基于回声状态网络的交通流预测模型及其相关研究
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摘要
随着经济的飞速发展以及城市化的快速推进,由车辆保有量的剧增而引发的交通堵塞、交通事故、能源浪费等问题已然成为制约城市发展的世界难题。作为解决交通问题最为有效的方法,智能交通系统(Intelligent Transportation System,简称ITS)近年来得到了越来越多的重视。而作为ITS最核心的子系统,交通控制和诱导系统需要依赖于准确的交通流预测。为此,实现精确、快速的交通流预测已成为了当前ITS发展的首要任务之一
然而,传统的模型在对采样间隔为2分钟的交通流时序进行单步预测时,其误差往往接近20%,过低的预测精度远不能满足ITS快速发展的需要。此外,由于交通流预测有着特殊的应用背景,人们期望实际应用的单步预测模型应同时满足速度、稳定性的需要,甚至还能用于多步预测中。多重条件的束缚令交通流预测的研究遇到极大困难。为此,我国科技部启动了973计划“大城市交通拥堵瓶颈的基础科学问题研究”,并在其核心子课题“智能化交通信息融合与集成的研究”中明确地将交通流预测作为研究的核心内容。通过研究我们发现,尽管近年来已有不少模型在交通流单步预测中取得了一定的成果,但由于模型过于集中在自身性能的优化上,而少有考虑交通流本身的物理特性,故最终难以突破预测精度过低的瓶颈,导致交通流的单步和多步预测至今仍是极具挑战且棘手的难点问题。
作为一种新型的机器学习方法,2004年《Science》中提出的回声状态网络(Echo State Networks,简称ESN)由于具备了独特的组织结构以及强大的短时记忆特性,故在对时间序列尤其是对由确定系统产生的无噪混沌时间序列,如Mackey-Glass、Lorenz等序列进行预测时,其预测精度能在以往模型的基础上提升上千倍。且由于采用伪逆法作为权值的训练方法,令ESN兼顾了训练快、稳定性高的优点。而正由于ESN集合了众多优点,它已逐渐地成为近年来机器学习的研究热点,被广泛地应用于时间序列的预测中。而本文被预测的实测交通流恰是具有混沌特性的一类时间序列,受经典混沌时间序列预测的启发,本文考虑将ESN模型引用至交通流的预测中。然而通过研究我们发现,由于受到交通流中复杂噪声成分的影响,在直接使用ESN对交通流进行预测时,其效果并不理想。
为了解决噪声干扰的问题,本文在交通流非线性动力学分析的基础上,融入了先进的信号处理方法,全新地构建了多个基于ESN的短时交通流单步和多步预测模型,且各模型在预测精度、训练速度和稳定性方面均有着不同程度的提升。基于对以上内容的研究,论文的主要工作及创新点将归纳如下：
(1)交通流复杂动力学的多角度分析。通过研究,我们发现交通流是含高噪且混沌的时间序列,复杂噪声成分的加入破坏了交通流混沌吸引子的性态,从而大幅地降低了交通流的可预测性。文中我们在交通流动力学分析的基础上,还详细地对交通流的可预测性进行了定量和定性的分析,从本质上揭示了交通流复杂的物理特性,其研究方法和结果也将为后文中新模型的构建奠定坚实的理论基础。
(2)提出基于ESN的交通流单步和多步预测模型。作为新型的预测模型,ESN能够高精度地对经典的混沌序列进行多步预测。本文在交通流动力学分析的基础上,提出了基于ESN的交通流单步和多步预测模型。并与多个经典模型的预测结果进行对比,验证了新模型在预测精度略有提升的同时,其训练速度和稳定性均占有绝对的优势。随后在完成模型的重要参数讨论后,给出了交通流预测中ESN模型的最优参数设置。此外,文中还着重地探讨了迭代法和直接法的多步预测性能。通过分析两者各自的优缺点,揭示了以往交通流多步预测模型中存在精度瓶颈的根源,其结果为后面解决多步预测难题提供了重要的理论支持。
(3)提出小波域的多尺度多核ESN模型(Multi-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Domain,简称MESNMW)实现了高精度的交通流预测。基于内容(2)中由于交通流噪声成分的干扰而尚未彻底解决的精度问题进行探索。研究发现,以往基于机器学习的交通流预测模型均集中于研究模型自身的泛化能力,忽视了由噪声成分引起交通流可预测性的降低对预测精度的巨大影响。为了不重蹈覆辙,本文全新地从信号处理的角度出发提出了一种新的MESNMW模型用于交通流的单步和多步预测。该模型利用小波多尺度分解方法,将交通流中的噪声成分屏蔽至权重较少的高频分量中,保障了主要分量特别是低频分量是具有高信噪比的混沌序列。在结合多核ESN进行预测后,其单步预测精度是单纯使用ESN模型的近20倍。另外,文中还着重对影响模型性能的重要参数进行了讨论,为模型参数的选择提供了理论的依据。
