Short-time traffic flow grey prediction method
By introducing first-order continuous medium equations and matrix sequences into the short-term traffic flow prediction model, combining gray difference information and partial differential equations, a multivariable gray prediction model is established, which solves the existing model's problem of processing complex traffic flow data. Inadequate, the prediction accuracy and stability are improved, and are suitable for short-term traffic flow prediction of intelligent transportation systems.
Patent Information
- Application Number
- CN202411122076.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-15
- Publication Date
- 2024-12-10
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The existing short-term traffic flow prediction model has problems that it is difficult to train data, difficult to understand the model and strong data dependence when processing complex multivariate traffic flow data, and the existing gray prediction model fails to effectively consider the traffic flow system. Multidimensionality of time and space leads to poor prediction results.
By introducing first-order continuous medium equations, using matrix sequences instead of point sequences, a short-term traffic flow partial gray prediction model is established, combining gray difference information and partial differential equations, a multivariable gray prediction model is constructed, taking into account the spatiotemporal characteristics of traffic flow data. , improve prediction accuracy.
It improves the stability and prediction accuracy of the model, broadens the scope of application of the gray prediction model, can effectively predict the development trend of short-term traffic flow, and demonstrates good stability and fitting effects, providing reliable traffic management information.
Smart Images
Figure CN119107797A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of traffic flow prediction and relates to a short-term traffic flow partial grey prediction method. Background Art
[0002] Intelligent Transportation System (ITS) has become a revolutionary force in the rapidly developing environment of modern transportation and is considered to be a system that can effectively alleviate urban traffic congestion. Short-term traffic flow prediction has always been an integral part of most intelligent transportation system research and applications. However, due to the increasing complexity of data and big data, as well as the randomness and dynamics of traffic conditions, short-term traffic flow prediction is very challenging. Accurate short-term traffic flow prediction can not only improve traffic management efficiency and traveler experience, but also promote the development of ITS and reduce the negative impact of emergencies. Therefore, how to improve the accuracy of short-term traffic flow prediction is crucial for ITS to help manage and reduce traffic congestion.
[0003] Existing traffic flow prediction models have achieved good results in actual road data applications. Summarizing and analyzing the currently proposed traffic flow prediction models, they can be roughly divided into statistical models, machine learning models, deep learning models, gray prediction models, etc. Statistical models perform statistical analysis on a large amount of historical traffic data, extract potential correlation patterns and features, and then predict future traffic flow information. Before the rise of artificial intelligence, traffic flow prediction methods have gradually shifted from traditional statistical models to computational intelligence, among which machine learning (ML) technology is more prominent. Compared with statistical models, it is better at processing multivariate data and capturing complex data relationships. With the exponential growth of traffic data volume and computing power, deep learning (DNN) has also been widely used in short-term traffic prediction in recent years.
[0004] Short-term traffic flow has the characteristics of randomness, nonlinearity, periodicity, uncertainty, etc. Statistical models, machine learning and its deep learning methods may have problems such as difficulty in training data, difficulty in understanding models and strong data dependence when predicting short-term traffic flow. Grey prediction models can solve the uncertainty problem caused by low data quality, but the existing grey prediction models basically use a single time series as input variable. Since traffic flow data has spatiotemporal multidimensionality, a single sequence input will affect the effect of the grey prediction model. The partial grey prediction model introduces matrix sequences as input objects to improve the applicability of the grey prediction model in traffic flow data. However, the partial grey prediction model is basically single variable and does not take into account other parameters in the traffic flow system. Faced with complex and changeable traffic flow data, it is not practical for short-term traffic flow prediction under intelligent systems. Summary of the invention
[0005] In view of this, the purpose of the present invention is to dynamically analyze the relationship between flow and speed, introduce the relationship between traffic flow and speed into the first-order continuous medium equation, replace the point sequence with a matrix sequence and establish a corresponding partial differential equation model based on the matrix sequence. Through the difference information between differential and difference, a short-term traffic flow partial gray prediction method is proposed to improve the prediction accuracy of the model and apply the new model to short-term traffic flow simulation and prediction.
[0006] In order to achieve the above object, the present invention provides the following technical solutions:
[0007] A short-term traffic flow partial grey prediction method comprises the following steps:
[0008] S1: Input the traffic volume q passing through a road segment (0) and speed u (0) The original matrix sequence of ;
[0009] S2: Process the original matrix sequence and calculate the first-order cumulative generation sequence q (1) and u (1) , calculate the first-order cumulative sequence q (1) The partial derivative of
[0010] S3: Constructing short-term traffic flow partial grey prediction model TFDMPGM(1,2) r , and construct matrices B and Y, and calculate the parameter estimation vector The value of
[0011] S4: Calculate simulated and predicted values
[0012] S5: The prediction effect is tested by the mean absolute percentage error MAPE;
[0013] S6: If the simulation result passes the error test, the iterative recursive method is used to predict the future trend, otherwise it returns to step S1.
