Bi-objective Optimization Design of Active and Nonlinear Vehicle Suspension System Under Combinatorial Random Road Profile

Document Type : Dynamics, Vibrations, and Control

Authors

1 M.Sc. Student, Department of mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran

2 Corresponding author: Assistant Professor, Department of mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran

Abstract

In this paper, effect of the different random road inputs in the form of combinatorial profile on the nonlinear and active quarter car model with two-degree of freedom has been analyzed. Bi-objective optimization processes using differential evolution algorithm with fuzzified mutation along with non-dominated sorting algorithm and crowding distance criterion have been carried out. Further, in current work, the hybrid usage of sliding mode control with skyhook and inertial delay control has been applied for modeling of the active suspension system with nonlinear parameters under the combination of three different random roads excitation, namely, class A, B and C. It is important to notice that the two objective functions which have been selected to be simultaneously optimized are, namely, vertical sprung mass acceleration and relative displacement between sprung mass and unsprung mass. The obtained results have been depicted in Pareto frontiers. Comparison of the results of this work with the ones in the literature has proved the superiority of methodology of this work. In fact, in 75% of outputs of application tests, the proposed design of this work has conquered the ones of previous works, and it shows the proper behavior of the suggested design of this work.

Highlights

  • Vehicle suspension design subject to road excitation using bi-objective optimization for achieving trade-off between ride comfort and road holding capability of vehicle
  • Applying combinatorial road profile in the form of random excitation