(4)提出小波包域的多尺度多核回声状态网络模型(Multi-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Packet Domain,简称MESNMWP)模型进一步地提高了交通流的预测精度。在MESNMW模型的基础上,提出了一种新的MESNMWP模型,该模型利用小波包多尺度分解方法能将交通流中的噪声成分屏蔽至权重更小的高频分量中,从而更大程度地保障了主要分量具有高信噪比。实验结果表明,MESNMWP模型的单步预测精度能在MESNMW模型的基础上再提升3倍多。另外,文中还采用MESNMW和MESNMWP模型完成了交通流的迭代多步预测和直接多步预测。而由于迭代法获得了更为精确的预测结果,因此修正了传统意识中认为“实测数据采用直接多步预测法更为有效”的片面观点,同时也为其它类似实测数据的多步预测提供了一种新的思路。
(5)提出基于小波域的多尺度单核ESN模型(Single-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Domain,简称SESNMW)和基于小波包域的多尺度单核回声状态网络(Single-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Packet Domain,简称SESNMWP)模型实现了高精度兼顾高效率的交通流预测。前面提出的MESNMW和MESNMWP模型虽能取得非常精确的预测结果,却是以高复杂计算为代价的,而过高的复杂度将引起训练时间的增长,极大地影响了MESNMW和MESNMWP模型在交通流预测中的实际应用。为了在保证预测精度的同时也兼顾运行时间效率,本文从信号平滑的角度上提出SESNMW和SESNMWP用于交通流的预测。文中还针对SESNMW和SESNMWP模型降噪中存在着相似性和可预测性之间矛盾,全新地提出多状态阈值法作为交通流的降噪模型应用于SESNMW和SESNMWP模型中。与传统的阈值法相比,该方法能更好地解决相似性和可预测性之间的矛盾,实现了在提高降噪后交通流拟合度的同时也提升了单核ESN的预测精度,从而全面地保障了SESNMW和SESNMW模型的预测精度和运行效率。
综上所述,本文以探索交通流预测模型为研究中心,在基于交通流动力学分析的基础上,首先提出了基于ESN的交通流单步和多步预测模型以解决交通流预测中运行效率和稳定性的问题；然后构建了MESNMW模型实现了高精度的交通流单步和多步预测；随后在MESNMW模型基础上创建了MESNMWP模型进一步地提升了交通流的预测精度,此精度已是现有方法的几十倍之多；最后提出了SESNMW和SESNMWP模型全方位地满足了交通流预测中精度、速度和稳定性的需要。本文上述所提的多个交通流预测模型具有较好的实用性,在科学研究和工程领域中具有重要的理论价值和实际价值。
With the rapid development of economy and urbanization, some traffic problems caused by the increasing vehicle inventory, such as traffic congestion, traffic accidents and energy dissipation, are becoming one of the world's biggest issues that hinder the urban development. As the most effective method for solving this problem, the Intelligent Transportation System (ITS) has been paid great attention in recent years. As one of the core part of ITS, the system of traffic control and guidance dependents on accurate prediction of traffic flow. Hence, realizing accurate and fast prediction of traffic flow has become one of the priorities of ITS development.
