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摘要: 深度学习（Deep learning，DL），特别是深度卷积神经网络（Convolutional neural networks，CNNs），能够从医学图像大数据中自动学习提取隐含的疾病诊断特征，近几年已迅速成为医学图像分析研究热点.本文首先简述医学图像分析特点；其次，论述深度学习基本原理，总结深度CNNs在医学图像分析中的分类、分割框架；然后，分别论述深度学习在医学图像分类、检测、分割等各应用领域的国内外研究现状；最后，探讨归纳医学图像分析深度学习方法挑战及其主要应对策略和开放的研究方向.Abstract: Deep learning (DL) algorithms, such as convolutional neural networks (CNNs), can automatically extract hidden disease diagnosis features from medical image data, and are being used to analyze medical images now. We review most of the deep learning methods for medical image analysis. Firstly, we introduce the characteristics of medical image analysis briefly. Then, we analyze the principles of deep learning, highlight the popular CNNs and summarize the frameworks of image classification and segmentation. Thirdly, we describe the state-of-the-art of the medical image analysis methods based on deep learning. Finally, we discuss the challenges and practicable strategies in deep learning for medical image analysis, as well as open research.
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城市道路交通运行状态的演变是一个复杂的动态过程, 交通状态特征参数与各运行状态之间具有复杂的映射关系.因此, 找到一种科学的道路交通运行状态辨识方法, 可以为城市交通系统的管理和有效控制提供理论基础, 为交通参与者的路径选择提供有力的保障[1-2].
道路交通的运行状态评估是交通拥堵状态辨识研究的核心内容, 国内外交通管理部门也以智能化的交通信息采集平台为依托, 建立了道路交通运行状态评价指标与模型.主要有欧洲大多数国家使用的基于路段速度计算拥堵性的INRIX Index指标, 美国提出的基于道路交通密度的道路拥堵指数(Roadway congestion index, RCI), 日本使用的基于交通量的拥堵度(Degree congestion, DC)指标.北京、广州、深圳等地也确定了交通运行状态评价指标, 可以归纳为基于拥堵里程比例、出行时间比和综合评价等几种计算方法.各评价指标和模型虽然表达形式不一样, 但都在一定程度上反映了路网交通运行状态和变化态势.
近年来, 国内外学者对交通拥堵状态辨识的研究主要集中在交通数据的获取与处理和辨识模型的构建与改进两个方面.王坤峰等[3]通过在图像中设置虚拟线圈, 提出了综合利用前景面积、纹理变化和像素运动的多特征融合车辆检测算法, 提高了不良天气和光照条件下交通信息采集的可靠性; Sun等[4]针对部分无价值浮动车数据造成的交通状态评价准确率降低情况, 通过调整数据选择, 添加数据过滤和使用数据加权处理对评价算法进行了优化, 提高了状态评估性能; Elhenawy等[5]将车流视为一个包含自由流速度分布和拥塞流速度分布的双组分模型, 通过自由流参数分布估计自由流速度阈值并实现交通拥堵状态的自动识别; Gong等[6]利用推特网普及型和大众化的特点, 有针对性地获取澳大利亚路网中的用户时空分布数据, 通过时空聚类算法计算道路潜在交通拥堵; Hu等[7]考虑到汽车时空轨迹的固有特性, 采用自相关提取拥堵波的传播速度, 提出了基于智能车路协同系统(Intelligent vehicle infrastructure cooperative systems, IVICS)道路交通拥堵状态辨识方法, 并通过NGSim验证了其有效性; Lu等[8]针对海量交通数据处理速度慢的问题, 基于遗传算法和C-means设计了一种大数据环境下拥堵辨识方法, 提高了处理速度; 赵玲等[9]针对山地城市路网交通亚健康状态的特点, 结合分形理论对路网交通亚健康状态下的短时交通流数据信号进行分析, 得到了亚健康状态下交通流信号非平稳信息的表征, 为山地城市路网亚健康状态下交通拥堵状态辨识和畅通控制提供了良好的理论支撑; 王卓等[10]使用图论中的最小路集法将路网简化为简单串并联路网, 提出了基于畅通可靠度的交通拥堵状态辨识方法; Widyantoro等[11]引入模糊理论方法, 以车辆占有率和平均速度为指标构建了一种交通拥堵状态辨识模型, 提高了拥堵状态辨识精确度; 张婧等[12]针对拥堵区域交通参数时空相关性的问题, 基于皮尔逊相关性指标构建了自适应分段的扩展相关性模型, 借助相关性状态变化刻画了拥堵在时空中扩散的定量特征, 为拥堵区域状态辨识奠定了基础; 何兆成等[13]研究了区域交通状态分析与评价方法, 引入交通拥堵时空累积指标对区域交通运行状态进行判别与定量计算, 并构建了区域交通状态可视化模型, 直观地描述了区域交通拥堵程度和分布情况以及空间层次上的城市区域交通运行规律, 并提出了基于数据可视化的区域路网交通拥堵状态辨识模型; Habtie等[14]提出一种三层神经网络模型用于估计完整的链路流量状态, 建立了实时道路交通状态辨识框架及模型; 乔少杰等[15]针对路网中移动对象难以进行准确描述的问题, 提出了基于隐马尔科夫链的自适应轨迹预测模型, 实现了较高的预测准确性.以上模型均在特定条件下取得了良好的效果.
