Abstract:The empirical envelope method based on amplitude modulation and frequency modulation decomposition is widely used in parameter identification of linear and nonlinear systems. However, in amplitude modulation and frequency modulation decomposition, multiple envelope iterations are to obtain pure amplitude modulation and frequency modulation signals, which will increase the cumulative error. In the empirical envelope method, the over envelope caused by the unsmooth derivative signal, which will increase the system parameter identification error. The idea of sliding window threshold denoising and moving average technology are used to solve the above two problems respectively. An improved empirical envelope method is proposed, and based on this method, the modal parameters of free attenuation vibration of single degree of freedom nonlinear system are identified. Through the analysis of several examples, it is proved that this method has good anti-noise performance and high recognition accuracy.
Key words: Modal parameter identification; Empirical envelope method; Nonlinear system; Threshold denoising; Moving average
曾华,许福友. 基于改进经验包络法的非线性系统参数识别[J]. 振动与冲击, 2022, 41(13): 180-188.
ZENG Hua, XU Fuyou. Parametric identification of nonlinear system based on improved empirical envelope method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(13): 180-188.
[1] Ibrahim S R. Random decrement technique for modal identification of structures[J]. Journal of Spacecraft and Rockets, 1977, 14(11): 696-700.
[2] Moaveni B, Asgarieh E. Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems[J]. Mechanical Systems and Signal Processing, 2012, 31: 40-55.
[3] Brincker R, Zhang L, Andersen P. Modal identification from ambient responses using frequency domain decomposition[C]//Proc. of the 18*‘International Modal Analysis Conference (IMAC), San Antonio, Texas. 2000.
[4] Brincker R, Zhang L, Andersen P. Output-only modal analysis by frequency domain decomposition[C]//Proceedings of the ISMA25 noise and vibration engineering. 2000, 11: 717-723.
[5] Brincker R, Andersen P, Jacobsen N J. Automated frequency domain decomposition for operational modal analysis[C]//Proceedings of The 25th International Modal Analysis Conference (IMAC), Orlando, Florida. 2007, 415.
[6] Kijewski T, Kareem A. Wavelet transforms for system identification in civil engineering[J]. Computer‐Aided Civil and Infrastructure Engineering, 2003, 18(5): 339-355.
[7] Yang J N, Lei Y, Pan S, et al. System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes[J]. Earthquake engineering & structural dynamics, 2003, 32(9): 1443-1467.
[8] Yang J N, Lei Y, Pan S, et al. System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes[J]. Earthquake engineering & structural dynamics, 2003, 32(10): 1533-1554.
[9] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London. Series A: mathematical, physical and engineering sciences, 1998, 454(1971): 903-995.
[10] Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms[C]//IEEE-EURASIP workshop on nonlinear signal and image processing. NSIP-03, Grado (I), 2003, 3(3): 8-11.
[11] Wang J L, Li Z J. Extreme-point symmetric mode decomposition method for data analysis[J]. Advances in Adaptive Data Analysis, 2013, 5(03): 1350015.
[12] Lian J, Liu Z, Wang H, et al. Adaptive variational mode decomposition method for signal processing based on mode characteristic[J]. Mechanical Systems and Signal Processing, 2018, 107: 53-77.
[13] 刘景良, 郑锦仰, 林友勤,等. 变分模态分解和同步挤压小波变换识别时变结构瞬时频率[J]. 振动与冲击, 2018, 37(20): 24-31.
LIU Jingliang, ZHENG Jinyang, LIN Youqin, et al.. Instantaneous frequency identification of time-varying structures using variational mode decomposition and synchrosqueezing wavelet transform. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(20): 24-31.
[14] 殷红, 董康立, 彭珍瑞. 基于VMD-SSI的结构模态参数识别[J]. 振动与冲击, 2020, 39(10): 81-91.
YIN Hong, DONG Kangli, PENG Zhenrui. Structural modal parameter identification based on VMD-SSI. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(10): 81-91.
[15] 孙猛猛, 郅伦海. 基于VMD的建筑结构模态参数识别[J]. 振动与冲击, 2020, 39(1): 175-183.
SUN Mengmeng, ZHI Lunhai. Modal parametric identification of building structures based on VMD. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(1): 175-183.
[16] Huang N E. Hilbert-Huang transform and its applications[M]. World Scientific, 2014.
[17] 张贤达, 非平稳信号分析与处理[M]. 1998: 国防工业出版社.
Zhang Xianda, nonstationary signal analysis and processing [M]. 1998: National Defense Industry Press.
[18] Maragos P, Kaiser J F, Quatieri T F. Energy separation in signal modulations with application to speech analysis[J]. IEEE transactions on signal processing, 1993, 41(10): 3024-3051.
[19] Kaiser J F. Some useful properties of Teager's energy operators[C]//1993 IEEE international conference on acoustics, speech, and signal processing. IEEE, 1993, 3: 149-152.
[20] Staszewski W J. Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform[J]. Journal of Sound and Vibration, 1998, 214(4): 639-658.
[21] Feldman M. Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method'Freevib'[J]. Mechanical systems and signal processing, 1994, 8(2): 119-127.
[22] 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.
[23] 郑近德, 程军圣, 杨宇. 一种新的估计瞬时频率的方法-经验包络法[J]. 振动与冲击, 2012, 31(17): 86-90.
Zheng Jinde, Cheng Junsheng, Yang Yu. A new method for estimating instantaneous frequency empirical envelope method [J]. JOURNAL OF VIBRATION AND SHOCK, 2012, 31 (17): 86-90.
[24] 程军圣,郑近德,杨宇.基于局部特征尺度分解的经验包络解调方法及其在机械故障诊断中的应用[J].机械工程学报,2012,48(19):87-94.
Cheng Junsheng, Zheng Jinde, Yang Yu. Empirical envelope demodulation method based on local feature scale decomposition and its application in mechanical fault diagnosis [J]. Journal of mechanical engineering, 2012,48 (19): 87-94.
[25] 赵斌,封周权,陈政清.环境激励下基于ESMD的结构模态参数识别方法[J].噪声与振动控制,2019,39(05):173-178.
Zhao Bin, Feng zhouquan, Chen Zhengqing. Structural modal parameter identification method based on ESMD under environmental excitation [J]. Noise and vibration control, 2019, 39 (05): 173-178
[26] Xu F, Ma Z, Zeng H, et al. A new method for studying wind engineering of bridges: Large-scale aeroelastic model test in natural wind[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2020: 104234.
[27] Zhang M, Xu F. Variational mode decomposition based modal parameter identification in civil engineering[J]. Frontiers of Structural and Civil Engineering, 2019, 13(5): 1082-1094.