基于小波变换的轨道不平顺数值模拟方法

Track Irregularity Simulation Based on Wavelet Transform

轨道不平顺时域模拟对轨道结构设计、工务养护维修及轮轨动力学计算均具有重要的意义。提出一种基于小波变换理论对轨道不平顺进行数值模拟的方法:对高斯白噪声进行小波分解,得到各层小波系数;根据轨道不平顺功率谱计算各个频段的伸缩比例,对小波系数进行比例伸缩;采用伸缩后的小波系数重构信号,得到轨道不平顺时域序列。以实际地铁轨道不平顺谱作为目标函数,将基于小波变换算法与白噪声滤波法、周期图法以及频域采样三角级数法等进行比较分析,结果表明,基于小波变换算法模拟的轨道不平顺波形满足随机性、非周期性、离散性特征,且呈现非平稳性和非正态性,更符合实际轨道不平顺分布特征规律。

Track irregularity simulation is very important for track structure design, track maintenance and repair works as well as wheel-rail dynamic calculation. A track ir- regularity simulation based on wavelet transform is pro- posed in this paper, the Gaussian white noise is wavelet de- composed for wavelet coefficients of each frequency band, the expanding ratios of the wavelet coefficients are calcu- lated according to track irregularity power spectrum, then wavelet coefficients is expanded according to these ratios to new wavelet coefficients. At last, the track irregularity time series are obtained by wavelet reconstruction according to new wavelet coefficients. The track irregularity simulation based on wavelet transform is compared with white noise filtering method, periodogram method, frequency domain sampling and trigonometric series method. The result shows that track irregularity simulation based on wavelet trans- form is stochastic, not periodic and discrete, is also non stationary and abnormal, it is more in line with the actual track irregularity distribution law.