基于时频切片分解的时变系统参数识别
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摘要
系统参数识别分为时不变系统参数识别和时变系统参数识别两大研究方向,其中时不变系统参数识别的研究已趋于成熟,而时变系统参数识别的研究则仍然处于起步阶段。对于多自由度时变结构,提出一种基于时频切片分解的时变系统参数识别方法。该方法采集结构的振动位移响应,根据时频分解计算得到响应在整个时频段内的时频能量分布图;依据结构的时频分布特性,选择多个时频切片窗分解响应信号,再对分解出的信号分别进行逆变换计算完成时域上的信号重构;重构出来的信号对应于结构的各阶模态位移响应信号,利用Hilbert变换提取信号瞬时频率,从而识别出结构各阶频率。通过一个三自由度的弹簧阻尼质量仿真实验,验证了该方法具有良好的识别精度和工程实用价值。
System parameter identification can be divided into two research directions: time-invariant system parameter identification and time-varying system parameter identification. The research on time-invariant system parameter identification has become mature, while the research on time-varying system parameter identification is still in its infancy. For multi-degree-of-freedom time-varying structures, a method for parameter identification based on time frequency slice decomposition is proposed. The first step of this method is to collect the displacement response of the structure, and then obtain the time-frequency energy distribution of the response in the whole time-frequency band. According to the time-frequency distribution characteristics of the structure, multiple time-frequency window signals are sliced out, and the inverse transform of FSWT is performed to reconstruct the signals in time domain. The reconstructed signal corresponds to each order modal displacement response signal of the structure. The instantaneous frequency of the signal is extracted by Hilbert transform, and the modal frequencies of each order of the structure are identified. According to a simulation experiment of the three-degree-of-freedom mass spring damping system, the method is proved to have good identification accuracy and practical engineering value.
System parameter identification can be divided into two research directions: time-invariant system parameter identification and time-varying system parameter identification. The research on time-invariant system parameter identification has become mature, while the research on time-varying system parameter identification is still in its infancy. For multi-degree-of-freedom time-varying structures, a method for parameter identification based on time frequency slice decomposition is proposed. The first step of this method is to collect the displacement response of the structure, and then obtain the time-frequency energy distribution of the response in the whole time-frequency band. According to the time-frequency distribution characteristics of the structure, multiple time-frequency window signals are sliced out, and the inverse transform of FSWT is performed to reconstruct the signals in time domain. The reconstructed signal corresponds to each order modal displacement response signal of the structure. The instantaneous frequency of the signal is extracted by Hilbert transform, and the modal frequencies of each order of the structure are identified. According to a simulation experiment of the three-degree-of-freedom mass spring damping system, the method is proved to have good identification accuracy and practical engineering value.
引文
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[2] Grossman A,Morlet J.Decomposition of hardy function into square integrable wavelets of constant shape[J].SIAM Journal on Mathematical Analysis,1984,15(4):736-783.
[3] Staszewski W J,Cooper J E.Flutter data analysis using the wavelet transform[C].Proceedings of International Congress on MV2:New Advances in Modal Synthesis of Large Structures,Non-linear,Damped and Non-Deterministic Cases,Lyon,France,1995:549-561.
[4] 许鑫,史治宇,Wieslaw J Staszewski,等.基于加速度响应的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,Wieslaw J Staszewski,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.(in Chinese)
[5] Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis[C].Proceedings of the Royal Society of London-Series A,1998,454:903-995.
[6] Huang N E,Shen Z,Long S R.A new view of nonlinear water waves:the Hilbert spectrum[J].Annual Review of Fluid Mechanics,1999,31:417-457.
[7] Feldman M.Non-linear system vibration analysis using Hilbert transform-Ⅰ:free vibration analysis method FREEV-IB[J].Mechanical Systems and Signal Processing,1994,8(2):119-127.
[8] Feldman M.Non-linear system vibration analysis using Hilbert transform-Ⅱ:forced vibration analysis method FORCEVIB[J].Mechanical Systems and Signal Processing,1994,8(3):309-318.
[9] Liu K.Identification of linear time-varying systems[J].Journal of Sound and Vibration,1997,206(4):487-505.
[10] Liu K.Extension of modal analysis to linear time-varying systems[J].Journal of Sound and Vibration,1999,226(1):149-167.
[11] 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-varing system identification using recursive subspace method based on free response data[J].Journal of Vibration Engineering,2005,18(2):233-237.(in Chinese)
[12] 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.(in Chinese)
[13] Raffy M,Gontier C.Statistical asymptotic error on modal parameters in combined deterministic-stochastic identification algorithm[J].Mechanical Systems and Signal Processing,2005,19(4):714-735.
[14] 雷亚国.基于改进Hilbert-Huang变换的机械故障诊断[J].机械工程学报,2011,47(5):71-77.Lei Yaguo.Machinery fault diagnosis based on improved Hilbert-Huang transform[J].Journal of Vibration Engineering,2011,47(5):71-77.(in Chinese)
[15] Yan Zhonghong,Ayaho Miyamoto,Jiang Zhongwei.Frequency slice wavelet transform for transient vibration response analysis[J].Mechanical Systems and Signal Processing,2009,23(5):1474-1489.
[16] 钟先友.旋转机械故障诊断的时频分析方法及其应用研究[D].武汉:武汉科技大学,2014.Zhong Xianyou.Time-frequency analysis method for fault diagnosis of rotating machinery and its application[D].Wuhan:Wuhan University of Science and Technology,2014.(in Chinese)
[17] 钟先友,赵春华,陈保家,等.基于形态自相关和时频切片分析的轴承故障诊断方法[J].振动与冲击,2014,33(4):11-16.Zhong Xianyou,Zhao Chunhua,Chen Baojia,et al.Bearing fault diagnosis method based on morphological filtering and time-delayed autocorrelation and time-frequency slice analysis[J].Journal of Vibration and Shock,2014,33(4):11-16.(in Chinese)
[18] 胡海岩,孙久厚,陈怀海.机械振动与冲击[M].北京:航空工业出版社,2002.Hu Haiyan,Sun Jiuhou,Chen Huaihai.Mechanical vibration and shock[M].Beijing:Aviation Industry Press,2002.(in Chinese)
[19] 钟佑明,秦树人,汤宝平.Hilbert-Huang变换中的理论研究[J].振动与冲击,2002,21(4):13-17.Zhong Youming,Qin Shuren,Tang Baoping.Study on the theory of Hilbert-Huang transform[J].Journal of Vibration and Shock,2002,21(4):13-17.(in Chinese)