脉动风速功率谱与随机Fourier幅值谱的关系研究

功率谱密度函数是随机过程在频域内的重要特征量,但由于其本质上是平稳过程的频域数值特征,致使其很难全面反映原始随机过程的概率信息,这就需要从更本源的意义上考察随机过程。本文试图从Fourier随机函数的角度反映随机过程,将经典的功率谱密度函数中具有物理意义的可测变量看作随机变量,利用功率谱与Fourier幅值谱的关系,定义了随机Fourier幅值谱;以Davenport谱为例,证实当地面粗糙度服从对数正态分布、10m高度基本风速服从极值Ⅰ型分布时,可通过功率谱构造具有物理意义的随机Fourier幅值谱。通过实测风速Fourier谱与随机Fourier幅值谱的比较,证明随机Fourier幅值谱的概念具有合理性。

A Study on the Relationship between Turbulence Power Spectrum and Stochastic Fourier Amplitude Spectrum

Power Spectrum is an important characteristic quantity of stochastic process in frequency domain. It can represent the power distribution of the stochastic process. However, because the power spectrum is only a numerical characteristics of stationary process in the frequency domain in nature, it is very difficult for it to involve all probability information of the original stochastic process. This shortcoming not only brings difficulties to the analysis of random vibration for the non-stationary process, but also causes that exact solutions of structure reliability wouldn't be obtained only by means of numerical characteristics solutions even for the stationary process. So it is necessary to investigate the stochastic process at a more frontal level. In this paper, the idea of Fourier stochastic function is adopted to reflect the stochastic process for the above purpose. Based on the relationship between the power spectrum and Fourier amplitude spectrum, the stochastic Fourier amplitude spectrum is defined. Then Davenport spectrum, which is used widely in wind engineering, is taken as an example to validate the proposed idea. The research finds that, when roughness length z_0 is characterized by log-normal distribution and basic wind speed U_(10) at height of ten meters is characterized by extreme value-Ⅰ distribution, the stochastic Fourier amplitude spectrum can be constructed by the power spectrum. Finally, the stochastic Fourier amplitude spectrum is proved to be rational by comparing measured wind speed Fourier spectrum with the stochastic Fourier amplitude spectrum.