CN111653084A - Short-term traffic flow prediction method based on space-time feature selection and Kalman filtering - Google Patents
Short-term traffic flow prediction method based on space-time feature selection and Kalman filtering Download PDFInfo
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Abstract
The invention discloses a short-term traffic flow prediction method based on space-time feature selection and Kalman filtering. According to the method, time sequences with different time lags of adjacent intersections are used as input characteristics of the model, and the defect that the space-time correlation among the time sequences of the traffic flow cannot be fully considered in the traditional model is overcome. Firstly, carrying out flow aggregation on original SCATS data; then, a multidimensional scaling method is applied to the predicted sections and the section groups in the adjacent areas of the predicted sections to find some sections with higher correlation with the predicted sections; then selecting the characteristics of the space-time characteristics formed by different time lags of the sections to determine the optimal input characteristics; and finally, obtaining a prediction result by considering a Kalman filtering model of the space-time correlation. The model can obtain higher prediction precision when short-time flow prediction is carried out on urban intersections, and has good robustness.
Description
Technical Field
The invention relates to the technical field of Kalman filtering algorithm, traffic flow prediction and the like, in particular to a short-time traffic flow prediction method based on space-time feature selection and Kalman filtering.
Background
An Intelligent Transportation System (ITS) is a general name for comprehensively establishing an all-around, wide-range, high-efficiency and intelligent transportation analysis and route selection management system by organically combining an advanced information technology, an electronic control technology, a data communication technology, an electronic positioning control technology and the like on the premise of researching a key basic theoretical model and aiming at relieving road congestion and reducing traffic accidents. The analysis and prediction of the short-term traffic flow of the road are key contents of an intelligent traffic system, the short-term traffic flow prediction theory and method research is pertinently developed, effective analysis and prediction data are obtained, and the traffic flow state of the road network is accurately predicted.
Sydney coordinated adaptive traffic control system (SCATS) is a very versatile system. The system utilizes a coil arranged at a position close to a downstream stop line of a lane to obtain parameters such as period, period duration, flow and the like in real time. The step length of the short-time traffic flow prediction is usually 5 minutes, but the period duration of the SCATS data is dynamically changed, and the data quality is not high. For this purpose, after data preprocessing, the raw SCATS data needs to be subjected to traffic aggregation to obtain traffic of a fixed time interval, which is called a virtual cycle. In SCATS, the cross-sections at the downstream stop line are called profiles, and the system assigns a profile number to each profile.
In urban roads, the cross sections of adjacent intersections tend to have higher spatial correlation. The set of sections in adjacent regions is called a section group. The sequence obtained by arranging the flow rates of the sections in time series is referred to as a traffic flow time series.
Multidimensional scaling is one type of multivariate statistical analysis method. In practical application, the RSQ value is selected as an evaluation index of a multi-dimensional scaling method.
In the field of traffic research, Euclidean distance is mostly adopted as an index for measuring traffic flow sequence similarity measure. The Euclidean distance matrix of the road network can be obtained by respectively calculating the Euclidean distance of the traffic flow time sequence on every two sections in the urban road network consisting of a plurality of sections.
There are many models for short-term traffic flow prediction at home and abroad, including four major categories: the first type is a model based on mathematical statistics, including a linear regression model, a historical average model, etc.; the second type is a nonlinear prediction theoretical model represented by a wavelet theoretical model; the third type is a neural network model, including an artificial neural network, a BP neural network, a fuzzy neural network model and the like; the fourth class is the combined predictive model. In the first type of model, a linear regression model has the defect of poor real-time performance, and a historical average model is simple, but the prediction precision is not high, so that sudden accidents cannot be processed; although the second type of model has higher prediction precision, the prediction takes longer time, and the defect of complicated parameter adjustment is obvious; the third type of model ensures the real-time performance of prediction through a real-time traffic flow updating model, but a large amount of historical data is needed for training, which is difficult to meet in practice; the fourth type of model meets the requirements on prediction accuracy and real-time performance, but the combined prediction model is difficult to be applied in practice. In addition, the existing models have the defect that the space-time correlation of the traffic flow cannot be fully considered.
Disclosure of Invention
The invention aims to provide a short-time traffic flow prediction method based on space-time feature selection and Kalman filtering.