[0014] Furthermore, the traffic volume passing through a road section in step S1 is q (0) , speed is u (0) They are all n m×m matrices, expressed as follows:
[0015] q (0) =(q (0) (1),q (0) (2),...,q (0) (n))
[0016] u (0) =(u (0) (1),u (0) (2),...,u (0) (n))
[0017] in
[0018]
[0019]
[0020] where k = 1, 2, ..., n, is the matrix q (0) (k) is the i-th row and j-th column, is the matrix u (0) (k) is the i-th row and j-th column.
[0021] Further, the step S2 includes the following contents:
[0022] Let q (1) (k) is the original sequence q (0) (k) is a cumulative generation sequence, let
[0023] q (1) =(q (1) (1),q (1) (2),...,q (1) (n))
[0024] in
[0025]
[0026] is the matrix q (1) (k) is the i-th row and j-th column, i, j = 1, 2, ..., m, k = 1, 2, ..., n; let u (1) (k) is the original sequence u (0) (k) is a cumulative generation sequence, let
[0027] u (1) =(u (1) (1),u (1) (2),...,u (1) (n))
[0028] in
[0029]
[0030] is the matrix u (1) (k) is the i-th row and j-th column;
[0031] make and Yes (1)(k) The partial derivative matrix sequence in the horizontal and vertical directions is
[0032]
[0033]
[0034] in yes The i-th row and j-th column of yes The i-th row and j-th column of .
[0035] Further, step S3 specifically includes the following steps:
[0036] Constructing short-term traffic flow partial grey prediction model TFDMPGM(1,2) r for:
[0037] q (0) (k)+k1u (0) (k)+k2q (1) (k)q x (1) (k)+k3q (1) (k)q y (1) (k) = u (1) (k)(a r u (1)r (k)+a r-1 u (1)r-1 (k)
[0038] The subscript r represents the highest degree of the polynomial g(x,t), k1, k2, k3, a r ,a r-1 ,…a1,a0 are parameter estimation variables, μ is an m×m-order constant matrix:
[0039]
[0040] TFDMPGM(1,2) r The whitened partial differential equation of the model is:
[0041]
[0042] TFDMPGM(1,2) r The least squares estimated parameter vector of the model:
[0043]
[0044] satisfy
[0045]
[0046] Where B is m 2 n×(r+4+n 2 )-order matrix, Y is m 2 An n×1 matrix:
[0047]
[0048]
[0049] In matrix B, They are q (1) (k),u (0) (k) is in the i-th row and j-th column of the matrix Y, is the matrix q (0) (k) is the i-th row and j-th column.
[0050] Further, in step S4, according to TFDMPGM(1,2) r The time response series of the model, the simulation and prediction matrix series, and the simulated and predicted values
[0051]
[0052] The beneficial effects of the present invention are:
[0053] 1. Starting from the first-order continuous medium equation in traffic flow dynamics, the dynamic relationship between traffic flow and speed is explored, the spatiotemporal characteristics of traffic flow data are considered, and a new dynamic partial differential equation for traffic flow and speed is established. This equation not only fully captures the details and characteristics of the data, but also gives it structural advantages and improves the stability of the model.
[0054] 2. Starting from the modeling mechanism of the grey prediction model, combining the characteristics of grey difference information and partial differential equations, a new multivariate partial grey prediction model of the relationship between traffic flow and speed variables is established. This model takes into account the spatiotemporal characteristics of traffic flow data, improves the prediction accuracy of the model, and broadens the structure and scope of application of the grey prediction model.
[0055] 3. From the application of the model, traffic flow data has periodicity and spatiotemporal characteristics, and the new model is applied to the short-term traffic flow prediction of highways. Through four cases and six comparative models, the data with weekly and daily periods are selected to illustrate the effectiveness of the model. The fitting results show that the new model can effectively predict the development trend of short-term traffic flow, and the model shows good stability, which can provide reliable and useful information for traffic management.
[0056] 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
[0057] 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:
[0058] Figure 1 It is a flow chart of steps of a short-term traffic flow partial grey prediction method;
[0059] Figure 2 This is a diagram for testing the effectiveness of the model of the present invention;
[0060] Figure 3 This is a trend chart of traffic flow prediction by the model of the present invention. DETAILED DESCRIPTION
[0061] 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.
