铁路轨道不平顺数据挖掘及其时间序列趋势预测研究
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摘要
铁路轨道状态的优劣直接决定列车运行是否安全。轨道的平顺性不仅是衡量轨道状态的重要指标,也是评价列车运行品质的基础。在轨道不平顺存在的情况下,轻则列车必须限速运行,重则会造成列车倾覆。因此,研究轨道不平顺变化的规律,掌握变化的趋势,防患于未然,无疑是铁路工务部门所迫切需要的。本文正是在这样的背景下,通过对轨道不平顺数据的研究和分析,挖掘轨道不平顺数据中隐含的规律,建立数学模型对未来趋势进行预测,最终为铁路工务各相关部门业务提供数据及状态变化模型上的支持,服务于铁路运输安全。
在轨道不平顺数据分析研究阶段,论文首先系统地对轨道不平顺数据特点进行分析,针对数据质量存在的问题,提出基于数据挖掘思想,具体操作上采用聚类分析方法进行异常数据识别,提出基于趋势相似性的数据偏移校正算法、基于异常度的局部异常值识别及消噪算法,对数据进行预处理。其次,提出采用小波分解与重构的方法对轨道不平顺时间序列进行分解与重构,为轨道不平顺预测建模奠定数据基础。最后,由于轨道几何不平顺数据反映轨道状态变化的动态特征,是一种典型的时态数据,论文通过数据挖掘概念及算法研究,对轨道不平顺序列进行聚类分析,发现轨道不平顺序列模式特征。在具体研究中,论文对原始数据、标准差数据、标准差小波分解数据和标准差近似序列数据进行聚类的实例分析,挖掘轨道不平顺序列模式特征,发现并描述了数据变化的趋势。
在轨道状态预测分析阶段,论文首先针对轨道状态变化的惯性特征,由于轨道状态具有记忆效应,轨道最新的检测状态与最近的上一次检测状态具有相似性,相邻时间检测状态具有相似趋势性。宏观上看,轨道状态变化在轨道整个生命周期内呈现非线性变化,但是在微观上,短时间内,如果进行频繁轨道检测,就会发现短相邻时间内轨道状态变化可以近似为线性特征。基于此假设,并结合轨道不平顺时间序列数据的非等时距特征,论文提出基于非等时距短期历史趋势的时间序列分段线性递推模型(PLRMSHT)。同时,为提高PLRMSHT模型的预测精度,对模型产生的残差项采用基于傅立叶三角变换的方法进行残差修正拟合,实例分析证明残差修正后的PLRMSHT具有较好的预测精度,模型取得了满意结果。其次,由于小波变换可以通过对时间(空间)频率的局部化分析和伸缩平移运算对信号(函数)逐步进行多尺度细化,最终达到高频处时间细分,低频处频率细分。小波的这个特征能自动适应时频信号分析的要求,从而可聚焦到信号的任意细节,把函数分解成一系列简单基函数的表示,无论是在理论上,还是实际应用中都有重要意义。因此,论文提出基于小波分解-重构的思想对轨道不平顺时间序列进行细分,分别对小波分解得到的细节信号、近似信号寻找最佳拟合预测模型。具体研究中,针对经过残差修正的ARIMA预测模型比原始ARIMA预测模型具有更高的预测精度,但残差修正过程不仅增加了模型的计算量和复杂度而且也不能反映其变化的本质的不足,本文提出基于小波分解-重构的分段线性-ARMA递推模型(PL-ARMARWDR)。通过小波分解变换,低频近似序列更加平缓顺滑,趋势性更加明显,高频细节序列更加平稳。模型中,低频近似序列采用线性递推模型,高频细节序列采用ARMA模型。由于轨道状态变化在实际上并不呈现线性变化趋势,其变化趋势是非线性的,研究表明轨道不平顺变化更符合指数趋势变化。由于灰色模型是一种采用指数函数近似的模型,因此论文提出基于小波分解-重构的分段灰色-ARMA递推模型(PG-ARMARWDR)。在模型中,低频近似序列采用灰色递推模型,高频细节序列采用ARMA模型。由于神经网络模型作为一种重要的非线性建模方法有着广泛的应用,神经网络模型可以近似任何非线性过程,因此论文提出基于小波分解-重构的分段神经网络-ARMA递推模型(PANN-ARMARWDR)。在模型中,低频近似序列采用神经网络递推模型,高频细节序列采用ARMA模型。经过“分解—建模—重构”过程,所提出的模型实现了轨道不平顺状态趋势变化的精确预测。
在本文结尾,论文通过实例对四种预测模型的预测精度进行分析,预测精度指标MSE和MAPE显示所提出模型都属于高精度预测,模型都取得了满意的结果,同时对模型的适用情况也进行比较和分析。
Track condition is directly related to the safe operation of trains. Track irregularity is not only an important indicator of track condition, but also the basis for measuring the quality of train operation. Where there is track irregularity, speed limit should be paid attention, and worst of all, overturning might occur. As a result, it is urgent for railway departments to study the law of track irregularity changes so as to master trends of track state changes and to take prevention measures. In this context, this doctoral dissertation analyses track irregularity data, explores the underlined rules of track irregularity, predicts future trends and ultimately, it provides support to relevant railway departments in models about data and track state changes, to ensure safety of railway transportation.
