A short-term traffic flow prediction method based on data volatility

Abstract

The invention relates to a short-term traffic flow prediction method based on data volatility, which belongs to the field of short-term traffic prediction and comprises the following steps: S1: collecting historical traffic flow data according to a set collection period to obtain an initial matrix sequence; S2: calculating a first-order cumulative sequence, a first-order cumulative subtraction sequence and a partial derivative sequence according to the initial matrix sequence; S3: using the initial matrix sequence, according to the traffic flow fluctuation characteristics and the modeling mechanism of the partial grey prediction model, constructing a whitening equation form of a second-order partial grey model of the traffic flow fluctuation equation, and obtaining a second-order partial grey model based on the traffic flow fluctuation equation by discretizing the whitening equation; S4: calculating model parameters by using the least squares method, and solving the prediction model by adopting an iterative recursive method.

Description

Technical Field

[0001] The invention belongs to the field of short-term traffic prediction and relates to a short-term traffic flow prediction method based on data volatility. Background Art

[0002] The operating status of various vehicles on the road varies with road conditions, traffic environment and driver characteristics. Although this change is complex, through a large number of observations and analyses, it is found that they have certain characteristic tendencies. Traffic flow exhibits volatility. Traffic flow volatility refers to the existence of a mutually dependent relationship between traffic flow density and speed. When the density of cars on the road reaches a certain level, the mutual influence between vehicles will lead to a decrease in speed and ultimately form traffic flow fluctuations. Due to the influence of external factors such as lane changes, traffic light changes, weather conditions, etc., the speed and density of vehicles are constantly changing, so traffic flow usually exhibits volatility.

[0003] Traffic flow theory is a marginal discipline that uses physics and applied mathematics to conduct qualitative and quantitative analysis of various parameters of traffic flow and their relationships in order to seek the changing laws of road traffic flow, thereby providing a basis for traffic planning, traffic management, road design, transportation administration, and road administration. Based on traffic flow theory, a traffic flow prediction model can be established, which can well analyze the volatility of traffic flow. The gray system theory takes the system of "partial information known and part of the information unknown" as the research object, mainly through the generation and development of "partial" known information, extracting valuable information, and realizing the correct description of the system operation behavior and evolution law. In the selection of prediction models, due to the short time span of short-term traffic flow data and the small number of data samples, experts and scholars have found that the use of gray prediction models for modeling and prediction can not only achieve the purpose of real-time calculation, but also have high calculation efficiency. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a short-term traffic flow prediction method based on data volatility.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A short-term traffic flow prediction method based on data volatility includes the following steps:

[0007] S1: Collect historical traffic flow data according to the set collection period to obtain an initial matrix sequence;

[0008] S2: Calculate the first-order cumulative sequence, the first-order cumulative sequence and the partial derivative sequence according to the initial matrix sequence;

[0009] S3: Using the initial matrix sequence, according to the traffic flow fluctuation characteristics and the modeling mechanism of the partial grey prediction model, the whitening equation form of the second-order partial grey model of the traffic flow fluctuation equation is constructed. By discretizing the whitening equation, the second-order partial grey model based on the traffic flow fluctuation equation is obtained;

[0010] S4: Calculate the model parameters using the least squares method and solve the prediction model using an iterative recursive approach.

[0011] Further, the step S2 calculates the first-order cumulative sequence, the first-order cumulative subtractive sequence and the partial derivative sequence according to the initial matrix sequence, specifically including:

[0012] S21: Establish an initial traffic flow matrix sequence based on traffic flow, recorded as:

[0013] X (0) =(x (0) (1),x (0) (2),…,x (0) (n)) (1)

[0014] Among them, X (0) It is composed of n m×m matrices, x (0) (k), (k=1,2,…,n) is an m×m matrix.

