A travel time distribution prediction method and system based on Copula

Abstract

The present invention relates to a travel time distribution prediction method and system based on Copula, wherein the method comprises: using the historical travel time data of the preceding and succeeding sections to construct the marginal distribution of the travel time of the preceding and succeeding sections, calibrating the parameters of the Copula function through the marginal distribution, and thereby establishing the joint distribution of the travel time of the preceding and succeeding sections based on Copula, taking the actual travel time experienced by the travelers on the way as the input of the prediction model, and using the joint distribution of the travel time of the preceding and succeeding sections based on Copula to obtain the conditional probability distribution of the travel time of the succeeding sections, thereby providing the travelers with the predicted travel time distribution of the future succeeding sections. The present invention makes full use of the existing section travel time information, dynamically predicts the travel time distribution, and can provide richer travel time distribution information to assist travelers in better planning routes and arranging itineraries.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation technology, and in particular to a Copula-based travel time distribution prediction method and system. Background Art

[0002] Traffic information is an indispensable part of the intelligent transportation system. Among the various types of traffic information, travel time information is an important reference indicator for planners to make decisions on investment in transportation projects, managers to evaluate the status of traffic operation, and travelers to plan their travel plans. Travel time information is the final manifestation of the comprehensive effects of the various components of the transportation system, including people, vehicles, roads, and the environment, and can intuitively reflect the operating status of the transportation system. Therefore, being able to provide accurate and rich travel time information is of great significance to the rational allocation of transportation system resources, identification and relief of traffic jams, and making wise travel choices.

[0003] Since there is inevitably uncertainty in the transportation system, travel time information is also uncertain. Most literature obtains travel time information by predicting the mean and variance of travel time, but travel time uncertainty has the basic characteristics of positive skewness and long tail, and a single mean and variance cannot provide complete travel time information. In addition, the rapid development of mobile Internet technology makes it possible to provide travelers with real-time in-transit traffic information. Therefore, the field of smart transportation needs to make full use of historical in-transit travel time information and incorporate travel time uncertainty into the prediction system to provide accurate and rich in-transit travel time prediction information.

[0004] With regard to the prediction of travel time in transit, existing technologies have defects such as complex prediction models, the need for a large number of data samples, and the inability to provide rich travel time uncertainty information. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a travel time distribution prediction method and system based on Copula, which makes full use of the actual travel time experienced on the way, establishes the joint distribution of travel time of the preceding and following sequence sections based on Copula, and predicts the travel time distribution of the future subsequent sections.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A travel time distribution prediction method based on Copula includes the following steps:

[0008] Get the actual travel time experienced during the journey;

[0009] Inputting the actual travel time experienced in transit into the prediction model to obtain the predicted distribution of travel time for subsequent road sections;

[0010] The construction of the prediction model includes the following steps:

[0011] S1. Obtain a historical data set of travel time between the previous and subsequent sections, and construct the marginal distribution of travel time between the previous and subsequent sections;

[0012] S2. Based on the marginal distribution of travel time of the preceding and succeeding road segments constructed in step S1, a joint distribution of travel time of the preceding and succeeding road segments based on Copula is established. The conditional probability distribution of travel time of the succeeding road segment can be obtained through the established joint distribution of travel time of the preceding and succeeding road segments. This conditional probability distribution is the predicted travel time distribution of the succeeding road segment.

[0013] Furthermore, in step S1, the steps of constructing the travel time distribution of the preceding road segment and the succeeding road segment are as follows:

[0014] S101, based on a data set T containing m pairs of travel time of a preceding road segment and a succeeding road segment, using statistical distribution to fit the marginal distribution of travel time of the preceding road segment and the succeeding road segment respectively;

[0015] S102. Using the goodness of fit index as a criterion, select the optimal marginal distribution. The optimal marginal distribution of the preceding road segment travel time is denoted as F u (u), the marginal distribution of the optimal subsequent segment travel time is denoted as F v (v).

[0016] Furthermore, the statistical distribution includes parametric distribution and non-parametric distribution.

