamic Constraints." International Journal of Computational Methods, Vol. 17, Issue. 6, pp. 1950016.
[8] Das, S., Saha, P. (2021).  "Performance of swarm intelligence based chaotic meta-heuristic algorithms in civil structural health monitoring." Measurement, Vol. 169, pp. 108533.
[9] Housseina, E., Saad, M.R., Hashim, F.A., Shaban, H., Hassaballah, M. (2020).  "Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems." Engineering Applications of Artificial Intelligence, Vol. 94, pp. 103731.
[10] Ficarella, E., Lamberti, L., Degertekin, F.O. (2021).  "Comparison of three novel hybrid metaheuristic algorithms for structural optimization problems." Computers & Structures, Vol. 244, pp. 106395.
[11] Fathi, H., Hoseini Vaez, S.R., Zhang, Q., Alavi, A.H. (2021).  "A new approach for crack detection in plate structures using an integrated extended finite element and enhanced vibrating particles system optimization methods." Structures, Vol. 29, pp. 638_651.
[12] Shabani, A, Asgarian, B, & Salido, M. (2019). "Search and rescue optimization algorithm for size optimization of truss structures with discrete variables. " Journal of Numerical Methods in Civil Engineering, Vol. 3, pp. 28_39.
[13] Shabani, A, Asgarian, B., Salido, M., & Gharebaghi, S. A. (2020). "Search and rescue optimization algorithm: A new optimization method for solving constrained engineering optimization problems". Expert Systems with Applications, Vol.161, 113698.
[14] Shabani, A., Asgarian, B., Gharebaghi, S. A., Salido, M. A., & Giret, A. (2019). "A new optimization algorithm based on search and rescue operations." Mathematical Problems in Engineering, Vol. 2019.
[15] Kaveh A, Hoseini Vaez SR, Hosseini P, Bakhtyari M. (2019). “Optimal design of steel curved roof frames by enhanced vibrating particles system algorithm”, Period Polytech Civil Eng; Vol. 63, Issue. 4, pp. 947-960.
[16] Asaad Samani, A., Fathali, M.A., Hoseini Vaez, S.R. (2022), “Optimal Seismic Design of 2D Steel Moment Frames with Set-back in Height Based on Structural Performance”, Journal of Rehabilitation in Civil Engineering, Vol. 10, Issue 2, pp. 35-55.
[17] Hosseini, P., Kaveh, A., Hatami, N., Hoseini Vaez, S.R. (2022), “The Optimization of Large-scale Dome Trusses on the Basis of the Probability of Failure”, International Journal of Optimization in Civil Engineering, Vol. 12, No. 3, pp. 457-475.
[18] Kaveh, A., Hosseini, P., Hatami, N., Hoseini Vaez, S.R. (2022), “Large-Scale Dome Truss Optimization With Frequency Constraints Using EVPS Algorithm”, International Journal of Optimization in Civil Engineering, Vol. 12, No. 1, pp. 105-123.
[19] Rezaee Manesh M., Ghasemi SH., Rezaee Manesh M. (2020). Dual Target Optimization of Two-Dimensional Truss Using Cost Efficiency and Structural Reliability Sufficiency. Journal of Soft Computing in Civil Engineering 4 (4), 96-109.
[20] Babaei A, Parker J, Moshaver P. Adaptive Neuro-Fuzzy Inference System (ANFIS) Integrated with Genetic Algorithm to Optimize Piezoelectric Cantilever-Oscillator-Spring Energy Harvester: Verification with Closed-Form Solution. Comput Eng Phys Model 2022;5:1–22.
[21] Li, F., Wu, T., Badiru, A., Hu, M. A. (2013).  "single-loop deterministic method for reliability-based design optimization." Engineering Optimization, Vol. 45, Issue. 4, pp. 435_458.
[22] Valdebenito, MA., Schuëller, GI. (2010).  "A survey on approaches for reliability-based optimization. " Structural and Multidisciplinary Optimization, Vol. 42, Issue. 5, pp. 645_663.
[23] Kaveh, A., Ilchi Ghazan, M. (2017).  "A new meta-heuristic algorithm: Vibrating particles system." Scientia Iranica. Transaction A, Civil Engineering, Vol. 24, Issue. 2, pp. 551_566.
[24] Kaveh, A., Khosravian, M. (2021).  "Size/Layout Optimization of Truss Structures Using Vibrating Particles System Meta-Heuristic Algorithm and its Improved Version." Periodica Polytechnica Civil Engineering, Vol. 66, Issue. 1, pp. 1_17.
