路面功率谱密度换算及不平度建模理论研究

Conversion of Spatial Power Spectral Density and Study on Road Irregularity Modeling Theory

为了明晰路面不平度空间域统计量的计算,以及几种重要功率谱密度(power spectral density,简称PSD)之间的关系,以帕塞瓦尔定理和维纳-辛钦定理为依据,在推导空间域自相关函数和PSD计算公式的基础上,导出了不平度空间域位移、速度与加速度PSD以及空间频率与角频率PSD之间的换算关系。另外,为了完善傅里叶逆变换法路面建模中PSD离散化的理论基础,以傅里叶级数与变换、离散傅里叶变换和频域卷积定理为依据,从离散化的原因、目的和结果验证出发论证了PSD离散化的正确性。就模拟路面验证问题,指出直接法谱估计的不合理之处,论证了平均周期图法谱估计时,空间与时间采样频率分别对应着空间域和时间域PSD输出。结果表明,上述换算关系和论证是正确的,可应用于路面不平度建模和汽车平顺性分析。

In order to clarify the spatial statistics calculation of road roughness and find out the relations among several important power spectral densities(PSD),Parseval′s theorem and the Wiener-Khintchine theorem are employed.Based on these theorems,the calculation formulas of spatial autocorrelation and PSD functions can be obtained,and a detailed derivation of the conversion relationships among spatial displacement,velocity and acceleration PSD is given.The relationships between spatial frequency PSD and angular frequency PSD can be obtained according to different Fourier transform patterns.Moreover,due to the lack of strictly theoretical analysis of PSD discretization for road irregularity modeling,it is thoroughly analyzed based on the frequency domain convolution theorem and the principles of six kinds of Fourier transform.In addition,the irrationality of the PSD verifying method in the literature is pointed out.It is also proved that Welch′s spectrum estimation method produces different kinds of road PSD depending on different parameters,such as spatial or temporal sampling frequency.Results show that the analysis and derivation are accurate and can be applied to road irregularity modeling and vehicle ride comfort analysis.