[0017] Furthermore, in step S2, establishing the joint distribution of travel time of the preceding and following sequence sections based on Copula includes the following steps:

[0018] S201, based on the optimal preceding road segment travel time edge distribution F obtained in step S102 u (u) and the marginal distribution of travel time of the optimal subsequent road segment F v (v) According to the Copula theory, the expression of the Copula probability density function is:

[0019] c(F u (u),F v (v); θ)

[0020] Where θ is the parameter space of the Copula function;

[0021] S202, using the maximum likelihood method to calibrate the relevant parameters θ of the Copula, constructing the log-likelihood function as follows:

[0022]

[0023] where t ui represents the observed travel time data of the previous segment in the historical previous segment-subsequent segment travel time dataset T, t vi represents the observed data of the i-th travel time of the subsequent road segment;

[0024] S203, based on the Copula related parameter θ calibrated in step S202, according to Sklar theorem, the joint distribution of the travel time of the preceding and following sequence sections is obtained as follows:

[0025] H(u,v;θ)=C(F u (u),F v (v); θ)

[0026] Where C is the Copula function with parameter θ.

[0027] Furthermore, in step S2, obtaining the conditional probability distribution of the travel time of the subsequent segment by using the established joint distribution of the travel time of the preceding and subsequent segments includes the following steps:

[0028] S204, let the travel time of the preceding road section be a random variable U, and the travel time of the succeeding road section be a random variable V, and transform the travel time distribution prediction scenario of the succeeding road section into a conditional probability problem of finding V when U=u, that is, finding:

[0029] P(V≤v|U=u)

[0030] S205. According to the Copula theory, the conditional probability P(V≤v|U=u) is expressed as follows through the joint distribution of the travel time of the preceding and following sequence sections based on the Copula:

[0031]

[0032] but That is, when the actual travel time experienced on the way is u, the predicted travel time distribution of the subsequent road sections in the future.

[0033] A travel time distribution prediction system based on Copula, comprising a data acquisition module, an edge distribution construction module, a joint distribution construction module and a prediction module;

[0034] The data acquisition module is used to obtain a historical preceding road segment-subsequent road segment travel time data set and to obtain the actual travel time experienced on the way;

[0035] The edge distribution construction module is used to construct the edge distribution of the travel time of the preceding road segment and the succeeding road segment based on the historical preceding road segment-successor road segment travel time data set;

[0036] The joint distribution construction module establishes a Copula-based joint distribution of travel time of the preceding and succeeding road segments based on the constructed marginal distribution of travel time of the preceding and succeeding road segments;

[0037] The prediction module uses the actual travel time experienced during the journey as the input of the prediction model, and uses the established joint distribution of the travel time of the preceding and following sections to obtain the conditional probability distribution of the travel time of the subsequent section. The conditional probability distribution is the predicted travel time distribution of the subsequent section.

[0038] Furthermore, in the edge distribution construction module, the steps of constructing the travel time distribution of the preceding road segment and the succeeding road segment are as follows:

[0039] S101, based on a data set T containing m pairs of travel time of a preceding road segment and a succeeding road segment, using statistical distribution to fit the marginal distribution of travel time of the preceding road segment and the succeeding road segment respectively;

[0040] S102. Using the goodness of fit index as a criterion, select the optimal marginal distribution. The optimal marginal distribution of the preceding road segment travel time is denoted as F u (u), the marginal distribution of the optimal subsequent segment travel time is denoted as F v (v).

[0041] Furthermore, the statistical distribution includes parametric distribution and non-parametric distribution.

[0042] Furthermore, in the joint distribution building module, establishing the joint distribution of travel time of the preceding and following road segments based on Copula includes the following steps:

[0043] S201, based on the optimal preceding road segment travel time edge distribution F obtained in step S102 u (u) and the marginal distribution of travel time of the optimal subsequent road segment F v (v) According to the Copula theory, the expression of the Copula probability density function is:

[0044] c(F u (u),F v (v); θ)

[0045] Where θ is the parameter space of the Copula function;

[0046] S202, using the maximum likelihood method to calibrate the relevant parameters θ of the Copula, constructing the log-likelihood function as follows:

[0047]

[0048] where t ui represents the observed travel time data of the previous segment in the historical previous segment-subsequent segment travel time dataset T, tvi represents the observed data of the i-th travel time of the subsequent road segment;

[0049] S203, based on the Copula related parameter θ calibrated in step S202, according to Sklar theorem, the joint distribution of the travel time of the preceding and following sequence sections is obtained as follows:

[0050] H(u,v;θ)=C(F u (u),F v (v); θ)

[0051] Where C is the Copula function with parameter θ.