然而, 单一的交通系统运行状态指标(例如饱和度、路网容量、行驶时间和延误等)往往难以正确描述和评价路网的运行状态, 给交通系统的宏观调控和管理带来一定的困难.特别是在智能交通系统(Intelligent transport system, ITS)装备普及化程度越来越高的后交通时代, 由于交通装备的复杂化和多样性, 使得现有城市路网交通监控的海量数据在随机因素和设备内生力影响(例如监控设备失常、路网结构不合理等)下发生异变, 降低了数据来源可靠性.在路网交通设备和通信网络无缝链接执行交通信息资源动态调配过程中, 保证路网畅通性的交通数据不仅种类繁多, 而且极其庞大, 在网络传输过程中还会存在丢包、时延等现象, 增加了交通状态特征参数的不确定性和不完整性.因此, 如何在海量交通数据处理的基础上, 融合、集成大量不确定和不完整的多源信息, 更加有效地进行路网交通拥堵状态的辨识以及动态预测, 提高路网的安全性和可靠性, 已成为交通拥堵研究必须解决的瓶颈问题之一.
为了解决海量数据下交通拥堵特征参数的不确定性和不完整性以及拥堵特征与拥堵状态之间映射关系复杂等问题, 本文将多元集对分析与证据理论相结合, 对拥堵状态辨识过程中的信息进行融合, 在构建路网交通拥堵状态刻画模型的基础上, 通过改进Dempster组合规则得到交通拥堵状态的概率及冲突系数计算方法, 并通过算例分析和实例仿真验证了算法的有效性与可靠性.
1. 交通路网拥堵状态刻画模型
1.1 集对分析简介
集对分析是赵克勤1989年在包头召开的全国系统理论会上提出的一种系统分析方法, 基本思路是在一定的问题背景下对两个集合所具有的特性作同异反分析并加以度量刻画, 得出这两个集合在所论问题背景下的同异反联系度表达式.
定义1 [16-20].给定2个集合 $A$ 和 $B$ , 并设这两个集合组成集对, 在某个具体的问题背景(设为 $W$ )下, 对集对 $H$ 的特性展开分析, 共得到 $N$ 个特性, 其中, 有 $S$ 个为集对 $H$ 中的两个集合 $A$ 和 $B$ 共同拥有; 在 $P$ 个特性上, 集合 $A$ 和 $B$ 相互对立, 在其余的 $F=N-S-P$ 个特性上既不互相独立, 也不互相统一, 又不为这2个集合所共同具有, 则: ${S}/{N}$ 称为这两个集合在集对 $u$ 中的统一度; ${P}/{N}$ 称为这两个集合在集对 $u$ 中的对立度; ${F}/{N}$ 称为这两个集合在集对 $u$ 中的差异度; 两个集合的联系度表示为
$ \begin{align} u = \frac{S}{N} + \frac{F}{N}i + \frac{P}{N}j \end{align} $
(1) 其中, $i$ 和 $j$ 分别为差异度 $F/N$ 和对立度 $P/N$ 的系数. $i$ 在 $[-1, 1]$ 区间视不同情况不确定取值; $j$ 在一般情况下规定其取 $-1, $ 以表示 $P/N$ 是与同一度 $S/N$ 相反的东西.为简便计算, 常用
$ \begin{align} u (W)= a + bi + cj \end{align} $
(2) 来表示, 式(2)满足 $ a + b + c = 1$ .
1.2 路网拥堵状态的集对分析刻画方法
为了探索和发现拥堵状态下路网暴露出来的问题和特征规律, 考虑到海量交通数据下城市交通路网拥堵状态难以推理及辨识的特性, 引入集对分析概念对路网交通状态进行刻画.
集合 $A$ 表示完全畅通状态时道路指标集, 集合 $B$ 表示当前道路交通状态指标集, 使这两个集合组成集对 $H = (A, B)$ , 在进行当前道路交通拥堵状态评估时, 它们的联系度可以表示为
$ \begin{align} u = a + bi + cj \end{align} $
(3) 其中, $a$ , $b$ , $c$ 为非负数, 且 $a + b + c = 1$ ; $j = -1$ , 为了不改变交通拥堵状态评判态势, 本文借用集对分析中顺势取值法对 $i$ 进行取值.顺势取值法又称比例取值法, 核心思想是把 $b$ 按原有 $a$ , $b$ , $c$ 的比例关系作分解, 再按此比例分给 $a$ , $c$ , $b.$ 若集对分为 $n$ 个态势, 则 $i$ 的取值为
$ \begin{align} i_m = 1 - \frac{{2m}}{{n - 1}} \end{align} $
(4) 在上述模型中, $b$ 部分可以通过道路交通的主动控制转换为 $a$ 部分, 此时式(3)可写为 $u=( a+ b )$ $+$ ; 如果道路交通没有及时疏导和管理, $b$ 部分可以转换为 $c$ 部分, 此时式(3)可写为 $u=a+( b$ $+$ $c ) j$ ; 另外, $c$ 部分也可以通过道路交通的主动控制转换为 $b$ 部分, 进而转换为 $a$ 部分, 此时联系度为 $u=$ $a$ $+$ $b+c=1$ .
