基于小波分解的宽带、非稳态信号激励下的结构响应计算
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摘要
随着大型工程机械工作环境的复杂化,其结构所受到的激励载荷也变得多样化,激励载荷由传统的窄带、稳态信号激励已逐渐走入了宽带、非稳态信号激励,对于宽带、非稳态信号激励下结构的动态响应分析也已经变得越来越迫切;另外,随着各种测试设备精度的大幅提高,结构在这种复杂激励下动力响应的测量也变为了可能。
计算机技术的发展,使有限元计算越来越多的应用于各种动力学领域的模拟、分析和计算中。文章第一部分研究了各种常用的数值方法对于宽带、非稳态信号激励下的结构响应计算的适应性,并得出以下结论:其对于窄带、稳态信号激励的计算能够得到高精度的结果,然而对于宽带、非稳态信号激励下的计算,还有很多值得改进的地方,有时甚至会出现错误的结果。针对这种问题,提出了基于信号分解和重组的方法,即把宽带、非稳态信号分解成不同频率段的窄带信号,而不同频率段的窄带激励信号采用不同的计算方法,分别得到其响应,进而得到原宽带、非稳态信号激励下结构的响应。
小波理论是近年来兴起的一种崭新的信号分析理论,一种可达到时间域或频率域局部化的时频分析方法,被称为数学上的“显微镜”。在文章第二部分,研究了如何利用小波变换的方法把宽带、非稳态信号分解成不同频率段的窄带、稳态信号。通过小波分解后不同频率段的信号,可以分别通过不同的计算方法求得其响应。对于高频信号还可以展开写成高频小波基的线性组合,利用系统对高频小波基的响应很快就可以得到系统的高频响应,进而通过叠加法原理就可以得到系统的响应。
文章的第三部分研究了在宽带、非稳态信号激励下,结构动力响应的数值模拟计算中时间步长的选取原则,以及把高频信号激励下的响应转化成对高频小波基的响应时,为了保证计算精度,计算时间截断的选取原则。通过计算发现,对于宽频、非稳态载荷激励的响应计算,文中提出的方法在满足高精度要求的前提下,能够大大提高计算效率。
文章最后,通过实验验证了:在宽频、非稳态信号激励下,通过小波分解的方法把激励信号分解到不同的频段上,进而通过叠加法得到原线性系统的响应的方法是确实可行的。
Along with complication of large-scale engineering machinery's working environment,exciting load of its structure has become diversification.Signals of exciting load has become wideband and non-stationary from narrow band and steady in tradition.The dynamic responseof structure in the excitation of wideband and non-stationary signals becomes more and more urgently. In addition, with a substantial increase in accuracy of test equipment, the measurement of dynamic response of structure in this complex excitation load signal also becomes possible.
With the development of computer technology, more and more finite element method applied to the variety simulation, analysis and calculation of dynamics.The first part discuss a variety of numerical methods commonly used for broadband, non-stationary signals excited by adaptive structural response calculations, and comes to the following conclusions: for the band, the calculation of steady-state excitation signal can get highly accurate results, however, for broadband and non-stationary signals incentive, it is difficult to get good results, even an error result. It is proposed based on signal decomposition and restructuring methods. The broadband, non-stationary signal is decomposed into narrowband signals of different frequencies, different frequency of excitation signals with different methods of calculation, the response and the original broadband, non-steady-state response excitation of the structure has obtained.
Wavelet theory is the rise in recent years, a new signal analysis theory, one can achieve the time domain or frequency domain analysis of time-frequency localization method, known as the mathematical "microscope." In the second part, the research studies how to use wavelet transform method decompose broadband, non-stationary signal into different frequency bands of narrow-band, steady signal. Through wavelet signals’decomposition of different frequencies can be separately obtained by different methods of calculation of its response. The high-frequency signal also can be written to a linear combination of high-frequency wavelet basis, using the system response on wavelet basis, high-frequency response of the system can be quickly obtained. And then through the superposition principle the response can be measured.
The third part research on with a broadband, non-stationary signal excitation, structural dynamic response of the numerical simulation time step selection principles, and the high frequency signal excitations translate into high-frequency response of wavelet bases, in order to ensure accuracy, computation time truncation selection principle.
Finally, validated by experiment: in the excitation of non-stationary broadband signals, through the wavelet method, decompose the excitation signal into different frequency bands, and then obtained by superposition of the response of the linear system is indeed feasible .
