Dynamic classification and prediction method of rail transit stations based on PDE and machine learning

Abstract

The present invention relates to the field of artificial intelligence classification technology, and specifically to a dynamic classification and prediction method for rail transit stations based on PDE and machine learning, comprising the following steps: S1: preprocessing the obtained NPRT index; S101: selecting node index and location index, and evaluating the comprehensive traffic value and location value of the station; S102: using information entropy weighting, and integrating the node index and location index into node value N and location value P respectively; S103: dividing the station by different clustering methods, and selecting the clustering model with the best performance as the final station division method; S104: predicting the passenger flow of each station by fitting method; S105: clustering analysis of the passenger flow of the station, and constructing a labeled data set; S2: introducing partial differential equations, establishing a PDE-NPRT model, and training the PDE-NPRT model. The present invention combines partial differential equations (PDE) with machine learning technology to improve the accuracy and reliability of traffic station classification.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence classification technology, and in particular to a rail transit station dynamic classification and prediction method based on PDE and machine learning. Background Art

[0002] Transit-oriented development (TOD) is an urban planning strategy that involves multifunctional, high-density development near public transportation hubs, which can effectively optimize land use, improve environmental conditions, and establish an efficient and reliable public transportation system.

[0003] As cities around the world grapple with rapid urbanization, congestion, and environmental degradation, the rail transit station classification (RTSC) model has become a powerful tool for urban planning and development. People usually use the rail transit station classification results to optimize land use, design transportation stations, plan transit development projects, and construct transportation networks. In other words, the accuracy of rail transit station classification has an important impact on TOD.

[0004] In order to improve the accuracy of rail transit station classification, existing technologies simulate the dynamics of transportation demand and supply by combining variables such as land use, population density and transportation network characteristics. For example, Ahad Amini Pishro et al. emphasized the importance of machine learning in rail transit classification and proposed the Node-Place-Passenger Flow-Time (NPRT) model for accurate station evaluation. Although it has improved the classification accuracy compared with the traditional RTSC model, it still has certain limitations in classification accuracy and reliability.

[0005] In summary, there is an urgent need for a NPRT model with high rail transit station classification accuracy and reliability. Summary of the invention

[0006] To solve the above problems, the present invention provides a rail transit station dynamic classification and prediction method based on PDE and machine learning, which is used to improve the classification accuracy and reliability of transportation stations, thereby realizing a detailed evaluation of station attributes.

[0007] In order to achieve the above object, the technical solution of the present invention is as follows: a rail transit station dynamic classification and prediction method based on PDE and machine learning, comprising the following steps:

[0008] S1: obtaining NPRT indicators and preprocessing the obtained NPRT indicators, wherein the NPRT indicators include node indicators, location indicators, passenger flow and time;

[0009] S101: Select node indicators and location indicators, and evaluate the comprehensive transportation value and location value of the station;

[0010] S102: using information entropy weighting, and integrating the node index and the position index into a node value N and a position value P respectively;

[0011] S103: using different clustering methods to divide sites based on the obtained NPRT index, and selecting the clustering model with the best performance as the final site division method;

[0012] S104: predicting the passenger flow of each station by a fitting method;

[0013] S105: By using different clustering methods and improving by adjusting hyperparameters and following the principles of clustering methods, cluster analysis is performed on the passenger flow of the station, and the clustering result with the best clustering effect is selected as the final clustering label to construct a labeled data set;

[0014] S2: Introduce partial differential equations to describe the changes in passenger flow in time and space in a continuous and dynamic way, and establish a PDE-NPRT model. Use a labeled data set to train the PDE-NPRT model, input the sites to be classified into the trained PDE-NPRT model, and output the site classification results.

[0015] Furthermore, it also includes S3: data analysis, which performs descriptive statistics on different passenger flow characteristics to understand the distribution and variability of passenger flow in different periods; calculates the minimum and maximum values ​​for each period to describe the range of observed passenger flow levels; calculates the mean as a central measure of the passenger flow distribution; and calculates the standard deviation to quantify the dispersion or variability of passenger flow levels within each time period.

