基于马尔可夫残差修正灰色模型的轨道质量指数及其分项预测  

Track Quality Index and Its Sub Items Prediction Based on Markov Residual Corrected Grey Model

作　　者：邓逸帆 李宵楠 李政 厚康恒[3] 肖杰灵 DENG Yifan;LI Xiaonan;LI Zheng;HOU Kangheng;XIAO Jieling(School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China;Key Laboratory of High-speed Railway Engineering of Ministry of Education,Southwest Jiaotong University,Chengdu 610031,China;Ning’an Railway Co.,Ltd.,Wuhu Anhui 241000,China)

机构地区：[1]西南交通大学土木工程学院,成都610031 [2]西南交通大学高速铁路线路工程教育部重点实验室,成都610031 [3]宁安铁路有限责任公司,安徽芜湖241000

出　　处：《铁道建筑》2024年第6期37-42,共6页Railway Engineering

基　　金：国家重点研发计划(2022YFB2602905);国家自然科学基金(52272441);宁安铁路有限责任公司科技研究开发计划[巢马(2023)其他-16]。

摘　　要：为研究轨道质量指数(Track Quality Index,TQI)及各分项值的变化趋势,本文考虑动检数据的非等时距特征,构建了关于TQI及各分项值的一阶灰色模型。原始数据经过累加变换后,利用最小二乘法求解模型的灰参数,并引入马尔可夫残差修正方法对灰色模型进行修正。通过对比修正前后灰色模型TQI及各分项的输出值(拟合值和预测值)与实测值,验证残差修正对提升模型预测精度和降低预测误差的改善效果。结果表明:经马尔可夫残差修正后,灰色模型TQI及各分项输出值可以较好反映其波动情况;与修正前灰色模型相比,修正后灰色模型TQI预测值与实测值的平均误差由1.59%降至0.89%,整体预测精度由2级提升到1级;TQI各分项预测值与实测值的平均误差由3.18%降至1.42%,整体精度由2~4级提升到1~2级。从降低误差和提升预测精度两方面看,修正后灰色模型的预测效果明显提升。To study the trend of changes in Track Quality Index(TQI)and its sub item values,this paper considered the unequal time interval characteristics of motion detection data and constructed a first-order grey model about TQI and its sub item values.After the original data was accumulated and transformed,the grey parameters of the model were solved using the least squares method,and the Markov residual correction method was introduced to correct the grey model.By comparing the output values(fitted value and predicted value)of the grey model TQI and each sub item before and after correction with the measured values,the improvement effect of residual correction on reducing errors and improving prediction accuracy was verified.The results show that after Markov residual correction,the grey model TQI and its sub item output values can better reflect its fluctuation situation.Compared with the pre-corrected grey model,the average error between the predicted TQI value and the measured value of the corrected grey model is decreased from 1.59%to 0.89%,and the overall prediction accuracy is improved from level 2 to level 1.The average error between the predicted value and measured value of each TQI sub item has been decreased from 3.18%to 1.42%,and the overall accuracy has been improved from level 2~4 to level 1~2.From the perspectives of reducing errors and improving prediction accuracy,the prediction performance of the corrected grey model has been significantly improved.

关 键 词：铁路轨道 TQI预测 理论分析 TQI TQI分项 灰色模型 非等时距 马尔可夫残差修正 

分 类 号：U213.2[交通运输工程—道路与铁道工程]