基于小波的非线性结构系统识别
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摘要
提出了一个基于小波变换的方法用于非线性结构系统识别。采用复Morlet小波,对非线性结构自由响应信号进行连续小波变换,根据小波系数模极大值的方法提取小波变换的脊线和小波骨架。提取的小波脊线和小波骨架被用来识别结构的瞬时频率和振幅,得到非线性结构的骨架曲线。为降低噪声的影响,采用一个基于奇异值分解(SVD)的方法对识别的结构进行处理。最后通过一个具有非线性刚度结构的数值模拟验证了该方法的有效性。
A method based on wavelet transformation for identifying a nonlinear structure system was presented.With it complex Morlet wavelet was adopted and continuous wavelet transformation on a free response signal of a nonlinear structure was performed.According to maximum value of modulus of wavelet coefficient,wavelet ridges and wavelet skeleton were extracted,which could be used to identify the instantaneous frequency and amplitude of the signal,then the skeleton curve of the nonlinear structure was obtained.In addition,a method based on singular value decomposition(SVD) was proceed to deal with the obtained result for dropping influence of noise.At last,the effectiveness of the proposed method was validated via numerical simulation of two structure models with nonlinear stiffness.
A method based on wavelet transformation for identifying a nonlinear structure system was presented.With it complex Morlet wavelet was adopted and continuous wavelet transformation on a free response signal of a nonlinear structure was performed.According to maximum value of modulus of wavelet coefficient,wavelet ridges and wavelet skeleton were extracted,which could be used to identify the instantaneous frequency and amplitude of the signal,then the skeleton curve of the nonlinear structure was obtained.In addition,a method based on singular value decomposition(SVD) was proceed to deal with the obtained result for dropping influence of noise.At last,the effectiveness of the proposed method was validated via numerical simulation of two structure models with nonlinear stiffness.
引文
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[10]Delprat N,Escudie B,et al.Asymptotic wavelet and gaboranalysis:extraction of instantaneous frequencies[J].IEEETrans on Information Theory,1992,38(2):644—664.
[11]Carmona R,Wen L H,Torrdsani B.Characteization of sig-nals by the ridges of their wavelet transforms[R].Califor-nia,Mar.22,1995.
[12]Wang Chao,Ren Weixin.A wavelet ridge and SVD-basedapproach for instantaneous frequency identification of struc-ture[A].Proceedings of the Second International Confer-ence on Structural Condition Assessment,Monitoring andImprovement,Changsha,Nov.19—21,2007,803—807.
[2]Feldman M.Non-linear system vibration analysis Hilberttransform-Ⅱ.Forced vibration analysis method‘Forcevib’[J].Mechanical systems and signal processing.1994,8(3):309—318.
[3]Feldman M.Identification of weakly nonlinearities in multiplecoupled oscillators[J].Journal of sound and vibration,2007,303:357—370.
[4]Shaw S W,Pierre C.Normal modes for non-linear vibratorysystems[J].Journal of sound and vibration,1993,164(1):85—124.
[5]黄天立,楼梦麟.基于HHT的非线性结构系统识别研究[J].地震工程与工程振动.2006,26(3):80—83.
[6]Kerschen G,Vakakis AF,et al.Toward a fundamental under-standing of the Hilbert-Huang transform in nonlinear structur-al dynamics[A].IMAC-XXIV Conference&exposition onstructural dynamics,St.Louis,Missouri,Jan.30-Feb.2,2006.
[7]Frank Pai P.Nonlinear vibration characterization by signaldecomposition[J].Journal of sound and vibration,2007,307:527—544.
[8]Staszewski W J.Identification of non-linear systems usingmult-scale ridges and skeletons of the wavelet transform[J].Journal of sound and vibration,1998,214(4):639—658.
[9]Ta M N,Lardies J.Identification of weak nonlinearities ondamping and stiffness by the continuous wavelet transform[J].Journal of sound and vibration,2006,293:16—37.
[10]Delprat N,Escudie B,et al.Asymptotic wavelet and gaboranalysis:extraction of instantaneous frequencies[J].IEEETrans on Information Theory,1992,38(2):644—664.
[11]Carmona R,Wen L H,Torrdsani B.Characteization of sig-nals by the ridges of their wavelet transforms[R].Califor-nia,Mar.22,1995.
[12]Wang Chao,Ren Weixin.A wavelet ridge and SVD-basedapproach for instantaneous frequency identification of struc-ture[A].Proceedings of the Second International Confer-ence on Structural Condition Assessment,Monitoring andImprovement,Changsha,Nov.19—21,2007,803—807.
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