CN116386330A - Copula-based travel time distribution prediction method and system - Google Patents
Copula-based travel time distribution prediction method and system Download PDFInfo
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- 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
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F17/15—Correlation function computation including computation of convolution operations
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- G—PHYSICS
- G08—SIGNALLING
- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/09—Arrangements for giving variable traffic instructions
- G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
- G08G1/0968—Systems involving transmission of navigation instructions to the vehicle
- G08G1/096833—Systems involving transmission of navigation instructions to the vehicle where different aspects are considered when computing the route
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- 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
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- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Abstract
The invention relates to a travel time distribution prediction method and a travel time distribution prediction system based on Copula, wherein the method comprises the following steps: and constructing travel time edge distribution of the preceding road section and the subsequent road section by utilizing travel time data of the historic preceding road section and the subsequent road section, calibrating parameters of a Copula function by the edge distribution, establishing a Copula-based joint distribution of the travel time of the preceding road section and the subsequent road section, taking the actual travel time of a traveler in transit as input of a prediction model, and obtaining the travel time conditional probability distribution of the subsequent road section by utilizing the Copula-based joint distribution of the travel time of the preceding road section and the subsequent road section, thereby providing predicted travel time distribution of the future subsequent road section for the traveler. The invention fully utilizes the existing road section travel time information to dynamically predict the travel time distribution, can provide richer travel time distribution information and assists travelers to better plan paths and schedule the travel.
Description
Technical Field
The invention relates to the technical field of intelligent traffic, in particular to a travel time distribution prediction method and system based on Copula.
Background
Traffic information is an indispensable component of an intelligent traffic system, and among a plurality of traffic information, journey time information is an important reference index for a planner to decide to invest in traffic projects, a manager to evaluate traffic running states and a traveler to plan journey schemes. The journey time information is the final expression of the comprehensive actions of people, vehicles, roads and all the components of the environment of the traffic system, and can intuitively reflect the running state of the traffic system. Therefore, accurate and rich travel time information can be provided, and the method has important significance for reasonably configuring, identifying and relieving traffic jam points and making intelligent travel selection of traffic system resources.
The travel time information also has uncertainty because of the unavoidable uncertainty of the traffic system. Most documents obtain travel time information by predicting the mean and variance of travel time, but travel time uncertainty has the fundamental feature of being forward biased and long-tailed, and a single mean and variance cannot provide complete travel time information. In addition, the rapid development of mobile interconnection technology makes it possible to provide real-time in-transit information for travelers. Therefore, the intelligent traffic field needs to fully utilize the historical on-road travel time information and incorporate the travel time uncertainty into the prediction system, thereby providing accurate and rich on-road travel time prediction information.
Aiming at the aspect of travel time prediction, the prior art has the defects that a prediction model is complex, a large number of data samples are needed to be used, rich travel time uncertainty information cannot be provided, and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a Copula-based travel time distribution prediction method and system, which fully utilize actual travel time which is already experienced in transit, establish the Copula-based joint distribution of travel time of a front road section and a rear road section, and predict the travel time distribution of a future road section and the rear road section.
The aim of the invention can be achieved by the following technical scheme:
a travel time distribution prediction method based on Copula comprises the following steps:
acquiring actual travel time which is already experienced in transit;
inputting the actual journey time which is already experienced in transit into a prediction model to obtain predicted journey time distribution of a subsequent road section;
the construction of the prediction model comprises the following steps:
s1, acquiring a travel time data set of a historic lead road section-a subsequent road section, and constructing the edge distribution of the travel time of the lead road section and the subsequent road section;
s2, establishing Copula-based joint distribution of travel time of the front road section and the rear road section through the edge distribution of the travel time of the front road section and the rear road section constructed in the step S1, and obtaining the travel time conditional probability distribution of the rear road section through the established joint distribution of the travel time of the front road section and the rear road section, wherein the conditional probability distribution is the predicted travel time distribution of the rear road section.
