Short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model

Abstract

The present invention relates to a short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial gray model, belonging to the field of intelligent transportation technology. The method comprises: constructing the original data form of a one-dimensional point sequence into a matrix original data sequence; calculating and accumulating a sequence X according to the original data matrix sequence; (r) and its corresponding mean sequence Z (r) and partial derivative sequences; establish a short-term traffic flow prediction model FPGM based on spatiotemporal data, and construct matrices B and Y to estimate model parameters; use particle swarm optimization to find the optimal fractional order accumulation order and parameters in the sine function; calculate the model simulation value X (r) , restore value X (0) ; Calculate the mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error and correlation coefficient of the FPGM (1,1|sin) model and the comparison model; If each indicator passes the error test, use the FPGM (1,1|sin) model to predict future trends, otherwise return to step S1. The present invention can provide data support for traffic flow data analysis and prediction.

Description

Technical Field

[0001] The invention belongs to the technical field of intelligent transportation, and relates to a short-term traffic flow prediction method based on spatiotemporal data and a fractional order cumulative partial grey model. Background Art

[0002] In recent years, Intelligent Transportation System (ITS) has been considered as an intelligent system that can effectively reduce traffic congestion. Traffic prediction is one of the necessary components of ITS, which can provide scientific support for urban traffic management system to arrange roads and is indispensable in traffic control and development. As an effective means to assist traffic planning, management and control, it has attracted more and more attention from researchers in various countries.

[0003] The traffic system is complex, and traffic flow data also has spatiotemporal, periodic and uncertain characteristics. Short-term road traffic flow prediction is a classic spatiotemporal research problem. Obviously, observations at adjacent locations and adjacent times are not independent of each other, but have close dynamic correlations. For example, from the perspective of the spatial dimension, different locations have different effects on fixed locations. Even if time changes, the same location will have different effects on fixed locations. From the perspective of the time dimension, traffic flow data at different time periods have different effects on the traffic status within a certain constant time period.

[0004] The traffic flow system is a complex dynamic system with human participation, time variation and high uncertainty. It is affected by uncertain realistic factors such as environment, weather, driver's psychological state, people's travel habits, etc., and has the characteristics of a gray system. At the same time, the observation scale of short-term traffic flow is generally less than 15 minutes, and the traffic induction cycle is generally 5 minutes, so there are only 12 data in one hour. Therefore, short-term traffic flow belongs to small sample data and has obvious gray system characteristics.

[0005] Reliable and accurate short-term traffic forecasting is a necessary condition for providing recent traffic status information and is also the key to traffic flow theory research. Therefore, the information provided by traffic forecasting can not only help traffic management departments arrange and direct traffic flow in advance, improve traffic efficiency and road safety, alleviate traffic congestion to a certain extent, reduce the occurrence of traffic accidents, and reduce exhaust emissions. It can also help travelers understand information in advance, arrange their trips reasonably, and choose the best route. However, spatiotemporal traffic flow forecasting faces many difficulties and challenges. First, mining the nonlinearity and complexity of spatiotemporal traffic data is a heavy task; second, it is constrained by the complex interaction between actual roads and monitoring systems.

[0006] For a complex and uncertain system like the traffic system, it is very necessary to study the information of multiple road sections to predict its overall development trend and evolution law. The multivariate model can partially make up for the shortcomings of the single variable model. In the modeling process, the impact of multiple variables on the changing trend of the traffic system can be fully considered, and the multivariate model has better structural compatibility. Therefore, a new spatiotemporal traffic flow prediction method is urgently needed to solve the above problems. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a short-term traffic flow prediction method based on spatiotemporal data and a fractional-order cumulative partial gray model, which constructs a matrix original data sequence in the form of the original data of a one-dimensional point sequence; at the same time, the particle swarm algorithm is used to optimize the fractional-order cumulative order and the parameters in the sine function to reduce the model error and improve the applicability of the model.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model, the prediction method includes:

[0010] S1: The original traffic flow data of one-dimensional point sequence is constructed into traffic flow data in the form of matrix sequence;

[0011] S2: Process the original matrix sequence and calculate and accumulate to generate the sequence X (r) and its corresponding mean sequence Z (r) and partial derivative sequences;

[0012] S3: Establish a short-term traffic flow prediction model FPGM based on spatiotemporal data; and construct matrices B and Y to estimate model parameters;

[0013] S4: Particle swarm optimization is used to find the fractional cumulative order and the parameters in the sine function;

[0014] S5: Calculate the simulation and restoration values ​​of the FPGM model; calculate the simulation value X through the time response formula (r) , calculate the restored value X by the reduction formula (0) ;

[0015] S6: Calculate the evaluation indicators of the model FPGM (1, M|sin) of the present invention and four comparative models PGM (1, 3), CMPGM (1, M), ARIMA and LSTM models, including: mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error and correlation coefficient;

[0016] S7: If all indicators pass the error test, the FPGM model is used to predict future trends, otherwise return to step S1.

