WO2023178581A1 - 一种基于量子游走的网约车流量多尺度特征解析方法 - Google Patents
一种基于量子游走的网约车流量多尺度特征解析方法 Download PDFInfo
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Definitions
- the invention belongs to the intersection of traffic geography and quantum mechanics, and specifically relates to a multi-scale feature analysis method for online car-hailing traffic based on quantum walks.
- the transportation system is a complex time-varying nonlinear system.
- urban traffic flow changes formed by trajectory aggregation have complex multi-scale spatiotemporal characteristics.
- the analysis of urban traffic flow characteristics is one of the key measures to build an intelligent transportation system.
- various data generated by vehicles during operation such as trajectories, traffic flow, speed, density, etc., are all indicators for measuring the potential patterns of spatiotemporal characteristics of urban traffic flow. Therefore, accurately mining the multi-scale characteristics of urban traffic flow can help to discover the spatial and temporal distribution patterns and structures implied by urban traffic flow types, which is of great significance to traffic management and even urban planning.
- time series-based methods are a typical traffic volume feature analysis and structure reconstruction method. It usually organizes variables such as traffic flow, speed and density into time series, and further extracts implicit information from these time series based on the information they contain. multi-scale features.
- Typical multi-scale structure analysis methods based on time series include time series analysis, empirical mode decomposition (EMD), wavelet analysis, multi-scale entropy, fractal spectrum analysis, principal component analysis (PCA), tensor method and combinations of the above methods. Methods etc.
- the above methods believe that traffic flow is composed of the superposition and aggregation of multiple components at different scales, thereby performing component simulation and multi-scale characteristic analysis of traffic flow.
- the multi-scale structure analysis method based on time series has the advantage of being good at mining the multi-scale structure implicit in traffic flow and capturing sudden changes in traffic flow.
- such methods are completely data-driven methods based on aggregated traffic flow time series, and rarely consider the impact of the dynamics of vehicle spatial distribution on traffic volume. Therefore, the analysis results of such methods may have pseudo-scale characteristics or "scale mixing" phenomena, which may lead to deviations between the understanding and recognition of the multi-scale structure of urban traffic flow and reality.
- the second category is multi-scale structural analysis methods based on regional units. This method studies the interaction mechanism between the transportation system and urban space based on the perspective of travel areas, analyzes the spatial constraints of urban space on individual behavior, and thereby analyzes the difference and diversity of urban transportation spatial structure.
- Louail et al. used second-order matrices to extract coarse-grained features of the travel network based on user location data obtained from mobile phones, and studied the relationship between the travel volume between residential areas and work areas and city size.
- Lee et al. used travel route data from 92 cities to study the interaction between urban street structure and functional use.
- some scholars have also explored the development process, evolution patterns and laws of transportation facility networks at multiple spatial scales.
- multi-scale structural analysis methods based on regional units are often used to explore the spatial patterns and characteristics of transportation systems, transportation modes, and urban spatial structures.
- most of these methods are macroscopic static methods, focusing on the correlation analysis between traffic flow and urban spatial structure.
- the dynamics of urban traffic flow especially online ride-hailing traffic flow, makes the traffic flow obtained by aggregating vehicle trajectories with significant spatiotemporal heterogeneity, which poses a challenge to effective urban traffic flow characteristic analysis.
- methods based on regional units rarely consider the dynamic evolution process of urban traffic flow in continuous time and space, and then insufficiently consider the multi-scale structure formed by the evolution. Therefore, methods based on regional units cannot intuitively explore the multi-scale characteristics of dynamic urban traffic flows.
- Purpose of the invention Propose a method for analyzing multi-scale characteristics of online car-hailing traffic based on quantum walks, which helps to deepen the understanding and understanding of the multi-scale evolution characteristics and spatial patterns of urban traffic flow.
- the present invention aims at a multi-scale feature analysis method for online car-hailing traffic based on quantum walks, which specifically includes the following steps:
- step (2) Screen the multi-scale probability model described in step (1) according to the spatiotemporal heterogeneity of online car-hailing traffic: use the observed online car-hailing traffic as the boundary constraint, and screen out the online car-hailing traffic at different locations based on stepwise regression.
- Multi-scale probabilistic patterns of car occurrence use the observed online car-hailing traffic as the boundary constraint, and screen out the online car-hailing traffic at different locations based on stepwise regression.
- step (1) is as follows:
- ⁇ (0) is the initial state of the wanderer
- ⁇ k is the scale factor, which represents the evolution model of online ride-hailing traffic flow.
- Mode( ⁇ kt) (Mode 1 ( ⁇ k t), Mode 2 ( ⁇ k t),..., Mode I ( ⁇ k t)) (2)
- the k-th row represents the probability pattern generated by the quantum walk on each sub-region
- the I column represents the probability pattern generated by adjusting the scale factor. All probability patterns generated on sub-region N i .
