Random dynamic analysis of vertical train–bridge systems under small probability by surrogate model and subset simulation with splitting

Abstract

The response of the train–bridge system has an obvious random behavior. A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge, and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track. Firstly, the coupling model of train–bridge systems is reviewed. Then, an ensemble method is presented, which can estimate the small probabilities of a dynamic system with stochastic excitations. The main idea of the ensemble method is to use the NARX (nonlinear autoregressive with exogenous input) model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution. Finally, the efficiency of the suggested method is compared with the direct Monte Carlo simulation method, and the probability exceedance of train responses under the vertical track irregularity is discussed. The results show that when the small probability of train responses under vertical track irregularity is estimated, the ensemble method can reduce both the calculation time of a single sample and the required number of samples.

A comprehensive review on coupling vibrations of train–bridge systems under external excitations

“…Although the time-domain method can consider the effect of various factors comprehensively, it is still difficult to evaluate the reliability of the train-bridge system. Therefore, an increasing number of random vibration methods are proposed recently, which includes the probability density evolution method (PDEM) [18], pseudoexcitation method (PEM) [19][20][21], statistical linearization [22], surrogate model approach [23,24], subset simulation [25], new point estimation method [26] and other theories or methods [27,28].…”

Probability distribution of derailment factor using identical probability distribution evolution method

“…The extreme value CDF is mainly used to establish the limit value of the derailment factor within the service life of a bridge, where n is the number of times a train runs over the bridge. Within the service life of the bridge, the total number of train operation can be predicted and the limit value of the derailment factor can be obtained using equation (11). Then, the safety of train operations can be judged by comparing the limit value with the relevant specification.…”

“…It mainly focuses on numerical algorithms, vehicle-bridge model optimization, and modeling various external excitations. [2][3][4][5][6][7] The main methods employed in researching the vehiclebridge system random vibrations include the Monte Carlo method (MCM), 8 extremum response surface method, 9 enhance MCM 10 , subset simulations, 11 probability density evolution theory, 12 and pseudo-excitation method (PEM). 13 Yu adopted the probability density evolution theory to study the dynamic response of a bridge considering the randomness of bridge mass, stiffness, and damping, and track irregularity.…”

Effect of long-wave deviation of stator plane on high-speed maglev train and guideway system

“…To realize the modeling and solution of the coupled train-guideway system, MATLAB is used to program the whole process. The train and guideway are regarded as two subsystems, and the corresponding dynamic response is solved by using Newmark- β method (Bao et al, 2021; Han et al, 2019; Xiang et al, 2020). The dynamic analysis of the coupled system mainly includes three steps: (1) the combination of mass, stiffness, and damping matrix of the train system and the guideway system; (2) the calculation of electromagnetic force; (3) the solution of dynamic equation (see Figure 5).…”