[0017] Further, in step S1, the original traffic flow data of the one-dimensional point sequence is constructed into traffic flow data in the form of a matrix sequence, and a matrix sequence X consisting of n m×m matrices is obtained. (0) :

[0018] X (0) =(X (0) (1),X (0) (2),…,X (0) (n))

[0019] Among them, X (0) (k)(k=1,2,…,n) is an m×m matrix, which is expressed as:

[0020]

[0021] Represents X (0) (k) The value in row i and column j.

[0022] Further, in step S2, the original sequence X (0) (k) r(r∈R + )-order cumulative generation sequence X (r) It is calculated as follows:

[0023] X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n))

[0024] Among them, X (r) (k)(k=1,2,…,n) is an m×m matrix, Represents X (r) (k) The value in row i and column j is as follows:

[0025]

[0026] and:

[0027]

[0028] α (r) X (0) (r∈R + ) is the sequence X (0) The fractional-order cumulative reduction operator of :

[0029] α (r) X (0) =(α (r) x (0)(1),α (r) x (0) (2),…,α (r) x (0) (n))

[0030] Among them, α (r) x (0) (k)(k=1,2,…,n) is an m×m matrix, and:

[0031]

[0032] Further, in step S2, the sequence X is generated by accumulation. (r) The mean value of the generated sequence Z (r) It is expressed as:

[0033] Z (r) =(Z (r) (2),…,Z (r) (n))

[0034] Among them, Z (r) (k)(k=2,3,…,n) is an m×m matrix, Represents Z (r) (k) the value in row i, column j, and The details are as follows:

[0035]

[0036] Accumulate and generate sequence X (r) The horizontal and vertical partial derivative sequence X x (r) and X y (r) Respectively expressed as:

[0037]

[0038]

[0039] express The value in row i and column j, express The value at row i and column j.

[0040] Further, in step S3, the expression of the FPGM model, FPGM(1,M|sin), is:

[0041]

[0042] Where M = 2m 2 +6; and its whitening equation is expressed as:

[0043]

[0044] Among them, a, b, c, r, ω, d are real constant parameter variables, t is X (r) The time variables, x, y are X (r) The spatial variable, β 0 ,β 1 It is an m×m-order constant matrix, as follows:

[0045]

[0046] β 011 ,β 012 ,…,β 0mm ,β 111 ,β 112 ,…,β 1mm is the matrix β 0 ,β 1 All elements in .

[0047] Further, in step S3, the constructed matrix B is m 2 (n-1)×(n 2 +3)-order matrix, which is expressed as:

[0048]

[0049] In matrix B, Z (i,j)x (r) (k),Z (i,j)y (r) (k),X (r) (k) is Z x (r) (k),Z y (r) (k),X (r) (k) The value in row i and column j;

[0050] The constructed matrix Y is m 2 The (n-1)×1 matrix is ​​expressed as:

[0051]

[0052] In the matrix Y, X (i,j) (0) (k) is X (0) (k) the value in row i and column j;

[0053] For the FPGM(1,M|sin) model, the least squares parameter estimate vector satisfy:

[0054]

[0055] in μ 011 ,μ 012 ,…,μ 0mm ,μ 111 ,μ 112 ,…,μ 1mm is the matrix β 0 ,β 1 All elements in .

[0056] Further, in step S4, a particle swarm optimization algorithm is used to find the optimal fractional cumulative order and the parameters in the sine function, and the process is as follows:

[0057] With the goal of minimizing the average relative error, considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established:

[0058]

[0059] The optimization model is optimized by using the particle swarm optimization algorithm to obtain the optimal fractional order r and the parameters ω and d in the sine function.