[0015] S22: Calculate the first-order cumulative sequence, recorded as:

[0016] X (1) =(x (1) (1),x (1) (2),…,x (1) (n)) (2)

[0017] in,

[0018] S23: Calculate the first-order cumulative decreasing sequence, recorded as:

[0019] α (1) X (0) =(α (1) x (0) (2),α (1) x (0) (3),…,α (1) x (0) (n)) (3)

[0020] Among them, α (1) x (0) (k) = x (0) (k)-x (0) (k-1),(k=2,3,…,n),

[0021] S24: Calculate the mean generation sequence, recorded as:

[0022] Z (1) =(z (1) (2),z (1) (3),…,z (1) (n)) (4)

[0023] in,

[0024] S25: Calculate the horizontal and vertical partial derivative sequences, recorded as:

[0025] X x (1) (k) = (X x (1) (2),X x (1) (3),…,X x (1) (n)) (5)

[0026] X y (1) (k) = (X y (1) (2),X y (1) (3),…,X y (1) (n)) (6)

[0027] Among them, X x (1) (k) and X y (1) (k) The following conditions are met:

[0028] Let X (i,j) (1) (k),X (i,j)x (1) (k),X (i,j)y (1) (k) represents X (1) (k),X x (1) (k),X y (1) (k) The value in row i and column j, then the partial derivative sequence satisfies the following partial accumulation generation operation P-AGO:

[0029] 1)X (i,j) (1) (k) = X (i,j) (0) (k)+X (i,j) (1) (k-1)

[0030] 2)X(i,j)x (1) (k) = X (i,j) (1) (k)-X (i-1,j) (1) (k)

[0031] 3)X (i,j)y (1) (k) = X (i,j) (1) (k)-X (i,j-1) (1) (k).

[0032] Furthermore, the second-order partial grey model based on the traffic flow wave equation in step S3 is specifically obtained in the following steps:

[0033] S31: Let u = u(x,y,t) be a measure of the wave intensity at a specific location (x,y) and a specific time t, then the wave equation for u is

[0034]

[0035] Here, a is usually a fixed constant, namely the propagation rate of the wave.

[0036] S32: Use the right side of equation (7) Substituting the second derivative, and setting u = X (1) (t), f(x,y,t)=dX (1) (t)+M, so equation (7) becomes:

[0037]

[0038] in,

[0039] S33: Let k = t, and obtain the second-order partial grey prediction model by the discrete grey model method as follows:

[0040] α (1) X (0) (k)+aX (0) (k)+bX x (1) (k)+cX y (1) (k)+dZ (1) (k) = M (9)

[0041] Formula (9) is the second-order partial grey prediction model WE-SPGM based on the traffic flow wave equation.

[0042] Furthermore, in step S4, the least square method is used to calculate the model parameters, and the prediction model is solved by an iterative recursive method, which specifically includes:

[0043] S41: Least squares parameter estimate vector satisfy

[0044]

[0045] Where B is m 2 (n-1)×(n 2 +4)-order matrix, Y is m 2 (n-1)×1 order matrix, expressed as:

[0046]

[0047] In B, X (i,j) (0) (k),X (i,j)x (1) (k),X (i,j)y (1) (k),Z (i,j) (1) (k) represents X (0) (k),X x (1) (k),X y (1) (k),Z (1) (k) The value in row i and column j; in Y, α (1) X (i,j) (0) (k) represents α (1) X (0) (k) the value in row i and column j;

[0048] S42: The following formula is derived from steps S2 and S3:

[0049]

[0050]

[0051] S43: Order

[0052]

[0053] Then formula (11) is transformed into the following form:

[0054]

[0055] S44: For equation (11), let λ0=1, λ1=β1, λ2=β1·β1+1·β2,…,λ τ =λ τ-1 β1+λ τ-2 ·β2, then formula (12)

[0056] It is expressed as:

[0057]

[0058] The restored value is obtained by cumulative subtraction:

[0059] X (0) (k) = X (1) (k)-X (1) (k-1)(k=3,4,…,n) (14).

[0060] The beneficial effects of the present invention are as follows: considering the fluid mechanics properties of traffic flow and the volatility of traffic flow data, the present invention starts from the principle of the traffic flow wave equation, combines the advantages of the gray prediction model, and proposes a short-term traffic flow prediction method and system based on data volatility. In the process of solving the system model, in order to improve the accuracy, the discretized gray differential equation is used instead of the whitening differential equation. Secondly, the model form is improved to increase the adaptability of the model and improve the model accuracy. In the solution of the model, an iterative recursive method is adopted to increase the weight of the adjacent matrix information, and predict the subsequent matrix, which effectively improves the accuracy of the prediction. Experiments show that when the data fluctuation is large, the method proposed by the present invention has achieved good results in the simulation and prediction of road traffic flow.

