Stochastic response analysis of uncertain train–bridge interaction system by stochastic pseudo excitation method

Abstract

The stochastic pseudo-excitation method (SPEM) is applied to improve the efficiency of the random vibration analysis of an uncertain train–bridge interaction (TBI) system. This method is combined with the first-order reliability method to handle the reliability analysis of the system. It is characterized by the introduction of a random variable of the amplitude coefficient based on the principle of the PEM, establishing stochastic excitation at each selected frequency point. Unlike the traditional PEM, the calculation results by the SPEM can consider the random characteristics of external loads and also reflect the effect of uncertain parameters. Two comparisons were conducted to verify the accuracy and efficiency of the proposed method for the dynamic analysis of an uncertain TBI system. First, the results calculated using the SPEM were compared with those calculated using the PEM, indicating that the SPEM can calculate the dynamic responses of the TBI system without uncertainties. Second, the stochastic responses of the uncertain TBI system obtained by the SPEM were compared with those obtained by the MCM, which exhibited good agreement and verified the efficiency of the proposed method. Third, the system response of the simplified TBI model was analyzed to determine the parametric sensitivity. Finally, the reliability of the TBI model was studied based on the selected sensitive parameters. These results indicated that the uncertain mass of the train played an essential role in the random vibration of the system. In addition, the safety index of the structure became more accurate with increasing number of samples, and the probabilistic distribution of the dynamic responses of the uncertain TBI system followed a Gaussian distribution extremely well, further verifying the appropriateness of the selected amplitude coefficient in the SPEM.