The technical solution for realizing the purpose of the invention is as follows: a short-time traffic flow prediction method based on space-time feature selection and Kalman filtering comprises the following steps:
step one, carrying out t-minute flow aggregation on original SCATS data;
step two, normalizing the aggregated data, and dividing the normalized data into a training set, a verification set and a test set;
step three, finding out n sections with highest correlation with the predicted sections by applying a multidimensional scaling method to the predicted sections and the section groups in the adjacent areas;
step four, performing feature selection on space-time features formed by different time lags of the predicted section and the n sections with the highest correlation with the predicted section by applying a space-time feature selection algorithm to determine the optimal input feature of the Kalman filtering model;
and step five, carrying out flow prediction on the test data set by using a Kalman filtering model for determining the optimal input characteristics to obtain a final prediction result.
Further, the raw data used is SCATS data, which is a data set including intersection number, strategic channel, coil number, cycle start time, phase duration, cycle duration, saturation, flow, date, and week.
Furthermore, the prediction step length of the short-time traffic flow prediction is t minutes, and the value range of t is {3,5,10,15 }.
Further, the flow rate polymerization in the first step is specifically carried out as follows:
t minutes of flow aggregation was performed for each coil by two parameters, cycle start time and flow. The flow rate per unit time in a single signal period is calculated as follows:
wherein
The average flow of the coil l at the intersection i in the kth period in unit time; q. q.si,l(k) Is the total flow of the coil l at the intersection i in the kth period; t isi,l(k) Is the cycle start time of coil i at intersection i at the kth cycle. The mapping relationship from the actual period to the aggregated virtual period is as follows:
wherein q isi,l(m) is the total flow of the coils l of the intersection i in the virtual period m; t is tkIs the duration of the virtual period m within the actual period k; n is the number of virtual periods m spanning the actual period.
Further, in step two, 80 percent of the normalized data set is used as a training set, 10 percent of the normalized data set is used as a verification set, and 10 percent of the normalized data set is used as a test set.
Further, in the third step, the step of finding the n sections with the highest correlation with the predicted section by applying the multidimensional scaling method to the predicted section and the section groups in the adjacent regions thereof is as follows:
3.1: normalizing the traffic flow time sequences on the predicted sections and the section groups in the adjacent areas of the predicted sections, and calculating the Euclidean distance between the traffic flow time sequences on every two sections to obtain an Euclidean distance matrix;
3.2: selecting RSQ as an evaluation index, checking the fitting degree under different dimensions, representing the traffic flow time sequence on a section through space points to obtain the coordinates of each space point under the dimension with the highest fitting degree, namely dimension s, and calling a coordinate graph formed by the coordinates of each space point under the dimension with the highest fitting degree as an s-dimensional coordinate perception graph;
3.3: in the obtained s-dimensional coordinate perception map, n sections with highest correlation with the predicted sections are obtained according to the judgment principle that the shorter the distance between two points is, the higher the correlation is, by using the distance between the points for representing the traffic flow time sequence, and the value range of n is {4,5, 6 }.
Further, the specific process of determining the optimal input features of the kalman filter model by applying the spatio-temporal feature selection algorithm in step four is as follows:
4.1: forming the flow sequences of the first Q periods of the n sections with highest correlation with the predicted sections in the test set into input characteristics of a Kalman filtering model, wherein the value range of Q is {2,3,4 };
4.2: and performing feature selection on the input features of the Kalman filtering model by using a feature selection algorithm based on a heuristic search strategy to obtain the optimal input features of the Kalman filtering model when verification set data is used.
Further, step 4.2 determines the optimal input features of the kalman filter model using a feature selection algorithm based on a heuristic search strategy as follows:
4.2.1: inputting a data set S, a characteristic F, a prediction algorithm A, a stop control parameter C and an initialization characteristic set FinitialAn error analysis function Validation using the MAPE as an evaluation index;
4.2.2: initializing an optimal feature set, and calculating an error obtained by using the optimal feature set;
4.2.3: adding 1 to the control parameter count C, if C is smaller than the stop control parameter C, turning to the step 4.2.4, otherwise, turning to the step 4.2.5;
4.2.4: generating in F a subset F containing features*And adding one more feature set F ', calculating to obtain the size D of the subset contained in the feature set F', traversing the feature set F ', not repeatedly searching the feature subset F' in the feature set F ', calculating an error for each searched feature subset F', and updating the optimal feature subset F if the error is less than the error obtained by using the initialized optimal feature set*If the initial error E is updated to be E', repeating the process until the traversal is finished;
4.2.5: outputting the optimal feature subset F*。
Further, the step five specifically comprises the following steps:
and carrying out flow prediction on the test data set by utilizing a Kalman filtering model for determining the optimal input characteristics to obtain a final prediction result.