在上述模型的基础上, 进一步考虑道路交通拥堵状态的多样性, 引入多元集对分析联系度对交通拥堵状态进行细致刻画, 具体模型为
$ \begin{align} u = a + b_1i_1 + b_2i_2 + \cdots + b_ni_n + c_j \end{align} $
(5) 当式(5)中的全体联系分量及其系数都有确定的值时, $u$ 有唯一确定值, 称为综合联系值, 综合联系值是综合参考了联系数中反部的负面影响以及异部的不确定性影响, 其可正可负, 也可以为零.本文使用综合联系值来描述当前道路交通拥堵状态及其变化趋势.
在此背景下, $u = -1$ 时, 说明当前道路交通拥堵状态与完全畅通状态对立, 即为完全拥堵状态; 当 $ - 1$ $<$ $u$ $<$ $1$ 时, 当前道路交通处于“些微拥堵”状态; 当 $u = 1$ 时, 当前道路处于“完全畅通”状态.考虑拥堵状态描述的精确性, 可根据 $u$ 的取值将“些微拥堵”状态进行细致划分.
得到单条道路拥堵值 $u_i$ 之后, 以路段的长度为权重系数对区域交通路网中各条道路的拥堵值进行加权平均, 得到区域交通路网的拥堵状态辨识评价指标 $C$ , 其计算公式为
$ \begin{align} C = \frac{{\sum\limits_{i = 1}^N {(u_i \times L_i)} }}{{\sum\limits_{i = 1}^N {L_i} }} \end{align} $
(6) 其中, $N$ 表示区域路网道路总数, $L_i$ 表示第 $i$ 条道路长度.
2. 拥堵状态相关参数的确定方法
在第1.2节的刻画模型中, $i_n$ 作为微观层次上不确定性的承载, 考虑到其对势级状态的影响, 采用顺势取值法可以得到具体值.而 $a$ , $b_n$ 和 $c$ 的值是各项检测指标相互作用的结果.在智能交通系统(ITS)普及的今天, 其信息采集系统形式越来越多样化, 基于单一的采集系统的监测信息得到的 $a, b_n$ 和 $c$ 的值不能准确描述当前时刻路网拥堵状态, 而且造成信息的丢失和浪费.本文采用D-S证据理论的方法, 将多源信息进行融合, 为当前交通拥堵状态的辨识提供依据.
2.1 证据理论的基本知识简介
D-S证据理论不需要先验信息, 并且可以处理由不知道或知识不准确而引起的不确定性, 在信息融合及目标识别领域的各种推理算法中具有独特的优势.
定义2 [21-25].设非空有限集合, $\cdots$ , $\theta_n\}$ 中包含 $n$ 个独立完备和排他的元素, 则称 $\Theta$ 为辨识框架.那么, $\Theta$ 的幂集可以表示为 $2^\Theta$ , 该幂集包含了辨识框架 $\Theta$ 中所有可能的子集, 即该幂集是由 $2^n$ 个命题子集组成, 它可以表示为
$ \begin{align} {2^\Theta } = &\ \{ \Phi, \{ \theta_1\}, \{ \theta_2\}, \cdots, \{ \theta_n\}, \notag \\ &\ \{ \theta_1 \cup \theta_2\}, \{ \theta_1 \cup \theta_3\} , \cdots, \Theta \} \end{align} $
(7) $A$ 为 $\Theta$ 的子集, 若映射 $m:{2^\Theta } \to [0, 1]$ 满足下列条件: $m(\Phi ) = 0$ , $m(A) \ge 0$ , $\sum\nolimits_{A \in {2^\Theta }} {m(A) = 1} $ .则称 $m$ 为 $\Theta$ 上的基本概率分配函数或基本信度分配函数, 也称为 $mass$ 函数或质量函数.对任意 $A$ $\subseteq$ $\Theta$ , $m(A)$ 表示证据对 $A$ 的支持程度, 不包括对 $A$ 的任何真子集的支持.另外, 如果, 那么将 $A$ 称为 $m$ 的焦元.
2.2 基于证据理论的交通拥堵辨识参数计算模型
考虑到证据理论在交通拥堵状态辨识的具体应用背景, 为简化计算复杂度, 利用以下引理可得出某交通拥堵状态概率和冲突因子计算公式.
引理1. 路网交通拥堵状态的幂集应表示为 ${2^\Theta }$ $=$ $\{ \{ \theta_1\}, \{ \theta_2\}, \cdots, \{ \theta_n\} \}$ , 其中 $\theta_i$ 表示路网处于第 $i$ 个拥堵状态.
证明. 路网交通拥堵状态是一个非空有限集合, 且包含 $n$ 个独立完备且排他元素, 用 $\Theta$ 表示交通拥堵状态的辨识框架, 则 $\Theta$ 的幂集可表示为式(7)样式.
然而, 考虑到路网交通拥堵状态的具体应用背景, 当前路网交通必处于且仅处于某个拥堵状态, 即在其幂集中不存在 $\Phi$ 和两两并发或多发的拥堵状态, 故路网交通拥堵状态的幂集应为
$ \begin{align} {2^\Theta } = \{ \{ \theta_1\}, \{ \theta_2\}, \cdots, \{ \theta_n\} \} \end{align} $
(8) 其满足: $m(\theta_i) \ge 0$ , , $\theta_i$ 为 $m$ 的焦元.
