基于小波和傅立叶变换的道路交通量预测研究
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摘要
道路交通量预测一直是道路交通管理的一项重要内容,本文在分析国内外研究现状的基础上,围绕道路交通量预测方法进行了深入和系统的理论和方法研究,并开展了实际应用。其中主要内容如下:
一、针对当前道路交通量时间序列中含有大量的异常数据,本文在阐述小波变换基本原理的基础上,提出了基于小波变换模极大值的异常数据识别和修正方法,该方法综合运用了小波变换和统计学相关理论,在实际异常数据的识别和纠正中取得了良好的效果。
二、由于本文在预测中大量使用小波变换,针对小波分解Mallat算法进行时间序列分解时所带来的边界误差问题,本文提出了基于最大能量周期的时间序列延拓方法,并将此方法应用到实际数据的延拓中,通过将延拓后的预测结果同采用对称延拓、补零延拓函数插值延拓所得数据的预测结果进行了比较表明,基于最大能量周期的时间序列延拓方法能很好的适合道路交通时间序列,对降低预测误差起到一定的作用。
三、针对道路交通量时间序列中含有大量的噪声,本文在对小波去噪理论进行探讨的基础上,提出了交通量序列去噪时阈值计算中σ确定的一种改进方法,并将之与其它的σ确定方式对预测所带来的影响进行了定量的对比分析,同时分析了软阈值、硬阈值、几乎硬阈值在交通量时间序列去噪中的优劣。
四、提出了道路交通量预测的小波分解组合预测方法。在对道路交通时间序列进行小波分解去噪后,利用傅立叶变换的频谱分析功能,本文对交通量时间序列周期进行了详细的分析,指出小时交通量时间序列中包含的周期有24小时,12小时,8小时和6小时,通过小波包变换把交通量时间序列中的各种周期特征分离出来,并且在对道路交通量时间序列中混沌特性进行分析的基础上,提出采用小波包分解来提取混沌特征,并将之应用于原始时间序列和ARIMA模型拟合残差中的混沌特性提取,然后对于小波包的各个分解项(各周期项、混沌项、随机项),在验证全部分别建模并不能提高预测精度的基础上,提出了基于倍周期的小波包分解项合并策略,并将之应用于实际的交通量预测中问题中,取得了良好的效果,并利用Dmeyer小波基来作小波分解以达到优化模型预测结果的目的。
五、对小波分解预测方法进行了优化。在对混沌预测的相关理论与方法
The traffic volume predicting is very important to the traffic management. This paper carry on deeply theory and method research about the traffic volume predicting based on the analyzes of the present situation in the domestic and foreign research. At the same time, this paper carries out the practical applicationin. The main content of this paper is as following:
First, beacuse there are massive unusual data in the road traffic volume time series, this paper proposed the recognition and the revision method of it based on the wavelet transformation mold maximum value after elaborating the basic principle of the wavelet transformation.This method utilizes theorise related on the wavelet transformation and statistics, and it has obtained the good effect in reality.
Second, for the much using of the wavelet transformation in the forecast, and facing the question of the boundary error made from the time series wavelet decomposes by the Mallat algorithm, this paper proposed the time series extension method which based on the biggest energy cycle. Through use it in extension of the actual data then forecast and compared the forecast result with that of extension by other method such as symmetry extension, makes up the zero extension, function interpolation extension, it indicated that the biggest energy cycle time series extension method is the very suitable for road traffic time series and is able to reduce the forecast error.
Third, in view of the massive noises in the road traffic volume time series, this paper proposed one improvement method to decide the value ofσin road traffic volume sequence denoise after the discussion of denosie theory. And a compare analysis between this method with other deterministic methods is carried on about the forecast result. Simultaneously the stand or fall of the soft threshold value, the hard threshold value, the nearly hard threshold value in road traffic volume time series denoise has been analyzed.
