非平稳风速的HHS时频状态表征
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摘要
为完整描述非平稳风速的时变特征,在传统时频分析手段的基础上,引入Holo-Hilbert谱(HHS),开展台风非平稳脉动风速的时频状态表征研究。以苏通桥址区记录的"海葵"台风风速样本为例,通过经验模式分解(EMD)将风速样本分解为多个正交单分量固有模式函数,并采用Huang氏标准化方法获得了各分量的解析信号表达。基于相位角恒增准则,计算了各分量在每一时刻的瞬时频率,并避免了解析信号出现负频率的问题。在此基础上,进一步对各分量的幅值进行Hilbert-Huang变换,将传统Hilbert时频谱拓展至四维状态,从而获得了实测非平稳风速的高阶时频谱。分析结果表明:高阶时频谱可完整描述非平稳风速的幅值调制特征,通过高阶边际谱可准确确定幅值调制的具体频率或频带范围;幅值频率与载体频率的尺度谱可表征非平稳风速在各载体频率处的幅值调制状态。
To fully describe the time-varying feature of non-stationary wind velocities and based on the traditional approaches of the time-frequency analysis,the Holo-Hilbert spectrum(HHS)is introduced to characterize the time-frequency state of typhoon fluctuating velocities.The wind sample of Typhoon Haikui recorded at Sutong Bridge site is taken as an example.By employing the empirical mode decomposition(EMD),the wind sample is decomposed into several orthogonal intrinsic modes,which are then written in analytical expressions using Huang′s normalization method.Based on the criterion that the phase angle is always increasing,the instantaneous frequency of each mode is calculated and the conventional negative frequency problem is avoided.Then,a Hilbert-Huang transform is further performed on the amplitude function,and the traditional Hilbert timefrequency spectrum is extended to be four dimensional.Thus the high-order time-frequency spectrum of the measured wind velocity is acquired.The analytical results indicate that the high-order time-frequency spectrum can fully describe the amplitudemodulating features of non-stationary wind velocities,and is able to accurately determine the specific frequency or frequency band of amplitude modulating.The scalogram of amplitude frequency and carrier frequency can characterize the amplitude-modulating state of the non-stationary wind velocity at each carrier frequency.
To fully describe the time-varying feature of non-stationary wind velocities and based on the traditional approaches of the time-frequency analysis,the Holo-Hilbert spectrum(HHS)is introduced to characterize the time-frequency state of typhoon fluctuating velocities.The wind sample of Typhoon Haikui recorded at Sutong Bridge site is taken as an example.By employing the empirical mode decomposition(EMD),the wind sample is decomposed into several orthogonal intrinsic modes,which are then written in analytical expressions using Huang′s normalization method.Based on the criterion that the phase angle is always increasing,the instantaneous frequency of each mode is calculated and the conventional negative frequency problem is avoided.Then,a Hilbert-Huang transform is further performed on the amplitude function,and the traditional Hilbert timefrequency spectrum is extended to be four dimensional.Thus the high-order time-frequency spectrum of the measured wind velocity is acquired.The analytical results indicate that the high-order time-frequency spectrum can fully describe the amplitudemodulating features of non-stationary wind velocities,and is able to accurately determine the specific frequency or frequency band of amplitude modulating.The scalogram of amplitude frequency and carrier frequency can characterize the amplitude-modulating state of the non-stationary wind velocity at each carrier frequency.
引文
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[10]Huang N E,Hu K,Yang A C C,et al.On Holo-Hilbert spectral analysis:a full informational spectral representation for nonlinear and non-stationary data[J].Philosophical Transactions of the Royal Society a Mathematical Physical and Engineering Sciences,374(2065):20150206.
[2]王浩,杨敏,陶天友,等.苏通大桥桥址区实测强风非平稳风特性分析[J].振动工程学报,2017,30(2):312-318.Wang Hao,Yang Min,Tao Tianyou,et al.Analysis of non-stationary wind characteristics of measured strong winds at the site of Sutong bridge[J].Journal of Vibration Engineering,2017,30(2):312-318.
[3]Kijewski-Correa T,Kareem A.Efficacy of Hilbert and wavelet transforms for time-frequency analysis[J].Journal of Engineering Mechanics,ASCE,2006,132(10):1037-1049.
[4]黄国庆,彭留留,廖海黎,等.普立特大桥桥位处山区风特性实测研究[J].西南交通大学学报,2016,51(2):349-356.Huang Guoqing,Peng Liuliu,Liao Haili,et al.Field measurement study on wind characteristics at Puli Great Bridge site in mountainous area[J].Journal of Southwest Jiaotong University,2016,51(2):349-356.
[5]Xu Y L,Chen J.Characterizing nonstationary wind speed using empirical mode decomposition[J].Journal of Structural Engineering,ASCE,2004,130(6):912-920.
[6]Su Y W,Huang G.Q,Xu Y L.Derivation of timevarying mean for non-stationary downburst winds[J].Journal of Wind Engineering and Industrial Aerodynamics,2015,141:39-48.
[7]Huang N E,Wu Z,Long S R,et al.On instantaneous frequency[J].Advances in Adaptive Data Analysis,2009,1(2):177-229.
[8]谢献忠,黄志刚,陈文新,等.基于峰频带通信号HHT变换的框架结构试验模态分析[J].工程力学,2012,29(5):134-140.Xie Xianzhong,Huang Zhigang,Chen Wenxin,et al.Experimental modal analysis of reinforced concrete frame structure by Hilbert-Huang transformation based on bandpass signals[J].Engineering Mechanics,2012,29(5):134-140.
[9]柯世堂,赵林,邵亚辉,等.Wavelet_Huang和Hilbert_Huang方法用于非高斯风压信号分析的比较研究[J].土木工程学报,2011,44(6):61-67.Ke Shitang,Zhao Lin,Shao Yahui,et al.Comparison of WHT and HHT methods for analyzing non-Gaussian wind pressure signals[J].China Civil Engineering Journal,2011,44(6):61-67.
[10]Huang N E,Hu K,Yang A C C,et al.On Holo-Hilbert spectral analysis:a full informational spectral representation for nonlinear and non-stationary data[J].Philosophical Transactions of the Royal Society a Mathematical Physical and Engineering Sciences,374(2065):20150206.