定理1. 基于引理1, 可以得出两个信源下交通拥堵状态 $\theta_i$ 的概率计算方法:
$ \begin{align} m(\theta_i) = \frac{{m_1(\theta_i) \times m_2(\theta_i)}}{{1 - k}}, \ \ \forall \theta_i \in \Theta \end{align} $
(9) 其中, $k$ 为交通拥堵状态辨识中的冲突系数, 且
$ \begin{align} k = \sum\limits_{\theta_i \cap \theta_j = \varphi } {m_1(\theta_i) \times m_2(\theta_j)}, \ \ i \ne j \end{align} $
(10) 证明. 在证据理论的原始定义中, 若 $\Theta$ 为辨识框架, $m_1$ 和 $m_2$ 是定义在 $\Theta$ 上的两个相互独立的质量函数, 它们的焦元集合分别为 $\{ A_1, A_2, \cdots, A_k\}$ 和, 对于所有基本概率分配中的非空集 $A$ , 由定义可以得出由两个证据共同作用产生的基本概率分配函数, Dempster运算如下:
$ \begin{align} m(A) = \frac{{\sum\limits_{A_i \cap B_j = A} {m_1(A_i)m_2(B_j)} }}{{1 - k}} \end{align} $
(11) 且
$ \begin{align} k = \sum\limits_{A_i \cap B_j = \varphi } {m_1(A_i) \times m_2(B_j)} \end{align} $
(12) 针对交通路网辨识框架 ${2^\Theta } = \{ \{ \theta_1\} $ , , $\cdots$ , $\{ \theta_n\} \}$ 下, $m_1$ 和 $m_2$ 是两个不同信息源产生的两个相互独立的质量函数, 但它们的焦元集合皆为 $\{ \theta_1$ , $\theta_2$ , $\cdots$ , $\theta_n\}$ , 根据上述方法可以得出两个证据共同产生的基本概率分配函数运算如下:
$ \begin{align} m(\theta_i) = \frac{{\sum\limits_{\theta_i \cap \theta_j = \theta_i} {m_1(\theta_i)m_2(\theta_j)} }}{{1 - k}} \end{align} $
(13) 其中,
$ \begin{align} k = \sum\limits_{\theta_i \cap \theta_j = \varphi } {m_1(\theta_i) \times m_2(\theta_j)} \end{align} $
(14) 当且仅当 $j=i$ 时, $\theta_i \cap \theta_j = \theta_i$ , 所以交通拥堵状态 $\theta_i$ 的计算方法如式(9)所示.
当且仅当 $i \ne j$ 时, $\theta_i \cap \theta_j = \phi $ , 所以冲突系数 $k$ 的计算方法如式(10)所示.
定理2. 在多源不确定信息情形下, 交通拥堵状态 $\theta_i$ 的概率计算式为
$ \begin{align} m(\theta_i) = \frac{{\prod\limits_{1 \le j \le n} {m_j(\theta_i)} }}{{1 - k}} \end{align} $
(15) 其中
$ \begin{align} k = 1 - \sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le n} {m_j(\theta_i)} } \end{align} $
(16) 证明. 已知, 在两个信源情形下, 有
$ \begin{align} &m(\theta_i) = \frac{{m_1(\theta_i) \times m_2(\theta_i)}}{{1 - k}} = \frac{{\prod\limits_{1 \le j \le 2} {m_j(\theta_i)} }}{{1 - k}} \end{align} $
(17) $ \begin{align} &k = \sum\limits_{\theta_i \cap \theta_j = \varphi } {m_1(\theta_i)\times m_2(\theta_j)} =\nonumber \\&\qquad 1 - \sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le 2}{m_j(\theta_i)} } \end{align} $
(18) 若在 $n$ 个信源情况下, 假设交通拥堵状态的概率计算式为
$ \begin{align} m(\theta_i) = \frac{{\prod\limits_{1 \le j \le n} {m_j(\theta_i)} }}{{1 - k}} \end{align} $
(19) 冲突系数 $k$ 的计算式为
$ \begin{align} k = 1 - \sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le n} {m_j(\theta_i)} } \end{align} $
(20) 将式(20)代入式(19), 得:
$ \begin{align} m(\theta_i) =&\ \frac{{\prod\limits_{1 \le j \le n} {m_j(\theta_i)} }}{{1 - k}} = \nonumber\\&\ \frac{{\prod\limits_{1 \le j \le n} {m_j(\theta_i)} }}{{\sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le n} {m_j(\theta_i)} } }} \end{align} $
(21) 在 $n+1$ 个信源情形下, 有
$ \begin{align} m(\theta_i) = \frac{{m_n(\theta_i) \times m_{n + 1}(\theta_i)}}{{\sum\limits_{1 \le i \le m} {m_n(\theta_i) \times m_{n + 1}(\theta_i)} }} \end{align} $
(22) 将式(21)代入式(20), 化简可得:
$ \begin{align} m(\theta_i) =&\frac{{\prod\limits_{1 \le j \le n + 1} {m_j(\theta_i)} }}{{\sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le n + 1} {m_j(\theta_i)} } }} = \nonumber\\&\frac{{\prod\limits_{1 \le j \le n + 1} {m_j(\theta_i)} }}{{1 - k}} \end{align} $
(23) 其中,
$ \begin{align} k = 1 - \sum\limits_{1 \le i \le m} {\prod\limits_{1 \le j \le n + 1} {m_j(\theta_i)} } \end{align} $
(24) 故可以得出结论:当信源个数 $n \ge 2$ 时, 都有式(15)和式(16)成立.