[25] Kaveh, A., Hoseini Vaez, S. R., Hosseini P. (2018).  "Matlab Code for an Enhanced Vibrating Particles System Algorithm." International Journal of Optimization in Civil Engineering, Vol. 8, Issue. 3, pp. 104_414.
[26] Kaveh, A., Hoseini Vaez, S. R., Hosseini, P. (2019).  "Enhanced vibrating particles system algorithm for damage identication of truss structures." Scientia Iranica, Vol. 26, Issue. 1, pp.  246_256.
[27] Kaveh, A., Hoseini Vaez, S. R., Hosseini, P. (2019).  "Performance of the Modified Dolphin Monitoring Operator for Weight Optimization of Skeletal Structures." Periodica Polytechnica Civil Engineering, Vol. 63, Issue. 1, pp. 30_45.
[28] Hoseini Vaez, S. R., Fathali, M.A., Mehanpour, H., (2022). "A two-step approach for reliability-based design optimization in power transmission line towers." International Journal on Interactive Design and Manufacturing.
[29] Kaveh, A., Hoseini Vaez, S. R., Hosseini, P., Fathali, M. A (2021). " Heuristic Operator for Reliability Assessment of Frame Structures", Periodica Polytechnica Civil Engineering, Vol. 65, Issue. 3, pp. 702_716.
[30] LRFD-AISC. (2016), "Manual of steel construction- load and resistance factor design", In: LRFD-AISC, American Institute of Steel Construction (AISC), Chicago, Illinois, USA, pp.
[31] Kaveh, A., Talatahari, S. (2009).  "Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. " Computers and Structures, Vol. 87, Issue. 5-6, pp. 267_283.
[32] Saka, M.P., Ulker, M. (1992).  "Optimum Design of Geometrically Nonlinear Space Trusses. " Computers and Structures, Vol. 42, Issue. 3, pp. 289_299.
[33] Naderi, A., Sohrabia, M.R., Ghasemi, M.R., Dizangian, B. "Total and partial updating technique: A Swift Approach for Cross-Section and Geometry Optimization of Truss Structures." KSCE Journal of Civil Engineering, Vol. 24, Issue. 4, pp. 1219_1227.
[34] Mai, T.H., Kang, J., Lee, J. (2021).  "A machine learning-based surrogate model for optimization of truss structures with geometrically nonlinear behavior." Finite Elements in Analysis and Design, Vol. 196, pp. 103572.
 [35] Soh, C.K., Yang, J. (1996).  "Fuzzy conntrolled genetic algorithm search for shape optimization." Journal of Computing in Civil Engineering, Vol. 10, Issue. 2, pp. 143_150.
[36] Lee, K.S., Geem, Z.W. (2004).  "A new structural optimization method based on the harmony search algorithm." Computers and Structures, Vol. 82, Issue. (9-10), pp. 781_798.
[37] Kaveh, A., Khayatazad, M. (2013). "Ray optimization for size and shape optimization of truss structures." Computers and Structures, Vol. 117, pp. 82_94.
[38] Kaveh, A., Mirzaei, B., Jafarvand, A. (2015).  "An improved magnetic charged system search for optimization of truss structures with continuous and discrete variables." Applied Soft Computing, Vol. 28, pp. 400_410.
[39] Pierezan, J., Coelho, L.S., Mariani, V.C., Segundo, E.H.V., Prayogo, D. (2021).  "Chaotic coyote algorithm applied to truss optimization problems." Computers & Structures, Vol. 242, pp. 106353.
 [40] Grecoa, M., Gesualdoa, F.A.R., Venturinib, W.S., Coda, H.B. (2006).  "Nonlinear positional formulation for space truss analysis." Finite Elements in Analysis and Design, Vol. 42, Issue. 12, pp. 1079_1086.
[41] Saffari, H., Maghami, A., Mansouri, I. (2014).  "Preconditioned improved bi-conjugate gradient in nonlinear analysis of space trusses." Asian Journal of Civil Engineering, Vol. 15, Issue. 4, pp. 547_561.
[42] Krishnamoorthy, C.S., Ramesh, G., Dinesh, K.U. (1996).  "Post-buckling analysis of structures by three-parameter constrained solution techniques." Finite Elements in Analysis and Design, Vol. 22, Issue. 2, pp. 109_142.
[43] Dharapuram, S.J., Howard, I., Christiano, P. (1975).  "Nonlinear analysis of reticulated space trusses." Journal of the Structural Division, Vol. 101, Issue. 12, pp. 2641-2658.