[0052] Furthermore, in the prediction module, obtaining the conditional probability distribution of the travel time of the subsequent road segment by using the established joint distribution of the travel time of the preceding and subsequent road segments comprises the following steps:

[0053] S204, let the travel time of the preceding road section be a random variable U, and the travel time of the succeeding road section be a random variable V, and transform the travel time distribution prediction scenario of the succeeding road section into a conditional probability problem of finding V when U=u, that is, finding:

[0054] P(V≤v|U=u)

[0055] S205. According to the Copula theory, the conditional probability P(V≤v|U=u) is expressed as follows through the joint distribution of the travel time of the preceding and following sequence sections based on the Copula:

[0056]

[0057] but That is, when the actual travel time experienced on the way is u, the predicted travel time distribution of the subsequent road sections in the future.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The method for predicting the travel time distribution of the in-transit road section provided by the present invention can make full use of the actual travel time experienced in transit to make an effective prediction of the subsequent travel time, but the requirement for the sample size of the data set is not strict, and effective prediction can still be made when the data volume is small. The present invention uses the Copula function to establish the joint distribution of the travel time of the preceding and following road sections, which has no specific assumptions on the marginal distribution of the preceding and following road sections, has high flexibility, and has a fast calculation speed. The obtained joint distribution can predict the complete information of the travel time uncertainty distribution on the one hand, and can also describe the correlation relationship information of the preceding and following road sections on the other hand, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1is a flow chart of a method for predicting travel time distribution of a route section based on Copula provided in an embodiment of the present invention;

[0061] Figure 2 The embodiment of the present invention provides a flow chart for constructing the edge distribution of travel time of the preceding and following road sections;

[0062] Figure 3 It is a flow chart of predicting the travel time distribution of a subsequent road segment based on the joint distribution of the travel time of the preceding and subsequent road segments based on Copula provided in an embodiment of the present invention;

[0063] Figure 4 It is a schematic diagram of the distribution of the predicted travel time of subsequent sections when the travel time of the current section is the median of its distribution provided in an embodiment of the present invention;

[0064] Figure 5 It is a schematic diagram of the distribution of the predicted travel time of subsequent sections when the travel time of the current section is the upper bound of its distribution provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0066] Example 1

[0067] In view of the defects in the prior art, the present invention proposes a travel time distribution prediction method and system based on Copula, wherein the method comprises the following steps:

[0068] Get the actual travel time experienced during the journey;

[0069] The actual travel time experienced during the journey is input into the prediction model to obtain the predicted travel time distribution of subsequent sections;

[0070] like Figure 1 As shown, it is a flow chart of constructing a Copula-based on-road segment travel time distribution prediction model provided by the present invention, comprising the following steps:

[0071] S1. Obtain a dataset T of travel time between a preceding road segment and a succeeding road segment containing m historical observations, and construct the marginal distribution of travel time between the preceding road segment and the succeeding road segment based on this dataset;

[0072] S2, calibrating the relevant parameters of the Copula function through the marginal distribution of the travel time of the preceding and succeeding road segments constructed in step S1, and establishing the joint distribution of the travel time of the preceding and succeeding road segments based on Copula;

[0073] The actual travel time experienced during the journey is used as the input of the prediction model, and the conditional probability distribution of the travel time of the subsequent section is obtained by using the established joint distribution of the travel time of the previous and subsequent sections. This conditional probability distribution is the predicted future travel time distribution of the subsequent section.

[0074] like Figure 2 As shown, step S1 specifically includes:

[0075] S101, based on the acquired historical preceding road segment-subsequent road segment travel time data, using statistical distribution to fit the travel time marginal distribution of the preceding road segment and the subsequent road segment respectively, wherein the statistical distribution includes parametric distribution and non-parametric distribution;

[0076] S102. Using the goodness of fit index as a criterion, select the optimal marginal distribution. The optimal marginal distribution of the preceding road segment travel time is denoted as F u (u), the marginal distribution of the optimal subsequent segment travel time is denoted as F v (v).

[0077] like Figure 3 As shown, step S2 specifically includes:

[0078] S201, based on the marginal distribution F of the travel time of the preceding road segment obtained in step S102 u (u), marginal distribution of travel time of subsequent sections F v (v) According to the Copula theory, the expression of the Copula probability density function is c(F u (u),F v (v); θ), where θ is the parameter space of the Copula function;

[0079] S202, use the maximum likelihood method to calibrate the relevant parameters θ of the Copula, and construct the log-likelihood function as follows: where t ui represents the observed travel time data of the previous segment in the historical previous segment-subsequent segment travel time dataset T, t vi represents the observed data of the i-th travel time of the subsequent road segment;

[0080] S203, based on the Copula related parameter θ calibrated in step S202, according to Sklar theorem, the joint distribution of the travel time of the preceding and following sequence sections is obtained as H(u,v;θ)=C(F u (u),F v (v); θ), where C is the Copula function with parameter θ;

[0081] S204, assuming that the travel time of the preceding road segment is a random variable U, and the travel time of the succeeding road segment is a random variable V, converting the travel time distribution prediction scenario of the succeeding road segment into a conditional probability problem of finding V when U=u, that is, finding P(V≤v|U=u);

[0082] S205. According to the Copula theory, the conditional probability P(V≤v|U=u) is expressed as follows through the joint distribution of the travel time of the preceding and following sequence sections based on the Copula:

[0083]

[0084] but That is, when the actual travel time experienced on the way is u, the predicted travel time distribution of the subsequent road sections in the future.

