WO2022104695A1 - 一种基于量子谐振子模型的交通流特征表达方法 - Google Patents

一种基于量子谐振子模型的交通流特征表达方法 Download PDF

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WO2022104695A1
WO2022104695A1 PCT/CN2020/130412 CN2020130412W WO2022104695A1 WO 2022104695 A1 WO2022104695 A1 WO 2022104695A1 CN 2020130412 W CN2020130412 W CN 2020130412W WO 2022104695 A1 WO2022104695 A1 WO 2022104695A1
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traffic flow
state
vehicle
probability
speed
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French (fr)
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罗文�
俞肇元
胡旭
袁林旺
王增杰
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南京师范大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137—Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • G08G1/0145—Measuring and analyzing of parameters relative to traffic conditions for specific applications for active traffic flow control
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G08G1/0133—Traffic data processing for classifying traffic situation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/20—Models of quantum computing, e.g. quantum circuits or universal quantum computers
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/052—Detecting movement of traffic to be counted or controlled with provision for determining speed or overspeed
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

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  • the invention relates to the technical fields of quantum mechanics and traffic geography, in particular to a method for expressing traffic flow characteristics based on a quantum harmonic oscillator model.
  • the expressway plays a vital role in the good operation of the inter-city traffic.
  • the traffic volume of small cars and large vehicles on the expressway has been increasing day by day. complex interactions.
  • different drivers adopt different driving strategies, such as driving at a constant speed, following a car, and abnormal driving strategies mainly based on overtaking.
  • the driving strategies of drivers in high-speed traffic flow are difficult to observe and change randomly, resulting in a high degree of complexity and uncertainty in high-speed traffic flow. Therefore, it is of great significance to extract the characteristic parameters of high-speed traffic flow for simplifying the expression of complex geographic space-time processes such as high-speed traffic flow.
  • the random oscillation in high-speed traffic flow will lead to the decrease of traffic capacity, and the accurate expression of the characteristics of high-speed traffic flow has become an important prerequisite for traffic management, prevention and regulation.
  • the existing traffic flow description feature extraction and expression methods are mainly based on the perspective of macro analysis, and the purpose of extracting traffic flow features and states is achieved by extracting the time-varying characteristics and spatial characteristics of traffic flow parameters and analyzing the traffic flow state.
  • the existing traffic state parameters mainly include two categories: (1) traffic flow, speed and density of traffic flow; (2) ratio of large vehicles, average speed difference between large and small vehicles, and saturation.
  • the expression methods of traffic flow characteristic parameters mainly include parameter relationship model and clustering method, as follows:
  • Parameter relationship model select the three basic parameters of speed, flow, and density to establish a three-parameter relationship model that conforms to specific traffic flow.
  • the traffic flow is divided into three states: smooth flow state, steady flow state and unstable flow state.
  • the methods of probability theory and regression analysis starting from different scales, based on the idea of combining qualitative and quantitative, the traffic flow state is divided.
  • driver's driving strategy is an important source of random oscillation of high-speed traffic flow, which shapes the main characteristics and structure of high-speed traffic flow.
  • Traditional methods can only analyze the overall situation or state of traffic flow from a macro perspective, lack of dynamic description of driver's driving strategy in traffic flow, and insufficient description of microscopic characteristics of traffic flow.
  • the technical problem to be solved by the present invention is to provide a traffic flow characteristic expression method based on the quantum harmonic oscillator model, which can analyze the regularity and difference of the traffic flow state characteristics on the time and space scale by visual expression of the traffic flow characteristic parameters. , to achieve in-depth exploration of traffic flow characteristics.
  • the present invention provides a method for expressing traffic flow characteristics based on a quantum harmonic oscillator model, comprising the following steps:
  • step (1) constructing the eigen equation of vehicle motion quantum harmonic oscillator energy and converting it into a Hermitian polynomial is as follows: the high-speed traffic flow is that all vehicles drive at a uniform speed v, then any vehicle i is at time t.
  • the ideal position of V is clear, denoted as S it ; and in the actual high-speed traffic flow, the driver will accelerate or decelerate according to the driving environment, personal decision-making and other comprehensive reasons, resulting in the actual speed greater than or less than the speed v, denoted as
  • ⁇ >; in the process of quantization description, the speed of the vehicle can be characterized as a superposition state V t a t
  • ⁇ >i, the position can be characterized as a superposition state S t c t
  • i is an imaginary unit
  • A is a constant describing the energy level distribution of an individual
  • ⁇ (x) is a wave function that characterizes the probability amplitude of an individual appearing at a specific location
  • the Hamiltonian quantity of is the core feature of system dynamics evolution
  • f(V t ), g(S t ) are the kinetic energy and potential energy of the harmonic oscillator, respectively.
  • Equation (2) can be transformed into the following Hermitian equation:
  • K represents the number of energy levels, which is represented by the number of different driving strategies that the driver can choose during driving
  • H n (x) is the n-order Hermitian polynomial
  • wn is the fitting parameter of the wave function, which characterizes the harmonic oscillator. The magnitude of the probability of being at different energy levels.
  • step (2) using the K-order Hermitian polynomial approximation to solve the traffic characteristic parameters is specifically: the probability in quantum mechanics can be expressed as the square of the wave function, so the probability of the vehicle appearing at a specific position in the high-speed traffic flow can be expressed as formula (4);
  • Equation (4) is the QHO model of long-distance high-speed traffic flow
  • h n (x) reflects the oscillation structure of different modes; let f(x) be the density function of the vehicle probability distribution, and the K-order Hermitian polynomial approximation is transformed into formula (5) optimization problem.
