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Electromagnetic buffer optimization based on Nash game

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Abstract

Aiming at the problem of unstable buffering process of electromagnetic buffer (EMB) under intensive impact load, a three-segment electromagnetic buffer is proposed. The inner tube and air-gap of EMB are divided into three segments. The finite element analysis and impact test results show that the resultant resistance force (RRF) curve has two hump-shaped peaks, which is the reason for the unstable buffering process. In order to stabilize the buffering process, a multi-objective optimization design method of EMB based on Nash game theory is proposed. Firstly, the optimization model is established by taking the two peaks of the RRF curve and the maximum buffer displacement as the optimization objectives. Secondly, the multi-objective optimization model is transformed into a game model by sensitivity analysis and fuzzy clustering. Then, a Nash equilibrium solution strategy of EMB Nash game model based on symmetric elitist information exchange is proposed, which integrates gene expression programming (GEP) surrogate model and genetic algorithm (GA) as an optimization solver. Finally, the Nash equilibrium of the game model is obtained. The results show that the smoothness of the RRF curve has been significantly improved, which proves the effectiveness of the game strategy.

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References

  1. Sodano, H.A.: Eddy current damping in structures. Shoc. Vib. Dig. 36, 469–478 (2004)

    Article  Google Scholar 

  2. Ebrahimi, B., Bolandhemmat, H., Khamesee, M.B., et al.: A hybrid electromagnetic shock absorber for active vehicle suspension systems. Vehicle. Syst. Dyn. 49, 311–332 (2011)

    Article  Google Scholar 

  3. Ebrahimi, B., Khamesee, M.B., Golnaraghi, F.: A novel eddy current damper: theory and experiment. J. Phys. D 42, 75001 (2009)

    Article  Google Scholar 

  4. Ebrahimi, B., Khamesee, M.B., Golnaraghi, F.: Eddy current damper feasibility in automobile suspension: modeling, simulation and testing. Smart. Mater. Struct. 18, 15017 (2009)

    Article  Google Scholar 

  5. Sodano, H.A., Inman, D.J., Belvin, W.K.: Development of a new passive-active magnetic damper for vibration suppression. J. Vib. Acoust. 128, 318–327 (2006)

    Article  Google Scholar 

  6. Shin, H.-J., Choi, J.-Y., Cho, H.-W., et al.: Analytical torque calculations and experimental testing of permanent magnet axial eddy current brake. IEEE. T. Magn. 49, 4152–4155 (2013)

    Article  Google Scholar 

  7. Jin, L., Zheng, J., Li, H., et al.: Effect of eddy current damper on the dynamic vibration characteristics of high-temperature superconducting maglev system. IEEE. T. Appl. Super. 27, 1–6 (2017)

    Google Scholar 

  8. Jiang, W., Han, X., Chen, L., et al.: Improving energy harvesting by internal resonance in a spring-pendulum system. Acta Mech. Sin. 36, 618–623 (2020)

    Article  MathSciNet  Google Scholar 

  9. Tan, T., Yan, Z., Ma, K., et al.: Nonlinear characterization and performance optimization for broadband bistable energy harvester. Acta Mech. Sin. 36, 578–591 (2020)

    Article  MathSciNet  Google Scholar 

  10. Qian, F., Zhou, S., Zuo, L.: Improving the off-resonance energy harvesting performance using dynamic magnetic preloading. Acta Mech. Sin. 36, 624–634 (2020)

    Article  MathSciNet  Google Scholar 

  11. Wang, J., Geng, L., Zhou, S., et al.: Design, modeling and experiments of broadband tristable galloping piezoelectric energy harvester. Acta Mech. Sin. 36, 592–605 (2020)

    Article  Google Scholar 

  12. Pan, Q., He, T., Xiao, D., et al.: Design and damping analysis of a new Eddy current damper for aerospace applications. Lat. Am. J. Solids. Stru. 13, 1997–2011 (2016)

    Article  Google Scholar 

  13. Perez-Diaz, J.L., Valiente-Blanco, I., Cristache, C., et al.: A novel high temperature eddy current damper with enhanced performance by means of impedance matching. Smart. Mater. Struct. 28, 25034 (2019)

    Article  Google Scholar 

  14. Zuo, L., Chen, X., Nayfeh, S.: Design and analysis of a new type of electromagnetic damper with increased energy density. J. Vib. Acoust. 133, 4 (2011)

    Article  Google Scholar 

  15. Saige, D., Engelhardt, J., Katz, S.: Application of eddy current damper technology for passive tuned mass damper systems within footbridges. Procedia Eng. 199, 1804–1809 (2017)

    Article  Google Scholar 

  16. Canova, A., F. Freschi, M. Repetto, et al.: Eddy current coupler optimization. In: International Conference on Power Electronics, Machines & Drives. London pp. 436–441 (2004).

  17. Aberoomand, V., Mirsalim, M., Fesharakifard, R.: Design optimization of double-sided permanent-magnet axial eddy-current couplers for use in dynamic applications. IEEE Trans. Energy Convers. 34, 909–920 (2019)

    Article  Google Scholar 

  18. Asl, R.T., Yüksel, H.M., Keysan, O.: Multi-objective design optimization of a permanent magnet axial flux eddy current brake. Turk. J. Electr. Eng. Co. 27, 998–1011 (2019)

    Google Scholar 

  19. Sohrabi, M.K.H.: Azgomi: A survey on the combined use of optimization methods and game theory. Arch. Comput. Method. Eng. 27, 59–80 (2018)