During the track irregularity data analysis, this doctoral dissertation first analyzes the characteristics of track irregularity data systematically based on data mining, employs clustering method to recognize abnormal data, proposes data variation calibration algorithm based on trends similarity, and algorithm of partial abnormal data recognition and noise elimination based on abnormality, preprocesses data. Next, wavelet decomposition and reconstruction model is proposed, so as to lay the data base for modeling for track irregularity time series. Finally, since track irregularity data reflects the dynamic characteristics of track state changes, it is an important temporal data. This doctoral dissertation conducts clustering analysis on track irregularity sequence and discovers pattern features with the application of data mining and algorithms. In concrete research, it conducts case analysis of data clustering based on the original data, standard deviation data, and standard deviation data after wavelet decomposition, similar standard deviation sequence, and finally discovers the trend in data changes.
During the track state prediction analysis, this doctoral dissertation first focuses on the inertia characteristics of the track state changes. Since track state has a memory effect, latest track state and the nearest previous state shares similarity, and the inspection state of the adjacent time points has a similar trend. From the macro perspective, the track state presents nonlinear changes throughout the whole life cycle of the track, but from the micro perspective, in a short time, track state changes at adjacent time will be close to linear features. Based on this assumption, combined with the non-isochronous features of track irregularity time series data, this paper proposes Piecewise Linear Recursive Model based on Short-term Historical Trends model (PLRMSHT). Also, to improve the prediction accuracy of PLRMSHT, residual correction is conducted based on Fourier delta transformation. Through case studies, models have achieved satisfactory results. Next, since wavelet transform can refine signal (function) in multiple aspects gradually through local analysis and stretching and panning on space (time) frequency, and ultimately realize time subdivision at high frequency points and frequency subdivision at low frequency points. This feature can adapt to signal analysis of time-frequency, and can focus on every detail of signal, and can divide the function into a series of simple basis functions. As a result, it is of significance both in theory and in practice. Therefore, based on wavelet decomposition-reconstruction, the thesis divides track irregularity time series, and finds the best fit forecast model to the details signal and the approximate signal of the wavelet decomposition. During concrete research, ARIMA forecast model after residual correction is of higher accuracy compared to the original ARIMA forecast model, but the correction itself increases the amount and complexity of computing, and can not reflect the inadequacy of changes. This thesis proposes Piecewise Linear-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PL-ARMARWDR). After wavelet decomposition and transformation, the low-frequency approximation sequence will be smoother, and its trend will be more obvious, and the high-frequency detail sequence will be more stable. In the model, the low-frequency approximation sequence uses linear recursive model and high-frequency detail sequence uses ARM A model. Since track status change is not a linear trend, in fact, the trend is nonlinear. Studies have shown that it more in line with exponential trends of track irregularity changes. Because the gray model is an exponential function approximation model, the thesis proposes Piecewise Gray-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PG-ARMARWDR). As an important non-linear modeling method, neural network model has been widely used. Because neural network model can be approximated by any non-linear process, so this thesis proposes Piecewise ANN-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PANN-ARMARWDR). In the model, the low-frequency approximation sequences uses recursive neural network model, and high-frequency detail sequence uses ARM A model. After the decomposition-modeling-recon structuring process, the proposed models have realized accurate prediction on trends of track irregularity state changes.