  • K is directly related to the understanding of the distribution characteristics of the traffic flow.
  • the best order should be selected according to the characteristics and states of the traffic flow itself, and Occam's razor should be followed.
  • three model parameters w 0 , w 1 , and w 2 can be obtained. These three parameters are the traffic flow characteristic parameters in the model. They correspond to the probability amplitudes of the wave function distribution modes of the ground state, the first excited state and the second excited state, respectively.
  • step (3) expressing the characteristic parameters of the traffic flow on a spherical surface is specifically: in the quantum harmonic oscillator model, the superposition structure of the wave functions of the different energy level states of the driving strategy of the traffic flow, according to the waveform of the Hermitian polynomial
  • three characteristic parameters w 0 , w 1 , and w 2 are selected, which correspond to the probability amplitudes of the wave function distribution modes of the ground state, the first excited state and the second excited state, and their squares are the three states respectively.
  • the present invention starts from the premise of autonomous decision-making of the driver's driving strategy, and aims at the objective limitation that the precise state information of the individual long-distance high-speed traffic flow cannot be observed, and uses the quantum state to describe the dynamic evolution of the vehicle speed and state.
  • the state is represented as a superposition state of three driving states, and the QHO model parameters are used to represent the probabilities of the three states. Realize in-depth exploration of traffic flow characteristics.
  • FIG. 1 is a schematic flow chart of the method of the present invention.
  • FIG. 2 is a schematic diagram of the high-speed traffic flow modeling based on the quantum harmonic oscillator model of the present invention.
  • FIG. 3 is a schematic diagram of the projection of the optimization solution of the present invention.
  • Fig. 4 is a schematic diagram showing the characteristic parameters of the traffic flow in 2015 for 225 stations in southern Jiangsu according to the present invention.
  • FIG. 5 is a schematic diagram of the expression of traffic flow characteristic parameters of Changzhou North Station in January, April, July and October in 2015 according to the present invention.
  • FIG. 6 is a schematic diagram showing the expression of traffic flow characteristic parameters under different time windows (2 minutes, 10 minutes, 30 minutes and 60 minutes) of Changzhou North Station in 2015 according to the present invention.
  • a traffic flow feature expression method based on the quantum harmonic oscillator model includes the following steps:
  • Vehicle travel in long-distance high-speed traffic flow has high complexity and uncertainty. It is assumed that the vehicle driving strategies mainly include three types, uniform driving, car-following driving and abnormal driving (mainly overtaking).
  • constant speed driving vehicles enter the station with a certain distribution and travel at a constant speed.
  • the highway which is the fundamental state of the entire traffic flow, thus serves as the energy ground state of the quantum harmonic oscillator.
  • long-distance expressway traffic-following the dynamic change between the following distance and speed of the front and rear vehicles is similar to the evolution law of two sliders connected by a virtual spring.
  • the acceleration/deceleration of the preceding vehicle will cause the virtual spring to stretch/decelerate. Squeeze, thereby creating a virtual force that accelerates/decelerates the car behind, and returns to the equilibrium state of the new speed after a period of time.
  • some drivers may adopt an overtaking strategy, which will interrupt the original traffic sequence and form random oscillations in long-distance high-speed traffic flow, which can be considered as quantum resonance. State transitions in submodels. For a single vehicle in long-distance high-speed traffic flow, its driving strategy will be adjusted over time, which makes the long-distance high-speed traffic flow produce obvious random oscillations.
  • the position is represented by a probability distribution described by a wave function that appears near a specific position, and the driving strategy is represented by three different energy levels.
  • the distribution superposition structure of the corresponding wave function namely the constant speed driving state, the car following driving state and the abnormal driving state.
  • the schematic diagram of the traffic flow feature expression modeling based on the QHO model is shown in Figure 2.
  • the traffic flow characteristic parameters (w 0 , w 1 , w 2 ) respectively represent the probability amplitudes of the three states, describe the waveform structure of the traffic flow wave function, and can accurately reflect the state changes of the entire traffic flow.
  • step (1) construct the quantum harmonic oscillator energy eigen equation of vehicle motion and convert it into a Hermitian polynomial.
  • the long-distance high-speed traffic flow is that all vehicles travel at a uniform speed v, then the ideal value of any vehicle i at time t is The position is clear, denoted as S it ; and in the actual high-speed traffic flow, the driver will accelerate or decelerate according to the driving environment, personal decision-making and other comprehensive reasons, resulting in the actual speed greater or less than the speed v, denoted as
  • ⁇ >; in the quantization description process, the speed of the vehicle can be characterized as a superposition state V t at t
  • ⁇ >i, the position can be characterized as a superposition state S t c t
  • Probability amplitude, c t and d t respectively represent the probability amplitude of the vehicle position leading and lagging behind the ideal position, and
  • 2
  • 2 1;
  • the motion process of the above-mentioned vehicle can be described as a quantum harmonic oscillator, and its energy eigen equation is shown in formula (1).
  • i is an imaginary unit
  • A is a constant describing the energy level distribution of an individual
  • ⁇ (x) is a wave function that characterizes the probability amplitude of an individual appearing at a specific location
  • the Hamiltonian quantity of is the core feature of system dynamics evolution
  • f(V t ), g(S t ) are the kinetic energy and potential energy of the harmonic oscillator, respectively.
