基于谱密度函数的轨道随机不平顺仿真

Simulation of Stochastic Railway Track Irregularity Based on Spectrum Density Function

通过蒙特卡罗方法得出高斯随机过程的相位概率分布类型,运用傅立叶变换进行时域信号的谱密度估计。基于时域采样原理,提出谱密度函数在频域内的采样方法,并利用傅立叶逆变换由谱密度函数得出轨道随机不平顺,使其符合时域分析的需要。仿真结果显示:高斯随机过程的相位符合均匀分布;轨道随机不平顺的模拟结果与频率下限和上限有很大关系,小的频率下限模拟结果表现为宽带波形,大的频率下限模拟结果表现为窄带波形,且频率上限越大,模拟结果中叠加的高频小幅成分越多。通过选择适当的模拟参数,可以使轨道随机不平顺的时域仿真结果与实测结果和频域仿真结果较好相符。

Probability distribution form of phase of Gaussian stochastic process was obtained by means of Monte Carlo method. Spectrum density of signal in time domain was evaluated through Fourier transform. Based on sampling rule of time domain, the sampling method of spectrum density function in frequency domain was put forward. By means of the inverse Fourier transform, stochastic railway track irregularity was obtained from spectrum density function to meet the requirements of the dynamics analysis in time domain. Simulation result shows that phase of Gaussian stochastic process accords with uniform distribution. The simulation results of track stochastic irregularity are quite dependent on frequency upper and lower limit. Simulation result is wideband wave with smaller lower limit and narrowband wave with bigger one. The bigger is upper limit, the more components of high frequency and small amplitude are superposed in simulation results. Selecting appropriate simulation parameters can make the simulation results in time domain of stochastic railway track irregularities agree well with the measured values and the simulation results in frequency domain.