- step (2) is as follows:
- the traffic flow in sub-region N i can be expressed as: Therefore, the simulation of online car-hailing traffic in each sub-region is:
- mapping parameter from the probability model to the online car-hailing flow which reflects the degree of influence of the probability model on the online car-hailing flow in the corresponding sub-region. is the residual term.
- step (3) is as follows:
- pair mapping parameters Arrange in descending order and rearrange the probability patterns corresponding to the mapping parameters in the same order It is called the first/.../four-scale probability model; combined with the spatiotemporal heterogeneity of online car-hailing traffic in different sub-regions, the characteristic analysis of multi-scale probability model coefficients of online car-hailing traffic is realized.
- the beneficial effects of the present invention are: the present invention considers the spatiotemporal heterogeneity of online car-hailing traffic flow caused by the dynamic evolution of urban traffic flow, and realizes the reconstruction and reconstruction of complex fluctuations of online car-hailing traffic flow. Inversion capability reveals the spatial distribution pattern of the influence of multi-scale probability patterns, and verifies the impact of urban spatial zoning structure on traffic flow; this invention helps to deepen the understanding of the multi-scale evolution characteristics of urban traffic flow and its spatial pattern. and understanding.
- Figure 1 is a flow chart of the present invention
- Figure 2 shows the study area and block division
- Figure 3 is the spatial distribution diagram of the influence degree of the multi-scale probability model; (a) to (d) are the spatial distribution diagrams of the influence degree of the first, second, third and fourth scale probability modes respectively;
- Figure 4 shows the proportion of influence of the multi-scale probability model and its standard deviation distribution
- Figure 5 shows the spatial pattern of urban traffic flow under the multi-scale probability model.
- the present invention proposes a multi-scale feature analysis method for online ride-hailing traffic based on quantum walks.
- quantum walks are used to simulate the dynamic evolution process of online ride-hailing in urban space, and based on this, the online ride-hailing traffic is generated.
- the multi-scale probability model that evolves with time when cars appear at different locations; secondly, the above multi-scale probability model is screened according to the spatiotemporal heterogeneity of online car-hailing flow; using the observed online car-hailing flow as the boundary condition, based on stepwise regression Screen out the multi-scale probability patterns that appear in online car-hailing at different locations; then, construct a mapping transformation mechanism between multi-scale probability patterns and online car-hailing traffic, thereby realizing multi-scale feature analysis of online car-hailing traffic; finally, based on Chengdu
- the online car-hailing traffic volume in the northeastern region of the city was used as experimental data to verify the applicability and feasibility of the present invention, which specifically includes the following steps.
- Step 1 Generate multi-scale probabilistic patterns.
- Quantum walk is an extension of the classic random walk and a typical uncertainty modeling tool.
- the vehicle Before observing, the vehicle can simultaneously select any possible node with different probabilities. When observations are applied to the system, the system will collapse to a specific state and the vehicle will appear at the node with the highest probability. Therefore, whether a vehicle visits a certain node forms a dynamically changing probability distribution.
- the dynamic evolution of the walker is determined by the wave function, which represents the dynamics of the probabilistic evolution of each node. Therefore, by changing the wave function parameters of the above theoretical model, multi-scale probability patterns with different structures can be generated, which can reflect the multi-scale characteristics formed by the dynamic evolution of online ride-hailing, and finally generate a model that can represent the multi-state and multi-situation behavior of online ride-hailing. Multi-scale probabilistic patterns formed by dynamic evolution.
- the probability pattern formed by the dynamic evolution of online car-hailing in each sub-region is generated through quantum walks.
- quantum walks the state of the walker at time t can be expressed as:
- ⁇ (0) is the initial state of the wanderer
- ⁇ k is the scale factor, which can characterize the evolution model of online ride-hailing traffic flow
- U( ⁇ k t) is the time evolution operator, which can be further expressed as
- H controls the dynamic evolution of quantum walks, and is usually represented by the adjacency matrix of the network.
- Mode ( ⁇ k t) (Mode 1 ( ⁇ k t), Mode 2 ( ⁇ k t),..., Mode I ( ⁇ k t)) (2)
- Step 2 Screen multi-scale probability patterns.
- the multi-scale probability model generated in step 1 is optimized and screened based on the actual observed online car-hailing traffic to obtain the online car-hailing flow characteristics in different regions. Based on this, it is clear how to select a multi-scale probability model to accurately reveal the complex characteristics of online car-hailing flow, such as sudden changes, peaks and valleys, and traffic congestion. It is of great significance to analyze the complex modal structure of online car-hailing flow.
- the k-th row represents the probability pattern generated by the quantum walk on each sub-region.
- Column I indicates that by adjusting the scaling factor All probability patterns generated on sub-region N i .
