基于演化谱理论的桥梁风致响应非平稳性分析
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摘要
基于Priestley演化谱理论,并结合小波变换原理,在理论上推导了非平稳随机过程演化谱估计的小波时域函数加权和法,从小波时域函数的角度建立了演化谱估计时域方法,弥补了传统演化谱估计方法需要小波频域函数这一不足。在此基础上,对实测台风"麦莎"全过程以及润扬大桥悬索桥在台风"麦莎"作用下的抖振响应进行了演化谱估计,分析了台风全过程及其风致响应的时频特性。研究结果表明:小波时域函数加权和法是一种估计非平稳随机过程演化谱的有效方法;台风"麦莎"全过程表现为强度强非平稳、频率弱非平稳,脉动风的脉动能量在整个台风过程中变化较大但主要频率成分变化较小;润扬大桥悬索桥主梁的风致抖振响应表现为强度非平稳、频率平稳,振动能量变化剧烈但频率成分基本不变。
Based on the principle of wavelet transform and the theory of evolutionary spectrum developed by Priestley,the property that the evolutionary spectrum was equal to the summation weighted wavelet functions in time domain was deduced.A method,which could overcome the shortage of the traditional method that the closed-form expression of wavelet in frequency domain was required,was established to estimate the evolutionary spectrum of nonstationary stochastic processes.Based on the field measurement data on Runyang Suspension Bridge,the evolutionary spectra of typhoon Matsa and wind-induced vibration in main girder were estimated and the timefrequency characteristics were analyzed.The results show that the proposed method can calculate the evolutionary spectrum of nonstationary stochastic processes accurately and effectively.The fluctuating wind of typhoon Matsa is high and nonstationary in intensity aspect but weak and nonstationary in frequency aspect.The energy of the fluctuating wind varies dramatically with the typhoon passing but the frequency components change little.The wind-induced vibration of the main girder of Runyang Suspension Bridge is nonstationary in intensity aspect and stationary in frequency aspect.When typhoon passing,the vibration energy changes obviously but the frequency components are constant.
Based on the principle of wavelet transform and the theory of evolutionary spectrum developed by Priestley,the property that the evolutionary spectrum was equal to the summation weighted wavelet functions in time domain was deduced.A method,which could overcome the shortage of the traditional method that the closed-form expression of wavelet in frequency domain was required,was established to estimate the evolutionary spectrum of nonstationary stochastic processes.Based on the field measurement data on Runyang Suspension Bridge,the evolutionary spectra of typhoon Matsa and wind-induced vibration in main girder were estimated and the timefrequency characteristics were analyzed.The results show that the proposed method can calculate the evolutionary spectrum of nonstationary stochastic processes accurately and effectively.The fluctuating wind of typhoon Matsa is high and nonstationary in intensity aspect but weak and nonstationary in frequency aspect.The energy of the fluctuating wind varies dramatically with the typhoon passing but the frequency components change little.The wind-induced vibration of the main girder of Runyang Suspension Bridge is nonstationary in intensity aspect and stationary in frequency aspect.When typhoon passing,the vibration energy changes obviously but the frequency components are constant.
引文
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[13]SPANOS P D,FAILLA G.Evolutionary Spectra Estimation Using Wavelets[J].Journal of Engineering Mechanics,2004,130(8):952-960.
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[15]赵杨,武岳,曹曙阳,等.利用HHT方法对非平稳风力的时频分析[J].振动与冲击,2011,30(2):5-9,14.ZHAO Yang,WU Yue,CAO Shu-yang,et al.Timefrequency Analysis of a Non-stationary Wind Pressure with HHT Method[J].Journal of Vibration and Shock,2011,30(2):5-9,14.
[2]马麟,刘健新,韩万水,等.基于Hilbert-Huang变换的大跨桥梁非线性抖振响应时频分析[J].振动与冲击,2010,29(11):237-242,265.MA Lin,LIU Jian-xin,HAN Wan-shui,et al.Timefrequency Analysis for Nonlinear Buffeting Response of a Long-span Bridge Based on HHT[J].Journal of Vibration and Shock,2010,29(11):237-242,265.
