关于非线性系统辨识的恢复力曲面法和希尔伯特变换法
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摘要
针对均匀薄板和压电双晶薄板进行了非线性辨识实验,比较了两种方法——恢复力曲面法和希尔伯特变换法。针对辨识数据的函数逼近问题,提出将位移-刚度函数而非位移-恢复力函数用于数据拟合。通过均匀薄板和压电双晶薄板的实验结果,验证了位移-刚度函数确实能提高小位移处的函数逼近精度并更加准确展现系统的非线性特性。还对比了恢复力曲面法和希尔伯特变换法在辨识精度和数据利用率方面的区别,结果显示希尔伯特变换法能有效抑制小位移处位移-刚度曲线的不规则振荡,并有着较高的数据利用率。
Two nonlinear system identification methods including the restoring force surface method and Hilbert transform one were compared based on experiments of a homogeneous plate and a piezoelectric bimorph one. The stiffnessdisplacement function was proposed to be used for data fitting instead of the restoring force-displacement function in the function approximation process. The experiment results of a homogeneous plate and a piezoelectric bimorph one showed that using the stiffness-displacement function can improve the function approximation accuracy at small displacements. The identification accuracy and data utilization rate obtained by the restoring force surface method were compared with those obtained by Hilbert transform one. The results showed that Hilbert transform method can effectively suppress irregular oscillations of the stiffness-displacement curve at small displacements,and it has a higher data utilization rate.
Two nonlinear system identification methods including the restoring force surface method and Hilbert transform one were compared based on experiments of a homogeneous plate and a piezoelectric bimorph one. The stiffnessdisplacement function was proposed to be used for data fitting instead of the restoring force-displacement function in the function approximation process. The experiment results of a homogeneous plate and a piezoelectric bimorph one showed that using the stiffness-displacement function can improve the function approximation accuracy at small displacements. The identification accuracy and data utilization rate obtained by the restoring force surface method were compared with those obtained by Hilbert transform one. The results showed that Hilbert transform method can effectively suppress irregular oscillations of the stiffness-displacement curve at small displacements,and it has a higher data utilization rate.
引文
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[2]KRAUSS R W,NAYFEH A H.Experimental nonlinear identification of a single mode of a transversely excited beam[J].Nonlinear Dynamics,1999,18(1):69-87.
[3]YASUDA K,KAWAMURA S,WATANABE K.Identification of nonlinear multi-degree-of-freedom systems:presentation of an identification technique[J].Japan Society of Mechanical Engineers International Journal series III,1987,53(495):8-14.
[4]AMABILI M,ALIJANI F,DELANNOY J.Damping for large-amplitude vibrations of plates and curved panels,part2:Identification and comparisons[J].International Journal of Non-Linear Mechanics,2016,85:226-240.
[5]MASRI S F,CAUGHEY T K.A nonparametric identification technique for nonlinear dynamic problems[J].Journal of Applied Mechanics,1979,46(2):433-447.
[6]FELDMAN M.Non-linear system vibration analysis using Hilbert Transform-I:Free vibration analysis method Freevib[J].Mechanical Systems&Signal Processing,1994,8(2):119-127.
[7]FELDMAN M.Non-linear system vibration analysis using Hilbert transform-II:Forced vibration analysis method Forcevib[J].Mechanical Systems&Signal Processing,1994,8(3):309-318.
[8]BRAUN S,FELDMAN M.Decomposition of non-stationary signals into varying time scales:Some aspects of the EMD and HVD methods[J].Mechanical Systems&Signal Processing,2011,25(7):2608-2630.
[9]邓杨,彭志科,杨杨,等.基于参数化时频分析的非线性振动系统参数辨识[J].力学学报,2013,45(6):992-996.DENG Yang,PENG Zhike,YANG Yang,et al.Identification of nonlinear vibration systems based on parametric TFA[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(6):992-996.
[10]FELDMAN M.Mapping nonlinear forces with congruent vibration functions[J].Mechanical Systems and Signal Processing,2013,37(1/2):315-337.
[11]闫蓓,王斌,李媛.基于最小二乘法的椭圆拟合改进算法[J].北京航空航天大学学报,2008,34(3):295-298.YAN Bei,WANG Bin,LI Yuan.Optimal ellipse fitting method base d on least-square principle[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(3):295-298.
[12]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.
[13]CHEN L Q,YUAN T C.Nonlinear oscillation of a circular plate energy harvester[C]∥XXVI International Congress of Theoretical and Applied Mechanics.Montrèal,Canada,2016.
[14]唐贵基,庞彬.基于改进的希尔伯特振动分解的机械故障诊断方法研究[J].振动与冲击,2015,34(3):167-182.TANG Guiji,PANG Bin.A mechanical fault diagnosis method based on improved Hilbert vibration decomposition[J].Journal of Vibration and Shock,2015,34(3):167-182.
[15]朱可恒,宋希庚,薛冬新.希尔伯特振动分解在滚动轴承故障诊断中应用[J].振动与冲击,2014,33(14):160-164.ZHU Keheng,SONG Xigeng,XUE Dongxin.Roller bearing fault diagnosis using Hilbert vibration decomposition[J].Journal of Vibration and Shock,2014,33(14):160-164.
[16]李辉,郑海起,杨绍普.基于EMD和Teager能量算子的轴承故障诊断研究[J].振动与冲击,2008,27(10):15-7.LI Hui,ZHENG Haiqi,YANG Shaopu.Bearing fault diagnosis based on EMD and Teager-Kaiser energy operator[J].Journal of Vibration and Shock,2008,27(10):15-17.
[17]FELDMAN M.Hilbert transform in vibration analysis[J].Mechanical Systems&Signal Processing,2011,25(3):735-802.