- Stepwise regression is a typical variable screening method and a possible way to screen significant probability patterns.
- the basic idea is to continuously introduce and delete variables in the multivariate linear model to build the optimal regression model. And decide whether a variable should be retained based on specific criteria and significance tests. This paper builds a forward stepwise regression model based on AIC to perform probabilistic pattern screening.
- the traffic flow in sub-region N i can be expressed as: Therefore, the online car-hailing traffic in each sub-region can be simulated as:
- Step 3 Analyze scale features.
- the "feature fingerprint" of online car-hailing traffic is constructed to display the complex structural characteristics of online car-hailing traffic in a simple and efficient manner.
- pair mapping parameters Arrange in descending order and rearrange the probability patterns corresponding to the mapping parameters in the same order and call it the first/.../four-scale probability pattern.
- This study selected the northeastern part of Chengdu City (i.e. 104.0421°E-104.1221°E, 30.65294°N-30.72294°N) as the experimental area.
- the area was gridded into 56 sub-areas with a spatial resolution of 0.01° ⁇ 0.01°, marked as N1, N2,...,N56.
- the study area and block division are shown in Figure 2.
- the online car-hailing traffic time series with a length of 144 in each sub-region was aggregated under a 10-minute time window to form the experimental data of this article .
- 2000 quantum walks were performed on the urban spatial topology based on the study area division structure, and the scale factor ⁇ k was increased from 0.01 to 20 with an interval of 0.01.
- the influence degree of the first-scale probability model is 0-128, among which the influence degree of this probability model is the highest in sub-region N22, which is 126.24, indicating that the first-scale probability model is the online ride-hailing in this sub-region.
- the influence degree of the second scale probability mode is 0-100.
- the first and second scale probability modes have a greater influence on sub-region N16, which are 116.86 and 96.83 respectively, indicating that the first and second scale probability modes determine the sub-region N16.
- the influence degree of the third-scale probability model is 0-40, and the influence degree of the fourth-scale probability model is 0-32.
- the influence of the third- and fourth-scale probability models on sub-region N11 The degree is larger, 37.57 and 30.38.
- the influence degrees of the first and second scale probability modes on this sub-region are 47.51 and 45.25 respectively.
- the four-scale probability model has a significant and balanced impact on sub-region N11, indicating that the traffic flow evolution in this sub-region is relatively stable. This is because there are many important places near this sub-region (such as Sichuan Science and Technology Museum, Tianfu Square and Chengdu Sports Center, etc.), the traffic flow density is high, most vehicles are in a following or slow-moving state, and the evolution is stable, so the degree of influence of the multi-scale probability model Uniform.
- the overall influence of the four-scale probability model shows a large-small distribution pattern from southwest to northeast. This is because in the process of extending from southwest to northeast, the main functional divisions of the study area have experienced the urban area.
- Urban traffic mainly adopts following or slow-moving strategies.
- the space for vehicles to adjust independently is small, the traffic flow structure evolves stably, and there are relatively few multi-scale probabilistic models. Therefore, the impact of multi-scale probabilistic models is greater.
- drivers have a certain amount of free control space and often engage in behaviors such as overtaking or changing lanes. This results in a complex suburban traffic structure and different probability patterns. Therefore, the average impact on a single-scale probability pattern is small.
- the influence proportion and standard deviation distribution of multi-scale probability models in each sub-region were also analyzed, as shown in Figure 4.
- the stacked histogram represents the proportion of influence of multi-scale probability modes. From the first scale to the fourth scale, the influence of probability modes shows a decreasing trend from strong to weak. In particular, it has the ability to measure the spatial pattern of urban traffic flow due to changes in the degree of influence of probability patterns at different scales. Therefore, the sub-regions are divided into three categories according to the difference in the degree of influence of the multi-scale probability pattern (here, one-quarter and three-quarters of the standard deviation are used as the dividing line), namely mutation sub-region and gradient sub-region.
- Sub-region and uniform sub-region (circle points, triangle points and square points in the figure respectively).
- the degree of influence of the multi-scale probability pattern is quite different, especially the absolute dominance of the first scale on the sub-region.
- There are certain differences in the degree of influence of the probability pattern in the gradient sub-region which basically shows a slowly changing degree of influence.
- the uniform sub-region is a further weakening of the gradient sub-region, and the influence of multi-scale probability modes in this sub-region is almost equal.
- FIG. 5 is another exploration of the spatial pattern of urban traffic flow.
- mutation sub-regions are mainly distributed in areas with complex urban traffic flow evolution, such as non-commercial areas and suburbs. This is because in non-commercial areas or suburbs, drivers have more opportunities to drive and control autonomously, and traffic flow evolution is complex, so the impact of multi-scale probabilistic patterns varies greatly.
- gradient and uniform subregions are more common and evenly distributed in the study area.