Further, in step S1, the steps of constructing the travel time distribution of the preceding road segment and the following road segment are as follows:
s101, respectively fitting travel time edge distribution of a preceding road section and a subsequent road section by using statistical distribution based on a travel time data set T of m pairs of preceding road sections and subsequent road sections;
s102, selecting the optimal edge distribution by taking the goodness-of-fit index as a criterion, and marking the optimal lead road section travel time edge distribution as F u (u) the optimal subsequent road segment travel time edge distribution is marked as F v (v)。
Further, the statistical distribution includes a parametric distribution and a non-parametric distribution.
Further, in step S2, establishing the Copula-based joint distribution of travel time of the preceding and following road segments includes the following steps:
s201, based on the optimal lead road section travel time edge distribution F obtained in the step S102 u (u) and optimal following road segment travel time edge distribution F v (v) According to the Copula theory, the expression of the Copula probability density function is obtained as follows:
c(F u (u),F v (v)；θ)
wherein θ is the parameter space of the Copula function;
s202, calibrating a relevant parameter theta of Copula by adopting a maximum likelihood method, and constructing a log likelihood function as follows:
wherein t is ui The i-th travel time observation data of the preceding road segment in the travel time data set T representing the historic preceding road segment and the subsequent road segment vi Representing the ith travel time observation data of the subsequent road section;
s203, based on the Copula related parameter theta calibrated in the step S202, obtaining the joint distribution of the travel time of the front and rear road sections according to the Sklar theorem, wherein the joint distribution is as follows:
H(u,v；θ)＝C(F u (u),F v (v)；θ)
where C is a Copula function with a parameter θ.
Further, in step S2, obtaining the travel time conditional probability distribution of the subsequent road segments by using the established joint distribution of the travel times of the preceding road segments and the subsequent road segments includes the following steps:
s204, recording the travel time of the preceding road section as a random variable U, recording the travel time of the following road section as a random variable V, and converting the predicted scene of the travel time distribution of the following road section into a conditional probability problem when the V is calculated as U=u, namely, calculating:
P(V≤v|U＝u)
s205, according to a Copula theory, expressing the required conditional probability P (V is less than or equal to v|U=u) as follows through the joint distribution of travel time of the front and rear road sections based on the Copula:
then
And when the actual journey time which is already experienced in the journey is u, the predicted journey time distribution of the future subsequent road section is obtained.
A travel time distribution prediction system based on Copula comprises a data acquisition module, an edge distribution construction module, a joint distribution construction module and a prediction module;
the data acquisition module is used for acquiring a travel time data set of a historic preface road section-a subsequent road section and acquiring actual travel time which is already experienced in transit;
the edge distribution construction module is used for constructing the front road section and the rear road section travel time edge distribution based on the historical front road section and rear road section travel time data set;
the joint distribution construction module is used for establishing joint distribution of travel time of the front and rear road sections based on Copula based on the constructed edge distribution of travel time of the front road section and the rear road section;
the prediction module takes the actual travel time which is already experienced in transit as the input of a prediction model, and obtains the travel time conditional probability distribution of the subsequent road section by utilizing the established joint distribution of the travel time of the preceding road section and the subsequent road section, wherein the conditional probability distribution is the predicted travel time distribution of the subsequent road section.
Further, in the edge distribution construction module, the steps of constructing the travel time distribution of the leading road section and the trailing road section are as follows:
s101, respectively fitting travel time edge distribution of a preceding road section and a subsequent road section by using statistical distribution based on a travel time data set T of m pairs of preceding road sections and subsequent road sections;
s102, selecting the optimal edge distribution by taking the goodness-of-fit index as a criterion, and marking the optimal lead road section travel time edge distribution as F u (u) the optimal subsequent road segment travel time edge distribution is marked as F v (v)。
Further, the statistical distribution includes a parametric distribution and a non-parametric distribution.
