周期时变转子系统参数识别技术研究
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摘要
针对周期时变转子振动系统,提出了基于方波脉冲函数展开的参数识别方法。将振动系统状态空间方程用方波脉冲级数展开,利用方波脉冲函数具有脱关性及正交性等性质,并根据矩阵分块与谱分解理论,推导出周期时变系统参数识别递推公式。通过对二自由度刚度周期时变系统仿真模型和实际非对称转子系统进行结构参数识别,结果表明,在合适计算步长下刚度值识别准确,平均绝对百分误差分别小于0.5%与1%,验证了该方法的正确性和有效性,有较大的工程应用价值。
For a periodic time-varying rotor system, parametric identification method based on the square wave pulse function was proposed. Firstly, the state-space matrix equation of the system was expanded with the square wave pulse function. Then recursion formulas for parametric identification of the system were derived adopting decorrelation and orthogonality of the square wave pulse function according to the matrix partition and spectral decomposition theory. Structural parametric identifications for a 2-DOF stiffness periodic time-varying system simulation model and an actual asymmetric rotor system were conducted with the proposed method. The results showed that their stiffness values are recognized correctly under appropriate calculation steps with the mean absolute percentage error of less than 0.5% and 1%, respectively; the correctness and effectiveness of the proposed method are verified, so it is valuable for engineering application.
For a periodic time-varying rotor system, parametric identification method based on the square wave pulse function was proposed. Firstly, the state-space matrix equation of the system was expanded with the square wave pulse function. Then recursion formulas for parametric identification of the system were derived adopting decorrelation and orthogonality of the square wave pulse function according to the matrix partition and spectral decomposition theory. Structural parametric identifications for a 2-DOF stiffness periodic time-varying system simulation model and an actual asymmetric rotor system were conducted with the proposed method. The results showed that their stiffness values are recognized correctly under appropriate calculation steps with the mean absolute percentage error of less than 0.5% and 1%, respectively; the correctness and effectiveness of the proposed method are verified, so it is valuable for engineering application.
引文
[1] 许鑫,史治宇.用于时变系统参数识别的状态空间小波方法[J]. 工程力学,2011(3): 23-28. XU Xin, SHI Zhiyu. Parameter identification for time-varying system using state space and wavelet method[J]. Engineering Mechanics, 2011(3): 23-28.
[2] 邹经湘,于开平,杨炳渊.时变结构的参数识别方法[J]. 力学进展, 2000(3): 370-377. ZOU Jingxiang, YU Kaiping, YANG Bingyuan. Methods of time-varying structural parameter identification[J]. Advances in Mechanics, 2000(3): 370-377.
[3] SHI Z Y, LAW S S, XU X. Identification of linear time-varying mdof dynamical systems from forced excitation using Hilbert transform and EMD method[J].Journal of Sound and Vibration, 2009, 321: 572―589.
[4] 许鑫,史治宇,STASZEWSKI W I,等.基于加速度响应连续小波变换的线性时变结构瞬时频率识别[J]. 振动与冲击, 2012,31(20): 166-171. XU Xin, SHI Zhiyu, STASZEWSKI W I, et al. Instantaneous frequencies identification of a linear time-varying structure using continuous wavelet transformation of free decay acceleration response[J]. Journal of Vibration and Shock, 2012,31(20): 166-171.
[5] 史治宇,沈林. 基于小波方法的时变动力系统参数识别[J]. 振动、测试与诊断, 2008(2): 108-112. SHI Zhiyu, SHEN Lin. Parameter identification of linear time-varying dynamical system based on wavelet method[J]. Journal of Vibration, Measurement & Diagnosis, 2008(2): 108-112.
[6] 黄东梅,周实,任伟新.基于小波变换的时变及典型非线性振动系统识别[J].振动与冲击,2014,33(13): 123-129. HUANG Dongmei,ZHOU Shi,REN Weixin. Parameter identification of time-varying and typical nonlinear vibration system based on wavelet transform[J]. Journal of Vibration And Shock, 2014,33(13): 123-129.