计算机技术的发展,使有限元计算越来越多的应用于各种动力学领域的模拟、分析和计算中。文章第一部分研究了各种常用的数值方法对于宽带、非稳态信号激励下的结构响应计算的适应性,并得出以下结论:其对于窄带、稳态信号激励的计算能够得到高精度的结果,然而对于宽带、非稳态信号激励下的计算,还有很多值得改进的地方,有时甚至会出现错误的结果。针对这种问题,提出了基于信号分解和重组的方法,即把宽带、非稳态信号分解成不同频率段的窄带信号,而不同频率段的窄带激励信号采用不同的计算方法,分别得到其响应,进而得到原宽带、非稳态信号激励下结构的响应。
小波理论是近年来兴起的一种崭新的信号分析理论,一种可达到时间域或频率域局部化的时频分析方法,被称为数学上的“显微镜”。在文章第二部分,研究了如何利用小波变换的方法把宽带、非稳态信号分解成不同频率段的窄带、稳态信号。通过小波分解后不同频率段的信号,可以分别通过不同的计算方法求得其响应。对于高频信号还可以展开写成高频小波基的线性组合,利用系统对高频小波基的响应很快就可以得到系统的高频响应,进而通过叠加法原理就可以得到系统的响应。
文章的第三部分研究了在宽带、非稳态信号激励下,结构动力响应的数值模拟计算中时间步长的选取原则,以及把高频信号激励下的响应转化成对高频小波基的响应时,为了保证计算精度,计算时间截断的选取原则。通过计算发现,对于宽频、非稳态载荷激励的响应计算,文中提出的方法在满足高精度要求的前提下,能够大大提高计算效率。
文章最后,通过实验验证了:在宽频、非稳态信号激励下,通过小波分解的方法把激励信号分解到不同的频段上,进而通过叠加法得到原线性系统的响应的方法是确实可行的。
Along with complication of large-scale engineering machinery's working environment,exciting load of its structure has become diversification.Signals of exciting load has become wideband and non-stationary from narrow band and steady in tradition.The dynamic responseof structure in the excitation of wideband and non-stationary signals becomes more and more urgently. In addition, with a substantial increase in accuracy of test equipment, the measurement of dynamic response of structure in this complex excitation load signal also becomes possible.
With the development of computer technology, more and more finite element method applied to the variety simulation, analysis and calculation of dynamics.The first part discuss a variety of numerical methods commonly used for broadband, non-stationary signals excited by adaptive structural response calculations, and comes to the following conclusions: for the band, the calculation of steady-state excitation signal can get highly accurate results, however, for broadband and non-stationary signals incentive, it is difficult to get good results, even an error result. It is proposed based on signal decomposition and restructuring methods. The broadband, non-stationary signal is decomposed into narrowband signals of different frequencies, different frequency of excitation signals with different methods of calculation, the response and the original broadband, non-steady-state response excitation of the structure has obtained.
Wavelet theory is the rise in recent years, a new signal analysis theory, one can achieve the time domain or frequency domain analysis of time-frequency localization method, known as the mathematical "microscope." In the second part, the research studies how to use wavelet transform method decompose broadband, non-stationary signal into different frequency bands of narrow-band, steady signal. Through wavelet signals’decomposition of different frequencies can be separately obtained by different methods of calculation of its response. The high-frequency signal also can be written to a linear combination of high-frequency wavelet basis, using the system response on wavelet basis, high-frequency response of the system can be quickly obtained. And then through the superposition principle the response can be measured.
The third part research on with a broadband, non-stationary signal excitation, structural dynamic response of the numerical simulation time step selection principles, and the high frequency signal excitations translate into high-frequency response of wavelet bases, in order to ensure accuracy, computation time truncation selection principle.
Finally, validated by experiment: in the excitation of non-stationary broadband signals, through the wavelet method, decompose the excitation signal into different frequency bands, and then obtained by superposition of the response of the linear system is indeed feasible .
引文
[1]包世华.结构动力学[M].武汉:武汉理工大学出版社,2005.
[2]张亚辉,林家浩.结构动力学基础[M].大连:大连理工大学出版社,2007.
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[6]李启月.工程机械[M].湖南:中南大学出版社.2007.
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[36]郑国强等.数字信号处理——理论与实践[M].西安:西安电子科技大学出版社,2009.
[37]赵淑清,郑薇.随机信号分析[M].哈尔滨:哈尔滨工业大学出版社,2007.
[38]孟庆丰,焦李成.回转机械低频振动的时频域识[J].振动工程学报,2004,17 (2):374-376 .
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[42]王勖成,邵敏.有限单元法基本原理与数值方法[M].北京:清华大学出版社,1995.
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[2]张亚辉,林家浩.结构动力学基础[M].大连:大连理工大学出版社,2007.
[3]李东旭.高等结构动力学[M].长沙:国防科学大学出版社,1997.
[4]刘延柱,陈文良,陈立群.振动力学[M].高等教育出版社,1998.