  • Equation (2) can be transformed into the following Hermitian equation:
  • K represents the number of energy levels, which is represented by the number of different driving strategies that the driver can choose during driving
  • H n (x) is the n-order Hermitian polynomial
  • wn is the fitting parameter of the wave function, which characterizes the harmonic oscillator. The magnitude of the probability of being at different energy levels.
  • step (2) using the K-order Hermitian polynomial approximation to solve the characteristic parameters is specifically: in quantum mechanics, the probability can be expressed as the square of the wave function, so the probability of the vehicle appearing at a specific position in the long-distance high-speed traffic flow can be expressed as formula (4 );
  • Equation (4) is the QHO model of long-distance high-speed traffic flow
  • h n (x) reflects the oscillation structure of different modes; let f(x) be the density function of the vehicle probability distribution, and the K-order Hermitian polynomial approximation is transformed into formula (5) optimization problem.
  • w n is the coefficient of the n-th order term of the Hermitian polynomial to be fitted, which characterizes the probability distribution of the wave function at the x position as the probability amplitude of h n ;
  • K is directly related to the understanding of the distribution characteristics of the traffic flow.
  • the best order should be selected according to the characteristics and states of the traffic flow itself, and Occam's razor should be followed.
  • three model parameters w 0 , w 1 , and w 2 can be obtained. These three parameters are the traffic flow characteristic parameters in the model. They correspond to the probability amplitudes of the wave function distribution modes of the ground state, the first excited state and the second excited state, respectively.
  • step (3) the characteristic parameters of the traffic flow are expressed on the spherical surface as follows: in the quantum harmonic oscillator model, the superposition structure of the wave functions of the different energy level states of the driving strategy of the traffic flow is selected according to the waveform analysis of the Hermitian polynomial.
  • w 0 , w 1 , w 2 Three characteristic parameters w 0 , w 1 , w 2 are obtained, which correspond to the probability amplitudes of the wave function distribution modes of the ground state, the first excited state and the second excited state respectively, and their squares are the probabilities of the three states, respectively, and In the actual situation, the absolute value of w 0 is the largest, which means that most of them are in a stable and uniform driving state during driving; a set of model parameters can accurately describe the driving state of the traffic flow at a specific time and place.
  • the fitting Hermitian polynomial is selected to be of order 2
  • the optimization method is L-BFGS
  • the traffic flow time series data of 225 expressway stations in southern Jiangsu in 2015 is selected as the experiment data.
  • the direct difference between the various stations lies mainly in the variation of their geographic location, that is, their distance from the incoming station.
  • the change of the vehicle's driving strategy must change according to the difference of its driving distance, and the spatial position is an important factor affecting the change of the characteristic parameters of the QHO model.
  • Time is another important factor affecting the change of the characteristic parameters of the QHO model.
  • the four seasons of the year in my country change significantly, and the driving strategies adopted on the highway will also change accordingly. Therefore, the characteristic parameters of traffic flow are expressed on the time scale. Analysis is very necessary.
  • the time window is the time frequency of data collection, that is, the number of vehicles passing through this station is counted in a certain period of time.
  • Time scale and spatial scale affect the characteristics of traffic flow from the perspective of the phenomenon of high-speed traffic, and the size of the time window affects the size of the scale selected by the basic data of traffic data. Therefore, the change of the time window will also affect the QHO traffic flow characteristic parameters. In order to better express and describe the traffic flow characteristics, the expression of the traffic characteristic parameters under the time window change is also essential.
  • the present invention selects the traffic flow time series data of 225 expressway stations in southern Jiangsu in 2015 as the experimental data, and the data collection time frequency/time window is 2 minutes, 10 minutes, 30 minutes and 60 minutes respectively.
  • Equation (6) can be transformed into the following Hermitian equation:
  • ⁇ K (x) is the wave function representing the magnitude of the probability of the vehicle appearing at position x.
  • the probability can be expressed as the square of the wave function, so the probability of a vehicle appearing at a specific location in a long-distance high-speed traffic flow can be expressed as formula (8).
  • the determination of the order K is directly related to the understanding of the traffic flow distribution characteristics. It is necessary to choose the best order according to the characteristics and state of the traffic flow itself. From the waveform characteristics of the Hermitian polynomial, the distribution structure of the ground state is described by the 0-order Hermitian polynomial, and its waveform structure is a uniformly transmitted single-peak wave packet, which approximates that each individual vehicle is kept in the condition of uniform oscillation near the equilibrium position and is relatively fixed. speed continues.
  • the distribution structure of the first excited state is described by a first-order Hermitian polynomial, and its waveform structure is superimposed oscillation with positive and negative feedback, which is manifested as a close-following process in which the vehicle accelerates/decelerates alternately near the equilibrium position.
  • Higher-level excited states can be characterized by higher-order Hermitian terms, showing higher frequency multimodal fluctuations, showing stronger vehicle interactions, reflecting abnormal driving behaviors such as aggressive driving, overtaking, etc. in traffic flow .
  • f(x) be the density function of the probability distribution of the vehicle, and its 2nd order Hermitian polynomial approximation is transformed into an optimization problem such as formula (9).
  • Equation (9) can be solved by constrained nonlinear optimization, but since the constraints are That is, the feasible solutions of w n are distributed on the unit sphere, making it difficult to search along the monotonic gradient.
  • the optimal solution W n on the unit sphere is transformed into the optimal solution ⁇ n on the two-dimensional plane. And after the optimal ⁇ n is solved, it can be transformed into an ascending dimension to realize the optimal solution of wn .