[7] 庞世伟,于开平, 邹经湘.识别时变结构模态参数的改进子空间方法[J].应用力学学报,2005, 22(2):184-188. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Improved subspace method with application in linear time-varying structural modal parameter identification[J]. Chinese Journal of Applied Mechanics, 2005,22(2):184-188.
[8] 庞世伟, 于开平, 邹经湘, 用于时变系统辨识的自由响应递推子空间方法[J].振动工程学报, 2005, 18(2):233-237. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Time-varying system identification using recursive subspace method based on free response data[J]. Journal of Vibration Engineering, 2005, 18(2):233-237.
[9] 庞世伟, 于开平, 邹经湘.用于时变结构模态参数识别的投影估计递推子空间方法[J].工程力学,2005, 22(5):115-119. PANG Shiwei, YU Kaiping, ZOU Jingxiang. A projection approximation recursive subspace method for identification of modal parameters of time-varying structures[J].Engineering Mechanics, 2005, 22(5):115-119.
[10] 庞世伟, 于开平, 邹经湘.用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法[J].机械工程学报, 2005, 41(10):117-122. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Using recursive subspace method based on projection approximation with moving window to estimate parameters of linear time-varying strucrure[J]. Chinese Journal of Mechanical Engineering, 2005, 41(10):117-122.
[11] SHAN X, BURL J B.Continuous wavelet based linear time-varying system identification[J]. Signal Processing, 2011, 91(6): 1476-1488.
[12] BAO C. Time-varying system identification using a newly improved HHT algorithm[J]. Computers & Amp, Structures, 2009, 87(23/24): 1611-1623.
[13] 王建军,李其汉,李润方. 齿轮系统非线性振动研究进展[J].力学进展,2005, 35(1): 37-51. WANG Jianjun, LI Qihan, LI Runfang. Research advances for nonlinear vibration of gear transmission systems[J]. Advances In Mechanics, 2005, 35(1): 37-51.
[14] WANG J J, LI R F, PENG X H. Survey of nonlinear vibration of gear transmission systems[J]. Applied Mechanics Reviews,2003, 56: 309-329.
[15] DUGUNDJI J,WENDELL J H. Some analysis methods for rotating systems with periodic coefficients[J]. AIAA Journal,1983, 21(6): 890-897.
[16] 肖锡武,肖光华,杨叔子. 不对称转子系统的参激强迫振动[J]. 振动工程学报, 2002, 15(3): 315-318. XAIO Xiwu, XIAO Guanghua, YANG Shuzi. Parametrically excited and forced oscillations of an unsymmetrical rotor system[J]. Journal of Vibration Engineering, 2002, 15(3): 315-318.
[17] SANNUTI B E. Analysis and synthesis of dynamic systems via block-pulse functions[J].Proc IEE, 1977, 124(6): 569-571.
[18] HAN Q K, WANG J J, LI Q H. Frequency response characteristics of parametrically excited systems[J]. Journal of Vibration and Acoustics, 2010,132(4):1154-1174.
[19] HAN Q K, WANG J J, LI Q H.Spectral properties for the vibrational response of parametrically excited system[J]. Archive of Applied Mechanics, 2010,80: 671-685.
[2] 邹经湘,于开平,杨炳渊.时变结构的参数识别方法[J]. 力学进展, 2000(3): 370-377. ZOU Jingxiang, YU Kaiping, YANG Bingyuan. Methods of time-varying structural parameter identification[J]. Advances in Mechanics, 2000(3): 370-377.
[3] SHI Z Y, LAW S S, XU X. Identification of linear time-varying mdof dynamical systems from forced excitation using Hilbert transform and EMD method[J].Journal of Sound and Vibration, 2009, 321: 572―589.
[4] 许鑫,史治宇,STASZEWSKI W I,等.基于加速度响应连续小波变换的线性时变结构瞬时频率识别[J]. 振动与冲击, 2012,31(20): 166-171. XU Xin, SHI Zhiyu, STASZEWSKI W I, et al. Instantaneous frequencies identification of a linear time-varying structure using continuous wavelet transformation of free decay acceleration response[J]. Journal of Vibration and Shock, 2012,31(20): 166-171.