[0062] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.
[0063] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.
[0064] Figure 1 The figure is a flow chart of the steps of a short-term traffic flow partial grey prediction method.
[0065] Assume that the traffic volume passing through a road section is q (0) , speed is u (0) are all n m×m matrices, let
[0066] q (0) =(q (0) (1),q (0) (2),...,q (0) (n)) (1)
[0067] u (0) =(u (0) (1),u (0) (2),...,u (0) (n)) (2)
[0068] in
[0069]
[0070]
[0071] in is the matrix q (0) (k) is the i-th row and j-th column, is the matrix u (0) (k) is the i-th row and j-th column.
[0072] Let q (1) (k) is the original sequence q (0) (k) is a cumulative generation sequence, let
[0073] q (1) =(q (1) (1),q (1) (2),...,q (1) (n)) (3)
[0074] in
[0075]
[0076] is the matrix q (1) (k) is the i-th row and j-th column. (1) (k) is the original sequence u (0) (k) is the cumulative generated sequence,
[0077] u (1) =(u (1) (1),u (1) (2),...,u (1) (n)) (4)
[0078] in
[0079]
[0080] is the matrix u (1) (k) is the i-th row and j-th column. and Yes (1) (k) The partial derivative matrix sequence in the horizontal and vertical directions is
[0081]
[0082]
[0083] in yes The i-th row and j-th column of
[0084] yes The i-th row and j-th column of .
[0085] The following are the relevant properties of the matrix sequence, which satisfies the following four conditions:
[0086] (1)
[0087] (2)
[0088] (3)
[0089] (4)
[0090] Q (0) (k)+k1u (0) (k)+k2q (1) (k)q x (1) (k)+k3q (1) (k)q y (1) (k) = u (1) (k)(a r u (1)r (k)+a r- 1u (1)r-1 (k)+…+a1u (1) (k)+a0)+μ.(k=1,2,…n) (5)
[0091] It is a short-term traffic flow partial grey prediction model, referred to as (TFDMPGM(1,2) r ), the subscript r represents the highest degree of the polynomial g(x,t).r ,a r-1 ,…a1,a0 are parameter estimation variables, μ is an m×m-order constant matrix:
[0092]
[0093]
[0094] is the whitened partial differential equation of the model.
[0095] The following theorem gives TFDMPGM(1,2) r The parameter estimates of the model are given by Theorem 1
[0096] Theorem 1: TFDMPGM(1,2) r The least squares estimated parameter vector of the model
[0097]
[0098] satisfy
[0099]
[0100] Where B is m 2 n×(r+4+n 2 )-order matrix, Y is m 2 n×1 matrix
[0101]
[0102]
[0103] In matrix B, They are u (0) (k) is in the i-th row and j-th column of the matrix Y, is the matrix q (0) (k) is the i-th row and j-th column.
[0104] The following theorem gives TFDMPGM(1,2) r The time response of the model
[0105] Theorem 2: TFDMPGM(1,2) r The time response sequence of the model is as follows:
[0106]
[0107] According to TFDMPGM(1,2) r Model the time response sequence and can simulate and predict matrix sequences.
[0108] Figure 2 The model of the present invention is applied to the British roads for testing, and compared with the value of the index MAPE, some results are shown in Table 1. The model error diagram and trend diagram are also drawn, as shown in Figure 2 shown.
[0109] Table 1
[0110]
[0111] It can be seen from Table 1 that the MAPE of the simulated values of the eight data sets are all below 5%. According to the MAPE values, it can be seen that the simulation accuracy of the model is high. Figure 2 The bar chart and box plot distribution of MAPE also show that TFDMPGM(1,2) r The errors of the model are relatively concentrated and the values are not large, which shows that the fitting effect of the new model is good. Figure 2 The line graph of the period from 6:14 to 12:14 from January 30 to February 3 shows more intuitively that the data fitted by TFDMPGM(1,2)3 is basically consistent with the real data, showing good fitting effect and stability. This method can better capture the changing trends and characteristics of traffic flow data, enrich the existing grey system theory, expand the research object of the grey prediction model, and can accurately predict traffic flow in real time.
[0112] Figure 3 The traffic flow from 7:59 to 13:59 on February 13 is predicted by using the short-term traffic flow partial gray prediction method proposed by the present invention. In order to more intuitively represent the predicted traffic flow trend, a traffic flow trend graph is produced.
[0113] From the prediction results, we can see that the original data shows obvious periodicity, and the data of each period is presented as a matrix. From the trend of the broken line, the trend of the predicted data is basically consistent with the actual data. In the early period of 7:59-13:59 on February 6, 7, 8, 9, and 10, when the traffic volume reached its peak, the predicted data also reached its peak, and then fluctuated around a certain traffic volume value, which shows that the prediction results of the model are effective.