Keywords


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[1] Bouazara mohamed, J.Richard marc. An optimization method designed to improve 3-D vehicle comfort and road holding capability through the use of active and semi-active suspensions. European Journal of Mechanics - A/Solids. 2001;20: 509-520. DOI :10.1016/S0997-7538(01)01138-X.
[2] Hać A, Youn I. Optimal semi-active suspension with preview based on a quarter car model. Journal of Vibration and Acoustics. 1992 ;114(1):84-92. DOI :10.1115/1.2930239.
[3] Fleps-Dezasse M, Brembeck M. LPV Control of Full-Vehicle Vertical Dynamics using Semi-Active Dampers. 2016; 49(11):432-39. DOI :10.1016/ j.ifacol. 016.08.064.
[4] Yildirim Ş. Vibration control of suspension systems using a proposed neural network, Journal of Sound and Vibration. (2004); 277(4-5):1059–69. DOI :10.1016/j.jsv.2003.09.057.
[5] Mendoza R, Nawarecki M, Sename O, Dugard L, M'Saad M. An optimal control approach for the design of an active suspension system. IFAC Proceedings. 1998; 3(1): 43-8. DOI :10.1016/S1474-6670(17)42175-6.
[6] Sepehri B, Hemati A. Active Suspension vibration control using Linear H-Infinity and optimal control. International Journal of Automotive Engineering. 2014; 4: 805-11.
[7] Yagiz N, Hacioglu Y. Backstepping control of a vehicle with active suspensions. Control Engineering Practice. 2008; 16(12): 1457-67. DOI :10.1016/j.conengprac.2008.04.003.
[8] D'Amato F, Viassolo D. Fuzzy control for active suspensions, Mechatronics. 2000; 10: 897-920. DOI :10.1016/S0957-4158(99)00079-3.
[9] Slotine J, Sliding controller design for nonlinear systems. International Journal of Control.1984; 40(2):421-34. DOI :10.1080/00207178 408933284.
[10] Yoshimura T, Isari Y, Li Q, Hino J. Active suspension of motor coaches using skyhook damper and fuzzy logic control. Control Engineering Practice. 1997; DOI 5(2):175-84. DOI :10.1016/S0967-0661 (97)00224-4.
[11] Deshpande V, Shendge P, Phadke S. Active suspension systems for vehicles based on a sliding-mode controller in combination with inertial delay control, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. 2013; 227(5):675-90. DOI :10.1177/0954407012462 953.
[12] Salehpour M, Jamali, A, Bagheri A, Nariman-Zadeh N. Optimum sliding mode controller design based on skyhook model for nonlinear vehicle vibration model. Automotive Science and Engineering. 2017;7(4):2537-50. DOI :10.22068/ijae. 7.4.2537.
[13] Kitayama S, Arakawa M, Yamazaki K. Differential evolution as the global optimization technique and its application to structural optimization, Applied Soft Computing.2011; 11(4): 3792–803. DOI :10.1016/ j.asoc.2011.02.012.
[14] Srinivas N, Deb K. Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation. 1994;2(3):221–48. DOI :10.1162/evco.1994.2.3.221.
[15] Toffolo A, Benini E. Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms. Evolutionary Computation. 2003; 11(2): 151-67.
[16] Guo L X, Zhang L P. Robust control of active vehicle suspension under nonstationary running. Journal of Sound and Vibration. 2012;331(26):5824–37. DOI :10.1162/106365603766646816.
[17] Kim C, Ro P I. A sliding mode controller for vehicle active suspension systems with nonlinearities. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. 1998;212(20):79-92. DOI :10.1243/0954407981525 812.
[18] Nariman-Zadeh N, Salehpour M, Jamali A, Haghgoo E. Pareto optimization of a five degree of freedom vehicle vibration model using a multi-objective uniform-diversity genetic algorithm (MUGA). Engineering Applications of Artificial Intelligence 2010;23(54):543–51. DOI :10.1016/ j.engappai.2009.08.008.
[19] Jamali A, Rammohan Mallipeddi, Salehpour M, Bagheri A. Multi-objective differential evolution algorithm with fuzzy inference-based adaptive mutation factor for Pareto optimum design of suspension system. Swarm and Evolutionary Computation. 2020; 54:100666. DOI :10.1016/ j.swevo.2020.100666.
[20] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objective genetic algorithm: , IEEE Transactions on Evolutionary Computation. (2002); 6(2): 182-97. DOI :10.1109/4235.996017.
[21] Jamali A, Salehpour M, Nariman-zadeh N. Robust Pareto active suspension design for vehicle vibration model with probabilistic uncertain parameters. Multibody System Dynamics. 2013; 30(3):265-85. DOI :10.1007/s11044-012-9337-4.
[22] Mohammadmoradi S, Akbari A, Mirzaei M. Robust Model Predictive Control for Active Suspension System using Linear Matrix Inequalities. Modares Mechanical Engineering 2018; 17 (12) :183-192. DOR :20.1001.1.10275940.1396.17.12.48.0.
[23] Ramezani Moghadam A, Kebriaei H. Design and stability analysis of optimal controller and observer for Itô stochastic model of active vehicle suspension system. Journal of Control. 2019;13(3):71-83. DOR :20.1001.1.20088345.1398.13.3.4.9.
[24] Abdi B, Mirzaei M, Rafatnia S, Akbari Alvanagh A. Analytical Design of Constrained Nonlinear Optimal Controller for Vehicle Active Suspension System considering the Limitation of Hydraulic Actuator. Journal of Control. 2017;11(3):25-34. DOR :20.1001.1.20088345.1396.11.3.4.5.
[25] Ghorbany M, Ebrahimi-Nejad S, Mollajafari M. Global-guidance chaotic multi-objective particle swarm optimization method for pneumatic suspension handling and ride quality enhancement on the basis of a thermodynamic model of a full vehicle. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. 2023;0(0). doi:10.1177/09544070221148287. DOI :10.1177/09544070221148287.
[26] Haiping Du, Nong Zhang. control of active vehicle suspensions with actuator time delay. Journal of Sound and Vibration 2007; 301:236–52. DOI :10.1016/j.jsv.2006.09.022.
[27] Liu G, Li Y, Nie X, Zheng H. A novel clustering-based differential evolution with 2 multi-parent crossovers for global optimization. Applied Soft Computing. 2012;12(2):663-81. DOI :10.1016/j.asoc. 2011.09.020.
[28] Zhang C, Chen J, Xin B. Distributed memetic differential evolution with the synergy of Lamarckian and Baldwinian learning. Applied Soft Computing. 2013;13(5):2947-59. DOI :10.1016/j.asoc.2012.02.028.
[29] Deng W, Yang X, Zou L, Wang M, Liu Y, Li Y. An improved self-adaptive differential evolution algorithm and its application. Chemometrics and Intelligent Laboratory Systems. 2013; 128:66–76. DOI :10.1016/j.chemolab.2013.07.004.
[30] Verros G, Natsiavas S, Papadimitriou C. Design optimization of quarter-car models with passive and semi-active suspensions under random road excitation. Journal of Vibration and Control. 2005; 11:581–606. DOI :10.1177/1077546305052315.
[31] International Standard, mechanical vibration-road surface profiles-reporting of measured data, is ISO8608:2016(E), ICS 17.160;93.080.10.
 
Volume 20, Issue 1 - Serial Number 75
Serial No. 75, Spring
April 2024
Pages 89-105
  • Receive Date: 03 September 2023
  • Revise Date: 26 September 2023
  • Accept Date: 16 October 2023
  • Publish Date: 15 April 2024