[0061] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0063] Figure 1 It is a flow chart of the method and system for predicting short-term traffic flow based on data volatility of the present invention;

[0064] Figure 2 It is a comparison diagram of the errors between the model of the present invention and other prediction models;

[0065] Figure 3 It is a simulation fitting curve diagram of the model of the present invention and other prediction models. DETAILED DESCRIPTION

[0066] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0067] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0068] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0069] The present invention provides a short-term traffic flow prediction method and system. Figure 1 As shown, the method specifically comprises the following steps:

[0070] S1: Input initial sequence: The historical traffic flow data is recorded by the traffic data collection system. The historical traffic flow data obtained is the number of vehicles passing through a specific observation point or road section within a certain time interval. The specified time interval can be specified according to the prediction requirements (for example, 15 minutes), so as to obtain the initial traffic flow matrix sequence X (0) ;

[0071] S2: Process the original matrix sequence. The sequence X can be generated by calculation and accumulation (1) , cumulatively generate sequence α (1) X (0) , mean sequence Z (1) and the partial derivative sequence X x (1) (k), X y (1)(k) specifically including:

[0072] S21: Establish an initial traffic flow matrix sequence based on traffic flow, recorded as:

[0073] X (0) =(x (0) (1),x (0) (2),…,x (0) (n)) (1)

[0074] Among them, X (0) It is composed of n m×m matrices, x (0) (k), (k=1,2,…,n) is an m×m matrix.

[0075] S22: Calculate the first-order cumulative sequence, recorded as:

[0076] X (1) =(x (1) (1),x (1) (2),…,x (1) (n)) (2)

[0077] in,

[0078] S23: Calculate the first-order cumulative decreasing sequence, recorded as:

[0079] α (1) X (0) =(α (1) x (0) (2),α (1) x (0) (3),…,α (1) x (0) (n)) (3)

[0080] Among them, α (1) x (0) (k) = x (0) (k)-x (0) (k-1),(k=2,3,…,n),

[0081] S24: Calculate the mean generation sequence, recorded as:

[0082] Z (1) =(z (1) (2),z (1) (3),…,z (1) (n)) (4)

[0083] in,

[0084] S25: Calculate the horizontal and vertical partial derivative sequences, recorded as:

[0085] X x (1) (k) = (X x (1) (2),X x (1) (3),…,X x (1) (n)) (5)

[0086] X y (1) (k) = (X y (1) (2),X y (1) (3),…,X y (1) (n)) (6)

[0087] Among them, X x (1) (k) and X y (1) (k) The following conditions are met:

[0088] Let X (i,j) (1) (k),X (i,j)x (1) (k),X (i,j)y (1) (k) represents X (1) (k),X x (1) (k),X y (1) (k) The value in row i and column j, then the partial derivative sequence satisfies the following partial accumulation generation operation P-AGO:

[0089] 1)X (i,j) (1) (k) = X (i,j) (0) (k)+X (i,j) (1) (k-1)

[0090] 2)X (i,j)x (1) (k) = X (i,j) (1) (k)-X (i-1,j) (1) (k)

[0091] 3)X (i,j)y (1) (k) = X (i,j) (1) (k)-X (i,j-1) (1) (k).

[0092] S3: Construct matrices, estimate parameters, and establish models: Construct matrices B and Y according to the matrix sequence required in S2, build a WE-SPGM model, and then calculate the parameter sequence by the least squares method. The specific steps to obtain the value are as follows:

[0093] S31: Let u = u(x,y,t) be a measure of the wave intensity at a specific location (x,y) and a specific time t, then the wave equation for u is

[0094]

[0095] Here, a is usually a fixed constant, namely the propagation rate of the wave.

[0096] S32: Use the right side of equation (7) Substituting the second derivative, and setting u = X (1) (t), f(x,y,t)=dX (1) (t)+M, so equation (7) becomes:

[0097]

[0098] in,

[0099] S33: Let k = t, and obtain the second-order partial grey prediction model by the discrete grey model method as follows:

[0100] α (1) X (0) (k)+aX (0) (k)+bX x (1) (k)+cX y (1) (k)+dZ (1) (k) = M (9)

[0101] Formula (9) is the second-order partial grey prediction model WE-SPGM based on the traffic flow wave equation.