Further, in the joint distribution construction module, establishing the Copula-based joint distribution of travel time of the front and rear road sections comprises the following steps:
s201, based on the optimal lead road section travel time edge distribution F obtained in the step S102 u (u) and optimal following road segment travel time edge distribution F v (v) According to the Copula theory, the expression of the Copula probability density function is obtained as follows:
c(F u (u),F v (v)；θ)
wherein θ is the parameter space of the Copula function;
s202, calibrating a relevant parameter theta of Copula by adopting a maximum likelihood method, and constructing a log likelihood function as follows:
wherein t is ui The i-th travel time observation data of the preceding road segment in the travel time data set T representing the historic preceding road segment and the subsequent road segment vi Representing the ith travel time observation data of the subsequent road section;
s203, based on the Copula related parameter theta calibrated in the step S202, obtaining the joint distribution of the travel time of the front and rear road sections according to the Sklar theorem, wherein the joint distribution is as follows:
H(u,v；θ)＝C(F u (u),F v (v)；θ)
where C is a Copula function with a parameter θ.
Further, in the prediction module, the method for obtaining the travel time conditional probability distribution of the subsequent road section by using the established joint distribution of the travel time of the previous road section and the subsequent road section comprises the following steps:
s204, recording the travel time of the preceding road section as a random variable U, recording the travel time of the following road section as a random variable V, and converting the predicted scene of the travel time distribution of the following road section into a conditional probability problem when the V is calculated as U=u, namely, calculating:
P(V≤v|U＝u)
s205, according to a Copula theory, expressing the required conditional probability P (V is less than or equal to v|U=u) as follows through the joint distribution of travel time of the front and rear road sections based on the Copula:
then
And when the actual journey time which is already experienced in the journey is u, the predicted journey time distribution of the future subsequent road section is obtained.
Compared with the prior art, the invention has the following beneficial effects:
the on-road section travel time distribution prediction method provided by the invention can make full use of the actual travel time which is already experienced in the on-road to make effective predictions on the subsequent travel time, but the requirements on the sample size of the data set are not strict, and the effective predictions can still be made when the data size is smaller. The invention utilizes the Copula function to establish the joint distribution of the travel time of the front and rear road sections, has no specific assumption on the edge distribution of the front and rear road sections, has higher flexibility and higher calculation speed, can predict the complete information of the uncertainty distribution of the travel time on the one hand, and can describe the correlation relation information of the front and rear road sections on the other hand, thereby having better application prospect.
Drawings
FIG. 1 is a flow chart of a method for predicting travel time distribution of a road segment based on Copula provided in an embodiment of the present invention;
FIG. 2 is a flow chart of the link travel time edge distribution of the build front and back sequence provided in an embodiment of the present invention;
FIG. 3 is a Copula-based front-rear road segment provided in an embodiment of the invention the travel time joint distribution predicts a travel time distribution flow chart of the subsequent road section;
FIG. 4 is a schematic diagram of a predicted travel time distribution of a subsequent road segment when the travel time of the current road segment is a median of the distribution provided in the embodiment of the present invention;
fig. 5 is a schematic diagram of predicted travel time distribution of a subsequent road segment when the travel time of the subsequent road segment is the upper bound of the distribution.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
Example 1
Aiming at the defects in the prior art, the invention provides a Copula-based travel time distribution prediction method and a Copula-based travel time distribution prediction system, wherein the method comprises the following steps:
acquiring actual travel time which is already experienced in transit;
inputting the actual journey time which is already experienced in the journey into a prediction model to obtain the predicted journey time distribution of the subsequent road section;
as shown in fig. 1, a flowchart for constructing a Copula-based on-road section travel time distribution prediction model provided by the invention comprises the following steps:
s1, acquiring a travel time data set T containing m historical observation precursor road sections and a subsequent road section, and respectively constructing the precursor road section and the subsequent road section travel time edge distribution based on the data set;
s2, calibrating related parameters of a Copula function through the route time edge distribution of the front road section and the rear road section constructed in the step S1, and establishing the route time joint distribution of the front road section and the rear road section based on the Copula;
and taking the actual journey time which is already experienced in transit as the input of a prediction model, and obtaining the journey time conditional probability distribution of the subsequent road section by utilizing the established journey time joint distribution of the preceding road section and the subsequent road section, wherein the conditional probability distribution is the predicted future journey time distribution of the subsequent road section.