  • the configuration of the optimal driving state that approximates the oscillating structure of the traffic flow can be obtained.
  • the characteristic parameters of different times, different sites, and different time windows are obtained, and the results of 6 sites are shown in Table 1.
  • the three characteristic parameters w 0 , w 1 and w 2 correspond to the probability amplitudes of the wave function distribution modes of the ground state, the first excited state and the second excited state respectively during the driving process of the vehicle.
  • this patent divides the spherical representation of feature parameters into space-based spherical feature representation, time-based spherical feature representation, and time-window-based spherical feature representation.
  • the traffic flow time series of Changzhou North Station in 2015 was taken as an example, and based on the principle of calculating a set of characteristic parameters every four hours, four time windows (2 minutes, 10 minutes, 30 minutes, and 60 minutes), and visualized the results on the unit sphere, forming the traffic flow feature expression under different time windows, as shown in Figure 6.
  • the time window gradually widens the aggregation degree of the feature parameters increases significantly, and even in the 60-minute time window, the feature parameters show a regular distribution shape.

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Abstract

一种基于量子谐振子模型的交通流特征表达方法，包括如下步骤：(1)构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式；(2)利用K阶厄米多项式逼近求解交通特征参数；(3)将交通流特征参数在球面进行表达。本方法从驾驶员行驶策略自主决策的前提出发，针对长程高速交通流个体精确状态信息不可观测的客观局限，利用量子态描述车辆速度和状态的动态演化，将车辆行驶状态表示为三种行驶状态的叠加态，利用QHO模型参数来表征三种状态的概率；通过将交通流特征参数的可视化表达，并分析交通流状态特征在时空尺度上的规律性和差异性，实现对交通流特征的深入探索。

Description

一种基于量子谐振子模型的交通流特征表达方法 技术领域
本发明涉及量子力学、交通地理技术领域，尤其是一种基于量子谐振子模型的交通流特征表达方法。
背景技术
高速公路作为城市间交通网络中的骨架，对城市间交通的良好运作起着至关重要的作用。近些年，随着网络和交通的发展，高速公路上的小车出行和大车运输的交通量与日俱增，高速交通流明显地表现出持续时间长、速度快且不均匀、交通密度高以及个体之间相互作用复杂等特点。在高速交通流中，不同的驾驶员采取的驾驶策略不同，诸如匀速行驶、跟车行驶以及以超车为主的异常行驶策略。高速交通流中驾驶员的驾驶策略难以观测且随机变化，导致高速交通流表现出高度的复杂性和不确定性。因此，提取高速交通流特征参数，对简化表达诸如高速交通流等复杂的地理时空过程具有重大意义。同时，高速交通流中的随机振荡会导致通行能力下降，对高速交通流特征的准确表达已成为交通管理、预防和调控的重要前提。
现有的交通流描述特征提取表达方法主要基于宏观分析视角，通过提取交通流参数的时变特性、空间特性以及交通流状态分析，达到提取交通流特征和状态的目的。现有的交通状态参数主要包括两类：(1)交通流量、速度和交通流密度；(2)大车比例、大小车平均速度差和饱和度。交通流特征参数表达方法主要有参数关系模型和聚类方法，具体如下：
(1)参数关系模型：选取速度、流量、密度三个基本参数，建立符合特定交通流的三参数关系模型。根据交通流运行机理不同，将交通流分为三种状态：畅行流状态、稳定流状态和不稳定流状态。并利用概率论及回归分析的方法，从不同尺度出发，基于定性与定量结合的思想，进行交通流状态的划分。
(2)聚类方法：基于在交通管理部门采集的交通流时间序列，提取其中的交通状态参数，对其进行聚类分析，以交通流运行的实际情况为参考，提取得到不同规模交通流的特征。
