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为揭示非平稳随机脉动风的时频特性,基于小波变换原理推导了时变功率谱的时间、频率和幅值与小波变换系数的关系,建立了非平稳随机脉动风时变功率谱估计的小波函数加权和法,并采用模拟非平稳脉动风和实测台风过程对理论推导结果进行了验证。研究结果表明:非平稳随机过程在某一时刻的不同尺度小波变换系数是一个以此非平稳随机过程的调制函数与小波函数的乘积为调制函数的非平稳随机过程的傅里叶变换,非平稳随机过程的时变功率谱等于不同尺度和不同时移的小波函数模平方的加权和,小波函数加权和法计算的非平稳随机脉动风的时变功率谱与理论结果具有良好的一致性。小波函数加权和法可有效地估计非平稳随机脉动风的时变功率谱,估计的时变功率谱可为进一步理解强(台)风的随机脉动特性奠定基础。
In order to reveal the time-frequency characteristics of nonstationary stochastic fluctuating wind, the relationship between time, frequency and amplitude of time-varying power spectrum and wavelet transform coefficients is deduced based on the principle of wavelet transform. Wavelet of time-varying power spectrum estimation of nonstationary stochastic fluctuating wind Function weighted sum method, and the theoretical derivation results are verified by simulating the non-stationary fluctuating wind and the measured typhoon process. The results show that the wavelet transform coefficients at different scales of a nonstationary stochastic process at a certain moment are a Fourier transform of a nonstationary stochastic process whose product is a modulation function of the nonstationary stochastic process and the function of the wavelet function is nonstationary The time-varying power spectrum of the random process is equal to the weighted sum of the squared squares of the wavelet functions of different scales and different time shifts. The time-varying power spectrum of the nonstationary stochastic fluctuating winds calculated by the weighted sum of the wavelet functions is in good agreement with the theoretical results. The weighted sum method of wavelet function can effectively estimate the time-varying power spectrum of nonstationary stochastic fluctuating wind. The estimated time-varying power spectrum can lay a foundation for further understanding of stochastic ripple characteristics of strong (typhoon) wind.