Compared with the prior art, the invention has the following remarkable advantages: (1) a large amount of historical data is not needed for model training, the requirement of flow prediction instantaneity is met, and the actual condition that the traffic data quality of the urban road network is not high is met. (2) The proposed model has strong practicability and takes short time for prediction. (3) The space-time correlation of the traffic flow is fully considered, and the prediction precision of the model is further improved.
Drawings
Fig. 1 is a flow chart of the short-term traffic flow prediction according to the present invention.
Fig. 2 is a schematic view of a flow aggregation region.
FIG. 3 is a coordinate sensing diagram of a cross-sectional group using a multidimensional scaling method
Fig. 4 is a flow prediction effect diagram.
Detailed Description
The invention is further described with reference to the drawings and examples.
A short-term traffic flow prediction method based on spatio-temporal feature selection and Kalman filtering is mainly shown in a flow chart shown in figure 1 and comprises the following steps:
step one, carrying out flow aggregation on original SCATS data for t minutes, wherein the value range of t is {3,5,10 and 15 };
step two, normalizing the aggregated data, and dividing the normalized data into a training set, a verification set and a test set;
step three, finding out n sections with highest correlation with the predicted sections by applying a multidimensional scaling method to the predicted sections and the section groups in the adjacent areas of the predicted sections, wherein the value range of n is {4,5, 6 };
step four, performing feature selection on space-time features formed by different time lags of the predicted section and the n sections with the highest correlation with the predicted section by applying a space-time feature selection algorithm to determine the optimal input feature of the Kalman filtering model;
and step five, carrying out flow prediction on the test data set by using a Kalman filtering model for determining the optimal input characteristics to obtain a final prediction result.
In this embodiment, the traffic data is acquired by the SCATS coil, and the acquired raw data is a data set including an intersection number, a strategic channel, a coil number, a cycle start time, a phase duration, a cycle duration, a saturation, a traffic, a date, and a week. In the present embodiment, the flow aggregation is performed on each coil at each intersection according to three field attributes, i.e., the coil number, the cycle start time, and the flow, and the time interval of the flow aggregation is 5 minutes. In the present embodiment, the prediction step size of the short-time traffic flow prediction is the same as the time interval of the flow aggregation, and both are 5 minutes.
The 5 minute flow aggregation was performed for each coil by both the cycle start time and the flow. The flow rate per unit time in a single signal period is calculated as follows:
wherein
The average flow of the coil l at the intersection i in the kth period in unit time; q. q.si，l(k) Is the total flow of the coil l at the intersection i in the kth period; t isi，l(k) Is the cycle start time of coil i at intersection i at the kth cycle. The mapping relationship from the actual period to the aggregated virtual period is as follows:
wherein q isi，l(m) is the total flow of the coils l of the intersection i in the virtual period m; t is tkIs the duration of the virtual period m within the actual period k; n is the number of virtual periods m spanning the actual period; the virtual period is the time interval of traffic aggregation.
Fig. 2 shows an aggregate area schematic, in this embodiment, the flow aggregation is performed at intersections numbered 802, 803, 821, 837 in the huntingstate SCATS system, and the coil composition of each cross section is shown in table 1.
TABLE 1 coil composition for each section
The section T821_2 is obtained by classifying the coil related to the intersection 821 into a virtual section according to the flow direction relationship between the upstream and downstream intersections with the intersection 803 as the downstream intersection and the intersection 821 as the upstream intersection, and the coil of the virtual section includes: coil 3 and coil 4 on the straight-going lane of section 821_1, coil 9 on the left-turn lane of section 821_3, and coil 13 on the left-turn lane of section 821_ 4.