[5] J.H.Ginsberg. Mechanical and Structural Vibrations-Theory and Applications[M]. JOHN WILEY&SONS.2001.
[6]李启月.工程机械[M].湖南:中南大学出版社.2007.
[7]张汝清等.现代计算力学[M].重庆:重庆大学出版社.2004.
[8]杨庆生,郑代华.高等计算力学[M].科学出版社.2009.
[9]曾攀.有限元分析及应用[M].北京:清华大学出版社.2004.
[10]王元汉,李丽娟,李银平.有限元法基础与程序设计[M].北京:清华大学出版社.2002.
[11]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[12]李建平.小波分析与信号处理——理论、应用及软件实现[M].重庆:重庆出版社,1997.
[13] B.H.Barbara.The World According to Wavelets:the Story of a Mathematical Technique in the Making[J].A K Peters Ltd.1998:90-95.
[14]李惠粉,蒋向前,李住.小波理论的发展及其在表面功能评定中的应用[J].现代计量测试,2001,5:5-8.
[15] E P Wigner.On the Quantum Correction for Thermodynamic Equilibrium[J].Physical Review,1932,40:749-759.
[16] D.Gabor.Theory of Communication[J].J.Inst.Elec.Eng. 1946,93:429-457.
[17] R.K.Potter,et al.Visible Speech[M].New York:Van Nostrand,1947.
[18] J.Ville.Theories et Applications de La notion de Signal Analytique[J].Cables et Transmission,1948,2A:61-74.
[19] C.H.Page.Instantaneous Power Spectra.J.Appl.Phys[J],1952.23:103-106.
[20] L.Cohen.Time-frequency Distributions—A Review,Proc[J].IEEE,1989,77:941-981.
[21] L.Cohen.Generalized Phase-space Distribution Functions.J.Math.Phys[J].,1966,7:781-786.
[22]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1999.
[23] V.Namias . The Fractional Order Fourier Transform and Its Application to Quantum Mechanics,J.Inst.Math[J].Applicat,1980,25:241-265.
[24] J.Morlet,G.Arens,E.Fourgeau,and D.Giard . Wave Propagation and Sampling Theory——PartⅡ:Sampling Theory and Complex Waves[J].Geophysics,1982,(2):222-236.
[25]秦前清,杨宗凯.实用小波分析[M].西安:西安电子科学出版社,1994.
[26] S.Mann, S.Haykin . Chirplets and Wavelets:Novel Time-frequency Methods[J].Electronic Letters,1992,28:114-116.
[27] D.Mihovilovic,R.N.Bracewell . Whistler Analysis in the Time-frequency Plane Using Chirplets[J].Geophysical Reasearch,1992,97:17 199-17 204.
[28] S.G.Mallat,Zhifeng Zhang.Matching Pursuits with Time-frequency Dictionaries[J].IEEE Trans.Signal Processing.1993,41(12):3397-3415.
[29]石钧.多小波:理论和应用[J].信号处理,1999,15(4):329-334.
[30] V.Strela.Multiwavelets:Theory and Application[J].Doctoral thesis,U.S.,Massachusetts Institudeof Technology,1996.
[31]刘贵忠,张志明,冯牧.由小波变换的模极大值快速重构信号[J].自然科学进展.2000, 10(7): 660-664.
[32]张茁生,刘贵忠,刘峰.一种新的信号二进小波变换模极大值重构信号的迭代算法[J].中国科学(E辑).2003, 33(6): 545-553.
[33] S. G. Mallat, Zhang Z. Matching Pursuit with Time-Frequency Dictionaries[J]. IEEE Trans, Singal Processing, Vol. 41, No. 12, 3397-3415, 1993.
[34]赵光宙.信号分析与处理(第二版)[M].机械工业出版社,2006.
[35]格拉法科斯.傅里叶分析(英文版)[M].机械工业出版社,2006.
[36]郑国强等.数字信号处理——理论与实践[M].西安:西安电子科技大学出版社,2009.
[37]赵淑清,郑薇.随机信号分析[M].哈尔滨:哈尔滨工业大学出版社,2007.
[38]孟庆丰,焦李成.回转机械低频振动的时频域识[J].振动工程学报,2004,17 (2):374-376 .
[39] S.G.Mallat. "A theory for multiresolution signal decompositions:the wavelet representation"[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.1989,7,11(7) :674-693.
[40] X .P.Zhang, et al. "From the wavelet series to the discrete wavelet transform the initialization"[J]. IEEE Trans.SP. 44(1).1996:129-133.
[41]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.
[42]王勖成,邵敏.有限单元法基本原理与数值方法[M].北京:清华大学出版社,1995.
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