In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cell...In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.展开更多
风速和风向是影响高速列车运行安全的重要因素,对高铁沿线的大风风速和风向进行有效预测有助于及时地对列车运行状况进行评估和预警。目前高铁大风领域的研究主要集中在风速的预测,尚未考虑风速风向的联合预测。基于深度循环神经网络—...风速和风向是影响高速列车运行安全的重要因素,对高铁沿线的大风风速和风向进行有效预测有助于及时地对列车运行状况进行评估和预警。目前高铁大风领域的研究主要集中在风速的预测,尚未考虑风速风向的联合预测。基于深度循环神经网络—长短记忆(LSTM)模型,提出独立预测法、分量预测法和多变量预测法等3种风速与风向联合预测方法,并利用兰新高铁大风监测实测数据对沿线多个基站的短期风速和风向进行同步联合预测。首先,通过归一化预处理原始风向和风速序列,并运用控制变量法确定最优时间步长和模型参数。其次,采用BPTT(Backpropagation Through Time)和Adam算法进行迭代训练,并结合早停法控制收敛,得到优化后的网络结构。最后,利用训练好的LSTM网络,采用3种方法对风速和风向进行联合预测。4个基站的实验结果表明,优化后的LSTM模型可以有效提取风速风向时间序列的长期依赖特征,结合联合预测方法能够实现对风速和风向的高精度同步预测;3种联合预测方法都能在较小范围内准确预测风速和风向,除5520基站外,风速预测误差在15%以内,风向预测误差在20%以内,其中多变量预测法表现出最优的整体预测精度,独立预测法次之。本研究为风速风向的联合预测提供了新的视角,对保障高铁列车运行的安全性具有参考价值。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124)
文摘In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.
基金The National Natural Science Foundation of China(11271086)he Natural Science Foundation of Guangxi Province(2011GXNSFD018022)he Innovation Group of Talents Highland of Guangxi Higher School
文摘风速和风向是影响高速列车运行安全的重要因素,对高铁沿线的大风风速和风向进行有效预测有助于及时地对列车运行状况进行评估和预警。目前高铁大风领域的研究主要集中在风速的预测,尚未考虑风速风向的联合预测。基于深度循环神经网络—长短记忆(LSTM)模型,提出独立预测法、分量预测法和多变量预测法等3种风速与风向联合预测方法,并利用兰新高铁大风监测实测数据对沿线多个基站的短期风速和风向进行同步联合预测。首先,通过归一化预处理原始风向和风速序列,并运用控制变量法确定最优时间步长和模型参数。其次,采用BPTT(Backpropagation Through Time)和Adam算法进行迭代训练,并结合早停法控制收敛,得到优化后的网络结构。最后,利用训练好的LSTM网络,采用3种方法对风速和风向进行联合预测。4个基站的实验结果表明,优化后的LSTM模型可以有效提取风速风向时间序列的长期依赖特征,结合联合预测方法能够实现对风速和风向的高精度同步预测;3种联合预测方法都能在较小范围内准确预测风速和风向,除5520基站外,风速预测误差在15%以内,风向预测误差在20%以内,其中多变量预测法表现出最优的整体预测精度,独立预测法次之。本研究为风速风向的联合预测提供了新的视角,对保障高铁列车运行的安全性具有参考价值。