In the present embodiment, the flow rate of the cross-section T803_1 is predicted using data of 10 consecutive tuesdays from 6 months in 2018 to 8 months in 2018 at each detection point. The data set is divided into the following rules: selecting data of one day as a test set and data of one day as a verification set; secondly, using the data of the remaining 8 days for multi-dimensional scale analysis; and thirdly, taking the data of the remaining 8 days as training data of each prediction model.
The embodiment is used for carrying out normalization processing on the traffic flow time sequence and mapping the flow to [0, 1 ]]After the interval, the Euclidean distance is used as an index for measuring the similarity measure of the traffic flow sequence. By calculating Euclidean distance of each two sections in the urban road network composed of a plurality of sections, the Euclidean distance matrix D ═ D (D) of the road network can be obtainedij) n × n, where n is the number of sections in the road network, after obtaining the Euclidean distance matrix of the road network, the section with higher spatial correlation with the predicted section can be found out from the plurality of sections by applying the multidimensional scaling method.
The example uses the SPSS software to apply a multidimensional scaling analysis to a slice group consisting of 12 slices selected from the slice T803_1 and 11 slices adjacent thereto. In the present embodiment, the dimension of the multidimensional scaling analysis is 2, and the index for evaluating the effect of the multidimensional scaling analysis is the RSQ value. After multidimensional scaling analysis of the cross-sectional groups, the RSQ value was 0.99341. The coordinate perception of the slice groups is shown in figure 3. According to the principle that the shorter the distance between two points is, the higher the correlation of the cross section is, 4 cross sections with higher correlation to the cross section T803_1 are screened out, and the 4 cross sections are: t803_3, T802_1, T837_1, T821_ 2.
To build a good prediction model, feature selection is usually required for the input features. The embodiment provides a feature selection algorithm based on a heuristic search strategy, and the average absolute percentage error (MAPE) of a prediction model is used as an evaluation standard of a feature subset.
In this embodiment, the feature set F is formed by combining different time lags of all cross sections obtained by a multidimensional scaling method, and the spatiotemporal feature selection algorithm can be expressed as:
wherein F*Is the best input feature subset; f' is a feature subset of F; a is a Kalman filtering prediction algorithm; s is a data set. The stopping control parameter of the algorithm can be found by the following formula:
C＝PQ (6)
wherein P is the number of sections; q is the number of values of different time lags. In order to simultaneously consider the time correlation and the space correlation among the traffic time sequences, the value of PQ is designed as a stopping parameter. In this embodiment, the value of P is 5, the value of Q is 3, and the time lags of different sections are the same in value sets, including: 5 minutes, 10 minutes, 15 minutes, corresponding to the first three cycles of the mth cycle: the m-1 st cycle, the m-2 nd cycle, and the m-3 rd cycle. The specific calculation process of the algorithm is as follows:
the algorithm 1 comprises the following steps:
the method comprises the following steps: inputting a data set S, a characteristic F, a prediction algorithm A, a stop control parameter C and an initialization characteristic set FinitialAn error analysis function Validation using the MAPE as an evaluation index;
step two: initializing an optimal feature set, and calculating an error obtained by using the optimal feature set;
step three: adding 1 to the control parameter count C, if C is smaller than the stop control parameter C, turning to the fourth step, otherwise, turning to the fifth step;
step four: generating in F a subset F containing features*And adding one more feature set F ', calculating to obtain the size D of the subset contained in the feature set F', traversing the feature set F ', not repeatedly searching the feature subset F' in the feature set F ', calculating an error for each searched feature subset F', and updating the optimal feature subset F if the error is less than the error obtained by using the initialized optimal feature set*If the initial error E is updated to be E', repeating the process until the traversal is finished;
step five: outputting the optimal feature subset F*。
In the present embodiment, the flow rate sequence of the section T803_1 in the T, T-1, T-2 periods is taken as the features 1, 6, 11; taking the flow sequence of the section T821_2 in T, T-1 and T-2 periods as characteristics 2, 7 and 12; taking the flow sequence of the section T837_1 in T, T-1 and T-2 periods as characteristics 3, 8 and 13; taking the flow sequence of the section T803_3 in T, T-1 and T-2 periods as characteristics 4, 9 and 14; the flow sequences of the section T802_1 in T, T-1 and T-2 periods are taken as characteristics 5,10 and 15. In this example, the set of best input features after feature selection is {1, 2,3,4, 6, 10, 13 }.