However, when traditional models are used to predict single-step traffic flow time series with the sampling interval of two minutes, their error is often close to20%, and this low prediction accuracy is far from being able to meet the needs of rapid development of ITS. Moreover, because of the special application background of traffic flow prediction, we expect that the single-step prediction model used in practice should not only satisfy the requirement of speed and stability but also be feasible for multiple step prediction. These constraints make the research of traffic flow prediction trap into great difficulty. Hence, China's Ministry of Science and Technology launched the973program Basic Science Research of Big City Traffic Congestion Bottleneck; in its core sub-topic Research of Intelligent Traffic Information Fusion and Integration, the traffic flow prediction is explicitly treated as its core content. We found that many models have achieved good results in the single-step prediction of traffic flow in recent years, but those models are over-focused on the optimization of their performance and seldom consider the physical characteristics of traffic flow, so it is difficult to break through the bottleneck of the low prediction accuracy, resulting in the difficulty and challenging of single-step and multi-step prediction of the traffic flow.
As a new machine learning method, Echo State Network (ESN) proposed in the journal of Science in2004has the characteristic of distinct organizational structure and a strong short-term memory. So ESN can get a thousand times more precise than previous models to predict time series, especially the noise-free chaotic time series generated by deterministic systems such as Mackey-Glass and Lorenz sequence. Moreover, since ESN adopts the pseudo-inverse method to train its weight, it has both characteristics of fast training speed and high stability. Because of its various advantages, ESN are becoming a research focus in the area of machine learning and has been widely used in time series prediction in recent years. Because the real-world traffic flow belongs to a kind of time series with chaotic property, inspired by the classical chaotic time series prediction approaches, we introduce the ESN model into the prediction of traffic flow. However, we found that, if we directly applied the ESN to the prediction of the traffic flow, the prediction effect is not good due to the affection of the complex noise components in the traffic flow.
In order to solve the problem of noise disturbance, based on the analysis of nonlinear dynamic of traffic flow, this paper integrates advanced signal processing methods and constructs several novel single-step or multi-step prediction models based on the ESN to predict short term traffic flow. Each of these models is able to improve the prediction accuracy, training speed and stability in certain degree. Based on the above research works, the main works and contributions can be summarized as follows:
(1) Complex dynamics of traffic flow are analyzed from multiple perspectives. According to our research, we find that traffic flow is chaotic time series with strong noise. These noise components destruct the behavior of chaotic attractor of traffic flow and significantly reduce its predictability. In this paper, we qualitatively and quantitatively analyze the predictability of traffic flow in detail on the basis of dynamics analysis on traffic flow. We revealed the complex physical properties of traffic flow in essence. Those research methods and results also provide a solid theoretical foundation for the further construction of new prediction models.
(2) ESN based single step and multiple step prediction models are proposed. As a novel prediction model, ESN is able to predict classical chaotic sequence in multi-step with a high precision. On the basis of dynamics analysis on traffic flow, this paper proposed traffic flow single step and multiple step prediction models based on ESN. Compared with the prediction results of several classic models, it is proved that the new models can improve the precision slightly and appear obvious advantages both in training speed and stability. After discussing some important parameters of the models, the optimal parameters of the ESN model for traffic flow prediction are assigned. In the meanwhile, this paper emphasizes the discussion of the performance of multi-step prediction while using the iterative method and direct method. Through analyzing their advantages and disadvantages, this paper revealed the source of the bottleneck of low prediction accuracy when using the traditional multi-step prediction models. This provides an important theoretical support for the following problem of multi-step prediction.
(3) The multi-reservoir echo state network model based on multi-scale decomposition of wavelet domain (MESNMW) model is proposed to precisely predict traffic flow. This paper investigates the prediction accuracy problem that is not well solved in Part (2) due to the interference of noise component in traffic flow. We found that previous machine learning methods based prediction models focus on the studies of the generalization ability of models while ignoring the tremendous influence of noise components on the prediction accuracy. In order to avoid this influence, this paper proposed a novel MESNMW model from the perspective of signal processing. Using multi-scale decomposition method based on wavelet, this model is able to shield the noise components in traffic flow by treating them as the high-frequency components with less weight such that guarantees the main components, especially the low-frequency components, are chaotic sequences with high signal-to-noise. Combined with multi-reservoir ESN, its single-step prediction accuracy is nearly20times of that obtained by the simple ESN model. Besides, this paper also discusses the influences of some important parameters on the model performances to provide a theoretical basis for the proper choice of model parameters.