- the traffic flow in these areas mostly evolves with slow-moving or car-following strategies.
- the space for vehicles to adjust independently is small, the traffic flow evolves stably, and the influence of multi-scale probability models is relatively uniform.
- the numbers of the three types of sub-regions are 14, 26 and 14 respectively, which also reveals the spatial pattern of traffic flow in the study area - mainly gradient, with both mutation types. and a uniform spatial pattern, which is also in line with the public’s perception of urban traffic flow.
Abstract
本发明公开了一种基于量子游走的网约车流量多尺度特征解析方法，首先，运用量子游走模拟网约车在城市空间中的动态演化过程，据此生成网约车出现在不同位置上的随时间演化的多尺度概率模式；其次，根据网约车流量的时空异质性来筛选上述多尺度概率模式；以观测的网约车流量作为边界条件，基于逐步回归筛选出不同位置上的网约车出现的多尺度概率模式；最后，构建多尺度概率模式与网约车流量间的映射转化机制，从而实现网约车流量的多尺度特征解析。本发明能准确解析网约车流量的多尺度特征，有助于挖掘城市交通流中隐含的时空分布格局和结构，对交通管理乃至城市规划具有重要意义。
Description
本发明属于交通地理和量子力学的交叉领域，具体涉及一种基于量子游走的网约车流量多尺度特征解析方法。
交通系统，尤其是城市交通系统，是一个复杂的时变非线性系统。实际上，由轨迹聚合形成的城市交通流量变化具有复杂的多尺度时空特征。目前，城市交通流量特征分析是建设智能交通系统的关键措施之一。此外，车辆在运行过程中产生的各种数据，如轨迹、交通流量以及速度、密度等，都是衡量城市交通流时空特征潜在规律的指标。因此，准确挖掘的城市交通流量的多尺度特征有助于挖掘城市交通流种隐含的时空分布格局和结构，对交通管理乃至城市规划具有重要意义。
目前，城市交通流量模拟与多尺度特征解析的方法可分为两类：基于时间序列的方法和基于区域单元的方法。基于时间序列的方法是一种典型的交通量特征分析和结构重构方法，通常将交通流量、速度和密度等变量组织成时间序列，并根据其包含的信息进一步从这些时间序列中提取隐含的多尺度特征。典型的，基于时间序列的多尺度结构分析方法有时间序列分析、经验模式分解(EMD)、小波分析、多尺度熵、分形谱分析、主成分分析(PCA)、张量方法以及上述方法的组合方法等。一般来说，上述方法认为了交通流量是由不同尺度的多个分量的叠加聚合而成，从而进行交通流量的成分模拟和多尺度特性分析。基于时间序列的多尺度结构分析方法具有善于挖掘交通流隐含的多尺度结构，捕捉交通流量突变的优点。但此类方法是完全基于聚合的交通流时间序列的数据驱动的方法，很少考虑车辆空间分布的动态性对交通量的影响。因此，此类方法的分析结果可能具有伪尺度特征或“尺度混合”现象，进而导致对城市交通流多尺度结构的理解和认识与现实存在偏差。
第二类是基于区域单元的多尺度结构分析方法。该方法基于出行区域的视角来研究交通系统与城市空间的交互机制，分析城市空间对个体行为的空间约束，从而解析城市交通空间结构的差异性和多元性。例如，Louail等基于手机获取的用户位置数据，使用二阶矩阵提取出行网络的粗粒度特征，研究了住宅区与工作 区之间的出行量与城市规模的关系。Lee等使用92个城市的出行路线数据﹐研究了城市街道结构与其功能使用之间的相互作用。此外，部分学者还探究了多空间尺度的交通设施网络的发展过程、演化模式与规律。通常，基于区域单元的多尺度结构分析方法常用于探索交通系统、交通出行模式和城市空间结构的空间格局和特征。然而，这些方法大多是宏观静态方法，侧重于交通流量与城市空间结构间的相关分析。事实上，城市交通流的动态性，尤其是网约车交通流，使得由车辆行驶轨迹聚合得到的交通流量具有显著的时空异质性，这对有效的城市交通流特征分析提出了挑战。也就是说，基于区域单元的方法很少考虑城市交通流在连续时间和空间上的动态演化过程，进而对由此演化形成的多尺度结构考虑不足。因此，基于区域单元的方法无法直观地探索动态的城市交通流的多尺度特征。