[0114] Due to the traffic congestion during peak hours, travelers are advised to choose different roads and travel during different peak hours to avoid traffic congestion and other problems. Traffic management departments can refer to the predicted traffic flow results to improve the operating efficiency and management level of the system, ensure traffic safety, and serve the public's efficient and smooth travel and economic sustainable development. TFDMPGM (1,2) r The model can effectively capture the changing trends and characteristics of traffic flow data and is therefore suitable for traffic flow prediction.
[0115] In the above embodiments, the description's reference to "this embodiment" indicates that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily all refer to the same embodiment.
[0116] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.
[0117] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, any one of the methods in this embodiment is implemented.
[0118] This embodiment also provides an electronic terminal, including: a processor and a memory;
[0119] The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the terminal executes any one of the methods in this embodiment.
[0120] The computer-readable storage medium in this embodiment can be understood by ordinary technicians in this field: all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.
[0121] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication with each other. The memory is used to store computer programs, the communication interface is used to communicate, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes each step of the above method.
[0122] In this embodiment, the memory may include a random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.
[0123] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.
[0124] The present invention can be used in many general or special computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like.
[0125] The present invention may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media, including storage devices.
[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 partial grey prediction method, characterized by: The following steps are involved: S1: Input the traffic volume q passing through a road segment (0) and speed u (0) The original matrix sequence of ; S2: Process the original matrix sequence and calculate the first-order cumulative generation sequence q (1) and u (1) , calculate the first-order cumulative sequence q (1) The partial derivative of S3: Constructing short-term traffic flow partial grey prediction model TFDMPGM(1,2) r , and construct matrices B and Y, and calculate the parameter estimation vector The value of S4: Calculate simulated and predicted values S5: The prediction effect is tested by the mean absolute percentage error MAPE; S6: If the simulation result passes the error test, the iterative recursive method is used to predict the future trend, otherwise it returns to step S1.
2. The short-term traffic flow gray prediction method according to claim 1 is characterized by: The traffic volume passing through a road section in step S1 is q (0) , speed is u (0) They are all n m×m matrices, expressed as follows: q (0) =(q (0) (1),q (0) (2),...,q (0) (n)) u (0) =(u (0) (1),u (0) (2),...,u (0) (n)) in where k = 1, 2, ..., n, is the matrix q (0) (k) is the i-th row and j-th column, is the matrix u (0) (k) is the i-th row and j-th column.
3. The short-term traffic flow gray prediction method according to claim 1 is characterized by: The step S2 includes the following contents: Let q (1) (k) is the original sequence q (0) (k) is a cumulative sequence generated by q (1) =(q (1) (1),q (1) (2),...,q (1) (n)) in is the matrix q (1) (k) is the i-th row and j-th column, i, j = 1, 2, ..., m, k = 1, 2, ..., n; Let u (1) (k) is the original sequence u (0) (k) is a cumulative sequence generated by u (1) =(u (1) (1),u (1) (2),...,u (1) (n)) in is the matrix u (1) (k) is the i-th row and j-th column; make and Yes (1) (k) The partial derivative matrix sequence in the horizontal and vertical directions is in yes The i-th row and j-th column of yes The i-th row and j-th column of .
4. The short-term traffic flow gray prediction method according to claim 1 is characterized by: Step S3 specifically includes the following steps: Constructing short-term traffic flow partial grey prediction model TFDMPGM(1,2) r for: q (0) (k)+k1u (0) (k)+k2q (1) (k)q x (1) (k)+k3q (1) (k)q y (1) (k)=u (1) (k)(a r u (1)r (k)+a r-1 u (1)r-1 (k) The subscript r represents the highest degree of the polynomial g(x,t), k1, k2, k3, a r ,a r-1 ,…a1,a0 are parameter estimation variables, μ is an m×m-order constant matrix: TFDMPGM(1,2) r The whitened partial differential equation of the model is: TFDMPGM(1,2) r The least squares estimated parameter vector of the model: satisfy Where B is m 2 n×(r+4+n 2 )-order matrix, Y is m 2 An n×1 matrix: In matrix B, They are u (0) (k) is in the i-th row and j-th column in the matrix Y, is the matrix q (0) (k) is the i-th row and j-th column.
5. The short-term traffic flow gray prediction method according to claim 1 is characterized by: In step S4, according to TFDMPGM(1,2) r The time response series of the model, the simulation and prediction matrix series, and the simulated and predicted values