(4) The multi-reservoir echo state network based on multi-scale of wavelet packet decomposition domain (MESNMWP) model is proposed to further improve the prediction precision of traffic flow. On the basis of MESNMW, this paper propose a novel MESNMWP model, which uses multi-scale decomposition approach based on wavelet packet to shield the noise components of traffic flow by treating them as high-frequency components with less weight, so that further guarantees the high signal-to-noise of the main components. The experimental results show that the prediction accuracy of MESNMWP single-step model can be increased to three times as that of MESNMW. In addition, this paper also adopts MESNMW and MESNMWP to complete both iterative and direct multi-step prediction of traffic flow. Since the iterative method can obtain more accurate prediction results, this study revises the one-sided traditional view "direct multi-step prediction method is more effective for real-world data". At the same time, it also provides a new way for multi-step prediction of other similar real-world data series.
(5)The single-reservoir echo state network model based on multi-scale of wavelet decomposition domain (SESNMW) and single-reservoir echo state network model based on multi-scale of wavelet packet decomposition domain (SESNMWP) are proposed to achieve high prediction accuracy and efficient on traffic flow. Although the above MESNMW and MESNMWP have high prediction accuracy, their computational costs are usually very high. This will lead to the growth of training time, which greatly hinders the practical application of MESNMW and MESNMWP for traffic flow prediction. In order to ensure both the prediction accuracy and the computational efficiency, this paper proposed SESNMW and SESNMWP from signal smoothing perspective. Aiming at the conflict of the similarity and predictability of the SESNMW and SESNMWP, the multi-state threshold method is introduced into the SESNMW and SESNMWP to reduce noise influences. Compared with other traditional threshold method, this model can more effectively solve the conflict of the similarity and predictability, increasing the fitting degree of the traffic flow after noise reduction process and enhancing the prediction accuracy of single-reservoir ESN. This method can comprehensively assure the prediction accuracy and operating efficiency of SESNMWand SESNMWP.
In summary, this paper focuses on exploring traffic flow prediction models. Firstly, based on the analysis of dynamics property of traffic flow, we propose several single and multi-steps models based on the ESN to improve the operating efficiency and stability of traffic flow prediction. Then, we establish MESNMWto implement high precise single and multi-step prediction of traffic flow. Based on MESNMW, we further create MESNMWPto improve the prediction accuracy. Finally, this paper proposes SESNMW and SESNMwp to satisfy the requirement of accuracy, speed and stability comprehensively for traffic flow prediction. The proposed traffic flow prediction models have good practicality, so they have important value of theoretical and practical application in the field of scientific research and engineering.
然而,传统的模型在对采样间隔为2分钟的交通流时序进行单步预测时,其误差往往接近20%,过低的预测精度远不能满足ITS快速发展的需要。此外,由于交通流预测有着特殊的应用背景,人们期望实际应用的单步预测模型应同时满足速度、稳定性的需要,甚至还能用于多步预测中。多重条件的束缚令交通流预测的研究遇到极大困难。为此,我国科技部启动了973计划“大城市交通拥堵瓶颈的基础科学问题研究”,并在其核心子课题“智能化交通信息融合与集成的研究”中明确地将交通流预测作为研究的核心内容。通过研究我们发现,尽管近年来已有不少模型在交通流单步预测中取得了一定的成果,但由于模型过于集中在自身性能的优化上,而少有考虑交通流本身的物理特性,故最终难以突破预测精度过低的瓶颈,导致交通流的单步和多步预测至今仍是极具挑战且棘手的难点问题。
