doi:

DOI: 10.3724/SP.J.1187.2009.10096

Journal of Electronic Measurement and Instrument (电子测量与仪器学报) 2009/23:10 PP.96-99

Improved harmonic-balance algorithms based on the genetic algorithms


Abstract:
As the slow of iterative convergence and large amount of calculation quantity in general harmonic balance algorithm (GHBA), an improved harmonic-balance algorithm which is based on the genetic algorithms’ implicit parallelism, overall superior solution and problem model independence for speeding up the convergence of iteration procedure is proposed. This method combines genetic algorithms’ stochastic self-adaptive optimization process and GHBA’s iterative process, it makes GHBA’s iterative calculation process is simplified and GHBA’s iterative convergence speed and calculation precision are improved. By using Duffing-Van Der Pol equations as example, approximate analytic solutions is obtained with this algorithm, acquired the better consistent with numerical value solution by using Runge-Kutta methods, which indicates that this algorithm is valid.

Key words:harmonic-balance algorithms,genetic algorithms,nonlinear equations,optimization

ReleaseDate:2014-07-21 14:58:15



[1] AL-SHYYAB A, KAHRAMAN A. Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: Sub-harmonic motions[J]. Journal of Sound and Vibration. 2005, 279(1-2): 417- 451.

[2] BESSER L, GILMORE R. Practical RF circuit design for modern wireless systems Vol. 2: Active Circuits and Systems[M]. Boston: Artech House, INC, 2003: 202- 207.

[3] 孔俊宝. 谐波平衡法及其改进[J]. 南京邮电学院学报. 1990, 10(2): 53-57.KONG J B. Harmonic balancing method and it’s im-provement[J]. Journal of Nanjing Institute of Posts and Telecommunications. 1990, 10(2): 53-57.

[4] 李鹏松, 周红庆. 牛顿谐波平衡法求解Euler杆大挠度屈曲问题[J]. 东北电力大学学报. 2008, 28(2): 19-22.LI P S, ZHOU H Q. Newton-Harmonic Balance Method for Solving Buckling Problem of the Euler’s Column with Large Deflection[J]. Journal of Northeast Dianli University. 2008, 28(2): 19-22.

[5] SHEN J H, LIN K C, CHEN S H, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method[J]. Nonlinear Dynamics, 2008, 52(4): 403-414.

[6] YAN G F, HUANG X H, TAN F. Research of process controls parameter optimal selection based on improved genetic algorithm[C]. World Forum on Smart Materials and Smart Structures Technology. London: Taylor & Francis Group, 2008, 392-393.

[7] 严刚峰, 赵宪生. 基于模拟退火—— 遗传算法的过程控制参数寻优研究[J]. 四川大学学报: 自然科学版. 2003, 40(5): 874-877.YAN G F, ZHAO X SH. The research of based on simu-lated annealing and genetic algorithm’s optimal selection of controls parameter[J]. Journal of Sichuan University: Natural Science Edition. 2003, 40(5): 874-877.

[8] 陈树辉. 强非线性振动系统的定量分析方法[M]. 北京: 科学出版社, 2007,115-122.CHEN SH H. The Definite Quantitative Methods for Strongly Non-Linear Vibration[M]. Beijing: Science Press, 2007, 115-122.

[9] 李庆扬. 科学计算方法基础[M]. 北京: 清华大学出版社, 2006,161-166.LI Q Y. Foundations of Science Computation Meth-ods[M]. Beijing: Tsinghua University Press, 2006, 161- 166.

[10] MARGALLO J G, BEJARANO J D. A generalization of the method of harmonic balance[J]. Journal of Sound and Vibration. 1987, 116(3): 591-595.

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