驾驶员驾驶策略动态调整是高速交通流随机振荡的重要来源，塑造了高速交通流的主要特征和结构。传统方法只能从宏观视角分析交通流的整体状况或状态，缺乏对交通流中驾驶员驾驶策略的动态描述，对交通流的微观特征描述不足。
发明内容
本发明所要解决的技术问题在于，提供一种基于量子谐振子模型的交通流特征表达方法，通过将交通流特征参数的可视化表达，并分析交通流状态特征在时空尺度上的规律性和差异性，实现对交通流特征的深入探索。
为解决上述技术问题，本发明提供一种基于量子谐振子模型的交通流特征表达方法，包括如下步骤：
(1)构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式；
(2)利用K阶厄米多项式逼近求解交通特征参数；
(3)将交通流特征参数在球面进行表达。
优选的，步骤(1)中，构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式具体为：高速交通流为所有车辆均以速度v匀速行驶，则任意车辆i在t时刻的理想位置是明确的，记为S it；而在实际高速交通流中，驾驶员会根据行驶环境、个人决策等综合原因，进行加速或者减速，导致实际速度大于或者小于速度v，记为|↑>和|↓>，进一步导致车辆实际位置超前或滞后于理想位置S it，记为|→>和|←>；在量子化描述过程中，车辆的速度可表征为叠加态V t＝a t|↑>+b t|↓>i，位置可表征为叠加态S t＝c t|→>+d t|←>i，其中，i是虚数单位，a t和b t分别表示加速和减速的概率幅，c t和d t分别表示车辆位置超前和滞后于理想位置的概率幅，且|a t| 2+|b t| 2＝|c t| 2+|d t| 2＝1；
据此可将上述车辆的运动过程描述为一个量子谐振子，其能量本征方程如公式(1)所示：
Figure PCTCN2020130412-appb-000001
其中，i是虚数单位；A是描述个体能级分布的常量；ψ(x)是波函数，表征个体出现在特定位置的概率幅；H＝f(V t)+g(S t)是系统的Hamiltonian量，是系统动力学演化的核心特征；f(V t)，g(S t)分别为谐振子的动能和势能。对于公式(1)，通过将其描述成形如
Figure PCTCN2020130412-appb-000002
的二阶非齐次线性微分方程，就能够得到如公式(2)的通解形式；
Figure PCTCN2020130412-appb-000003
式(2)可转化为如下的厄米方程：
Figure PCTCN2020130412-appb-000004
其中，K代表能级数，表征为驾驶过程中驾驶员可以选择的不同驾驶策略的个数，H n(x)是n阶厄米多项式，w n是波函数的拟合参数，表征谐振子处于不同能级的概率幅大小。
优选的，步骤(2)中，利用K阶厄米多项式逼近求解交通特征参数具体为：量子力学中概率可表示为波函数的平方，因此高速交通流中车辆出现在特定位置的概率可表示为公式(4)；
Figure PCTCN2020130412-appb-000005
式(4)为长程高速交通流的QHO模型；
考虑到
Figure PCTCN2020130412-appb-000006
是标准正态分布函数的概率密度函数，将
Figure PCTCN2020130412-appb-000007
转化为厄米多项式的概率表达，h n(x)反映不同模态的振荡结构；设f(x)为车辆概率分布的密度函数，其K阶的厄米多项式逼近转化为如公式(5)的优化问题。
Figure PCTCN2020130412-appb-000008
对于公式(5)能够通过约束的非线性优化进行求解，由于特征参数的约束条件为
Figure PCTCN2020130412-appb-000009
利用单位球面和平面之间映射的方法进行求解；
在QHO模型中，阶数K的确定直接关系到对交通流分布特性的理解，应尽可能根据交通流自身的特点和状态选择最佳的阶数，遵循奥卡姆剃刀法则，如非必要情况下，通常选择K＝2构造二阶QHO模型，通过2阶厄米多项式逼近转化，能够得到w 0、w 1、w 2 三个模型参数，这三个参数就是模型中的交通流特征参数，他们分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅。
优选的，步骤(3)中，将交通流特征参数在球面进行表达具体为：在量子谐振子模型中，交通流的驾驶策略不同能级状态的波函数的叠加结构，根据厄米多项式的波形分析，选择了三个特征参数w 0、w 1、w 2，分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅，他们的平方分别是三种状态的概率，且
Figure PCTCN2020130412-appb-000010
在实际情况下，w 0的绝对值是最大的，表示在行驶中大部分处于平稳匀速行驶状态；一组模型参数能够准确的描述在特定时刻特定地点的交通流的行驶状态；通过引入在三维坐标系下中心点为(0,0,0)的一个球，位于球面上的点坐标的平方和始终为1，即x 2+y 2+z 2＝1；将交通流特征参数(w 0,w 1,w 2)分别映射到这个球面上，就能够很直观地观察特征参数之间的关系；球面参数坐标点之间的分布能够比较直观地描述交通流状态的聚类情况和差异变化，根据具体数据分析交通流状态变化的原因。
本发明的有益效果为：本发明从驾驶员行驶策略自主决策的前提出发，针对长程高速交通流个体精确状态信息不可观测的客观局限，利用量子态描述车辆速度和状态的动态演化，将车辆行驶状态表示为三种行驶状态的叠加态，利用QHO模型参数来表征三种状态的概率；通过将交通流特征参数的可视化表达，并分析交通流状态特征在时空尺度上的规律性和差异性，实现对交通流特征的深入探索。
附图说明
图1为本发明的方法流程示意图。
图2为本发明基于量子谐振子模型的高速交通流建模示意图。
图3为本发明优化求解的投影示意图。
图4为本发明苏南地区225个站点2015年全年交通流特征参数表达示意图。