As a state space model, the Kalman filter may predict the processes that can be represented in state space through a unified algorithm. Therefore, it is undoubtedly appropriate to establish an urban short-term traffic flow prediction model by kalman filtering theory.
The embodiment improves the existing model, and the state equation and the observation equation of the improved state space model are as follows:
wherein X (m) ═ P1(m)，P2(m)，…PM(m)]T；B(m)＝[V1(m)，V2(m)，…VM(m)](ii) a C (m) is a state transition matrix; u (m-1) isProcess noise; ω (m) is the observation noise; pi(M) (i ═ 1,2, … M) is the correlation coefficient for the M-th cycle; vi(M) (i ═ 1,2, …, M) is the flow ratio of the ith input characteristic in the mth cycle; y (m +1) is the flow ratio of the predicted flow for the m +1 th cycle. In this embodiment, the state transition matrix, the process noise, the observation noise, and the correlation coefficient are all obtained by presetting. Vi(m) and y (m +1) are defined as follows:
wherein q isi(m) is the flow observed for the ith input feature in the mth cycle, with 5 minutes as one cycle;
is the flow history average of the ith input characteristic in the mth period; q. q.sp(m +1) is the predicted flow of the m +1 th period of the predicted section; q. q.sM(m +1) is the flow history average of the m +1 th period of the predicted section. Using an iterative process of kalman filtering, the following set of equations is obtained:
in the formula
Is a prior estimate of the state vector;
is a posterior estimate of the state vector;
is a prior estimate of the error covariance;
is a posteriori estimate of the error covariance; k (m) is the Kalman gain; q (m-1) is the covariance matrix of the process noise; r (m) is a covariance matrix of observed noise; i is a unit array; y isobserve(m +1) is the flow ratio of the observed flow in the m +1 th period of the predicted section, which is defined as:
wherein q (m +1) is a flow rate observed value of the m +1 th cycle of the predicted cross section.
The flow predicted value of the m +1 th period of the predicted section obtained according to the iteration process is as follows:
in the present embodiment, the error analysis is performed on the prediction data through the mean percent error (MAPE), and the calculation formula is as follows:
wherein n represents the number of co-selected test data, viIs the actual vehicle flow value of the ith period,
the resulting flow is predicted for the model for the ith cycle. A comparison of predicted flow versus actual flow for the method of the present invention is shown in fig. 4.
In summary, the present invention overcomes the following problems in the prior art: the prediction real-time performance is poor and the prediction precision is not high based on a mathematical statistical model; nonlinear model prediction takes long time; the neural network model requires a large amount of training data and the combined prediction model has poor actual usability; the existing model cannot fully consider the defect of the space-time correlation of traffic flow. The method can be well suitable for the intersection flow prediction under the urban road environment.
Claims (9)
1. A short-time traffic flow prediction method based on space-time feature selection and Kalman filtering is characterized by comprising the following steps:
step one, carrying out t-minute flow aggregation on original SCATS data;
step two, normalizing the aggregated data, and dividing the normalized data into a training set, a verification set and a test set;
step three, finding out n sections with highest correlation with the predicted sections by applying a multidimensional scaling method to the predicted sections and the section groups in the adjacent areas;
step four, performing feature selection on space-time features formed by different time lags of the predicted section and the n sections with the highest correlation with the predicted section by applying a space-time feature selection algorithm to determine the optimal input feature of the Kalman filtering model;
and step five, carrying out flow prediction on the test data set by using a Kalman filtering model for determining the optimal input characteristics to obtain a final prediction result.
2. The short-time traffic flow prediction method based on spatiotemporal feature selection and Kalman filtering according to claim 1, characterized in that: the original SCATS data comprises data sets of intersection numbers, strategic channels, coil numbers, cycle start time, phase start time, phases, phase duration, cycle duration, saturation, flow, date and week.
3. The short-time traffic flow prediction method based on spatiotemporal feature selection and Kalman filtering according to claim 1, characterized in that: in the step one, the value range of t is {3,5,10,15 }.