In the final part of this doctoral dissertation, the accuracy of four prediction models are analyzed by examples, and MSE and MAPE are used as forecasting accuracy index and the results show that all models belong to high-precision prediction, and the proposed models have achieved satisfactory results. Also, the applicability of all models are also compared and analyzed.
在轨道不平顺数据分析研究阶段,论文首先系统地对轨道不平顺数据特点进行分析,针对数据质量存在的问题,提出基于数据挖掘思想,具体操作上采用聚类分析方法进行异常数据识别,提出基于趋势相似性的数据偏移校正算法、基于异常度的局部异常值识别及消噪算法,对数据进行预处理。其次,提出采用小波分解与重构的方法对轨道不平顺时间序列进行分解与重构,为轨道不平顺预测建模奠定数据基础。最后,由于轨道几何不平顺数据反映轨道状态变化的动态特征,是一种典型的时态数据,论文通过数据挖掘概念及算法研究,对轨道不平顺序列进行聚类分析,发现轨道不平顺序列模式特征。在具体研究中,论文对原始数据、标准差数据、标准差小波分解数据和标准差近似序列数据进行聚类的实例分析,挖掘轨道不平顺序列模式特征,发现并描述了数据变化的趋势。
在轨道状态预测分析阶段,论文首先针对轨道状态变化的惯性特征,由于轨道状态具有记忆效应,轨道最新的检测状态与最近的上一次检测状态具有相似性,相邻时间检测状态具有相似趋势性。宏观上看,轨道状态变化在轨道整个生命周期内呈现非线性变化,但是在微观上,短时间内,如果进行频繁轨道检测,就会发现短相邻时间内轨道状态变化可以近似为线性特征。基于此假设,并结合轨道不平顺时间序列数据的非等时距特征,论文提出基于非等时距短期历史趋势的时间序列分段线性递推模型(PLRMSHT)。同时,为提高PLRMSHT模型的预测精度,对模型产生的残差项采用基于傅立叶三角变换的方法进行残差修正拟合,实例分析证明残差修正后的PLRMSHT具有较好的预测精度,模型取得了满意结果。其次,由于小波变换可以通过对时间(空间)频率的局部化分析和伸缩平移运算对信号(函数)逐步进行多尺度细化,最终达到高频处时间细分,低频处频率细分。小波的这个特征能自动适应时频信号分析的要求,从而可聚焦到信号的任意细节,把函数分解成一系列简单基函数的表示,无论是在理论上,还是实际应用中都有重要意义。因此,论文提出基于小波分解-重构的思想对轨道不平顺时间序列进行细分,分别对小波分解得到的细节信号、近似信号寻找最佳拟合预测模型。具体研究中,针对经过残差修正的ARIMA预测模型比原始ARIMA预测模型具有更高的预测精度,但残差修正过程不仅增加了模型的计算量和复杂度而且也不能反映其变化的本质的不足,本文提出基于小波分解-重构的分段线性-ARMA递推模型(PL-ARMARWDR)。通过小波分解变换,低频近似序列更加平缓顺滑,趋势性更加明显,高频细节序列更加平稳。模型中,低频近似序列采用线性递推模型,高频细节序列采用ARMA模型。由于轨道状态变化在实际上并不呈现线性变化趋势,其变化趋势是非线性的,研究表明轨道不平顺变化更符合指数趋势变化。由于灰色模型是一种采用指数函数近似的模型,因此论文提出基于小波分解-重构的分段灰色-ARMA递推模型(PG-ARMARWDR)。在模型中,低频近似序列采用灰色递推模型,高频细节序列采用ARMA模型。由于神经网络模型作为一种重要的非线性建模方法有着广泛的应用,神经网络模型可以近似任何非线性过程,因此论文提出基于小波分解-重构的分段神经网络-ARMA递推模型(PANN-ARMARWDR)。在模型中,低频近似序列采用神经网络递推模型,高频细节序列采用ARMA模型。经过“分解—建模—重构”过程,所提出的模型实现了轨道不平顺状态趋势变化的精确预测。
在本文结尾,论文通过实例对四种预测模型的预测精度进行分析,预测精度指标MSE和MAPE显示所提出模型都属于高精度预测,模型都取得了满意的结果,同时对模型的适用情况也进行比较和分析。
Track condition is directly related to the safe operation of trains. Track irregularity is not only an important indicator of track condition, but also the basis for measuring the quality of train operation. Where there is track irregularity, speed limit should be paid attention, and worst of all, overturning might occur. As a result, it is urgent for railway departments to study the law of track irregularity changes so as to master trends of track state changes and to take prevention measures. In this context, this doctoral dissertation analyses track irregularity data, explores the underlined rules of track irregularity, predicts future trends and ultimately, it provides support to relevant railway departments in models about data and track state changes, to ensure safety of railway transportation.