图5为本发明常州北站2015年1月、4月、7月和10月交通流特征参数表达示意图。
图6为本发明常州北站2015年全年不同时间窗口(2分钟、10分钟、30分钟和60分钟)下交通流特征参数表达示意图。
具体实施方式
如图1所示，一种基于量子谐振子模型的交通流特征表达方法，包括如下步骤：
(1)构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式；
(2)利用K阶厄米多项式逼近求解特征参数；
(3)将交通流特征参数在球面进行表达。
长程高速交通流中车辆行驶具有很高的复杂性和不确定性。假设车辆驾驶策略主要包括三种，匀速行驶、跟驰行驶和异常行驶(以超车情况为主)。在匀速行驶过程中，车辆以一定的分布驶入站点并匀速行驶，在整个高速交通过程中，车辆之间不存在相互作用，直到车辆匀速驶出站点，交通流以一定的车辆序列分布驶出高速公路，这是整个交通流的基本状态，因此可作为量子谐振子的能量基态。在长程高速公路交通流跟驰行驶中，前后车辆跟驰距离与速度之间的动态变化类似于虚拟弹簧连接的两个滑块的演化规律，前车加速/减速运动会导致虚拟弹簧发生拉伸/挤压，从而会产生一个虚拟力使后车加速/减速，并且在一段时间之后回归新速度的平衡状态。在长程高速交通流中，当前方车辆车速较慢或者减速时候，部分驾驶员可能会采取超车策略，这样会打断原来的车流顺序，形成长程高速交通流中的随机振荡，可认为是量子谐振子模型中的状态跃迁。对于长程高速交通流单个车辆而言，其行驶策略会随着时间的变化而发生调整，这样就使得长程高速交通流产生明显的随机振荡。在量子化描述过程中，各车辆的明确位置和驾驶状态均不可精确测定，其中位置表现为以波函数描述的概率分布出现在特定的位置附近，而驾驶策略表现为三种不同能级状态下对应的波函数的分布叠加结构，即匀速行驶状态、跟驰行驶状态和异常行驶状态。基于QHO模型的交通流特征表达建模示意图如图2所示。交通流特征参数(w 0,w 1,w 2)分别表示的是三种状态的概率幅，描述的是交通流波函数的波形结构，能够准确的反映整个交通流的状态变化。通过这个特征参数组，能够直接识别出交通状态的特征，且不同地区、不同时间、不同尺度的高速交通流的差异性和相似性也能够被识别和解释。
步骤(1)中，构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式具体为：长程高速交通流为所有车辆均以速度v匀速行驶，则任意车辆i在t时刻的理想位置是明确的，记为S it；而在实际高速交通流中，驾驶员会根据行驶环境，个人决策等综合原因，进行加速或者减速，导致实际速度大于或者小于速度v，记为|↑>和|↓>，进 一步导致车辆实际位置超前或滞后于理想位置S it，记为|→>和|←>；在量子化描述过程中，车辆的速度可表征为叠加态V t＝a t|↑>+b t|↓>i，位置可表征为叠加态S t＝c t|→>+d t|←>i，其中，i是虚数单位，a t和b t分别表示加速和减速的概率幅，c t和d t分别表示车辆位置超前和滞后于理想位置的概率幅，且|a t| 2+|b t| 2＝|c t| 2+|d t| 2＝1；
据此可将上述车辆的运动过程描述为一个量子谐振子，其能量本征方程如公式(1)所示。
Figure PCTCN2020130412-appb-000011
其中，i是虚数单位；A是描述个体能级分布的常量；ψ(x)是波函数，表征个体出现在特定位置的概率幅；H＝f(V t)+g(S t)是系统的Hamiltonian量，是系统动力学演化的核心特征；f(V t)，g(S t)分别为谐振子的动能和势能。对于公式(1)，通过将其描述成形如
Figure PCTCN2020130412-appb-000012
的二阶非齐次线性微分方程，就能够得到如公式(2)的通解形式；
Figure PCTCN2020130412-appb-000013
式(2)可转化为如下的厄米方程：
Figure PCTCN2020130412-appb-000014
其中，K代表能级数，表征为驾驶过程中驾驶员可以选择的不同驾驶策略的个数，H n(x)是n阶厄米多项式，w n是波函数的拟合参数，表征谐振子处于不同能级的概率幅大小。
步骤(2)中，利用K阶厄米多项式逼近求解特征参数具体为：量子力学中概率可表示为波函数的平方，因此长程高速交通流中车辆出现在特定位置的概率可表示为公式(4)；
Figure PCTCN2020130412-appb-000015
式(4)为长程高速交通流的QHO模型；
考虑到
Figure PCTCN2020130412-appb-000016
是标准正态分布函数的概率密度函数，将
Figure PCTCN2020130412-appb-000017
转化为厄米多项式的概率表达，h n(x)反映不同模态的振荡结构；设f(x)为车辆概率分布的密度函数，其K阶的厄米多项式逼近转化为如公式(5)的优化问题。
Figure PCTCN2020130412-appb-000018
其中，w n是待拟合的厄米多项式n阶项的系数，表征x位置上波函数的概率分布为h n的概率幅；
对于公式(5)能够通过约束的非线性优化进行求解，由于特征参数的约束条件为
Figure PCTCN2020130412-appb-000019
利用单位球面和平面之间映射的方法进行求解；
在QHO模型中，阶数K的确定直接关系到对交通流分布特性的理解，应尽可能根据交通流自身的特点和状态选择最佳的阶数，遵循奥卡姆剃刀法则，如非必要情况下，通常选择K＝2构造二阶QHO模型，通过2阶厄米多项式逼近转化，能够得到w 0、w 1、w 2三个模型参数，这三个参数就是模型中的交通流特征参数，他们分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅。
步骤(3)中，将交通流特征参数在球面进行表达具体为：在量子谐振子模型中，交通流的驾驶策略不同能级状态的波函数的叠加结构，根据厄米多项式的波形分析，选择了三个特征参数w 0、w 1、w 2，分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅，他们的平方分别是三种状态的概率，且
