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...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.展开更多
车-桥系统的失效属于小概率事件,采用子集分裂模拟方法(Subset Simulation with Splitting,SS/S)对车-桥系统响应进行了分析。首先,采用MATLAB编制了车-桥系统的分析程序,并通过数值算例进行了验证。其次,回顾了SS/S法的基本原理,采用...车-桥系统的失效属于小概率事件,采用子集分裂模拟方法(Subset Simulation with Splitting,SS/S)对车-桥系统响应进行了分析。首先,采用MATLAB编制了车-桥系统的分析程序,并通过数值算例进行了验证。其次,回顾了SS/S法的基本原理,采用自回归模型(Autoregressive Models,AR模型),对轨道不平顺进行条件模拟,给出了车-桥系统响应的SS/S统计分析框架,并采用数值算例进行了验证。最后,针对车-桥系统,利用SS/S得到了车体竖向和横向加速度超越概率,并与蒙特卡洛法(MCS法)进行了对比验证。结果表明:相较于直接MCS方法,SS/S方法可大幅度减少车-桥系统响应极值超越概率曲线估计时所需的样本,显著提高计算效率。展开更多
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51978589,51778544,and 51525804).
文摘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.
文摘车-桥系统的失效属于小概率事件,采用子集分裂模拟方法(Subset Simulation with Splitting,SS/S)对车-桥系统响应进行了分析。首先,采用MATLAB编制了车-桥系统的分析程序,并通过数值算例进行了验证。其次,回顾了SS/S法的基本原理,采用自回归模型(Autoregressive Models,AR模型),对轨道不平顺进行条件模拟,给出了车-桥系统响应的SS/S统计分析框架,并采用数值算例进行了验证。最后,针对车-桥系统,利用SS/S得到了车体竖向和横向加速度超越概率,并与蒙特卡洛法(MCS法)进行了对比验证。结果表明:相较于直接MCS方法,SS/S方法可大幅度减少车-桥系统响应极值超越概率曲线估计时所需的样本,显著提高计算效率。