[5] 史治宇,沈林. 基于小波方法的时变动力系统参数识别[J]. 振动、测试与诊断, 2008(2): 108-112. SHI Zhiyu, SHEN Lin. Parameter identification of linear time-varying dynamical system based on wavelet method[J]. Journal of Vibration, Measurement & Diagnosis, 2008(2): 108-112.
[6] 黄东梅,周实,任伟新.基于小波变换的时变及典型非线性振动系统识别[J].振动与冲击,2014,33(13): 123-129. HUANG Dongmei,ZHOU Shi,REN Weixin. Parameter identification of time-varying and typical nonlinear vibration system based on wavelet transform[J]. Journal of Vibration And Shock, 2014,33(13): 123-129.
[7] 庞世伟,于开平, 邹经湘.识别时变结构模态参数的改进子空间方法[J].应用力学学报,2005, 22(2):184-188. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Improved subspace method with application in linear time-varying structural modal parameter identification[J]. Chinese Journal of Applied Mechanics, 2005,22(2):184-188.
[8] 庞世伟, 于开平, 邹经湘, 用于时变系统辨识的自由响应递推子空间方法[J].振动工程学报, 2005, 18(2):233-237. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Time-varying system identification using recursive subspace method based on free response data[J]. Journal of Vibration Engineering, 2005, 18(2):233-237.
[9] 庞世伟, 于开平, 邹经湘.用于时变结构模态参数识别的投影估计递推子空间方法[J].工程力学,2005, 22(5):115-119. PANG Shiwei, YU Kaiping, ZOU Jingxiang. A projection approximation recursive subspace method for identification of modal parameters of time-varying structures[J].Engineering Mechanics, 2005, 22(5):115-119.
[10] 庞世伟, 于开平, 邹经湘.用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法[J].机械工程学报, 2005, 41(10):117-122. PANG Shiwei, YU Kaiping, ZOU Jingxiang. Using recursive subspace method based on projection approximation with moving window to estimate parameters of linear time-varying strucrure[J]. Chinese Journal of Mechanical Engineering, 2005, 41(10):117-122.
[11] SHAN X, BURL J B.Continuous wavelet based linear time-varying system identification[J]. Signal Processing, 2011, 91(6): 1476-1488.
[12] BAO C. Time-varying system identification using a newly improved HHT algorithm[J]. Computers & Amp, Structures, 2009, 87(23/24): 1611-1623.
[13] 王建军,李其汉,李润方. 齿轮系统非线性振动研究进展[J].力学进展,2005, 35(1): 37-51. WANG Jianjun, LI Qihan, LI Runfang. Research advances for nonlinear vibration of gear transmission systems[J]. Advances In Mechanics, 2005, 35(1): 37-51.
[14] WANG J J, LI R F, PENG X H. Survey of nonlinear vibration of gear transmission systems[J]. Applied Mechanics Reviews,2003, 56: 309-329.
[15] DUGUNDJI J,WENDELL J H. Some analysis methods for rotating systems with periodic coefficients[J]. AIAA Journal,1983, 21(6): 890-897.
[16] 肖锡武,肖光华,杨叔子. 不对称转子系统的参激强迫振动[J]. 振动工程学报, 2002, 15(3): 315-318. XAIO Xiwu, XIAO Guanghua, YANG Shuzi. Parametrically excited and forced oscillations of an unsymmetrical rotor system[J]. Journal of Vibration Engineering, 2002, 15(3): 315-318.
[17] SANNUTI B E. Analysis and synthesis of dynamic systems via block-pulse functions[J].Proc IEE, 1977, 124(6): 569-571.
[18] HAN Q K, WANG J J, LI Q H. Frequency response characteristics of parametrically excited systems[J]. Journal of Vibration and Acoustics, 2010,132(4):1154-1174.
[19] HAN Q K, WANG J J, LI Q H.Spectral properties for the vibrational response of parametrically excited system[J]. Archive of Applied Mechanics, 2010,80: 671-685.