As shown in fig. 2, step S1 specifically includes:
s101, based on acquired historical travel time data of a front road section and a rear road section, fitting the travel time edge distribution of the front road section and the rear road section respectively by using statistical distribution, wherein the statistical distribution comprises parameter distribution and non-parameter distribution;
s102, selecting the optimal edge distribution by taking the goodness-of-fit index as a criterion, and marking the optimal lead road section travel time edge distribution as F u (u) the optimal subsequent road segment travel time edge distribution is marked as F v (v)。
As shown in fig. 3, step S2 specifically includes:
s201, based on the lead road section travel time edge distribution F obtained in the step S102 u (u) subsequent road segment travel time edge distribution F v (v) According to the Copula theory, the expression of the Copula probability density function is c (F u (u),F v (v) The method comprises the steps of carrying out a first treatment on the surface of the θ), where θ is the parameter space of the Copula function;
s202, calibrating relevant parameters theta of Copula by adopting a maximum likelihood method, and constructing a log likelihood function as
Wherein t is ui The i-th travel time observation data of the preceding road segment in the travel time data set T representing the historic preceding road segment and the subsequent road segment vi Representing the ith travel time observation data of the subsequent road section;
s203, based on the Copula related parameter θ calibrated in the step S202, obtaining the joint distribution of the travel time of the front and rear road sections as H (u, v; θ) =C (F) u (u),F v (v) The method comprises the steps of carrying out a first treatment on the surface of the θ), wherein C is a Copula function with a parameter θ;
s204, setting the travel time of a preceding road section as a random variable U, setting the travel time of a following road section as a random variable V, and converting a predicted scene of travel time distribution of the following road section in the journey into a conditional probability problem when V is U=u, namely solving P (V is less than or equal to v|U=u);
s205, according to a Copula theory, expressing the required conditional probability P (V is less than or equal to v|U=u) as follows through the joint distribution of travel time of the front and rear road sections based on the Copula:
then
And when the actual journey time which is already experienced in the journey is u, the predicted journey time distribution of the future subsequent road section is obtained.
The embodiment verifies the effectiveness of the Copula-based on-road section travel time distribution prediction method based on the actual travel time data set of the license plate system of the expressway in a certain city. The data set comprises 4 paths (each path consists of 2 road segments, namely a preceding road segment and a following road segment), which cover 3 days to 5 days (Tuesday to Tuesday) and 7 days (Saturday) of a year, and travel time data of 4 days are included, and the data acquisition time period is 6:00 to 10:00 in the morning. For a 30 minute analysis time window, 8 sets of data were taken per day for each path, and 128 sets of data were taken for 4 days for 4 paths. The road section travel time edge distribution is fitted by using kernel density estimation, and the Copula function is BB7-Copula.
As can be seen from fig. 4, when the travel time of the preceding road section is 159s, the travel time of the following road section is {180s,184s,191s,213s,184s,211s,195s,184s,194s, 178 s,193s }, and the probability that the observed value is obtained by the Copula-based joint distribution is {0.19,0.33,0.58,0.96,0.33,0.95,0.71,0.33,0.68,0.17,0.65}.
As can be seen from fig. 5, when the travel time of the current road segment is the upper bound 445s of the distribution, the current road segment has only one travel time observation 312s with a probability of 0.25. According to the prediction result of the invention, the travel time distribution of the subsequent road section is 80 th The fractional number can reach 647s. Therefore, the method provided by the invention can effectively predict the on-road travel time distribution and provide richer travel time uncertainty information.