[0085] This embodiment is based on a data set of actual travel time of a city expressway license plate system to verify the effectiveness of the Copula-based on-road segment travel time distribution prediction method provided by the present invention. The data set includes 4 paths (each path consists of 2 segments, namely the preceding segment and the succeeding segment), covering 4 days of travel time data from December 3 to 5 (Tuesday to Thursday) and December 7 (Saturday) in a certain year, and the data collection period is from 6:00 to 10:00 in the morning. With 30 minutes as the analysis time window, there are 8 sets of data per day for each path, and 128 sets of data for 4 paths and 4 days. The marginal distribution of segment travel time is fitted by kernel density estimation, and the Copula function adopts BB7-Copula.

[0086] from Figure 4 It can be seen that when the travel time of the current section is the mode of its distribution 159s, the observed travel time of the subsequent sections is {180s, 184s, 191s, 213s, 184s, 211s, 195s, 184s, 194s, 179s, 193s}. Through the Copula-based joint distribution, the probabilities of the above observations are {0.19, 0.33, 0.58, 0.96, 0.33, 0.95, 0.71, 0.33, 0.68, 0.17, 0.65} respectively.

[0087] from Figure 5 It can be seen that when the travel time of the current segment is the upper bound of its distribution, 445s, the current subsequent segment has only one travel time observation value of 312s with a probability of 0.25. th The quantile can reach 647s. This shows that the method proposed in the present invention can effectively predict the distribution of travel time in transit and provide more abundant travel time uncertainty information.

[0088] also, Figure 4 The prediction results of only rely on the observation data of 112 sample pairs. Figure 5 The prediction results only rely on the observation data of 178 sample pairs. For the traffic capacity of the urban expressway exceeding 7000pcu / h, the above sample size is very small and has high availability. This shows that the method proposed in the present invention does not have strict requirements on the sample size of the data set, and can still be effectively predicted when the data volume is small, and is less restricted by the sample size in practical applications.

[0089] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A travel time distribution prediction method based on Copula, characterized in that: The following steps are involved: Get the actual travel time experienced during the journey; Inputting the actual travel time experienced in transit into the prediction model to obtain the predicted distribution of travel time for subsequent road sections; The construction of the prediction model includes the following steps: S1. Obtain a historical data set of travel time between the previous and subsequent sections, and construct the marginal distribution of travel time between the previous and subsequent sections; S2, using the marginal distribution of the travel time of the preceding and succeeding sections constructed in step S1, a joint distribution of the travel time of the preceding and succeeding sections based on Copula is established, and the conditional probability distribution of the travel time of the succeeding section can be obtained through the established joint distribution of the travel time of the preceding and succeeding sections, and the conditional probability distribution is the predicted travel time distribution of the succeeding section; In step S1, the steps of constructing the travel time distribution of the preceding road segment and the succeeding road segment are as follows: S101, based on a data set T containing m pairs of travel time of a preceding road segment and a succeeding road segment, using statistical distribution to fit the marginal distribution of travel time of the preceding road segment and the succeeding road segment respectively; S102. Using the goodness of fit index as a criterion, select the optimal marginal distribution. The optimal marginal distribution of the preceding road segment travel time is denoted as F u (u), the marginal distribution of the optimal subsequent segment travel time is denoted as F v (v); In step S2, establishing the joint distribution of travel time of the preceding and following road segments based on Copula includes the following steps: S201, based on the optimal preceding road segment travel time edge distribution F obtained in step S102 u (u) and the marginal distribution of travel time of the optimal subsequent road segment F v (v) According to the Copula theory, the expression of the Copula probability density function is: c(F u (u),F v (v);θ) Where θ is the parameter space of the Copula function; S202, using the maximum likelihood method to calibrate the relevant parameters θ of the Copula, constructing the log-likelihood function as follows: where t ui represents the observed travel time data of the previous segment in the historical previous segment-subsequent segment travel time dataset T, t vi represents the observed data of the i-th travel time of the subsequent road segment; S203, based on the Copula related parameter θ calibrated in step S202, according to Sklar theorem, the joint distribution of the travel time of the preceding and following sequence sections is obtained as follows: H(u,v;θ)=C(F u (u),F v (v);θ) Where C is the Copula function with parameter θ; In step S2, obtaining the conditional probability distribution of the travel time of the subsequent segment by using the established joint distribution of the travel time of the preceding and subsequent segments includes the following steps: S204, let the travel time of the preceding road section be a random variable U, and the travel time of the succeeding road section be a random variable V, and transform the travel time distribution prediction scenario of the succeeding road section into a conditional probability problem of finding V when U=u, that is, finding: P(V≤v|U=u) S205. According to the Copula theory, the conditional probability P(V≤v|U=u) is expressed as follows through the joint distribution of the travel time of the preceding and following sequence sections based on the Copula: but That is, when the actual travel time experienced on the way is u, the predicted travel time distribution of the subsequent road sections in the future.