作为一种新型的机器学习方法,2004年《Science》中提出的回声状态网络(Echo State Networks,简称ESN)由于具备了独特的组织结构以及强大的短时记忆特性,故在对时间序列尤其是对由确定系统产生的无噪混沌时间序列,如Mackey-Glass、Lorenz等序列进行预测时,其预测精度能在以往模型的基础上提升上千倍。且由于采用伪逆法作为权值的训练方法,令ESN兼顾了训练快、稳定性高的优点。而正由于ESN集合了众多优点,它已逐渐地成为近年来机器学习的研究热点,被广泛地应用于时间序列的预测中。而本文被预测的实测交通流恰是具有混沌特性的一类时间序列,受经典混沌时间序列预测的启发,本文考虑将ESN模型引用至交通流的预测中。然而通过研究我们发现,由于受到交通流中复杂噪声成分的影响,在直接使用ESN对交通流进行预测时,其效果并不理想。
为了解决噪声干扰的问题,本文在交通流非线性动力学分析的基础上,融入了先进的信号处理方法,全新地构建了多个基于ESN的短时交通流单步和多步预测模型,且各模型在预测精度、训练速度和稳定性方面均有着不同程度的提升。基于对以上内容的研究,论文的主要工作及创新点将归纳如下：
(1)交通流复杂动力学的多角度分析。通过研究,我们发现交通流是含高噪且混沌的时间序列,复杂噪声成分的加入破坏了交通流混沌吸引子的性态,从而大幅地降低了交通流的可预测性。文中我们在交通流动力学分析的基础上,还详细地对交通流的可预测性进行了定量和定性的分析,从本质上揭示了交通流复杂的物理特性,其研究方法和结果也将为后文中新模型的构建奠定坚实的理论基础。
(2)提出基于ESN的交通流单步和多步预测模型。作为新型的预测模型,ESN能够高精度地对经典的混沌序列进行多步预测。本文在交通流动力学分析的基础上,提出了基于ESN的交通流单步和多步预测模型。并与多个经典模型的预测结果进行对比,验证了新模型在预测精度略有提升的同时,其训练速度和稳定性均占有绝对的优势。随后在完成模型的重要参数讨论后,给出了交通流预测中ESN模型的最优参数设置。此外,文中还着重地探讨了迭代法和直接法的多步预测性能。通过分析两者各自的优缺点,揭示了以往交通流多步预测模型中存在精度瓶颈的根源,其结果为后面解决多步预测难题提供了重要的理论支持。
(3)提出小波域的多尺度多核ESN模型(Multi-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Domain,简称MESNMW)实现了高精度的交通流预测。基于内容(2)中由于交通流噪声成分的干扰而尚未彻底解决的精度问题进行探索。研究发现,以往基于机器学习的交通流预测模型均集中于研究模型自身的泛化能力,忽视了由噪声成分引起交通流可预测性的降低对预测精度的巨大影响。为了不重蹈覆辙,本文全新地从信号处理的角度出发提出了一种新的MESNMW模型用于交通流的单步和多步预测。该模型利用小波多尺度分解方法,将交通流中的噪声成分屏蔽至权重较少的高频分量中,保障了主要分量特别是低频分量是具有高信噪比的混沌序列。在结合多核ESN进行预测后,其单步预测精度是单纯使用ESN模型的近20倍。另外,文中还着重对影响模型性能的重要参数进行了讨论,为模型参数的选择提供了理论的依据。
(4)提出小波包域的多尺度多核回声状态网络模型(Multi-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Packet Domain,简称MESNMWP)模型进一步地提高了交通流的预测精度。在MESNMW模型的基础上,提出了一种新的MESNMWP模型,该模型利用小波包多尺度分解方法能将交通流中的噪声成分屏蔽至权重更小的高频分量中,从而更大程度地保障了主要分量具有高信噪比。实验结果表明,MESNMWP模型的单步预测精度能在MESNMW模型的基础上再提升3倍多。另外,文中还采用MESNMW和MESNMWP模型完成了交通流的迭代多步预测和直接多步预测。而由于迭代法获得了更为精确的预测结果,因此修正了传统意识中认为“实测数据采用直接多步预测法更为有效”的片面观点,同时也为其它类似实测数据的多步预测提供了一种新的思路。
(5)提出基于小波域的多尺度单核ESN模型(Single-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Domain,简称SESNMW)和基于小波包域的多尺度单核回声状态网络(Single-reservoir Echo State Networks based on Multi-scale Decomposition of Wavelet Packet Domain,简称SESNMWP)模型实现了高精度兼顾高效率的交通流预测。前面提出的MESNMW和MESNMWP模型虽能取得非常精确的预测结果,却是以高复杂计算为代价的,而过高的复杂度将引起训练时间的增长,极大地影响了MESNMW和MESNMWP模型在交通流预测中的实际应用。为了在保证预测精度的同时也兼顾运行时间效率,本文从信号平滑的角度上提出SESNMW和SESNMWP用于交通流的预测。文中还针对SESNMW和SESNMWP模型降噪中存在着相似性和可预测性之间矛盾,全新地提出多状态阈值法作为交通流的降噪模型应用于SESNMW和SESNMWP模型中。与传统的阈值法相比,该方法能更好地解决相似性和可预测性之间的矛盾,实现了在提高降噪后交通流拟合度的同时也提升了单核ESN的预测精度,从而全面地保障了SESNMW和SESNMW模型的预测精度和运行效率。
综上所述,本文以探索交通流预测模型为研究中心,在基于交通流动力学分析的基础上,首先提出了基于ESN的交通流单步和多步预测模型以解决交通流预测中运行效率和稳定性的问题；然后构建了MESNMW模型实现了高精度的交通流单步和多步预测；随后在MESNMW模型基础上创建了MESNMWP模型进一步地提升了交通流的预测精度,此精度已是现有方法的几十倍之多；最后提出了SESNMW和SESNMWP模型全方位地满足了交通流预测中精度、速度和稳定性的需要。本文上述所提的多个交通流预测模型具有较好的实用性,在科学研究和工程领域中具有重要的理论价值和实际价值。
With the rapid development of economy and urbanization, some traffic problems caused by the increasing vehicle inventory, such as traffic congestion, traffic accidents and energy dissipation, are becoming one of the world's biggest issues that hinder the urban development. As the most effective method for solving this problem, the Intelligent Transportation System (ITS) has been paid great attention in recent years. As one of the core part of ITS, the system of traffic control and guidance dependents on accurate prediction of traffic flow. Hence, realizing accurate and fast prediction of traffic flow has become one of the priorities of ITS development.
