时滞多维轨道不平顺激励的一致白噪声模型

Uniform White Noise Model for Time-Delay Multi-dimensional Rail Irregularity Excitation

为获得各轮轴处轨道不平顺,用于列车-桥梁振动控制和随机振动分析,研究了轨道不平顺的模拟方法.采用白噪声滤波法生成单轮轴的轨道不平顺;为实现不平顺波长选择,提出了成型滤波器参数的宽频带识别法.为考虑各轮轴间的时延,利用相邻轮轴间的短时滞,构造了基于高阶Pade近似的累次时滞系统.将成型滤波器与时滞系统相结合,得到了以白噪声为输入、列车各轮轴处轨道不平顺为输出的状态方程.算例表明,模拟样本与轨道不平顺目标谱密度相符,且满足各轮轴处轨道不平顺之间的时滞关系.

To obtain rail irregularity samples for train-bridge vibration control and stochastic analyses, a simulation method of irregularities at all axles of a train was investigated. Rail irregularity at the first axle was generated by the white noise filtration method. To achieve wavelength selection of rail irregularity, a wideband identification method was proposed for the design of a shape filter. To take time-delay among different axles into account, a step-wised time delay system based on a high order Pade＇s approximation of the short time-delay between adjacent axles was constructed. By combining the shape filter with the time-delay system, a state equation with uniform white noise as input and irregularities at all axles of a train as output was obtained. A numerical example shows that simulated irregularity samples accord well with the target irregularity power spectral density （PSD） and satisfy the time-delay relation among irregularities at different axles.