发明内容
发明目的：提出了一种基于量子游走的网约车流量多尺度特征解析方法，有助于加深对城市交通流的多尺度演化特征及其空间格局的理解与认识。
技术方案：本发明旨在一种基于量子游走的网约车流量多尺度特征解析方法，具体包括以下步骤：
(1)运用量子游走模拟网约车在城市空间中的动态演化过程，生成网约车出现在不同位置上的随时间演化的多尺度概率模式；
(2)根据网约车流量的时空异质性来筛选步骤(1)所述的多尺度概率模式：以观测的网约车流量作为边界约束条件，基于逐步回归筛选出不同位置上的网约车出现的多尺度概率模式；
(3)构建多尺度概率模式与网约车流量间的映射转化机制，实现网约车流量的多尺度特征解析。
进一步地，所述步骤(1)实现过程如下：
在量子游走中，游走者在t时刻的状态为：
ψ(δ
kt)＝U(δ
kt)ψ(0) (1)
其中，ψ(0)是游走者的初始状态，δ
k为尺度因子，表征网约车交通流的演化模式，
是时间演化算子，哈密顿量H控制着量子游走的动态演化；在固定尺度因子δ
k的情况下，计算出复数状态向量ψ(δ
kt)，共有I项，I为 子区域数目，对于第i项ψ
i(δ
kt)，其平方表示在时刻t车辆出现在子区域N
i的概率，并将其记为Mode
i(δ
kt)＝|ψ
i(δ
kt)|
2；将所有子区域的概率模式进行汇总，得到以下概率模式：
Mode(
δkt)＝(Mode
1(δ
kt),Mode
2(δ
kt),…,Mode
I(δ
kt)) (2)
且∑Mode(δ
kt)＝1；此外，根据参数集
不断调整尺度因子，生成各子区域所有的概率模式
对于固定的尺度因子δ
k，第k行表示量子游走在各子区域上生成的概率模式，第I列表示通过调整尺度因子
在子区域N
i上生成的所有概率模式。
进一步地，所述步骤(2)实现过程如下：
在多元线性模型中不断引入和删除变量构建最优的回归模型，并基于特定的准则和显著性检验决定变量是否保留；基于各子区域的网约车流量
和概率模式
进行逐步回归概率模式筛选；假设各子区域均筛选S个显著的概率模式，则筛选得到的概率模式为：
称这些概率模式为网约车流量的多尺度概率模式，并将其表示为：
基于上述多尺度概率模式，子区域N
i上的交通流量能够表示为：
因此，各子区域的网约车流量模拟为：
其中，
为模拟的网约车流量，
为概率模式到网约车流量的映射参数，反映了概率模式在对应子区域网约车流量的影响程度，
为残差项。
进一步地，所述步骤(3)实现过程如下：
对映射参数
进行降序排列，并按照相同的顺序重新排列与映射参数对应的概率模式
并将其称为第一/…/四尺度概率模式；结合不同子区域网约车流量的时空异质性，实现网约车流量多尺度概率模式系数的特征分析。
有益效果：与现有技术相比，本发明的有益效果：本发明考虑了城市交通流动态演化导致的网约车交通流量的时空异质性，实现对网约车流量复杂波动的重构与反演能力，揭示了多尺度概率模式影响程度的空间分布格局，验证了城市空间分区结构对交通流的影响；本发明有助于加深对城市交通流的多尺度演化特征及其空间格局的理解与认识。
图1为本发明的流程图；
图2为研究区域与区块划分；
图3为多尺度概率模式的影响程度空间分布图；其中(a)～(d)分别为第一、第二、第三和第四尺度概率模式影响程度的空间分布图；
图4为多尺度概率模式的影响程度占比及其标准差分布；
图5为多尺度概率模式下城市交通流的空间格局。
下面结合附图对本发明作进一步详细说明。
如图1所示，本发明提出一种基于量子游走的网约车流量多尺度特征解析方 法，首先，运用量子游走模拟网约车在城市空间中的动态演化过程，据此生成网约车出现在不同位置上的随时间演化的多尺度概率模式；其次，根据网约车流量的时空异质性来筛选上述多尺度概率模式；以观测的网约车流量作为边界条件，基于逐步回归筛选出不同位置上的网约车出现的多尺度概率模式；然后，构建多尺度概率模式与网约车流量间的映射转化机制，从而实现网约车流量的多尺度特征解析；最后，以成都市东北部区域的网约车流量作为实验数据，验证了本发明的适用性与可行性，具体包括以下步骤。
步骤1：生成多尺度概率模式。
量子游走是经典随机游走的拓展，是一种典型的不确定性建模工具。在观测之前，车辆可以同时选择任何具有不同概率的可能的节点。当对系统施加观测后，系统将坍塌到特定状态，车辆将出现在概率最高的节点。因此，车辆是否访问某个节点形成了一个动态变化的概率分布。在量子游走中，游走者的动态演化由波函数决定，波函数表示每个节点概率演化的动力学。因此，通过改变上述理论模型的波函数参数，可以生成不同结构的多尺度概率模式，据此反映网约车动态演化所形成的多尺度特征，最终生成能够表征网约车在多状态多情境下动态演化形成的多尺度概率模式。
通过量子游走来生成网约车在各子区域上动态演化形成的概率模式。在量子游走中，游走者在t时刻的状态可表示为：
ψ(δ