Fourth, a wavelet decomposition combination forecast method is proposed to predict the road future traffic volume. After the road traffic time series is decomposed by wavelet and denoised, , this article has carried on the detailed
一、针对当前道路交通量时间序列中含有大量的异常数据,本文在阐述小波变换基本原理的基础上,提出了基于小波变换模极大值的异常数据识别和修正方法,该方法综合运用了小波变换和统计学相关理论,在实际异常数据的识别和纠正中取得了良好的效果。
二、由于本文在预测中大量使用小波变换,针对小波分解Mallat算法进行时间序列分解时所带来的边界误差问题,本文提出了基于最大能量周期的时间序列延拓方法,并将此方法应用到实际数据的延拓中,通过将延拓后的预测结果同采用对称延拓、补零延拓函数插值延拓所得数据的预测结果进行了比较表明,基于最大能量周期的时间序列延拓方法能很好的适合道路交通时间序列,对降低预测误差起到一定的作用。
三、针对道路交通量时间序列中含有大量的噪声,本文在对小波去噪理论进行探讨的基础上,提出了交通量序列去噪时阈值计算中σ确定的一种改进方法,并将之与其它的σ确定方式对预测所带来的影响进行了定量的对比分析,同时分析了软阈值、硬阈值、几乎硬阈值在交通量时间序列去噪中的优劣。
四、提出了道路交通量预测的小波分解组合预测方法。在对道路交通时间序列进行小波分解去噪后,利用傅立叶变换的频谱分析功能,本文对交通量时间序列周期进行了详细的分析,指出小时交通量时间序列中包含的周期有24小时,12小时,8小时和6小时,通过小波包变换把交通量时间序列中的各种周期特征分离出来,并且在对道路交通量时间序列中混沌特性进行分析的基础上,提出采用小波包分解来提取混沌特征,并将之应用于原始时间序列和ARIMA模型拟合残差中的混沌特性提取,然后对于小波包的各个分解项(各周期项、混沌项、随机项),在验证全部分别建模并不能提高预测精度的基础上,提出了基于倍周期的小波包分解项合并策略,并将之应用于实际的交通量预测中问题中,取得了良好的效果,并利用Dmeyer小波基来作小波分解以达到优化模型预测结果的目的。
五、对小波分解预测方法进行了优化。在对混沌预测的相关理论与方法
The traffic volume predicting is very important to the traffic management. This paper carry on deeply theory and method research about the traffic volume predicting based on the analyzes of the present situation in the domestic and foreign research. At the same time, this paper carries out the practical applicationin. The main content of this paper is as following:
First, beacuse there are massive unusual data in the road traffic volume time series, this paper proposed the recognition and the revision method of it based on the wavelet transformation mold maximum value after elaborating the basic principle of the wavelet transformation.This method utilizes theorise related on the wavelet transformation and statistics, and it has obtained the good effect in reality.
Second, for the much using of the wavelet transformation in the forecast, and facing the question of the boundary error made from the time series wavelet decomposes by the Mallat algorithm, this paper proposed the time series extension method which based on the biggest energy cycle. Through use it in extension of the actual data then forecast and compared the forecast result with that of extension by other method such as symmetry extension, makes up the zero extension, function interpolation extension, it indicated that the biggest energy cycle time series extension method is the very suitable for road traffic time series and is able to reduce the forecast error.
Third, in view of the massive noises in the road traffic volume time series, this paper proposed one improvement method to decide the value ofσin road traffic volume sequence denoise after the discussion of denosie theory. And a compare analysis between this method with other deterministic methods is carried on about the forecast result. Simultaneously the stand or fall of the soft threshold value, the hard threshold value, the nearly hard threshold value in road traffic volume time series denoise has been analyzed.
Fourth, a wavelet decomposition combination forecast method is proposed to predict the road future traffic volume. After the road traffic time series is decomposed by wavelet and denoised, , this article has carried on the detailed
引文
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