[0060] Further, in step S5, the time response formula is:

[0061]

[0062] in, is the simulated value of the FPGM(1,M|sin) model The value in row i and column j;

[0063] The final reduction formula:

[0064]

[0065] in, is the restored value of the FPGM(1,M|sin) model The value at the coordinate (i, j). Further, in step S6, the calculation formula of the mean square error MSE is:

[0066]

[0067] The calculation formula for the mean absolute simulation percentage error MAPE is:

[0068]

[0069] The calculation formula for the root mean square percentage error RMSPE is:

[0070]

[0071] The calculation formula for the mean absolute error MAE is:

[0072]

[0073] The calculation formula of the correlation coefficient R is:

[0074]

[0075] Where cov(·) represents covariance and Var(·) represents variance.

[0076] Furthermore, in step S7, the various indicators of the model FPGM (1, M|sin) calculated in step S6 are compared with the comparison models PGM (1, 3), CMPGM (1, M), ARIMA and LSTM models. If the above parameters all meet the accuracy requirements, FPGM (1, M|sin) is used to predict the future development of traffic flow; if there are parameters that do not meet the accuracy requirements, return to step S1 to adjust the prediction model parameters again.

[0077] The beneficial effects of the present invention are:

[0078] The present invention innovates on the basis of the traditional grey prediction model, introduces partial differential theory and fractional order accumulation operator to more accurately predict short-term traffic flow. By combining the sine function correction term and the particle swarm optimization algorithm, the present invention significantly improves the accuracy and stability of the prediction. The FPGM (1, M|sin) model outperforms the existing grey prediction model, statistical analysis method and deep learning method in multiple experimental cases, showing its practical value in intelligent transportation systems. The application of this model can provide more scientific and effective data support for urban traffic management and planning, and is particularly suitable for the analysis and prediction of the spatiotemporal characteristics of traffic flow data.

[0079] 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

[0080] 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:

[0081] Figure 1 A flow chart of a short-term traffic flow prediction method based on spatiotemporal data of the present invention;

[0082] Figure 2 A trend comparison chart of the prediction model of the present invention and other models;

[0083] Figure 3 It is a comparison chart of APE between the prediction model of the present invention and other models. DETAILED DESCRIPTION

[0084] 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.

[0085] 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.

[0086] 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.

[0087] See also Figure 1 to Figure 3 , which is a short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model.

[0088] The present invention provides a short-term traffic flow prediction method based on spatiotemporal data. The grey prediction model is mainly established through the differential information between the ordinary differential equation and the differential equation. The differential equation is generally the whitening equation of the grey prediction model. Figure 1 As shown, the method specifically comprises the following steps:

[0089] S1: The original traffic flow data of one-dimensional point sequence is constructed into traffic flow data in the form of matrix sequence;

[0090] S2: Process the original matrix sequence, that is, calculate and accumulate to generate the sequence X (r) , mean sequence Z (r) and partial derivative sequences;

[0091] S3: Establish a short-term traffic flow prediction model based on spatiotemporal data, abbreviated as FPGM model; construct matrices B and Y, and estimate model parameters;

[0092] S4: Particle swarm algorithm is used to find the best fractional cumulative order and parameters in the sine function;

[0093] S5: Calculate the simulation and restoration values ​​of the FPGM model; calculate the simulation value X through the time response formula (r) , calculate the restored value X by the reduction formula (0) ;

[0094] S6: Calculate the evaluation indicators of the model: MSE, MAPE, RMSPE, MAE, and R;

[0095] S7: If all indicators pass the error test, the FPGM model is used to predict future trends, otherwise return to step S1.

[0096] Further, in step S1, the original traffic flow data of the one-dimensional point sequence is constructed into traffic flow data in the form of a matrix sequence, and a matrix sequence X consisting of n m=m-order matrices is obtained. (0) :

[0097] X (0) ×(X (0) (1),X (0) (2),…,X (0) (n))

[0098] Among them, X (0) (k)(k=1,2,…,n) is an m×m matrix, Represents X (0) (k) The value in row i and column j is as follows:

[0099]

[0100] Further, in step S2, the original matrix sequence is processed, specifically including:

[0101] X (r) is the original sequence X (0) (k) r(r∈R + )-order cumulative generation sequence:

[0102] X (r) =(X (r) (1),X (r)(2),...,X (r) (k),...,X (r) (n))

[0103] Among them, X (r) (k)(k=1,2,…,n) is an m×m matrix, Represents X (r) (k) The value in row i and column j is as follows:

[0104]

[0105] and (i, j=1,2,...,m; k=1,2,...,n).