[3]赵杨,曹曙阳,武岳,等.几种非平稳分析方法对非平稳风力时程的比较分析[J].土木工程学报,2011,44(9):51-57.ZHAO Yang,CAO Shu-yang,WU Yue,et al.Comparison of Several Non-stationary Methods for Analysis of Time History of Non-stationary Wind Pressure[J].China Civil Engineering Journal,2011,44(9):51-57.
[4]樊剑,刘铁,胡亮.基于现代时频分析技术的地震波时变谱估计[J].振动与冲击,2007,26(11):79-82,98,184.FAN Jian,LIU Tie,HU Liang.Time-varying Spectrum Estimation of Earthquake Ground Motion via Modern Time-frequency Analysis[J].Journal of Vibration and Shock,2007,26(11):79-82,98,184.
[5]IYAMA J,KUWAMURA H.Application of Wavelets to Analysis and Simulation of Earthquake Motions[J].Earthquake Engineering&Structural Dynamics,1999,28(3):255-272.
[6]BASU B,GUPTA V K.Stochastic Seismic Response of Single-degree-of-freedom Systems Through Wavelets[J].Engineering Structures,2000,22(12):1714-1722.
[7]GURLEY K,KAREEM A.Application of Wavelet Transforms in Earthquake,Wind,and Ocean Engineering[J].Engineering Structures,1999,21(2):149-167.
[8]曹晖,赖明,白绍良.地震地面运动局部谱密度的小波变换估计[J].工程力学,2004,21(5):109-115.CAO Hui,LAI Ming,BAI Shao-liang.Estimation of Local Special Density of Earthquake Ground Motion Based on Wavelet Transform[J].Engineering Mechanics,2004,21(5):109-115.
[9]马瑞恒,时党勇.爆破振动信号的时频分析[J].振动与冲击,2005,24(4):92-95.MA Rui-heng,SHI Dang-yong.Time-frequency Analysis of Blasting Vibration Signal[J].Journal of Vibration and Shock,2005,24(4):92-95.
[10]赵明生,张建华,易长平.基于小波分解的爆破振动信号RSPWVD二次型时频分析[J].振动与冲击,2011,30(2):44-47.ZHAO Ming-sheng,ZHANG Jian-hua,YI Changping.Blasting Vibration Signal RSPWVD Quadratic Time-frequency Analysis Based on Wavelet Decomposition[J].Journal of Vibration and Shock,2011,30(2):44-47.
[11]PRIESTLEY M B.Power Spectral Analysis of Nonstationary Random Processes[J].Journal of Sound and Vibration,1967,6(1):86-97.
[12]白泉,鲍文博,金生吉.基于小波变换的地震波时变功率谱估计[J].沈阳工业大学学报,2010,32(3):342-348.BAI Quan,BAO Wen-bo,JIN Sheng-ji.Estimation of Time-dependent Power Spectral Density of Seismic Wave Based on Wavelet Transform[J].Journal of Shenyang University of Technology,2010,32(3):342-348.
[13]SPANOS P D,FAILLA G.Evolutionary Spectra Estimation Using Wavelets[J].Journal of Engineering Mechanics,2004,130(8):952-960.
[14]FAILLA G,PAPPATICO M,CUNDARI G A.A Wavelet-based Spectrum for Non-stationary Processes[J].Mechanics Research Communications,2011,38(5):361-367.
[15]赵杨,武岳,曹曙阳,等.利用HHT方法对非平稳风力的时频分析[J].振动与冲击,2011,30(2):5-9,14.ZHAO Yang,WU Yue,CAO Shu-yang,et al.Timefrequency Analysis of a Non-stationary Wind Pressure with HHT Method[J].Journal of Vibration and Shock,2011,30(2):5-9,14.
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