Wavelet_Huang和Hilbert_Huang方法用于非高斯风压信号分析的比较研究
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摘要
非高斯风压时程具有间歇性的大脉冲信号和不对称性,传统的傅里叶变换无法得到信号的频谱特性随时间的变化过程,也不能识别出不同频段处信号的变异性。采用一种结合经验模式分解(EMD)和小波变换(WaveletTransform)的方法(简称WHT)对非高斯风压信号进行时-频-谱联合特性分析,随后讨论了不同频段处信号的奇异性、冲击性和分辨率;并和Hilbert_Huang变换(简称HHT)分析的结果进行对比。两种方法处理非高斯信号都能很好地提取信号的主要特征和分解、重构;由于小波基尺度有限并受到测不准原理的限制,WHT方法得到的小波谱的能量在频率范围内分布较宽,而HHT方法得到的Hilbert能量谱大多都集中在有限的能量谱线上;WHT方法进行不同频段处信号的变异性检测是对EMD分解得到的IMF分量进行小波分解,其更能反映原始数据的固有特性,在任意感兴趣的频段捕捉到信号的局部特征。研究结果表明,HHT方法可以更好地进行非高斯信号的谱特性分析,而WHT方法在信号的分解、重构和变异性检测时效果更好。
The non-Gaussian wind pressure signal has intermittent high pulses and asymmetric characteristics,while traditional Fourier transform cannot get the signal spectrum characteristics over time and the variability in different frequencies.In this paper,the empirical mode decomposition(EMD) and wavelet transform methods are employed in combination to analyze the time-frequency-spectrum of non-Gaussian wind pressure signals,the singularity and impact characteristics of different frequencies are discussed,and the results are compared with those calculated by using Hilbert_Huang transform.The study shows that both WHT and HHT are efficient ways of analyzing the main characteristics and decomposing the non-Gaussian signals.Due to the limit wavelet scale and Heisenberg principle,the wavelet spectrum lines by WHT are distributed in a wide frequency range,but Hilbert energy spectrum by HHT clearly expresses the energy distribution with time and frequency.With WHT method,the intrinsic mode function obtained with EMD can reflect the intrinsic physical characteristics with wavelet transform,and local characteristics of arbitrary frequency can be obtained.It can be concluded that the HHT method is more adaptive than WHT method in analyzing the spectrum characteristics of non-Gaussian signal,while WHT method has a wide range of application for decomposition,restructuring and measurement of variabilities.
The non-Gaussian wind pressure signal has intermittent high pulses and asymmetric characteristics,while traditional Fourier transform cannot get the signal spectrum characteristics over time and the variability in different frequencies.In this paper,the empirical mode decomposition(EMD) and wavelet transform methods are employed in combination to analyze the time-frequency-spectrum of non-Gaussian wind pressure signals,the singularity and impact characteristics of different frequencies are discussed,and the results are compared with those calculated by using Hilbert_Huang transform.The study shows that both WHT and HHT are efficient ways of analyzing the main characteristics and decomposing the non-Gaussian signals.Due to the limit wavelet scale and Heisenberg principle,the wavelet spectrum lines by WHT are distributed in a wide frequency range,but Hilbert energy spectrum by HHT clearly expresses the energy distribution with time and frequency.With WHT method,the intrinsic mode function obtained with EMD can reflect the intrinsic physical characteristics with wavelet transform,and local characteristics of arbitrary frequency can be obtained.It can be concluded that the HHT method is more adaptive than WHT method in analyzing the spectrum characteristics of non-Gaussian signal,while WHT method has a wide range of application for decomposition,restructuring and measurement of variabilities.
引文
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[2]Kumar K S,Stathopulos T.Wind loads on low buildingroofs:a stochastic perspective[J].Journal of StructuralEingineering,2000,126(8):944-956
[3]柯世堂,赵林,葛耀君,等.超大型排烟冷却塔风压分布及双孔道位置优化[J].建筑科学与工程学报,2009,26(2):52-56(Ke Shitang,Zhao Lin,Ge Yaojun,et al.Windpressure distribution and double holes position optimizationfor super large-scale cooling towers with flue gas[J].Journal of Architecture and Civil Engineering,2009,26(2):52-56(in Chinese))
[4]Gioffre M,Gusella V,Grigoriu M.Non-Gaussian windpressure on prismatic buildings.Ⅱ:numerical simulation[J].Journal of Structural Engineering,2001,127(9):990-995
[5]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis[C]//Proceedings of theRoyal Society of London.Series A:Mathematical,Physicaland Engineering Sciences,1998:903-995
[6]Huang N E,Shen Z,Long S R.A new view of nonlinearwater waves:the Hilbert spectrum[J].Annual Review ofFluid Mechanics,1999,31:417-457
[7]Liang H,Lin Z,McCallum R W.Artifact reduction inelectrogastrogram based on empirical mode decompositionmethod[J].Medical and Biological Engineering andComputing,2000,38(1):35-41
[8]Vincent H T,Hu S L J,Hou Z.Damage detection usingempirical mode decomposition method and a comparisonwith wavelet analysis[C]//Proceedings of the 2ndInternational Workshopon Structural Health Monitoring.Stanford:Stanford University,1999:891-900
[9]陈隽,徐幼麟,李杰.Hilbert-Huang变换在密频结构阻尼识别中的应用[J].地震工程与工程振动,2003,23(4):34-42(Chen Jun,Xu Youlin,Li Jie.Hilbert-Huangtransform for damping ratio identification of structures withclosely spaced modes of vibration[J].EarthquakeEngineering and Engineering Vibration,2003,23(4):34-42(in Chinese))
[10]Feldman M.Non-linear system vibration analysis usingHilbert transform.I:free vibration analysis method‘Freevib’[J].Mechanical Systems and SignalProcessing,1994,8(2):119-127
[11]Chui C K.An introduction to wavelets[M].London:Academic Press,1992
[12]郭亚,应怀樵,武颖奎.小波在频率发生较小变化识别中的应用研究[J].振动与冲击,2005,24(5):99-100(Guo Ya,Ying Huaiqiao,Wu Yingkui.Study on waveletapplication in the identification of frequency’s indistinctivechange[J].Journal of Vibration and Shock,2005,24(5):99-100(in Chinese))
[13]柯世堂,赵林,张军锋,等.冷却塔表面脉动风压的非高斯特性及风压极值[C]//第十四届全国结构风工程学术会议论文集.北京:中国土木工程学会,2009:354-362
[14]仲佑明,秦树人,汤宝平.一种振动信号新变换法的研究[J].振动工程学报,2002,15(2):233-238(ZhongYouming,Qin Shuren,Tang Baoping.Study on a newtransform method for vibration signal[J].Journal ofVibration Engineering,2002,15(2):233-238(inChinese))
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