[0106] α (r) X (0) (r∈R + ) is the sequence X (0) The fractional-order cumulative reduction operator of :

[0107] α (r) X (0) =(α (r) x (0) (1),α (r) x (0) (2),…,α (r) x (0) (n))

[0108] Among them, α (r) x (0) (k)(k=1,2,…,n) is an m×m matrix, and

[0109]

[0110] Z (r) Yes X (r) The mean of generated sequence is:

[0111] Z (r) =(Z (r) (2),…,Z (r) (n))

[0112] Among them, Z (r) (k)(k=2,3,…,n) is an m×m matrix, Represents Z (r) (k) The value in row i and column j is as follows:

[0113]

[0114] and

[0115] Xx (r) and X y (r) They are X (r) The sequence of horizontal and vertical partial derivatives of :

[0116]

[0117] express The value in row i and column j, express The value at row i and column j.

[0118] Further, in step S3, a FPGM model is established, and the expression of the FPGM model, namely FPGM(1,M|sin), is:

[0119]

[0120] Where M = 2m 2 +6; and its whitening equation is expressed as:

[0121]

[0122] Among them, a, b, c, r, ω, d are real constant parameter variables, β 0 ,β 1 is an m×m-order constant matrix, t is X (r) The time variables, x, y are X (r) spatial variables.

[0123] Further, in step S3, a matrix is ​​constructed to estimate the model parameters, specifically including: for the FPGM (1, M | sin) model, the least squares parameter estimation vector satisfy:

[0124]

[0125] B is an m 2 (n-1)×(n 2 +3)-order matrix, Y is an m 2 (n-1)×1 matrix:

[0126]

[0127] In matrix B, Z (i,j)x (r) (k),Z (i,j)y (r) (k),X (r) (k) is Z x (r) (k),Z y(r) (k),X (r) (k) is the value in row i and column j. In matrix Y, X (i,j) (0) (k) is X (0) (k) The value in row i, column j.

[0128] Further, in step S4, the particle swarm algorithm searches for the optimal fractional cumulative order and the parameters in the sine function, and the process is as follows:

[0129] Since the FPGM (1, M|sin) model is established based on cumulative order and specific parameters. Different values ​​of parameters will affect the simulation accuracy of the model. The average relative error is the main criterion for measuring the simulation effect of the grey prediction model. In order to optimize the simulation effect, the present invention takes minimizing the average relative error as the goal, considers the relationship between model parameters and the range of parameter values, and establishes the following nonlinear optimization model:

[0130]

[0131] By using the particle swarm optimization algorithm to optimize the optimization model, the optimal fractional order r and the parameters ω and d in the sine function are obtained.

[0132] Further, in step S5, the time response formula is:

[0133]

[0134] in, is the simulated value of the FPGM(1,M|sin) model The value in row i and column j;

[0135] The final reduction formula:

[0136]

[0137] in, is the restored value of the FPGM(1,M|sin) model The value at the coordinate (i, j). Further, in step S6, the formulas for calculating the values ​​of the FPGM (1, M | sin) model and the two partial gray models PGM (1, 3), CMPGM (1, M), and the evaluation indicators MSE, MAPE, RMSPE, MAE, and R of ARIMA and LSTM are shown in Table 1 below:

[0138] Table 1

[0139]

[0140] The MSE, MAPE, RMSPE and MAE values ​​are all greater than 0. The smaller the values ​​of these indicators, the higher the model accuracy. The range of R value is [0,1], where the closer the R value is to 1, the better the model effect.

[0141] Further, in step S7, the various indices of the model FPGM (1, M|sin) of the present invention and the four comparative models PGM (1, 3), CMPGM (1, M), ARIMA and LSTM models calculated in step S6 are compared in turn. When the MAPE index value of the present model FPGM (1, M|sin) is smaller than that of the other four models, it means that the simulation accuracy of the present model is high and it has an advantage over the other models. At the same time, if the R index value of the present model FPGM (1, M|sin) is higher than that of the other four models, it means that the simulation accuracy of the present model is high and it has an advantage over the other models. In general, if the above parameters make the MSE, MAPE, RMSPE and MAE values ​​of the present model smaller than those of the other four models, and the R index value is higher than those of the other four models, it means that the parameters meet the accuracy requirements, and FPGM (1, M|sin) is used to predict the future development of traffic flow; if there are parameters that do not meet the accuracy requirements, return to step S1 to adjust the prediction model parameters again.