However, when traditional models are used to predict single-step traffic flow time series with the sampling interval of two minutes, their error is often close to20%, and this low prediction accuracy is far from being able to meet the needs of rapid development of ITS. Moreover, because of the special application background of traffic flow prediction, we expect that the single-step prediction model used in practice should not only satisfy the requirement of speed and stability but also be feasible for multiple step prediction. These constraints make the research of traffic flow prediction trap into great difficulty. Hence, China's Ministry of Science and Technology launched the973program Basic Science Research of Big City Traffic Congestion Bottleneck; in its core sub-topic Research of Intelligent Traffic Information Fusion and Integration, the traffic flow prediction is explicitly treated as its core content. We found that many models have achieved good results in the single-step prediction of traffic flow in recent years, but those models are over-focused on the optimization of their performance and seldom consider the physical characteristics of traffic flow, so it is difficult to break through the bottleneck of the low prediction accuracy, resulting in the difficulty and challenging of single-step and multi-step prediction of the traffic flow.
As a new machine learning method, Echo State Network (ESN) proposed in the journal of Science in2004has the characteristic of distinct organizational structure and a strong short-term memory. So ESN can get a thousand times more precise than previous models to predict time series, especially the noise-free chaotic time series generated by deterministic systems such as Mackey-Glass and Lorenz sequence. Moreover, since ESN adopts the pseudo-inverse method to train its weight, it has both characteristics of fast training speed and high stability. Because of its various advantages, ESN are becoming a research focus in the area of machine learning and has been widely used in time series prediction in recent years. Because the real-world traffic flow belongs to a kind of time series with chaotic property, inspired by the classical chaotic time series prediction approaches, we introduce the ESN model into the prediction of traffic flow. However, we found that, if we directly applied the ESN to the prediction of the traffic flow, the prediction effect is not good due to the affection of the complex noise components in the traffic flow.
In order to solve the problem of noise disturbance, based on the analysis of nonlinear dynamic of traffic flow, this paper integrates advanced signal processing methods and constructs several novel single-step or multi-step prediction models based on the ESN to predict short term traffic flow. Each of these models is able to improve the prediction accuracy, training speed and stability in certain degree. Based on the above research works, the main works and contributions can be summarized as follows:
(1) Complex dynamics of traffic flow are analyzed from multiple perspectives. According to our research, we find that traffic flow is chaotic time series with strong noise. These noise components destruct the behavior of chaotic attractor of traffic flow and significantly reduce its predictability. In this paper, we qualitatively and quantitatively analyze the predictability of traffic flow in detail on the basis of dynamics analysis on traffic flow. We revealed the complex physical properties of traffic flow in essence. Those research methods and results also provide a solid theoretical foundation for the further construction of new prediction models.
