Archive | 2021
Hamiltonian Monte Carlo with application to train-track-bridge coupled interactions subjected to seismic excitation with uncertainties
Abstract
\n Numerical models of train running over the bridge are prone to errors and random excitation sources, which inevitably influence the capacity of such models to accurately predict the observed behaviour. Finite element (FE) updating method can be employed to fit the numerical models through the observed model. This paper proposes a new method to predict the random vibration of train-track-bridge system under earthquakes based on Hamiltonian Monte Carlo (HMC) method. The system identification is performed based on data recorded in situ. FE model is calibrated by minimizing the difference between the FE results and the natural frequencies of a real train-bridge coupled system. Naïve stochastic gradient descent is introduced to optimize the fitting process, avoiding over fitting and under fitting performance. The correlation matrix is built to calculate the correlation score between the measured and the HMC models. Based on above framework, results show that the HMC method has great effectiveness and accuracy with comparisons to the Monte Carlo method (MCM) and the popular probability density evolution method (PDEM). Moreover, the roles of bridge random parameters, track irregularities, and the seismic actions on the random responses are comprehensively investigated. Finally, the updating coefficients reduce the errors to less than 10%.