Predictions Of Random Response Of Train On Long-Span Bridge Under Crosswind Based On Surrogate Model

With the rapid development of transportation construction,the number of long-span railway bridges crossing long rivers and valleys is increasing.The wind load of train running on longspan bridge is more obvious.Random track irregularity and wind load make the response of train on long-span bridge show strong random characteristics.Based on the coupling vibration theory of wind-vehicle-bridge(WVB)system and surrogate model method,this dissertation focuses on the cross-wind random response of train on long-span bridge,the influence of random excitation and random system parameters on train running safety was studied.Main research works are as follows:(1)With regard to the problems of low efficiency and large error in aerodynamic wind tunnel test,a synchronous test device for testing the aerodynamic characteristics of vehiclebridge(VB)system was proposed,and the aerodynamic test method of VB system was improved.Based on the synchronous test device,the section model wind tunnel tests were used to measure the aerodynamic force of VB system,and two large-span truss bridges with typical cross-section were taken as the research objects.The influence of special factors,such as asymmetric layout of railway lines,automobile,and turbulent wind,were discussed.The aerodynamic characteristics of VB system,which are measured more efficiently and accurately by the proposed device,provide calculation parameters for WVB coupled vibration analysis.(2)The WVB coupling vibration model,considering the additional moments caused by lift and drag forces,was established.Then the WVB analysis program is compiled based on the MATLAB,and the reliability of WVB program was verified by measured data and the existing software.The wind environment around the multi-limb towers was measured through aeroelastic model wind tunnel test.Based on the study above,the influence of the wind shielding effect of bridge tower with multiple limbs on the VB system was studied,and the factors,such as the nonuniform wind load model,wind speed,and wind direction angle,on the response of the train were discussed.The results indicate that the responses of train,considering wind shielding effect of multi-limb bridge tower,show two consecutive and significant sudden changes in a short time,and the train response increases by about 50%.(3)The random response of train on long-span bridge subjected to random track irregularity was studied by surrogate model.The response of vertical train-bridge system was predicted by the surrogate model combining important sample and NARX-neural network model,and the prediction accuracy was verified by Monte Carlo simulation(MCS).Parts of wheel-rail contact geometric parameter of three-dimensional VB system were linearized to weaken the nonlinearity.The train response was predicted by NARX-regression model,and important sample was used to improve the prediction performance of surrogate model.Results show that the NARX-neural network and the NARX-regression models are in good agreement with the results of MCS,and calculation efficiency is improved by 2～3 order of magnitudes.Important sample significantly improves the prediction accuracy of surrogate model.(4)The surrogate model for predicting the dynamic random response of trains on long-span bridges considering the parameter uncertainty was proposed.The analysis framework based on the polynomial chaos expansions and autoregressive moving-average with exogenous inputs(PC-ARMAX)surrogate model,that can consider the parameter uncertainty of dynamic timevarying system,was proposed,and the prediction accuracy was improved through important sample.The effect of parameter uncertainty,such as the car body mass,the stiffness and damping of the secondary suspension,on response of VB system was discussed.Then the combined influence of random track irregularity and parameter uncertainty was further considered.Some conclusions are drawn: the PC-ARMAX model not only significantly improves calculation efficiency by 2～3 order of magnitudes but also ensures the prediction accuracy.The difference of random response caused by stochastic vehicle parameter can reach more than 40%.The PCARMAX surrogate model based on important sample is suitable for parameter sensitivity analysis of train on long-span bridge.(5)The surrogate model based on high-order difference and ARMAX was used to predict and analyze the random cross-wind response of train on long-span bridge.The WVB model was simplified by the wind spectra relative to moving train and the equivalent static wind loading.Based on the simplified WVB model,the ARMAX surrogate model of multivariate time series combining high-order difference method and important sample was established,and the effects of wind speed and vehicle speed on the random characteristic of cross-wind response of train were discussed.The results show that the prediction performance of ARMAX model is significantly improved by high-order difference method and important sample,and the proposed ARMAX model improves the calculation efficiency of WVB system by about 100 times,which is suitable for running safety of train on long-span bridge under crosswind.