2.3 质量函数的确定方法
质量函数的确定是信息融合过程中的重要环节.通常情况下, 质量函数的确定是由专家经验给出, 或根据传感器的数据构造而来.本文采用基于历史数据库的统计分析方法确定各交通参数的质量函数.
设 $U$ 为交通观测过程中某传感器的观测参量, 首先对其进行离散化.鉴于各交通指标在其取值范围内为非均匀分布, 若按等间距均匀划分的方式进行数据离散化处理, 会使数据密度大的区域信息量损失, 为保证各数据所含信息量基本一致, 采用基于概率密度函数的方式进行离散处理.
设 $f(U, x)$ 为参量 $U$ 的概率密度函数, 则 $f(U, x)$ 具有下列性质:
$ \begin{align*} \begin{cases} f(U, x) \ge 0\\[2mm] \int_{ - \infty }^{ + \infty } {f(U, x){\rm d}x = 1} \\[2mm] P(a < x \le b) = \int_a^b {f(x){\rm d}x} \end{cases} \end{align*} $
若要将指标 $U$ 离散化为 $n$ 个等级, 则划分之后每个区间的概率密度函数面积为 $1/n$ , 设为离散化之后第 $i$ 个等级区间的左边界值, $x_i$ 为离散化后第 $i$ 个等级区间的右边界值, 则
$ \begin{align*} &\int_{x_0}^{x_1} {f(U, x){\rm d}x = } \int_{x_1}^{x_2} {f(U, x){\rm d}x = } \cdots=\\ & \qquad\int_{x_{n - 1}}^{x_n} {f(U, x)}{\rm d}x = \dfrac{1}{n} \end{align*} $
依次对上述定积分进行求解, 可分别求的各区间边界值.
依据上述方法对历史数据库中的参量进行离散化, 统计历史数据中参量所属区间出现概率以及参量属于该区间且当前交通拥堵状态为 $\theta_i$ 的概率, 两者比值作为该传感器的质量函数值.即
$ \begin{align} m(\theta_i) = \frac{{P\{ U \in [x_{i-1}, x_i] \cap \theta \in \theta_i\} }}{{P(U \in [x_{i-1}, x_i])}} \end{align} $
(25) 3. 算法的验证与分析
将重庆市南岸区2016年2月15 ~ 21日每天6:00 ~ 21:00的历史监测数据作为数据源, 对重庆市南岸区路网交通运行状态进行分析与评价.监测区域为南岸区主干路网, 包括15条主干道, 全长约146.205 km, 覆盖区域面积约为263.09 ${\rm km}^2$ .
图 1中, 横向粗线条标识为海峡路, 纵向粗线条标识为桃源路.海峡路成东西走向:东接重庆市重要的交通枢纽四公里立交区域, 并直通内环快速至重庆江北机场; 西接通往重庆高新科技园区的鹅公岩大桥, 并直达成渝高速.该条路径途经南岸区诸多居民生活聚集区, 是市民工作出行的必经道路, 日交通量巨大.桃源路大体为南北走向:南临南岸区重要观光旅游地南滨路, 北达南岸区商业中心南坪步行街, 是该区居民观光、休闲、购物的主选道路之一.在南岸区整体交通网络主干道中, 海峡路与桃源路极具代表性, 因此, 本文实例验证部分主要以这两条主干道的监测数据作为仿真分析的基础.
对南岸区15条主干道进行监测, 在主干道交叉口位置的各个方向道路上安装数据监测系统, 每个数据监测系统设置5个断面.其中, 排队长度观测断面所用设备为照相机, 通过图像处理的方法检测出道路上的车辆位置, 预估排队长度, 图像采集间隔为2.5分钟; 车速观测断面所用设备为雷达枪, 它依靠车辆对它发出的雷达射线产生的多普勒效应来测量车辆的速度, 数据回传间隔为5分钟; 时间占有率观测断面所用设备为地磁线圈, 车辆通过埋设在路面下的环形线圈, 引起线圈的磁场变化, 检测器据此计算出车辆的时间占有率, 数据回传间隔为5分钟.摄影机观测断面所用设备为摄像机, 其所摄制的视频数据不直接作为本文数据来源, 当由于某些原因导致上述三个观测断面数据缺失时, 可调取视频并通过人工观察与分析的方法将缺失数据补齐, 同时摄制视频也有利于场景还原和结果验证.观测示意图如图 2所示.