Figure PCTCN2020130412-appb-000020
在实际情况下，w 0的绝对值是最大的，表示在行驶中大部分处于平稳匀速行驶状态；一组模型参数能够准确的描述在特定时刻特定地点的交通流的行驶状态。通过引入在三维坐标系下中心点为(0,0,0)的一个球，位于球面上的点坐标的平方和始终为1，即x 2+y 2+z 2＝1；将交 通流特征参数(w 0,w 1,w 2)分别映射到这个球面上，就能够很直观地观察特征参数之间的关系；球面参数坐标点之间的分布能够比较直观地描述交通流状态的聚类情况和差异变化，根据具体数据分析交通流状态变化的原因。
根据前文假定的三种驾驶策略，选定拟合的厄米多项式为2阶，优化方法选择L-BFGS，并选择苏南地区225个高速公路站点2015年全年的交通流时间序列数据作为实验数据。
各个站点之间直接的不同主要在于其地理位置的变化，即它们距离进站点的距离。在长程高速交通流中，车辆的行驶策略变化一定根据其行驶距离的不同而产生变化，空间位置是影响QHO模型特征参数变化的一个重要因素。通过将交通流特征参数表达，更加直观地分析和描述不同站点之间的相似性和差异性变化，进而分析交通流特征基于空间位置的变化，为描述交通流特征提供数据基础。
时间是影响QHO模型特征参数变化的另一个重要因素，我国的一年四季变化明显，高速公路上采取的驾驶策略也会随之发生一些变化，因此，对交通流特征参数进行时间尺度下的表达分析是非常有必要的。
时间窗口就是数据采集时间频率，即在一定时间段内统计通过此站点的车辆数。时间尺度和空间尺度是从高速交通这个现象的角度对交通流特征产生影响的，而时间窗口的大小影响的是交通数据的基层数据选择的尺度大小。因此时间窗口的变化也会影响QHO交通流特征参数，为了能够更好的对交通流特征表达和描述，对时间窗口变化下的交通特征参数表达也是必不可少的。
本发明选择苏南地区225个高速公路站点2015年全年的交通流时间序列数据作为实验数据，数据采集时间频率/时间窗口分别为2分钟、10分钟、30分钟和60分钟。
将上述车辆的运动过程描述为一个量子谐振子，最终将高速公路交通流描述成如下的形式：
Figure PCTCN2020130412-appb-000021
式(6)可转化为如下的厄米方程：
Figure PCTCN2020130412-appb-000022
其中，x代表车辆在高速公路中的位置，即距离驶入站点的距离。ψ K(x)是波函数，代表车辆出现在x位置的概率幅。
量子力学中概率可表示为波函数的平方，因此长程高速交通流中车辆出现在特定位置的概率可表示为公式(8)。
Figure PCTCN2020130412-appb-000023
我们通过获取观测到车辆在特定空间位置出现的概率P，通过函数逼近的方法求解(w 0,w 1,w 2)。
在QHO的交通流特征表达方法中，阶数K的确定直接关系到对交通流分布特性的理解。需要根据交通流自身的特点和状态选择最佳的阶数。从厄米多项式的波形特点看，基态的分布结构由0阶厄米多项式描述，其波形结构为均匀传递的单峰波包，近似于各个体车辆保持在平衡位置附近均匀振荡条件下以相对固定的速度持续行驶。第一激发态的分布结构由1阶厄米多项式描述，其波形结构为存在正负反馈的叠加振荡，表现为车辆在平衡位置附近加速/减速交替进行的紧密跟驰过程。更高能级的激发态可以用高阶的厄米项加以表征，表现为更高频率的多峰波动，显示了更为强烈的车辆交互作用，反应交通流中诸如激烈驾驶、超车等异常驾驶行为。在遵循奥卡姆剃刀法则的情况下，最终选择K＝2构造二阶QHO模型。
设f(x)为车辆概率分布的密度函数，其2阶的厄米多项式逼近转化为如公式(9)的优化问题。
Figure PCTCN2020130412-appb-000024
对于公式(9)可以通过约束的非线性优化进行求解，但是由于约束条件为
Figure PCTCN2020130412-appb-000025
即w n的可行解分布在单位球上，使得其搜索很难沿着单调的梯度进行。为降低求解的复杂性，可以通过反向赤平投影将N维球面
Figure PCTCN2020130412-appb-000026
上的点投影至
Figure PCTCN2020130412-appb-000027
的平面上，进而在该 平面上进行无约束的优化求解，如图3所示。为此，以W 0(1,0,0)为原点，将单位球上的可行解投影到x＝-1平面上，即将W 1投影为γ 1，W n投影为γ n，实现对可行域的降维变换，在单位球上优化求解W n转化为在二维平面上的优化求解γ n。并在求解出最优γ n后，将其进行升维变换，即可实现对w n的优化求解。
基于以上优化求解，可以得到逼近交通流振荡结构的最优驾驶状态的配置情况。最终得到了不同时间、不同站点、不同时间窗口的特征参数，其中6个站点的结果如表1所示。w 0、w 1、w 2三个特征参数，他们分别对应的是车辆行驶过程中的基态、第一激发态和第二激发态的波函数分布模态的概率幅。
表1 沪宁高速南京至无锡段6个站点的特征参数求解结果
Figure PCTCN2020130412-appb-000028
基于交通流特征参数平方和为1的性质，因此可将计算所得的交通流特征参数绘制在单位球上，实现抽象参数的可视化表达。同时，基于不同的分析目的，本专利将特征参数的球面表达分为基于空间的球面特征表达、基于时间的球面特征表达和基于时间窗口的球面特征表达。
为探究不同站点交通流的变化规律，选取苏南地区225个站点2015年10分钟时间窗口的交通流时间序列实现了交通流特征参数求解，并将结果可视化在单位球上，形成了空间尺度上的交通流特征表达，如图4所示。
为探究交通流在时间尺度上的变化规律，以常州北站2015年1月、4月、7月和10月的交通流时间序列(时间窗口为10分钟)为例，并基于每四个小时计算一组特征参数的原则(即每个月180个左右特征参数)，计算得到了四个月的交通流特征参数，并将结果可视化在单位球上，形成了时间尺度上的交通流特征表达，如图5所示。