4. The short-time traffic flow prediction method based on spatio-temporal feature selection and Kalman filtering according to claim 1, characterized in that, the specific method for realizing flow aggregation in the first step is as follows:
and (3) carrying out t-minute flow aggregation on each coil through two parameters of the cycle starting time and the flow, wherein the flow calculation formula of unit time in a single signal cycle is as follows:
wherein the content of the first and second substances,
the average flow of the coil l at the intersection i in the kth period in unit time; q. q.si,l(k) Is the total flow of the coil l at the intersection i in the kth period; t isi,l(k) Is the cycle start time of the coil l of the intersection i in the kth cycle; the mapping relationship from the actual period to the aggregated virtual period is as follows:
wherein q isi,l(m) is the total flow of the coils l of the intersection i in the virtual period m; t is tkIs the duration of the virtual period m within the actual period k; n is the number of virtual periods m spanning the actual period.
5. The short-time traffic flow prediction method based on spatiotemporal feature selection and Kalman filtering according to claim 1, characterized in that: in the second step, 80 percent of data in the data set is used as a training set, 10 percent of data is used as a verification set, and 10 percent of data is used as a test set.
6. The short-time traffic flow prediction method based on spatio-temporal feature selection and Kalman filtering according to claim 1, characterized in that in the third step, by applying a multidimensional scaling method to the predicted sections and the section groups in the adjacent areas thereof, n sections with highest correlation with the predicted sections are found out by the following specific steps:
3.1: normalizing the traffic flow time sequences on the predicted sections and the section groups in the adjacent areas of the predicted sections, and calculating the Euclidean distance between the traffic flow time sequences on every two sections to obtain an Euclidean distance matrix;
3.2: selecting RSQ as an evaluation index, checking fitting degrees under different dimensions to obtain coordinates of each space point under the dimension with the highest fitting degree, namely dimension s, and calling a coordinate graph formed by the coordinates of each space point under the dimension with the highest fitting degree as an s-dimensional coordinate perception graph;
3.3: in the obtained s-dimensional coordinate perception map, n sections with the highest correlation with the predicted sections are found out according to the judgment principle that the shorter the distance between two points is, the higher the correlation is through the distance between the points for representing the traffic flow time sequence, and the value range of n is {4,5, 6 }.
7. The short-time traffic flow prediction method based on spatio-temporal feature selection and Kalman filtering according to claim 1, characterized in that the step of applying spatio-temporal feature selection algorithm to determine the optimal input features of the model in the fourth step is as follows:
4.1: forming the flow sequences of the first Q periods of the n sections with highest correlation with the predicted sections in the test set into input characteristics of a Kalman filtering model, wherein the value range of Q is {2,3,4 };
4.2: and performing feature selection on the input features of the Kalman filtering model by using a feature selection algorithm based on a heuristic search strategy to obtain the optimal input features of the Kalman filtering model when verification set data is used.
8. The short-time traffic flow prediction method based on spatiotemporal feature selection and kalman filtering according to claim 7, characterized in that: step 4.2 the step of determining the optimal input features of the kalman filter model by using the feature selection algorithm based on the heuristic search strategy is as follows:
4.2.1: inputting a data set S, a characteristic F, a prediction algorithm A, a stop control parameter C and an initialization characteristic set FinitialAn error analysis function Validation using the MAPE as an evaluation index;
4.2.2: initializing an optimal feature set, and calculating an error obtained by using the optimal feature set;
4.2.3: adding 1 to the control parameter count C, if C is smaller than the stop control parameter C, executing the step 4.2.4, otherwise, turning to the step 4.2.5;
4.2.4: generating in F a subset F containing features*And adding one more feature set F ', calculating to obtain the size D of the subset contained in the feature set F', traversing the feature set F ', not repeatedly searching the feature subset F' in the feature set F ', calculating an error for each searched feature subset F', and updating the optimal feature subset F if the error is less than the error obtained by using the initialized optimal feature set*If the initial error E is updated to be E', repeating the process until the traversal is finished;
4.2.5: outputting the optimal feature subset F*。
9. The short-time traffic flow prediction method based on spatiotemporal feature selection and Kalman filtering according to claim 1, characterized in that: and in the fifth step, according to the optimal input characteristics determined by the verification set, flow prediction is carried out on the test data set by using a Kalman filtering prediction model, and a final prediction result is obtained.
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