3.1 算例分析
为清楚地表明信息融合过程及验证定理2的正确性, 首先以本文模型对某时刻传感器的回传数据为例进行算例分析.假设路网交通拥堵分为 $\theta_1$ , $\theta_2$ , $\theta_3$ , $\theta_4$ 和 $\theta_5$ 5个状态, 分别表示畅通、基本畅通、轻度拥堵、中度拥堵和严重拥堵, 则该路段的刻画模型可写为
$ u = a + b_1i_1 + b_2i_2 + b_3i_3 + cj $
采用顺势取值法, 得 $i_1 = 0.5$ , $i_2 = 0$ , $i_3 = - 0.5$ , $j = - 1$ .该路段安装的传感器有3个, 根据当前检测到的参数, 以历史统计数据中当前参数下交通状态属于各状态的概率为质量函数, 得
$ \begin{align*}m_1 =&\ (\theta_1, \theta_2, \theta_3, \theta_4, \theta_5) =\\&\ (0.2, 0.4, 0.2, 0.1, 0.1)\\[1mm] m_2 =&\ (\theta_1, \theta_2, \theta_3, \theta_4, \theta_5) =\\&\ (0.1, 0.4, 0.3, 0.1, 0.1)\\[1mm]m_3 =&\ (\theta_1, \theta_2, \theta_3, \theta_4, \theta_5) =\\&\ (0.1, 0.5, 0.2, 0.1, 0.1)\end{align*} $
利用定理1的融合规则对质量函数进行两两融合.首先对 $m_1$ 和 $m_2$ 进行融合, 结果如表 1所示.
表 1 $m_1$ 与 $m_2$ 的融合过程Table 1 Fusion process of $m_1$ and $m_2$$\theta_1(0.2)$ $\theta_2(0.4)$ $\theta_3(0.2)$ $\theta_4(0.1)$ $\theta_5(0.1)$ $\theta_1(0.1)$ 0.02 0.04 0.02 0.01 0.01 $\theta_2(0.4)$ 0.08 0.16 0.08 0.04 0.04 $\theta_3(0.3)$ 0.06 0.12 0.06 0.03 0.03 $\theta_4(0.1)$ 0.02 0.04 0.02 0.01 0.01 $\theta_5(0.1)$ 0.02 0.04 0.02 0.01 0.01 计算冲突系数得
$ k = \sum\limits_{\theta_i \cap \theta_j = \varphi } {m_1(\theta_i) \times m_2(\theta_j)} = 0.74 $
再计算融合后各状态的质量函数, 得
$ \begin{align*}m_{1, 2}(\theta_1) =&\ \frac{{m_1(\theta_1) \times m_2(\theta_1)}}{{1 - k}} = \\[1mm]&\ \frac{{0.02}}{{1 - 0.74}} = 0.08\end{align*} $
$ \begin{align*} m_{1, 2}(\theta_2) =&\ \frac{{m_1(\theta_2) \times m_2(\theta_2)}}{{1 - k}} = \\[1mm]&\ \frac{{0.16}}{{1 - 0.74}} = 0.61\\[3mm] m_{1, 2}(\theta_3) =&\ \frac{{m_1(\theta_3) \times m_2(\theta_3)}}{{1 - k}} = \\[1mm]&\ \frac{{0.06}}{{1 - 0.74}} = 0.23\\[3mm] m_{1, 2}(\theta_4) =&\ \frac{{m_1(\theta_4) \times m_2(\theta_4)}}{{1 - k}} = \\[1mm]&\ \frac{{0.01}}{{1 - 0.74}} = 0.04\\[3mm] m_{1, 2}(\theta_5) =&\ \frac{{m_1(\theta_5) \times m_2(\theta_5)}}{{1 - k}} = \\[1mm]&\ \frac{{0.02}}{{1 - 0.74}} = 0.08\end{align*} $
令上述融合结果与 $m_3$ 进行融合计算, 结果如表 2所示.
表 2 $m_{1, 2}$ 与 $m_3$ 的融合过程Table 2 Fusion process of $m_{1, 2}$ and $m_3$$\theta_1(0.08)$ $\theta_2(0.61)$ $\theta_3(0.23)$ $\theta_4(0.04)$ $\theta_5(0.04)$ $\theta_1(0.1)$ 0.008 0.061 0.023 0.004 0.004 $\theta_2(0.5)$ 0.040 0.305 0.115 0.020 0.020 $\theta_3(0.2)$ 0.016 0.112 0.046 0.008 0.008 $\theta_4(0.1)$ 0.008 0.061 0.023 0.004 0.004 $\theta_5(0.1)$ 0.008 0.061 0.023 0.004 0.004 计算冲突系数, 得
$ k = \sum\limits_{\theta_i \cap \theta_j = \varphi } {m_{1, 2}(\theta_i) \times m_3(\theta_j)} = 0.633 $
计算融合后各状态的质量函数, 得
$ \begin{align*}m(\theta_1) =&\ \frac{{m_{1, 2}(\theta_1) \times m_3(\theta_1)}}{{1 - k}} = \\[1mm]&\ \frac{{0.008}}{{1 - 0.633}} = 0.022\\[3mm] m(\theta_2) =&\ \frac{{m_{1, 2}(\theta_2) \times m_3(\theta_2)}}{{1 - k}} = \\[1mm]&\ \frac{{0.305}}{{1 - 0.633}} = 0.831\\ m(\theta_3) = &\ \frac{{m_{1, 2}(\theta_3) \times m_3(\theta_3)}}{{1 - k}} = \\[1mm]&\ \frac{{0.046}}{{1 - 0.633}} = 0.125\\[3mm] m(\theta_4) = &\ \frac{{m_{1, 2}(\theta_4) \times m_3(\theta_4)}}{{1 - k}} = \\[1mm]&\ \frac{{0.004}}{{1 - 0.633}} = 0.011\\[3mm] m(\theta_5) = &\ \frac{{m_{1, 2}(\theta_5) \times m_3(\theta_5)}}{{1 - k}} = \\[1mm]&\ \frac{{0.004}}{{1 - 0.633}} = 0.011\end{align*} $
两次融合后, 即可得到该路段处于各拥堵状态的概率取值.
