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.

Probability distribution of derailment factor using identical probability distribution evolution method

“…The standard deviation can be obtained by the PEM. 27 Thus, the random forces and moments are as follows…”

“…The standard deviation can be obtained by the PEM. 27 Thus, the random forces and moments are as followswhere Fnormaly(w,t), Fnormalz(w,t) and Fθ(w,t) represent the virtual wheel/rail forces and moments in the y, z and θ -directions, respectively; Kz1 and Cz1 are the stiffness and damping, respectively; Mnormalw represents the wheel-set mass; Cnormalc represents the creep damping; w is the frequency; i stands for the complex unit; Γ(t) is the transition matrix, which distributes the wheel-rail force to the bridge nodes; G(t) is the modulation function matrix; V(t)…”

Influence mechanism of vertical dynamic track irregularity on train operation stability of long-span suspension bridge

“…The track structure usually needs to maintain sufficient foundation stiffness to ensure the smoothness of the track and the operation stability of train, especially for the high-speed train. 1–3…”