[0016] Furthermore, it also includes S201: solving, equating the PDE-NPRT equation to a heat equation; assuming that the solution of the PDE-NPRT equation is expressed as the sum of a series of sine waves or cosine waves, solving each sine wave component separately, and simplifying the calculation by using the second-order derivative properties of sine waves and cosine waves; selecting the frequency according to the boundary conditions of the NPRT model, and adjusting the amplitude of each sine wave or cosine wave through the initial conditions and boundary conditions; superimposing the solutions of all sine wave or cosine wave components to form a complete solution to the PDE-NPRT equation.

[0017] Further, in S101, the node indicators include the number of entrances and exits of each subway station N1, the number of subway stations that a station can reach within 20 minutes N2, the first central business district N3, the second central business district N4, the distance from the first central business district N5, the distance from the second central business district N6, the degree centrality N7, and the proximity centrality N8; the location indicators include the average price of office land within a 1000m radius catchment area P1, the number of offices within a 1000m radius P2, the average price of commercial land within a 1000m radius catchment area P3, the number of stores within a 1000m radius P4, the average price of residential land within a 1000m radius catchment area P5, the number of residences within a 1000m radius P6, the number of public facilities within a 1000m radius catchment area P7, the number of parking lots within a 500m radius catchment area P8, and the number of bus stops within a 500m radius catchment area P9;

[0018] The N7 is measured by the number of chains connected to the station, as shown in the following formula: , where Indicates the station and another station The connection relationship between Representing a collection Total number of stations in;

[0019] The N8 is determined by the inverse sum of the shortest transit distances from the station to all other stations, as shown in the following formula: , where Indicates the station and another station The shortest distance between.

[0020] Furthermore, in the above 105, the clustering methods used include K-Means, AGNES, DBSCAN, and GMM, and are improved respectively; for K-Means and GMM, the number of clusters k is adjusted; for AGNES, the k value and the distance definition method are determined; for DBSCAN, the maximum neighborhood radius eps and the minimum number of samples within the radius min_samples are modified.

[0021] Further, in S201, the small change in passenger flow after a small change in time is expressed by the following formula: ;

[0022] The change in passenger flow after a small step in a node is expressed by the following formula: , where N is the node value, R is the passenger flow function, and T is the time.

[0023] Further, in S201, the passenger flow rate change rate per unit distance is expressed by the following formula: , where N is the node value and R is the passenger flow function.

[0024] Further, the heat equation is: , where is the proportional constant, T is the temperature, For time.

[0025] Further, the equation of the PDE-NPRT model is: , where N is the node value, P is the location value, R is the passenger flow function, and T is the time. is the proportionality constant.

[0026] Furthermore, the method further includes S202: optimizing the equation of the PDE-NPRT model, and expressing the optimized objective function as follows: In the formula, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period, N is the node value, P is the location value, R is the passenger flow function, and T is the time;

[0027] In the formula, express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express The theoretical passenger flow during this period, N is the node value, P is the position value, R is the passenger flow function, and T is time;

[0028] Then, all objective functions are minimized iteratively through the BFGS algorithm, and the minimum objective of the optimization model is integrated and compared with the mean square error (MSE) between the actual passenger flow and the theoretical passenger flow.

[0029] The above scheme has the following beneficial effects:

[0030] 1. This scheme combines partial differential equations (PDE) with machine learning technology to introduce a continuous and dynamic way to describe the changes in passenger flow in time and space, thereby improving the accuracy and reliability of traffic station classification. Traditional classification methods are often based on static data or simple time series analysis, which is difficult to capture complex spatiotemporal dynamics.

[0031] 2. This solution, by introducing NPRT indicators (node ​​indicators, location indicators, passenger flow, time), can more comprehensively evaluate the comprehensive traffic value and location value of the station, thereby achieving a detailed evaluation of the station attributes. This detailed evaluation helps to better understand the role and influence of different stations in the transportation network.

[0032] 3. In this solution, the established PDE-NPRT model significantly improves the prediction ability of the model by fitting and predicting the passenger flow in different time periods. At the same time, the model is iteratively optimized through optimization algorithms (such as BFGS), which further reduces the prediction error and makes the model more accurate and reliable in practical applications.