[0142] This embodiment compares the prediction model of the present invention with other models. The trend comparison diagram of the prediction model of the present invention and other models is shown in FIG. Figure 2 As shown in the APE comparison chart Figure 3 As shown. The data for this case selects the traffic flow data of the M54 Expressway, which is selected from the traffic flow data on the expressway website on weekdays, and the traffic flow data is separated by 15 minutes. The traffic flow data of the same section for 15 minutes from 6:59 to 12:59 every Tuesday of November 2022, that is, November 1, 8, 15, 22, and 29, are selected, for a total of 125 data. The 25 traffic flow data with a 15-minute interval between 6:59 and 12:59 on November 1 constitute the matrix of the first matrix in the matrix sequence, and the remaining four matrices are analogous. The FPGM(1,M|sin) model is still compared with the CMPGM(1,M) model, the PGM(1,3) model, the ARIMA model, and the LSTM model. In this embodiment, the ARIMA model structure calculated based on the original data is the ARIMA (4, 0, 3) model, and the FPGM (1, M|sin) model parameters are r = 1, ω = 16.0956, d = 13.852. Five models are simulated and compared. The evaluation index calculation results of the five models are shown in Table 2.

[0143] Table 2

[0144]

[0145] As can be seen from Table 2, the MSE, MAPE, RMSPE and MAE values ​​of the PGM(1,3) model are the highest, and the R index value is the lowest, and the overall performance is very poor. The index results of the ARIMA model and the LSTM model are not much different. The MAPE of the FPGM(1,M|sin) model is better than that of the CMPGM(1,M) model, and the other indicators are also the best among the five models. In general, by comparing the evaluation indicators with the comparison model, it can be seen that the simulation accuracy of this model is the highest.

[0146] In order to see the advantages of the FPGM (1, M|sin) model more clearly, the calculation results of the above indicators are plotted as images. Figure 2 , APE comparison chart see Figure 3 . Note that the simulation results of the PGM(1,3) model and the ARIMA model are poor, so we do not draw the trend graph and APE comparison graph of these two models. Figure 2 As shown in the figure, the fitting trend of LSTM is quite different from the trend of the real data set, and there is a large deviation. Compared with the CMPGM(1,M) model, the data simulation trend of the FPGM(1,M|sin) model is worse than that of the CMPGM(1,M). At some points, the simulation effect of the CMPGM(1,M) model is not as good as that of the FPGM(1,M|sin) model. In general, the simulation error of the FPGM(1,M|sin) model is the smallest and the effect is the best.

[0147] In summary, the FPGM (1, M|sin) model not only enriches the existing grey system theory, but also provides a method for real-time and accurate short-term traffic flow prediction. It can be effectively applied to traffic control and guidance, providing reliable and effective information for traffic managers and travelers, improving travel efficiency and reducing traffic congestion.