kt)＝U(δ
kt)ψ(0) (1)
其中，ψ(0)是游走者的初始状态，δ
k为尺度因子，能够表征网约车交通流的演化模式，U(δ
kt)是时间演化算子，可将其进一步表示为
且哈密顿量H控制着量子游走的动态演化，通常以网络的邻接矩阵来表示哈密顿量H。
因此，在固定尺度因子δ
k的情况下，能够计算出ψ(δ
kt)。它是一个复数状态向量，共有I项(I为子区域数目)。对于第i项ψ
i(δ
kt)，其平方表示在时刻t车辆出现在子区域N
i的概率，并将其记为Mode
i(δ
kt)＝|ψ
i(δ
kt)|
2。将所有子区域的概率模式进行汇总，能够得到以下概率模式：
Mode(δ
kt)＝(Mode
1(δ
kt),Mode
2(δ
kt),…,Mode
I(δ
kt)) (2)
且∑Mode(δ
kt)＝1。此外，根据参数集
不断调整尺度因子，能够生成各子区域所有的概率模式
步骤2：筛选多尺度概率模式。
由于网约车流量具有明显的时空分异性，因此根据实际观测的网约车流量对步骤1生成的多尺度概率模式进行优化筛选，得到不同区域的网约车流量特征。据此明晰如何选取多尺度概率模式来准确揭示网约车流量的诸如突变、峰值谷值以及交通拥堵等复杂特征，对解析网约车流量的复杂模态结构有重大意义。
通过上述概率模式的生成，获得了研究区域内所有的概率模式
它几乎囊括了网约车交通流中所有驾驶模式对应的概率模式。并将这些概率模式表示为：
对于固定的尺度因子δ
k，第k行表示量子游走在各子区域上生成的概率模式。第I列表示通过调整尺度因子
在子区域N
i上生成的所有概率模式。
虽然网约车交通流结构复杂，是众多驾驶模式组合形成的复杂巨系统。但网约车交通流的演化结构具有显著的空间异质性，也就是说不同子区域的概率模式不完全相同。因此，基于实际观测的网约车流量来筛选各子区域存在的显著概率模式是解析网约车流量多尺度特征的关键。逐步回归是一种典型的变量筛选方法，是显著概率模式筛选的可能途径。其基本思想是在多元线性模型中不断引入和删除变量来构建最优的回归模型。并基于特定的准则和显著性检验决定变量是否保留。本文基于AIC构建了向前逐步回归模型来进行概率模式筛选。
基于各子区域的网约车流量
和概率模式
进行了逐步回归概率模式筛选。假设各子区域均筛选S个显著的概率模式，则筛选得到的概率模 式为：
称这些概率模式为网约车流量的多尺度概率模式，并将其表示为：
基于上述多尺度概率模式，子区域N
i上的交通流量能够表示为：
因此，各子区域的网约车流量可模拟为：
其中，
为模拟的网约车流量；
为概率模式到网约车流量的映射参数，反映了概率模式在对应子区域网约车流量的影响程度；
为残差项。
步骤3：对尺度特征解析。
研究多尺度概率模式与网约车流量间的特征提取与映射表达机制，据此突破如何选取网约车流量中的多尺度概率模式来准确揭示网约车流量的复杂特征这一难点。进而基于上述多尺度概率模式构建网约车流量的“特征指纹”，以简洁高效的原则展示网约车流量的复杂结构特征。通过综合运用微观与宏观、确定与随机分析相结合的研究方法，以及对城市交通流的“形”“数”“理”特征的深入分析，尝试揭示网约车动态演化和复杂特征结构的内在机理。
为了探索多尺度概率模式对网约车流量的影响以及多尺度概率模式系数的分布特征。对映射参数
进行降序排列，并按照相同的顺序重新排列与映射参数对应的概率模式
并将其称为第一/…/四尺度概率模式。最后，结合不同子区域网约车流量的时空异质性，实现网约车流量多尺度概率模式系数的特征分析。
本发选取成都市东北部(即104.0421°E-104.1221°E,30.65294°N-30.72294°N) 为实验区域。并以0.01°×0.01°的空间分辨率将该区域格网化处理为56个子区域，记为N1,N2,…,N56，研究区域及区块划分如图2所示。对于实验数据的处理，基于2016年11月1日研究区域内的网约车轨迹数据，在10分钟的时间窗口下聚合得到各子区域长度为144的网约车流量时间序列，形成本文实验数据。此外，在生成多尺度概率模式时，在基于研究区域划分构造的城市空间拓扑结构上进行2000次量子游走，尺度因子δ
k从0.01增加至20，且间隔为0.01。
基于上述网约车流量时间序列，开展了以下实验：(1)影响程度特征分析。分别分析第一/第二/…/第四尺度概率模式的影响程度的空间分布，解析网约车流量的结构特征。(2)探索多尺度概率模式下城市交通流的空间格局。计算各子区域多尺度概率模式的影响程度的标准差，根据其差异性实现城市交通流空间格局的揭示。