In addition, the prediction result of fig. 4 depends on the observation data of only 112 sample pairs, and the prediction result of fig. 5 depends on the observation data of only 178 sample pairs. For the traffic capacity of the urban expressway exceeding 7000pcu/h, the sample size is small and the availability is high. Therefore, the method provided by the invention has no strict requirement on the sample size of the data set, can still effectively predict the data set when the data volume is smaller, and is less limited by the sample size in practical application.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (10)
1. The travel time distribution prediction method based on Copula is characterized by comprising the following steps of:
acquiring actual travel time which is already experienced in transit;
inputting the actual journey time which is already experienced in transit into a prediction model to obtain predicted journey time distribution of a subsequent road section;
the construction of the prediction model comprises the following steps:
s1, acquiring a travel time data set of a historic lead road section-a subsequent road section, and constructing the edge distribution of the travel time of the lead road section and the subsequent road section;
s2, establishing Copula-based joint distribution of travel time of the front road section and the rear road section through the edge distribution of the travel time of the front road section and the rear road section constructed in the step S1, and obtaining the travel time conditional probability distribution of the rear road section through the established joint distribution of the travel time of the front road section and the rear road section, wherein the conditional probability distribution is the predicted travel time distribution of the rear road section.
2. The Copula-based travel time distribution prediction method according to claim 1, wherein in step S1, the steps of constructing the travel time distribution of the preceding link and the following link are as follows:
s101, respectively fitting travel time edge distribution of a preceding road section and a subsequent road section by using statistical distribution based on a travel time data set T of m pairs of preceding road sections and subsequent road sections;
s102, selecting the optimal edge distribution by taking the goodness-of-fit index as a criterion, and marking the optimal lead road section travel time edge distribution as F u (u) the optimal subsequent road segment travel time edge distribution is marked as F v (v)。
3. The Copula-based travel time distribution prediction method according to claim 2, wherein the statistical distribution comprises a parameter distribution and a non-parameter distribution.
4. The Copula-based travel time distribution prediction method according to claim 2, wherein in step S2, establishing a Copula-based joint distribution of travel times of the preceding and following road segments comprises the steps of:
s201, based on the optimal lead road section travel time edge distribution F obtained in the step S102 u (u) and optimal following road segment travel time edge distribution F v (v) According to the Copula theory, the expression of the Copula probability density function is obtained as follows:
c(F u (u)，F v (v)；θ)
wherein θ is the parameter space of the Copula function;
s202, calibrating a relevant parameter theta of Copula by adopting a maximum likelihood method, and constructing a log likelihood function as follows:
wherein t is ui The i-th travel time observation data of the preceding road segment in the travel time data set T representing the historic preceding road segment and the subsequent road segment vi Representing the ith travel time observation data of the subsequent road section;
s203, based on the Copula related parameter theta calibrated in the step S202, obtaining the joint distribution of the travel time of the front and rear road sections according to the Sklar theorem, wherein the joint distribution is as follows:
H(u，v；θ)＝C(F u (u)，F v (v)；θ)
where C is a Copula function with a parameter θ.
5. The Copula-based travel time distribution prediction method according to claim 4, wherein in step S2, the travel time conditional probability distribution of the subsequent road segment is obtained by using the established joint distribution of travel times of the preceding road segment and the subsequent road segment, comprising the steps of:
s204, recording the travel time of the preceding road section as a random variable U, recording the travel time of the following road section as a random variable V, and converting the predicted scene of the travel time distribution of the following road section into a conditional probability problem when the V is calculated as U=u, namely, calculating:
P(V≤v|U＝u)
s205, according to a Copula theory, expressing the required conditional probability P (V is less than or equal to v|U=u) as follows through the joint distribution of travel time of the front and rear road sections based on the Copula:
then
And when the actual journey time which is already experienced in the journey is u, the predicted journey time distribution of the future subsequent road section is obtained.