[0148] 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 spatiotemporal data and fractional order cumulative partial grey model, characterized by: The prediction method comprises: S1: The original traffic flow data of one-dimensional point sequence is constructed into traffic flow data in the form of matrix sequence; S2: Process the original matrix sequence and calculate and accumulate to generate the sequence X (r) and its corresponding mean sequence Z (r) and partial derivative sequences; S3: Establish a short-term traffic flow prediction model FPGM based on spatiotemporal data; and construct matrices B and Y to estimate model parameters; S4: Particle swarm optimization is used to find the fractional cumulative order and the parameters in the sine function; S5: Calculate the simulation and restoration values ​​of the FPGM model; calculate the simulation value by the time response formula, and calculate the restoration value by the restoration formula; S6: Calculate the evaluation indicators of the model FPGM (1, M|sin) and the comparison model, including: mean square error, mean absolute simulation percentage error, root mean square percentage error, mean absolute error and correlation coefficient; S7: If all indicators pass the error test, the FPGM (1, M|sin) model is used to predict future trends, otherwise, return to step S1; In step S1, the original traffic flow data of the one-dimensional point sequence is constructed into traffic flow data in the form of a matrix sequence, and a matrix sequence X consisting of n m×m matrices is obtained. (0) : X (0) =(X (0) (1),X (0) (2),…,X (0) (n)) Among them, X (0) (k), k = 1, 2, ..., n is an m × m matrix, which is expressed as: Represents X (0) (k) The value in row i and column j, i,j = 1,2,…,m; k = 1,2,=,n; In step S2, the original sequence X (0) (k) is the r-order cumulative generation sequence X (r) It is calculated as follows: X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n)) Where r∈R + ;X (r) (k), k=1,2,…,n is an m×m matrix, Represents X (r) (k) The value in row i and column j, i, j = 1, 2, ..., m; k = 1, 2, ..., n, as follows: and: α (r) X (0) For sequence X (0) The fractional order cumulative reduction operator, r∈R + : a (r) X (0) =(a (r) x (0) (1),a (r) x (0) (2),…,a (r) x (0) (n)) Among them, α (r) x (0) (k), k = 1, 2, ..., n is an m × m matrix, and: In step S2, the sequence X is generated by accumulation (r) The mean of the generated sequence Z (r) It is expressed as: WITH (r) =(From (r) (2),…,From (r) (n)) Among them, Z (r) (k), k = 2, 3, ..., n is an m × m matrix, Represents Z (r) (k) The value in row i and column j, i, j = 1, 2, ..., m; k = 2, 3, ..., n, and The details are as follows: Accumulate and generate sequence X (r) The horizontal and vertical partial derivative sequence X x (r) and X y (r) Respectively expressed as: express The value in row i and column j, express The value in row i and column j, where i, j = 1, 2, ..., m, k = 1, 2, ..., n; In step S3, the expression of the FPGM model, FPGM(1,M|sin), is: Where M = 2m 2 +6; and its whitening equation is expressed as: Among them, a, b, c, r, ω, d are real constant parameter variables, t is X (r) The time variables, x, y are X (r) The spatial variables, β0, β1 are m×m order constant matrices, as follows: β 011 ,β 012 ,…,β 0mm ,β 111 ,β 112 ,…,β 1mm are all elements in the matrices β0,β1; In step S3, the constructed matrix B is m 2 (n-1)×(n 2 +3)-order matrix, which is expressed as: In matrix B, Z (i,j)x (r) (k),Z (i,j)y (r) (k), Z x (r) (k),Z y (r) (k),X (r) (k) The value in row i and column j; The constructed matrix Y is m 2 The (n-1)×1 matrix is ​​expressed as: In the matrix Y, X (i,j) (0) (k) is X (0) (k) the value in row i and column j; For the FPGM(1,M|sin) model, the least squares parameter estimate vector satisfy: in μ 011 ,μ 012 ,…,μ 0mm ,μ 111 ,μ 112 ,…,μ 1mm are all elements in the matrices β0,β1; In step S5, the time response formula is: in, is the simulated value of the FPGM(1,M|sin) model The value in row i and column j; The final reduction formula: in, is the restored value of the FPGM(1,M|sin) model The value at coordinate (i,j).

2. The short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model according to claim 1 is characterized by: In step S4, a particle swarm optimization algorithm is used to find the optimal fractional cumulative order and parameters in the sine function, and the process is as follows: With the goal of minimizing the average relative error, considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established: The optimization model is optimized by using the particle swarm optimization algorithm to obtain the optimal fractional order r and the parameters ω and d in the sine function.

3. The short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model according to claim 2 is characterized by: In step S6, the calculation formula of mean square error MSE is: The calculation formula for the mean absolute simulation percentage error MAPE is: The calculation formula for the root mean square percentage error RMSPE is: The calculation formula for the mean absolute error MAE is: The calculation formula of the correlation coefficient R is: Where cov(·) represents covariance and Var(·) represents variance.

4. The short-term traffic flow prediction method based on spatiotemporal data and fractional order cumulative partial grey model according to claim 3 is characterized by: In step S7, the model FPGM (1, M|sin) calculated in step S6 is compared with the indicators of the comparison models PGM (1, 3), ARIMA and LSTM models. If the above parameters meet the accuracy requirements, FPGM (1, M|sin) is used to predict the future development of traffic flow; if there are parameters that do not meet the accuracy requirements, return to step S1 to adjust the prediction model parameters again.

Images