各子区域前四尺度概率模式的影响程度空间分布如图3所示，(a)～(d)分别为第一、第二、第三和第四尺度概率模式影响程度的空间分布；其中，颜色由深到浅表示概率模式的影响程度由弱到强。特别地，由于本发明主要以数据驱动机制进行概率模式筛选与交通流量重构，导致子区域N47和N55的影响程度存在负值，在本发明中的研究价值不高，因此舍弃对这两个子区域的讨论。就单个概率模式而言，第一尺度概率模式的影响程度为0-128，其中该概率模式在子区域N22的影响程度最高，为126.24，表明第一尺度概率模式是该子区域内网约车流量的主要演化模式。第二尺度概率模式的影响程度为0-100，第一和第二尺度概率模式对子区域N16的影响程度较大，分别为116.86和96.83，表明第一和第二尺度概率模式决定了该子区域内网约车流量的整体演化结构。第三尺度概率模式的影响程度为0-40，第四尺度概率模式的影响程度为0-32，同样地，相较于其他子区域，第三和第四尺度概率模式对子区域N11的影响程度较大，为37.57和30.38。而第一和第二尺度概率模式对该子区域的影响程度分别为47.51和45.25。四个尺度的概率模式对子区域N11的影响程度较为显著且均衡，表明该子区域内交通流演化较为稳定。这是由于该子区域附近有众多重要场所(如四川科技馆、天府广场和成都体育中心等)，交通流密度大，车辆大多处于跟驰或缓行状态，演化稳定，因此多尺度概率模式影响程度均一。
就整体而言，四个尺度的概率模式的整体影响程度由西南-东北呈现出大-小 的分布格局，这是由于从西南延申至东北的过程中，研究区域的主要功能分区经历了城区-郊区的过渡，交通流总体结构由高密度的城区交通逐步过渡为相对高自由度的郊区交通。城区交通以跟驰或缓行策略为主，车辆可自主调节的空间较小，交通流结构演化稳定，多尺度概率模式相对较少，因此多尺度概率模式的影响程度较大。对于郊区交通，驾驶员有一定的自由控制空间，多出现超车或变道等行为，导致郊区交通结构复杂，存在形态各异的概率模式，因此平均到单一尺度概率模式上的影响程度较小。
为探究多尺度概率模式作用下城市交通流的空间分布格局，还分析了各子区域多尺度概率模式的影响程度占比及其标准差分布，如图4所示。其中堆叠柱状图表示多尺度概率模式的影响程度占比，概率模式从第一尺度到第四尺度，其影响程度呈现出由强到弱的递减趋势。特别地，由于不同尺度概率模式的影响程度的变化情况具有衡量城市交通流空间格局的能力。因此根据多尺度概率模式影响程度的差异性(此处以标准差的四分之一和四分之三分位数作为分界线)将子区域分为三类，分别为突变型子区域、渐变型子区域和均匀型子区域(分别为图中圆点、三角形点和正方形点)。对于突变型子区域，其多尺度概率模式影响程度差异较大，特别是第一尺度对该子区域的绝对主导作用。渐变型子区域的概率模式影响程度存在一定差异，基本呈现出缓变的影响程度。均匀型子区域则是渐变型子区域的进一步弱化，多尺度概率模式在该子区域的影响程度几乎相等。
上述三种类型子区域的空间分布如图5所示，是对城市交通流空间格局的又一探索。其中，突变型子区域主要分布于城市交通流演化复杂的区域，如非商业区和郊区。这是由于在非商业区或郊区，驾驶员有更多的机会进行自主驾驶和控制，交通流演化复杂，因此多尺度概率模式影响程度差异较大。然而，渐变型和均匀型子区域则较为常见，均匀分布于研究区域。这些区域的交通流大多以缓行或跟车策略演化，车辆可自主调节的空间较小，交通流演化稳定，多尺度概率模式的影响程度较为均一。此外，三种类型子区域(突变型、渐变型和均匀型)的个数分别为14、26和14，也揭示了研究区域的交通流的空间格局—以渐变型为主，兼有突变型和均匀型的空间格局，这也符合公众对城市交通流的认知。
Claims (4)
- 一种基于量子游走的网约车流量多尺度特征解析方法，其特征在于，包括以下步骤：(1)运用量子游走模拟网约车在城市空间中的动态演化过程，生成网约车出现在不同位置上的随时间演化的多尺度概率模式；(2)根据网约车流量的时空异质性来筛选步骤(1)所述的多尺度概率模式：以观测的网约车流量作为边界约束条件，基于逐步回归筛选出不同位置上的网约车出现的多尺度概率模式；(3)构建多尺度概率模式与网约车流量间的映射转化机制，实现网约车流量的多尺度特征解析。
- 根据权利要求1所述的基于量子游走的网约车流量多尺度特征解析方法，其特征在于，所述步骤(1)实现过程如下：在量子游走中，游走者在t时刻的状态为：ψ(δ kt)＝U(δ kt)ψ(0) (1)其中，ψ(0)是游走者的初始状态，δ k为尺度因子，表征网约车交通流的演化模式，是时间演化算子，哈密顿量H控制着量子游走的动态演化；在固定尺度因子δ k的情况下，计算出复数状态向量ψ(δ kt)，共有I项，I为子区域数目，对于第i项ψ i(δ kt)，其平方表示在时刻t车辆出现在子区域N i的概率，并将其记为Mode i(δ kt)＝|ψ i(δ kt)| 2；将所有子区域的概率模式进行汇总，得到以下概率模式：
Mode(δ kt)＝(Mode 1(δ kt),Mode 2(δ kt),…,Mode I(δ kt)) (2)且∑Mode(δ kt)＝1；此外，根据参数集不断调整尺度因子，生成各子区域所有的概率模式