直接采用式(14)计算拥堵状态的概率取值, 可得
$ \begin{align*} &m(\theta_1) = \frac{{0.002}}{{0.096}} = 0.021\\[2mm] &m(\theta_2) = \frac{{0.08}}{{0.096}} = 0.833\\[2mm] &m(\theta_3) = \frac{{0.012}}{{0.096}} = 0.125\\[2mm] &m(\theta_4) = \frac{{0.001}}{{0.096}} = 0.010\\[2mm] &m(\theta_5) = \frac{{0.001}}{{0.096}} = 0.010\end{align*} $
其结果与两两融合所得结果基本一致, 考虑到两两融合计算过程中四舍五入的情况对其结果的影响, 可以得出本文中定理是正确的.
融合后的信息表示与未融合的信息表示出现较大的差异, 可以判定当前时刻该路段处于基本畅通状态.下面采用集对分析理论对其进行细致刻画, 将 $a$ $=$ $0.022$ , $b_1 = 0.831$ , $b_2 = 0.125$ , $ b_3 = 0.011$ , $c=$ $0.011$ 代入 $u = a + b_1i_1 + b_2i_2 + b_3i_3 + cj$ 中.可得
$ \begin{align*} u = &\ 0.022 \times 1 + 0.831 \times 0.5 +\\ &\ 0.125 \times 0 + 0.011 \times ( - 0.5) +\\ &\ 0.011 \times ( - 1) = 0.421 \end{align*} $
因为 $0 \le 0.421 \le 0.5$ , 且 $|0.5 - 0.421| \le |0.421$ $-$ $0|$ , 根据上述结果得出结论:当前时刻该路段的拥堵状态处于基本畅通和轻度拥堵之间, 且更偏向于基本畅通状态.
3.2 实例验证
为验证模型的可靠性与实用价值, 利用本文模型对南岸区路网主干道海峡路2月15日的监测数据进行处理, 并结合交通部门提供的二次处理后的监测数据, 与典型的基于路段速度计算拥堵性指标的INRIX Index模型进行比较, 结果如下:
在图 3中, 实线为INRIX Index模型交通拥堵状态辨识结果, 虚线为本文模型辨识结果.对比可知, 两条曲线数值及变化趋势基本一致, 验证了本文模型的正确性.且本文模型结果曲线变化相对平缓, 避免了依靠单一指标判断过程中的数据波动, 也在一定程度上降低了单一指标检测错误、数据丢失和异变对辨识结果产生的不良影响.
从图 3可以看出, 2月15日6:00 ~ 8:00海峡路路况良好, 8:00过后道路交通拥堵状态逐渐向严重拥堵转变, 早高峰持续时间约为半小时, 后逐渐转变为基本畅通. 10:00 ~ 15:00虽有小幅度波动, 但道路状况基本畅通. 15:00左右出现短时中度拥堵, 后迅速恢复.晚高峰出现在18:00 ~ 19:00, 之后恢复畅通.该路段从畅通状态到严重拥堵状态耗时较短, 说明其对异常事件较为敏感, 道路交通的拥堵容错能力较差.
为了更加直观地展现 $u$ 值与交通拥堵状态的关联性与有效性, 截取图 3中从轻度拥堵状态到重度拥堵状态的时间段内(14:00 ~ 15:00)的海峡路与桃源路交叉口的交通数据, 输入仿真软件进行情景再现, 模拟十字路口的车辆行驶情况.仿真界面中的交叉口每条道路中的矩形颜色表示该道路的交通指示灯颜色, 绿色表示允许通行, 红色表示禁止通行, 黄色表示允许转向.在未输入数据之前, 十字路口显示无车辆行驶状态, 作为该软件的初始状态.将该段时间内的交通监测数据输入软件, 当路网处于各拥堵状态时, 软件界面如图 4~7所示.
通过仿真界面可知, 当图 3中曲线从轻度拥堵状态向重度拥堵状态转化时, 该十字路口的车辆滞留量和排队长度也在增加, 直接证明了模型的可靠性.
利用上述方法分别对南岸区15条主干道交通检测信息进行融合处理, 并通过式(5)得到2月15日南岸区路网交通拥堵状态辨识结果, 如图 8所示.
分析可知, 2月15日南岸区路网交通状态大部分时间处于基本畅通和轻度拥堵之间, 路网早高峰出现在10:00左右, 晚高峰出现在18:00 ~ 19:00, 晚高峰比早高峰拥堵程度严重, 但持续时间较短.对比两种模型结果可知, 单纯依靠速度计算拥堵性的INRIX Index模型波动较大, 且参数的变化敏感度极高.而本文模型对多源信息进行融合, 变化较为平缓, 在一定程度上降低了由单一参数的不确定性和不完整性造成的拥堵状态辨识错误的概率.分析区域路网交通拥堵状态的整体变化趋势, 有利于交通部门从宏观角度出发, 制定调控方案, 缓解区域交通拥堵.