(2) ESN based single step and multiple step prediction models are proposed. As a novel prediction model, ESN is able to predict classical chaotic sequence in multi-step with a high precision. On the basis of dynamics analysis on traffic flow, this paper proposed traffic flow single step and multiple step prediction models based on ESN. Compared with the prediction results of several classic models, it is proved that the new models can improve the precision slightly and appear obvious advantages both in training speed and stability. After discussing some important parameters of the models, the optimal parameters of the ESN model for traffic flow prediction are assigned. In the meanwhile, this paper emphasizes the discussion of the performance of multi-step prediction while using the iterative method and direct method. Through analyzing their advantages and disadvantages, this paper revealed the source of the bottleneck of low prediction accuracy when using the traditional multi-step prediction models. This provides an important theoretical support for the following problem of multi-step prediction.
(3) The multi-reservoir echo state network model based on multi-scale decomposition of wavelet domain (MESNMW) model is proposed to precisely predict traffic flow. This paper investigates the prediction accuracy problem that is not well solved in Part (2) due to the interference of noise component in traffic flow. We found that previous machine learning methods based prediction models focus on the studies of the generalization ability of models while ignoring the tremendous influence of noise components on the prediction accuracy. In order to avoid this influence, this paper proposed a novel MESNMW model from the perspective of signal processing. Using multi-scale decomposition method based on wavelet, this model is able to shield the noise components in traffic flow by treating them as the high-frequency components with less weight such that guarantees the main components, especially the low-frequency components, are chaotic sequences with high signal-to-noise. Combined with multi-reservoir ESN, its single-step prediction accuracy is nearly20times of that obtained by the simple ESN model. Besides, this paper also discusses the influences of some important parameters on the model performances to provide a theoretical basis for the proper choice of model parameters.
(4) The multi-reservoir echo state network based on multi-scale of wavelet packet decomposition domain (MESNMWP) model is proposed to further improve the prediction precision of traffic flow. On the basis of MESNMW, this paper propose a novel MESNMWP model, which uses multi-scale decomposition approach based on wavelet packet to shield the noise components of traffic flow by treating them as high-frequency components with less weight, so that further guarantees the high signal-to-noise of the main components. The experimental results show that the prediction accuracy of MESNMWP single-step model can be increased to three times as that of MESNMW. In addition, this paper also adopts MESNMW and MESNMWP to complete both iterative and direct multi-step prediction of traffic flow. Since the iterative method can obtain more accurate prediction results, this study revises the one-sided traditional view "direct multi-step prediction method is more effective for real-world data". At the same time, it also provides a new way for multi-step prediction of other similar real-world data series.
(5)The single-reservoir echo state network model based on multi-scale of wavelet decomposition domain (SESNMW) and single-reservoir echo state network model based on multi-scale of wavelet packet decomposition domain (SESNMWP) are proposed to achieve high prediction accuracy and efficient on traffic flow. Although the above MESNMW and MESNMWP have high prediction accuracy, their computational costs are usually very high. This will lead to the growth of training time, which greatly hinders the practical application of MESNMW and MESNMWP for traffic flow prediction. In order to ensure both the prediction accuracy and the computational efficiency, this paper proposed SESNMW and SESNMWP from signal smoothing perspective. Aiming at the conflict of the similarity and predictability of the SESNMW and SESNMWP, the multi-state threshold method is introduced into the SESNMW and SESNMWP to reduce noise influences. Compared with other traditional threshold method, this model can more effectively solve the conflict of the similarity and predictability, increasing the fitting degree of the traffic flow after noise reduction process and enhancing the prediction accuracy of single-reservoir ESN. This method can comprehensively assure the prediction accuracy and operating efficiency of SESNMWand SESNMWP.
In summary, this paper focuses on exploring traffic flow prediction models. Firstly, based on the analysis of dynamics property of traffic flow, we propose several single and multi-steps models based on the ESN to improve the operating efficiency and stability of traffic flow prediction. Then, we establish MESNMWto implement high precise single and multi-step prediction of traffic flow. Based on MESNMW, we further create MESNMWPto improve the prediction accuracy. Finally, this paper proposes SESNMW and SESNMwp to satisfy the requirement of accuracy, speed and stability comprehensively for traffic flow prediction. The proposed traffic flow prediction models have good practicality, so they have important value of theoretical and practical application in the field of scientific research and engineering.
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