中文摘要：

轨道几何形状检测数据是一个随时间变化具有随机特征的时间序列,反映轨道几何状态的变化.在本文中,灰色关联度理论用于研究轨道水平不平顺时间序列数据,挖掘时间序列数据之间隐含的关系;经过普遍适应性改进和残差修正改进的灰色GM（1,1）模型预测固定测点轨道不平顺长期状态变化趋势,随机线性AR和卡尔曼滤波模型分析单元区段轨道不平顺短期变化趋势,探索轨道状态变化随机数据序列中隐藏的规律并进行预测.短期和长期预测模型验证结果表明,三种模型是有效的,能够达到预期的精度.

英文摘要：

Track geometry inspection data reflects the change of track geometry state.It is a time series which changes over time with random characteristics.In this paper,seven gray incidence degree models are used to analyze track irregularity time series data and to examine the implied relationship between the time series data.The improved grey GM（1,1） after residual error correction and adaptive improvement,stochastic linear AR and Kalman filtering models are applied to analyze track irregularity of cross level in fixed measuring point and unit section,to explore the hidden laws among data from the random data sequence of the track cross level state changes and predict track state in short-term and long-term by applying the models.The results show that the model is feeeasible and meet the intended accuracy.