利用本文方法对15 ~ 21日的主干道交通监测信息进行融合, 计算出工作日和双休日各个时刻的拥堵值均值, 得到南岸区区域路网工作日与双休日的拥堵对比曲线, 如图 9所示.
从图 9可以看出, 本周工作日期间南岸区区域路网路况较为良好, 早高峰出现在8:00 ~ 9:00, 晚高峰出现在18:00 ~ 19:00.双休日的路网交通拥堵较为严重, 无明显的早、晚高峰特性.分析原因可能为本周为春节假期的第一个工作周, 部分返乡人员未归, 减轻了路网交通压力. 2月22日为元宵节, 19日与20日两天大量人员踏上归途, 导致区域路网交通拥堵较为严重.
4. 结论
本文提出了一种考虑多源不确定信息的路网拥堵状态辨识方法.首先引入集对分析概念给出了路网交通拥堵状态刻画模型, 然后通过改进证据理论中Dempster组合规则给出刻画模型中相关参数的确定方法.通过算例计算和实例仿真, 验证了本文提出方法的合理有效性.主要结论如下:
1) 结合集对分析与证据理论的交通拥堵状态辨识方法, 不仅适用于少量数据情况下路网交通运行状态的评估, 而且适用于海量不确定和不完整数据情况下的拥堵状态有效辨识.因此本文方法具有一般性.
2) 通过算例分析两两融合的结果与直接采用文中定理计算的结果进行比较, 验证了本文结论的正确性, 且采用定理2直接进行信息融合计算, 得到的结果更准确.
3) 证据理论的组合规则具有良好的证据聚焦能力, 其在不确定信息表达及合成方面的优势, 使经组合后的交通拥堵状态概率分布向有利于证据的子集分布移动, 在一定程度上降低了信息的不确定性.
总之, 相对于传统的依靠单一交通拥堵状态运行指标来描述路网运行状态的方法, 本文提出的方法具有比较明显的优越性, 具有潜在的应用价值.但是, 如何将这种辨识方法应用到路网交通多模式拥堵预测, 以便从宏观层面了解道路运行状态的态势变化, 是需要进一步研究的内容.
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图 2 受限玻尔兹曼机RBM及基于RBM的深度网络
Fig. 2 Restricted Boltzmann machine (RBM) and deep networks based RBM
表 1 基于CNN的计算机视觉分类任务经典框架
Table 1 Classical CNN frameworks for computer vision classification tasks
网络结构 特点 备注 LeNet[9] 多个卷积层和子采样层 美国手写数字识别 AlexNet[60] 提出了ReLU和Dropout 刷新了2012年ImageNet ILSVRC物体分类竞赛的世界纪录 VGGNet[62] 提出采用小卷积核实现更深的网络以及多尺度融合 获ILSVRC 2014定位任务冠军、分类任务亚军 GoogleNet[65] 22层网络, 多个Inception结构串联 获ILSVRC 2014分类和检测任务冠军 ResNet[14] 提出了残差网络, 引入跳转连接, 深达152层 2015年ILSVRC物体检测与物体识别竞赛冠军 Inception ResNet[67] Inception结构与Residual Net结合 可获得与ResNet相当的性能, 但收敛速度加快 FCN[68] 密集性预测, 实现了像素级分类 避免了图像块之间的重叠而导致重复卷积计算的问题 DenseNet[70] 任何两层之间都有直接的连接 缓解梯度消失, 强化特征传播, 支持特征重用, 并降低网络参数数量 SqueezeNet[72] 简化网络结构和减少网络参数 仅需1/50的AlexNet参数量即可达到了AlexNet相同的精度 DCNN[73] 提出可变形深度卷积神经网络 增强了网络对于几何变换的建模能力 DPN[71] 结合了ResNet和DenseNet优势 基于DPN的团队取得2017年ILSVRC物体检测与物体识别竞赛冠军 SENet[74] 学习每个特征通道的重要程度, 强化有用特征 2017年ILSVRC图像分类任务竞赛冠军 
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表 2 脑瘤分割方法比较(使用BRATS数据集验证)
Table 2 Comparison of methods for brain tumor segmentation (validation on BRATS database)
作者 方法 DICE 总肿瘤区 核心肿瘤区 活性肿瘤区 专家评定 医学训练和经验 0.88 0.93 0.74 Urban[174] 多模态输入, 训练3D CNN 0.87 0.77 0.73 Zikic[175] 将3D立方体图像块转换成2D图像块, 训练2D CNN网络 0.837 0.736 0.69 Havaei[82] 2D多模态输入, 双路径级联CNN架构, 综合了局部细节和更全局信息 0.88 0.79 0.73 Pereira[176] 3×3的小的小卷积核, 更多的CNN层数和非线性运算, 更少的滤波器权重 0.88 0.83 0.77 Kamnitsas[168] 采用深度为11层的小滤波器3D CNN的双路径网络框架 0.898 0.75 0.721
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