[0102] S4: Calculate the model parameters using the least squares method and solve the prediction model using an iterative recursive method, including:

[0103] S41: Least squares parameter estimate vector satisfy

[0104]

[0105] Where B is m 2 (n-1)×(n 2 +4)-order matrix, Y is m2 (n-1)×1 order matrix, expressed as:

[0106]

[0107] In B, X (i,j) (0) (k),X (i,j)x (1) (k),X (i,j)y (1) (k),Z (i,j) (1) (k) represents X (0) (k),X x (1) (k),X y (1) (k),Z (1) (k) The value in row i and column j; in Y, α (1) X (i,j) (0) (k) represents α (1) X (0) (k) the value in row i and column j;

[0108] S42: The following formula is derived from steps S2 and S3:

[0109]

[0110] S43: Order

[0111]

[0112] Then formula (11) is transformed into the following form:

[0113]

[0114] S44: For equation (11), let λ0=1, λ1=β1, λ2=β1·β1+1·β2,…,λ τ =λ τ-1 β1+λ τ-2 ·β2, then formula (12)

[0115] It is expressed as:

[0116]

[0117] The restored value is obtained by cumulative subtraction:

[0118] X (0) (k) = X (1) (k)-X (1) (k-1)(k=3,4,…,n) (14).

[0119] The simulation results are compared with the actual traffic flow data to verify the accuracy and reliability of the model.

[0120] S5: Apply the model to actual cases to verify its excellent performance in the cases and the predictive performance of the model. If the indicator results pass the error test, substitute the partial derivative sequence predicted by the GM(1,1) model into the WE-SPGM model to predict the future. If the calculated indicator results do not pass the error test, return to step S1.

[0121] According to the public data set of British road traffic, the traffic flow from 4:59 to 12:29 for five consecutive days from April 3 to 7 was selected, and the traffic flow data with an interval of 15 minutes was used for modeling as a validity analysis case of the present invention. The model of the present invention was compared with other prediction models, and the measured prediction performance index used was MAPE. The calculated results are shown in Table 1. Plot a graph, such as Figure 2 shown.

[0122] Table 1

[0123] serial number time WE-SPGM ANN ARIMA LSTM 1 4：59-10：59 8.6706 11.4729 29.2485 11.8896 2 5：14-11：14 7.9970 13.2765 24.7275 10.2628 3 5：29-11：29 6.8664 13.5348 20.1435 10.0770 4 5：44-11：44 5.5523 12.7827 17.0666 11.9654 5 5：59-11：59 6.0231 12.1181 12.8697 10.4202 6 6：14-12：14 5.6971 11.5945 11.4495 8.1644 7 6：29-12：29 6.0491 10.6860 8.9296 7.9803

[0124] As can be seen from Table 1, the MAPE values ​​of the WE-SPGM model are all below 10%, indicating that the model has high accuracy; the error values ​​of the ANN model and the LSTM model are basically around 10%, which is a category of high accuracy, and even the accuracy of individual error values ​​is below 10%, reflecting a good fitting effect; in the fitting of the seven sets of data, the error value fluctuation range of the ARIMA model is large, and the fitting effect is average. Compared with the other three models, the error values ​​of the WE-SPGM model are the smallest, indicating that the model has a better simulation effect than other models. In order to more intuitively illustrate the effectiveness of the model in fitting the morning peak data, select No. 4 to draw Figure 3 The graph depicts the comparison between the four models and the traffic flow data from 5:44 to 11:44 on April 3 and 4.