对于固定的尺度因子δ k，第k行表示量子游走在各子区域上生成的概率模式， 第I列表示通过调整尺度因子在子区域N i上生成的所有概率模式。
- 根据权利要求1所述的基于量子游走的网约车流量多尺度特征解析方法，其特征在于，所述步骤(2)实现过程如下：在多元线性模型中不断引入和删除变量构建最优的回归模型，并基于特定的准则和显著性检验决定变量是否保留；基于各子区域的网约车流量和概率模式
进行逐步回归概率模式筛选；假设各子区域均筛选S个显著的概率模式，则筛选得到的概率模式为：
称这些概率模式为网约车流量的多尺度概率模式，并将其表示为：
基于上述多尺度概率模式，子区域N i上的交通流量能够表示为：因此，各子区域的网约车流量模拟为：
其中，为模拟的网约车流量，
为概率模式到网约车流量的映射参数，反映了概率模式在对应子区域网约车流量的影响程度，
为残差项。
- 根据权利要求1所述的基于量子游走的网约车流量多尺度特征解析方法，其特征在于，所述步骤(3)实现过程如下：对映射参数进行降序排列，并按照相同的顺序重新排列与映射参数对应的概率模式
并将其称为第一/…/四尺度概率模式；结合不同子区域网约车流量的时空异质性，实现网约车流量多尺度概率模式系数的特 征分析。
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| EP2590151A1 (en) * | 2011-11-03 | 2013-05-08 | Deutsche Telekom AG | A framework for the systematic study of vehicular mobility and the analysis of city dynamics using public web cameras |
| CN110111575A (zh) * | 2019-05-16 | 2019-08-09 | 北京航空航天大学 | 一种基于复杂网络理论的城市交通流量网络分析方法 |
| US10733877B2 (en) * | 2017-11-30 | 2020-08-04 | Volkswagen Ag | System and method for predicting and maximizing traffic flow |
| CN112614336A (zh) * | 2020-11-19 | 2021-04-06 | 南京师范大学 | 一种基于量子随机游走的交通流模态拟合方法 |
| CN113327079A (zh) * | 2021-05-28 | 2021-08-31 | 东北师范大学 | 一种基于网约车轨迹的路径选择潜在因素可视分析方法 |
| CN113393488A (zh) * | 2021-06-08 | 2021-09-14 | 南京师范大学 | 一种基于量子游走的行为轨迹序列多特征模拟方法 |
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| EP2590151A1 (en) * | 2011-11-03 | 2013-05-08 | Deutsche Telekom AG | A framework for the systematic study of vehicular mobility and the analysis of city dynamics using public web cameras |
| US10733877B2 (en) * | 2017-11-30 | 2020-08-04 | Volkswagen Ag | System and method for predicting and maximizing traffic flow |
| CN110111575A (zh) * | 2019-05-16 | 2019-08-09 | 北京航空航天大学 | 一种基于复杂网络理论的城市交通流量网络分析方法 |
| CN112614336A (zh) * | 2020-11-19 | 2021-04-06 | 南京师范大学 | 一种基于量子随机游走的交通流模态拟合方法 |
| CN113327079A (zh) * | 2021-05-28 | 2021-08-31 | 东北师范大学 | 一种基于网约车轨迹的路径选择潜在因素可视分析方法 |
| CN113393488A (zh) * | 2021-06-08 | 2021-09-14 | 南京师范大学 | 一种基于量子游走的行为轨迹序列多特征模拟方法 |
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