为探究不同时间窗口下交通流的变化规律，以常州北站2015年全年的交通流时间序列为例，并基于每四个小时计算一组特征参数的原则，分别计算四个时间窗口(2分钟、10分钟、30分钟和60分钟)下的特征参数，并将结果可视化在单位球上，形成了不同时间窗口下的交通流特征表达，如图6所示。随着时间窗口逐渐拓宽，特征参数的聚集度明显提高，甚至在60分钟时间窗口下，特征参数呈现出规则的分布形状。

Claims (4)

  1. 一种基于量子谐振子模型的交通流特征表达方法，其特征在于，包括如下步骤：
    (1)构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式；
    (2)利用K阶厄米多项式逼近求解交通特征参数；
    (3)将交通流特征参数在球面进行表达。
  2. 如权利要求1所述的基于量子谐振子模型的交通流特征表达方法，其特征在于，步骤(1)中，构建车辆运动量子谐振子能量本征方程并将其转化为厄米多项式具体为：高速交通流为所有车辆均以速度v匀速行驶，则任意车辆i在t时刻的理想位置是明确的，记为S it；而在实际高速交通流中，驾驶员会根据行驶环境、个人决策等综合原因，进行加速或者减速，导致实际速度大于或者小于速度v，记为|↑>和|↓>，进一步导致车辆实际位置超前或滞后于理想位置S it，记为|→>和|←>；在量子化描述过程中，车辆的速度可表征为叠加态V t＝a t|↑>+b t|↓>i，位置可表征为叠加态S t＝c t|→>+d t|←>i，其中，i是虚数单位，a t和b t分别表示加速和减速的概率幅，c t和d t分别表示车辆位置超前和滞后于理想位置的概率幅，且|a t| 2+|b t| 2＝|c t| 2+|d t| 2＝1；
    据此可将上述车辆的运动过程描述为一个量子谐振子，其能量本征方程如公式(1)所示：
    Figure PCTCN2020130412-appb-100001
    其中，i是虚数单位；A是描述个体能级分布的常量；ψ(x)是波函数，表征个体出现在特定位置的概率幅；f(V t)，g(S t)分别为谐振子的动能和势能；H＝f(V t)+g(S t)是系统的Hamiltonian量，是系统动力学演化的核心特征；对于公式(1)，通过将其描述成形如
    Figure PCTCN2020130412-appb-100002
    的二阶非齐次线性微分方程，就能够得到如公式(2)的通解形式；
    Figure PCTCN2020130412-appb-100003
    式(2)可转化为如下的厄米方程：
    Figure PCTCN2020130412-appb-100004
    其中，K代表能级数，表征为驾驶过程中驾驶员可以选择的不同驾驶策略的个数，H n(x)是n阶厄米多项式，w n是波函数的拟合参数，表征谐振子处于不同能级的概率幅大小。
  3. 如权利要求1所述的基于量子谐振子模型的交通流特征表达方法，其特征在于，步骤(2)中，利用K阶厄米多项式逼近求解交通特征参数具体为：量子力学中概率可表示为波函数的平方，因此高速交通流中车辆出现在特定位置的概率可表示为公式(4)；
    Figure PCTCN2020130412-appb-100005
    式(4)为长程高速交通流的QHO模型；
    考虑到
    Figure PCTCN2020130412-appb-100006
    是标准正态分布函数的概率密度函数，将
    Figure PCTCN2020130412-appb-100007
    转化为厄米多项式的概率表达，h n(x)反映不同模态的振荡结构；设f(x)为车辆概率分布的密度函数，其K阶的厄米多项式逼近转化为如公式(5)的优化问题。
    Figure PCTCN2020130412-appb-100008
    对于公式(5)能够通过约束的非线性优化进行求解，由于特征参数的约束条件为
    Figure PCTCN2020130412-appb-100009
    利用单位球面和平面之间映射的方法进行求解；
    在QHO模型中，阶数K的确定直接关系到对交通流分布特性的理解，应尽可能根据交通流自身的特点和状态选择最佳的阶数，遵循奥卡姆剃刀法则，如非必要情况下，通常选择K＝2构造二阶QHO模型，通过2阶厄米多项式逼近转化，能够得到w 0、w 1、w 2三个模型参数，这三个参数就是模型中的交通流特征参数，他们分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅。
  4. 如权利要求1所述的基于量子谐振子模型的交通流特征表达方法，其特征在于，步骤(3)中，将交通流特征参数在球面进行表达具体为：在量子谐振子模型中，交通流的驾驶策略不同能级状态的波函数的叠加结构，根据厄米多项式的波形分析，选择了三个特征参数w 0、w 1、w 2，分别对应的是基态、第一激发态和第二激发态的波函数分布模态的概率幅，他们的平方分别是三种状态的概率，且
    Figure PCTCN2020130412-appb-100010
    在实际情况下，w 0的绝对值是最大的，表示在行驶中大部分处于平稳匀速行驶状态；一组模型参数能够准确的描述在特定时刻特定地点的交通流的行驶状态；通过引入在三维坐标系下中心点为(0,0,0)的一个球，位于球面上的点坐标的平方和始终为1，即x 2+y 2+z 2＝1；将交通流特征参数(w 0,w 1,w 2)分别映射到这个球面上，就能够很直观地观察特征参数之间的关系；球面参数坐标点之间的分布能够比较直观地描述交通流状态的聚类情况和差异变化，根据具体数据分析交通流状态变化的原因。
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