2. The travel time distribution prediction method based on Copula according to claim 1, characterized in that: The statistical distribution includes parametric distribution and non-parametric distribution.

3. A travel time distribution prediction system based on Copula, characterized in that: It includes a data acquisition module, an edge distribution building module, a joint distribution building module and a prediction module; The data acquisition module is used to obtain a historical preceding road segment-subsequent road segment travel time data set and to obtain the actual travel time experienced on the way; The edge distribution construction module is used to construct the edge distribution of the travel time of the preceding road segment and the succeeding road segment based on the historical preceding road segment-successor road segment travel time data set; The joint distribution construction module establishes a Copula-based joint distribution of travel time of the preceding and succeeding road segments based on the constructed marginal distribution of travel time of the preceding and succeeding road segments; The prediction module uses the actual travel time experienced during the journey as the input of the prediction model, and uses the established joint distribution of the travel time of the preceding and following sequence sections to obtain the conditional probability distribution of the travel time of the subsequent section, and the conditional probability distribution is the predicted travel time distribution of the subsequent section; In the edge distribution construction module, the steps of constructing the travel time distribution of the preceding road segment and the succeeding road segment are as follows: S101, based on a data set T containing m pairs of travel time of a preceding road segment and a succeeding road segment, using statistical distribution to fit the marginal distribution of travel time of the preceding road segment and the succeeding road segment respectively; S102. Using the goodness of fit index as a criterion, select the optimal marginal distribution. The optimal marginal distribution of the preceding road segment travel time is denoted as F u (u), the marginal distribution of the optimal subsequent segment travel time is denoted as F v (v); In the joint distribution building module, establishing the joint distribution of travel time of the preceding and following road segments based on Copula includes the following steps: S201, based on the optimal preceding road segment travel time edge distribution F obtained in step S102 u (u) and the marginal distribution of travel time of the optimal subsequent road segment F v (v) According to the Copula theory, the expression of the Copula probability density function is: c(F u (u),F v (v);θ) Where θ is the parameter space of the Copula function; S202, using the maximum likelihood method to calibrate the relevant parameters θ of the Copula, constructing the log-likelihood function as follows: where t ui represents the observed travel time data of the previous segment in the historical previous segment-subsequent segment travel time dataset T, t vi represents the observed data of the i-th travel time of the subsequent road segment; S203, based on the Copula related parameter θ calibrated in step S202, according to Sklar theorem, the joint distribution of the travel time of the preceding and following sequence sections is obtained as follows: H(u,v;θ)=C(F u (v),F v (v);θ) Where C is the Copula function with parameter θ; In the prediction module, obtaining the conditional probability distribution of the travel time of the subsequent segment by using the established joint distribution of the travel time of the preceding and subsequent segments includes the following steps: S204, let the travel time of the preceding road section be a random variable U, and the travel time of the succeeding road section be a random variable V, and transform the travel time distribution prediction scenario of the succeeding road section into a conditional probability problem of finding V when U=u, that is, finding: P(V≤v|U=u) S205. According to the Copula theory, the conditional probability P(v≤v|U=u) is expressed as follows through the joint distribution of the travel time of the preceding and following sequence sections based on the Copula: but That is, when the actual travel time experienced on the way is u, the predicted travel time distribution of the subsequent road sections in the future.

4. The travel time distribution prediction system based on Copula according to claim 3, characterized in that: The statistical distribution includes parametric distribution and non-parametric distribution.

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