    Article  Google Scholar 

  20. Li, Y., Lin, L., Dai, Q., et al.: Allocating common costs of multinational companies based on arm’s length principle and Nash non-cooperative game. Eur. J. Oper. Res. 283, 1002–1010 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Sun, Q., Yang, G., Wang, X., et al.: Cooperative game-oriented optimal design in constraint-following control of mechanical systems. Nonlinear Dyn. 101, 977–995 (2020)

    Article  Google Scholar 

  22. Yin, H., Chen, Y.-H., Yu, D.: Rendering optimal design in controlling fuzzy dynamical systems: a cooperative game approach. IEEE. Trans. Ind. Inform. 15, 4430–4441 (2018)

    Article  Google Scholar 

  23. Nash, J.F.: Equilibrium points in n-Person games. Proc. Natl. Acad. Sci. USA 36, 48–49 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yin, H., Chen, Y.H., Yu, D.: Stackelberg-theoretic approach for performance improvement in fuzzy systems. IEEE Trans. Cybern. 50, 2223–2236 (2020)

    Article  Google Scholar 

  25. Li, C., Chen, Y.-H., Zhao, H., et al.: Stackelberg game theory-based optimization of high-order robust control for fuzzy dynamical systems. IEEE Trans. Syst. Man Cybern. Syst. 1, 1–12 (2020)

    Google Scholar 

  26. Latifi, M., Rakhshandehroo, G., Nikoo, M.R., et al.: A game theoretical low impact development optimization model for urban storm water management. J. Clean. Prod. 241, 118323 (2019)

    Article  Google Scholar 

  27. Yin, H., Chen, Y.-H., Yu, D., et al.: Nash game oriented optimal design in controlling fuzzy dynamical systems. IEEE. Trans. Fuzzy Syst. 27, 1659–1673 (2018)

    Article  Google Scholar 

  28. Yu, Y.G.Q.: Huang: Nash game model for optimizing market strategies, configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family. Eur. J. Oper. Res. 206, 361–373 (2010)

    Article  MATH  Google Scholar 

  29. Belkov, S., Evstigneev, I.V., Hens, T., et al.: Nash equilibrium strategies and survival portfolio rules in evolutionary models of asset markets. Math. Finance Econ. 14, 249–262 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tang, Z.L.: A new Nash optimization method based on alternate elitist information exchange for multi-objective aerodynamic shape design. Appl. Math. Model. 68, 244–266 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Tang, Z.L.: Nash equilibrium and multi criterion aerodynamic optimization. J. Comput. Phys. 314, 107–126 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  32. Tang, Z., Chen, Y., Zhang, L.: Natural laminar flow shape optimization in transonic regime with competitive Nash game strategy. Appl. Math. Model. 48, 534–547 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. Léon, E.R., Pape, A.L., Costes, M., et al.: Concurrent aerodynamic optimization of rotor blades using a Nash game method. J. Am. Helicopter. Soc. 61, 1–13 (2016)

    Article  Google Scholar 

  34. Oliveira, E., Petraglia, H.A.A.: Solving generalized Nash equilibrium problems through stochastic global optimization. Appl. Soft. Comput. 39, 21–35 (2016)

    Article  Google Scholar 

  35. Hou, F., Zhai, Y., You, X.: An equilibrium in group decision and its association with the Nash equilibrium in game theory. Comput. Ind. Eng. 139, 106138 (2020)

    Article  Google Scholar 

  36. Diaz-Manriquez, A., Toscano, G., Barron-Zambrano, J.H., et al.: A review of surrogate assisted multiobjective evolutionary algorithms. Comput. Intell. Neurosci. 2016, 9420460 (2016)

    Article  Google Scholar 

  37. Wang, G.G.S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Design. 129, 370–380 (2007)

    Article  Google Scholar 

  38. Martí, P., Shiri, J., Duran-Ros, M., et al.: Artificial neural networks vs. gene expression programming for estimating outlet dissolved oxygen in micro-irrigation sand filters fed with effluents. Comput. Electron. Agron. 99, 176–185 (2013)

    Article  Google Scholar 

  39. Ferreira, C.: Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst. 13, 87–129 (2001)

    MathSciNet  MATH  Google Scholar 

  40. Furlani, E.P.: Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications. Academic Press, London (2001)

    Google Scholar 

  41. Craik, D.J.: Magnetism: principles and applications. Phys. Today 49, 57–57 (1996)

    Article  Google Scholar 

  42. Dey, P.A.K.: A utilization of GEP (gene expression programming) metamodel and PSO (particle swarm optimization) tool to predict and optimize the forced convection around a cylinder. Energy 95, 447–458 (2016)

    Article  Google Scholar 

  43. Hong, T., Jeong, K., Koo, C.: An optimized gene expression programming model for forecasting the national CO2 emissions in 2030 using the metaheuristic algorithms. Appl. Energy 228, 808–820 (2018)

    Article  Google Scholar 

  44. Hamby, D.M.: A review of techniques for parameter sensitivity analysis of environmental models. Environ. Monit. Assess. 32, 135–154 (1994)

    Article  Google Scholar 

Download references

Funding

This work was financially supported by the China Postdoctoral Science Foundation (Grant No. BX2021126).

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Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Fengjie Xu, Guolai Yang, Zixuan Li, Liqun Wang & Quanzhao Sun

  2. School of Mechanical Engineering, Shandong University of Technology, Zibo, 255000, China

    Zixuan Li

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  1. Fengjie Xu
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  2. Guolai Yang
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  3. Zixuan Li
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  4. Liqun Wang
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  5. Quanzhao Sun
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Correspondence to Guolai Yang.

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Executive Editor: Jian Xu.

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Xu, F., Yang, G., Li, Z. et al. Electromagnetic buffer optimization based on Nash game. Acta Mech. Sin. 37, 1331–1344 (2021). https://doi.org/10.1007/s10409-021-01101-2

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