During the track irregularity data analysis, this doctoral dissertation first analyzes the characteristics of track irregularity data systematically based on data mining, employs clustering method to recognize abnormal data, proposes data variation calibration algorithm based on trends similarity, and algorithm of partial abnormal data recognition and noise elimination based on abnormality, preprocesses data. Next, wavelet decomposition and reconstruction model is proposed, so as to lay the data base for modeling for track irregularity time series. Finally, since track irregularity data reflects the dynamic characteristics of track state changes, it is an important temporal data. This doctoral dissertation conducts clustering analysis on track irregularity sequence and discovers pattern features with the application of data mining and algorithms. In concrete research, it conducts case analysis of data clustering based on the original data, standard deviation data, and standard deviation data after wavelet decomposition, similar standard deviation sequence, and finally discovers the trend in data changes.
During the track state prediction analysis, this doctoral dissertation first focuses on the inertia characteristics of the track state changes. Since track state has a memory effect, latest track state and the nearest previous state shares similarity, and the inspection state of the adjacent time points has a similar trend. From the macro perspective, the track state presents nonlinear changes throughout the whole life cycle of the track, but from the micro perspective, in a short time, track state changes at adjacent time will be close to linear features. Based on this assumption, combined with the non-isochronous features of track irregularity time series data, this paper proposes Piecewise Linear Recursive Model based on Short-term Historical Trends model (PLRMSHT). Also, to improve the prediction accuracy of PLRMSHT, residual correction is conducted based on Fourier delta transformation. Through case studies, models have achieved satisfactory results. Next, since wavelet transform can refine signal (function) in multiple aspects gradually through local analysis and stretching and panning on space (time) frequency, and ultimately realize time subdivision at high frequency points and frequency subdivision at low frequency points. This feature can adapt to signal analysis of time-frequency, and can focus on every detail of signal, and can divide the function into a series of simple basis functions. As a result, it is of significance both in theory and in practice. Therefore, based on wavelet decomposition-reconstruction, the thesis divides track irregularity time series, and finds the best fit forecast model to the details signal and the approximate signal of the wavelet decomposition. During concrete research, ARIMA forecast model after residual correction is of higher accuracy compared to the original ARIMA forecast model, but the correction itself increases the amount and complexity of computing, and can not reflect the inadequacy of changes. This thesis proposes Piecewise Linear-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PL-ARMARWDR). After wavelet decomposition and transformation, the low-frequency approximation sequence will be smoother, and its trend will be more obvious, and the high-frequency detail sequence will be more stable. In the model, the low-frequency approximation sequence uses linear recursive model and high-frequency detail sequence uses ARM A model. Since track status change is not a linear trend, in fact, the trend is nonlinear. Studies have shown that it more in line with exponential trends of track irregularity changes. Because the gray model is an exponential function approximation model, the thesis proposes Piecewise Gray-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PG-ARMARWDR). As an important non-linear modeling method, neural network model has been widely used. Because neural network model can be approximated by any non-linear process, so this thesis proposes Piecewise ANN-ARMA Recursive based on Wavelet Decomposition and Reconstruction model (PANN-ARMARWDR). In the model, the low-frequency approximation sequences uses recursive neural network model, and high-frequency detail sequence uses ARM A model. After the decomposition-modeling-recon structuring process, the proposed models have realized accurate prediction on trends of track irregularity state changes.
In the final part of this doctoral dissertation, the accuracy of four prediction models are analyzed by examples, and MSE and MAPE are used as forecasting accuracy index and the results show that all models belong to high-precision prediction, and the proposed models have achieved satisfactory results. Also, the applicability of all models are also compared and analyzed.
引文
[1]http://news.china.com.cnytxt/2013-01/17/content_27712460.htm
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