[0125] A person skilled in the art can understand that all or part of the steps in the above-mentioned implementation case method can be completed by instructing related hardware through a program. The program can be stored in a computer-readable storage medium. When the program is executed, the steps of the method can be implemented. The storage medium, such as ROM / RAM, disk, CD, etc.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A short-term traffic flow prediction method based on data volatility, characterized by: The following steps are involved: S1: Collect historical traffic flow data according to the set collection period to obtain an initial matrix sequence; S2: Calculate the first-order cumulative sequence, the first-order cumulative subtraction sequence and the partial derivative sequence according to the initial matrix sequence; Step S2, according to the initial matrix sequence, calculates the first-order cumulative sequence, the first-order cumulative subtraction sequence and the partial derivative sequence, specifically including: S21: Establish an initial traffic flow matrix sequence based on traffic flow, recorded as: X (0) =(X (0) (1),X (0) (2),…,X (0) (n)) (1) Among them, X (0) It is composed of n m×m matrices, X (0) (k), k=1,2,…,n is an m×m matrix; S22: Calculate the first-order cumulative sequence, recorded as: X (1) =(X (1) (1),X (1) (2),…,X (1) (n)) (2) in, S23: Calculate the first-order cumulative decreasing sequence, recorded as: a (1) X (0) =(a (1) X (0) (2),a (1) X (0) (3),…,a (1) X (0) (n)) (3) Among them, α (1) X (0) (k)=X (0) (k)-X (0) (k-1),k=2,3,…,n; S24: Calculate the mean generation sequence, recorded as: WITH (1) =(From (1) (2),With (1) (3),…,From (1) (n)) (4) in, S25: Calculate the horizontal and vertical partial derivative sequences, recorded as: Among them, X x (1) (k) and X y (1) (k) The following conditions are met: Let X (i,j) (1) (k),X (i,j)x (1) (k),X (i,j)y (1) (k) respectively represent X (1) (k),X x (1) (k),X y (1) (k) The value in row i and column j, then the partial derivative sequence satisfies the following partial accumulation generation operation P-AGO: 1)X (i,j) (1) (k)=X (i,j) (0) (k)+X (i,j) (1) (k-1) 2)X (i,j)x (1) (k)=X (i,j) (1) (k)-X (i-1,j) (1) (k) 3)X (i,j)y (1) (k)=X (i,j) (1) (k)-X (i,j-1) (1) (k) S3: Using the initial matrix sequence, according to the traffic flow fluctuation characteristics and the modeling mechanism of the partial gray prediction model, a whitening equation form of the second-order partial gray model of the traffic flow fluctuation equation is constructed, and the second-order partial gray model based on the traffic flow fluctuation equation is obtained by discretizing the whitening equation; the second-order partial gray model based on the traffic flow fluctuation equation in step S3 is specifically obtained as follows: S31: Let u = u(x,y,t) be a measure of the wave intensity at position (x,y) and time t, then the wave equation for u is Among them, a is usually a fixed constant, that is, the propagation rate of the wave; S32: Use the right side of equation (7) Substituting the second derivative, and setting u = X (1) (t), f(x,y,t)=dX (1) (t)+M, so equation (7) becomes: in, S33: Let k = t, and obtain the second-order partial grey prediction model by the discrete grey model method as follows: Formula (9) is the second-order partial grey prediction model WE-SPGM based on the traffic flow wave equation; S4: Calculate the model parameters using the least squares method and solve the prediction model using an iterative recursive approach.

2. The short-term traffic flow prediction method based on data volatility according to claim 1 is characterized by: Step S4 uses the least squares method to calculate the model parameters and uses an iterative recursive method to solve the prediction model, which specifically includes: S41: Least squares parameter estimate vector satisfy Where B is m 2 (n-1)×(n 2 +4)-order matrix, Y is m 2 (n-1)×1 order matrix, expressed as: In B, X (i,j) (0) (k),X (i,j)x (1) (k),X (i,j)y (1) (k),Z (i,j) (1) (k) respectively represent X (0) (k),X x (1) (k),X y (1) (k),Z (1) (k) The value in row i and column j; in Y, α (1) X (i,j) (0) (k) represents α (1) X (0) (k) the value in row i and column j; S42: The following formula is derived from steps S2 and S3: S43: Order Then formula (11) is transformed into the following form: S44: For formula (11), let λ0 = 1, λ1 = β1, λ2 = β1·β1 + 1·β2, …, λ τ = λ τ-1 ·β1 + λ τ-2 ·β2, then formula (12) It is expressed as: The restored value is obtained by cumulative subtraction: X (0) (k)=X (1) (k)-X (1) (k-1),k=3,4,…,n (14)。

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