Research on probability statistics of train running safety indices based on pseudo-excitation method

Abstract

In order to explore the random nature of high-speed railway train operation safety indices, the pseudo-excitation method, extreme value theory, and non-stationary harmonic superposition theory are used in this paper to study the statistics of train operation safety indices. The pseudo-excitation load formulation for track irregularity is obtained by the pseudo-excitation method, and the resulting non-stationary random vibration problem is transformed into a deterministic time history problem. The pseudo-excitation method is used to establish the dynamic equations of motion, and the separation iteration method is used to solve the equations, so as to obtain the power spectral density of the wheel-rail interaction forces. The wheel-rail interaction forces are obtained by using a modulation function and the harmonic superposition method. By fitting an extreme value distribution, the maximum values of the train running safety indices are explored. The proposed numerical approach is validated experimentally using the data from a 24.6 m long simply supported concrete bridge by studying the extreme value distributions of driving safety indices. Additional numerical simulation are conducted for varying train speeds and bridge spans. The results show that the Gumbel distribution can fit the extreme value of driving safety parameters for different speeds and different bridge span lengths. It is observed that the higher the speed, the sharper the extreme value distribution of train running safety indices, and the larger the train running safety index values corresponding to 99.87% confidence level. The corresponding extreme values at the 99.87% confidence level are greater than the maximum value of each time-domain sample.