System identification of folding rudders with freeplay nonlinearity under base excitation

PDF(2175 KB)

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (4) : 122-128.

WANG Bo1,2，MA Zhisai1,2，DING Qian1,2，ZHANG Xin3，YANG Ning3

Author information +

History +

Abstract

Freeplay nonlinearity is ubiquitous in folding rudders of flight vehicles, which is difficult to be accurately described.It is necessary to obtain the real nonlinear characteristics of freeplays by using system identification methods.The identified model of the nonlinear system with freeplays under base excitation was first built using direct parameter estimation.Nonlinear restoring force was expressed by polynomials of relative velocity and displacement.A significance factor was defined to determine whether a term is an important part of the identified model, and the coefficients of the polynomials were solved by the least squares method.Finally, the completed system model can be obtained based on the relationship between different degrees of freedom, and the identification accuracy can be validated via the mean-square error between the estimated and measured responses.Identification results of a three degree of freedom numerical example demonstrate that the restoring force of a nonlinear system with freeplays can be accurately approximated by adding cubic stiffness.Furthermore, the dynamic characteristics of two measuring points on the folding rudder can be well described by the identified model, which is of importance to discretization modeling and dynamic analysis of folding rudders with freeplays.

Key words

folding rudders / base excitation / freeplay nonlinearity / system identification

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WANG Bo1,2，MA Zhisai1,2，DING Qian1,2，ZHANG Xin3，YANG Ning3. System identification of folding rudders with freeplay nonlinearity under base excitation[J]. Journal of Vibration and Shock, 2020, 39(4): 122-128

References

[1] 赵永辉，胡海岩. 具有操纵面间隙非线性二维翼段的气动弹性分析[J]. 航空学报, 2003, 24(6): 521-525.
Zhao Yonghui, Hu Haiyan. Aeroelastic Analysis of a Two-Dimensional Airfoil with Control Surface Freeplay Nonlinearity[J]. Acta Aeronautica Et Astronautica Sinica, 2003, 24(6): 521-525.
[2] 丁千，陈予恕. 机翼颤振的非线性动力学和控制研究[J]. 科技导报, 2009, 27(2): 53-61.
DING Qian, Chen Yushu. Non-linear Dynamics and Control of Flutter of Airfoil[J]. Science & Technology Review, 2009, 27(2):53-61.
[3] 贾尚帅，丁千. 含间隙超音速二元弹翼非线性颤振与主动控制[J]. 中国科学:物理学力学天文学, 2013, 43(4): 390-400.
Jia Shangshuai, Ding Qian. Nonlinear flutter and active control of the supersonic two-dimensional missile wings with a freeplay[J]. Scientia Sinica （Physica,Mechanica & Astronomica）, 2013, 43(4): 390-400.
[4] 刘芳，丁千. 含间隙折叠舵面的主共振响应分析[J]. 航空动力学报, 2016, 31(12): 2965-2971.
Liu Fang, Ding Qian. Primary resonance response analysis on folding rudder with gaps[J]. Hangkong Dongli Xuebao/journal of Aerospace Power, 2016, 31(12):2965-2971.
[5] Kerschen G，Worden K，Vakakis A F，et al. Past, present and future of nonlinear system identification in structural dynamics[J]. Mechanical Systems & Signal Processing, 2006, 20(3): 505-592.
[6] Noël J P，Kerschen G. Nonlinear system identification in structural dynamics: 10 more years of progress[J]. Mechanical Systems & Signal Processing, 2016, 832-35.
[7] Masri S F，Caughey T K. A nonparametric identification technique for nonlinear dynamic problems[J]. Journal of Applied Mechanics, 1979, 46(2): 433-447.
[8] Masri S F，Sassi H，Caughey T K. Nonparametric identification of nearly arbitrary nonlinear systems[J]. Journal of Applied Mechanics, 1982, 49(3): 619-628.
[9] Meskell C，Fitzpatrick J A，Rice H J. Application of force-state mapping to a non-linear fluid–elastic system[J]. Mechanical Systems & Signal Processing, 2001, 15(1): 75-85.
[10] Worden K，Hickey D，Haroon M，et al. Nonlinear system identification of automotive dampers: A time and frequency-domain analysis[J]. Mechanical Systems & Signal Processing, 2009, 23(1): 104-126.
[11] 杨永新，S.R.Ibrahim. 非线性集总参数振动系统的一个非参数识别方法[J]. 振动与冲击, 1985, 5(1): 19-31.
Yang Yongxin, S.R.Ibrahxim. A nonparametric identification technique for a variety of discrete nonlinear vibrating systems[J]. Journal of Vibration & Shock, 1985, 5(1):19-31.
[12] Al-Hadid M A，Wright J R. Application of the force-state mapping approach to the identification of non-linear systems[J]. Mechanical Systems & Signal Processing, 1990, 4(6): 463-482.
[13] Mohammad K S，Worden K，Tomlinson G R. Direct parameter estimation for linear and non-linear structures[J]. Journal of Sound & Vibration, 1992, 152(3): 471-499.
[14] Bonisoli E，Vigliani A. Identification techniques applied to a passive elasto-magnetic suspension[J]. Mechanical Systems & Signal Processing, 2007, 21(3): 1479-1488.
[15] 许斌，贺佳. 部分输入未知条件下结构参数及激励识别[J]. 土木工程学报, 2012, 45(6): 13-22.
Xu Bin, He Jia. Structural parameters and dynamic loading identification with partially unknown excitations[J]. China Civil Engineering Journal, 2012, 45(6):13-22.
[16] Xu B，He J，Dyke S J. Model-free nonlinear restoring force identification for sma dampers with double chebyshev polynomials: Approach and validation[J]. Nonlinear Dynamics, 2015, 82(3): 1-16.
[17] 许斌，王云. 利用部分加速度测量的结构滞回特性免模型识别[J]. 工程力学, 2018, 35(02): 180-187.
Xu Bin, Wang Yun. Model free structural hysteritic behavior identification with limited acceleration measurements[J]. Engineering Mechanics, 2018, 35(02): 180-187.