6. The travel time distribution prediction system based on Copula is characterized by comprising a data acquisition module, an edge distribution construction module, a joint distribution construction module and a prediction module;
the data acquisition module is used for acquiring a travel time data set of a historic preface road section-a subsequent road section and acquiring actual travel time which is already experienced in transit;
the edge distribution construction module is used for constructing the front road section and the rear road section travel time edge distribution based on the historical front road section and rear road section travel time data set;
the joint distribution construction module is used for establishing joint distribution of travel time of the front and rear road sections based on Copula based on the constructed edge distribution of travel time of the front road section and the rear road section;
the prediction module takes the actual travel time which is already experienced in transit as the input of a prediction model, and obtains the travel time conditional probability distribution of the subsequent road section by utilizing the established joint distribution of the travel time of the preceding road section and the subsequent road section, wherein the conditional probability distribution is the predicted travel time distribution of the subsequent road section.
7. The Copula-based travel time distribution prediction system according to claim 6, wherein the edge distribution construction module constructs the travel time distribution of the preceding road segment and the following road segment as follows:
s101, respectively fitting travel time edge distribution of a preceding road section and a subsequent road section by using statistical distribution based on a travel time data set T of m pairs of preceding road sections and subsequent road sections;
s102, selecting the optimal edge distribution by taking the goodness-of-fit index as a criterion, and marking the optimal lead road section travel time edge distribution as F u (u) the optimal subsequent road segment travel time edge distribution is marked as F v (v)。
8. The Copula-based travel time distribution prediction system of claim 7, wherein the statistical distribution comprises a parametric distribution and a non-parametric distribution.
9. The Copula-based travel time distribution prediction system according to claim 7, wherein the joint distribution construction module establishes a Copula-based joint distribution of travel times of the preceding and following road segments, comprising the steps of:
s201, based on the optimal lead road section travel time edge distribution F obtained in the step S102 u (u) and optimal following road segment travel time edge distribution F v (v) According to the Copula theory, the expression of the Copula probability density function is obtained as follows:
c(F u (u)，F v (v)；θ)
wherein θ is the parameter space of the Copula function;
s202, calibrating a relevant parameter theta of Copula by adopting a maximum likelihood method, and constructing a log likelihood function as follows:
wherein t is ui The i-th travel time observation data of the preceding road segment in the travel time data set T representing the historic preceding road segment and the subsequent road segment vi Representing the ith travel time observation data of the subsequent road section;
s203, based on the Copula related parameter theta calibrated in the step S202, obtaining the joint distribution of the travel time of the front and rear road sections according to the Sklar theorem, wherein the joint distribution is as follows:
H(u，v；θ)＝c(F u (u)，F v (v)；θ)
where C is a Copula function with a parameter θ.
10. The Copula-based travel time distribution prediction system according to claim 9, wherein the prediction module obtains a travel time conditional probability distribution of a subsequent road segment by using the established joint distribution of travel times of the previous and subsequent road segments, and the method comprises the following steps:
s204, recording the travel time of the preceding road section as a random variable U, recording the travel time of the following road section as a random variable V, and converting the predicted scene of the travel time distribution of the following road section into a conditional probability problem when the V is calculated as U=u, namely, calculating:
P(V≤v|U＝u)
s205, according to a Copula theory, expressing the required conditional probability P (V is less than or equal to v|U=u) as follows through the joint distribution of travel time of the front and rear road sections based on the Copula:
then
And when the actual journey time which is already experienced in the journey is u, the predicted journey time distribution of the future subsequent road section is obtained.
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| CN116935655B (en) * | 2023-09-15 | 2023-12-05 | 武汉市规划研究院 | Traffic state judging method and system for complex urban road network |
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