[0033] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of an embodiment of a method for dynamic classification and prediction of rail transit stations based on PDE and machine learning of the present invention;

[0035] Figure 2 A 1-norm distance distribution histogram between each two stations of an embodiment of a rail transit station dynamic classification and prediction method based on PDE and machine learning of the present invention;

[0036] Figure 3-Figure 6 It is an IT1 cluster scatter plot under the optimal model of an embodiment of a rail transit station dynamic classification and prediction method based on PDE and machine learning of the present invention;

[0037] Figure 7-Figure 14 This is a comparison chart between actual passenger flow and simulated passenger flow in an embodiment of the method for dynamic classification and prediction of rail transit stations based on PDE and machine learning of the present invention. DETAILED DESCRIPTION

[0038] The following is further described in detail through specific implementation methods:

[0039] Example: As shown in the attached Figure 1 -Attached Fig.14 As shown: A rail transit station dynamic classification and prediction method based on PDE and machine learning includes the following steps: S1: obtaining NPRT indicators and preprocessing the obtained NPRT indicators, wherein the NPRT indicators include node indicators, location indicators, passenger flow and time;

[0040] S101: Select node indicators and location indicators, and evaluate the comprehensive transportation value and location value of the station;

[0041] Specifically, this embodiment takes Chengdu subway transportation as an example, and evaluates the comprehensive transportation value of the station according to the facilities, nearby transportation options, accessibility to the destination and the importance of the network. Further, in S101, the node indicators include the number of entrances and exits of each subway station N1, the number of subway stations that a station can reach within 20 minutes N2, the first central business district N3, the second central business district N4, the distance from the first central business district N5, the distance from the second central business district N6, the degree centrality N7, and the near centrality N8; the location indicators include 100 The average price of office land within a 0m radius catchment area is P1, the number of offices within a 1000m radius is P2, the average price of commercial land within a 1000m radius catchment area is P3, the number of shops within a 1000m radius is P4, the average price of residential land within a 1000m radius catchment area is P5, the number of residential houses within a 1000m radius is P6, the number of public facilities within a 1000m radius catchment area is P7, the number of parking lots within a 500m radius catchment area is P8, the number of bus stops within a 500m radius catchment area is P9;

[0042] The N7 is measured by the number of chains connected to the station, as shown in the following formula: , in formula (1), Indicates the station and another station The connection relationship between Representing a collection Total number of stations in;

[0043] The N8 is determined by the inverse sum of the shortest transit distances from the station to all other stations, as shown in the following formula: , in formula (2), Indicates the station and another station The shortest distance between.

[0044] As shown in Table 1, facilities are measured by the number of entrances and exits of each subway station (N1). Transportation accessibility considers the number of subway stations that can be reached within a 20-minute travel time, the connection with Chunxi Road CBD (N3) and the connection with Tianfu Third Street CBD (N4). To reflect Chengdu's dual taxis, we calculated the number of stations and the distance to each CBD, with Chunxi Road represented by (N5) and Tianfu Third Street represented by (N6). Network centrality includes degree centrality (N7) and closeness centrality (N8). Graph modeling is used to utilize network centrality to evaluate the importance of stations within the transportation network; Chengdu's rail transit network can be represented by a graph as , where the vertices in V represent stations and the edges in E represent the connections between stations. The weight of the edge is determined by the rail transit travel distance. The degree centrality (N7) of a station v ∈ V in the Chengdu network is measured by the number of links connected to station v, as defined in Equation (1), where represents the connection between station v and another station t ∈ V, and K represents the total number of stations in set V. Closeness centrality represents the proximity and accessibility of nodes within a network component. The closeness centrality (N8) of station v is determined by the inverse of the sum of the shortest transportation distances from station v to all other stations in set V, as shown in Equation (2).

[0045] Table 1 Node location indicator

[0046]

[0047] S102: using information entropy weighting, and integrating the node index and the position index into a node value N and a position value P respectively;

[0048] Specifically, in order to enhance data analysis and establish indicators, the information entropy weighting method (IEW) is used to merge N1-N8 into node value N and P1-P9 into position value P. A lower information entropy means that the indicator is less important in providing information, and thus plays a weaker role in the comprehensive evaluation. Therefore, it should be assigned a lower weight. Therefore, information entropy can determine the weight of each indicator, taking N as an example. Similarly, the weight of P can also be determined. If there is Stations and Node indicators, get : In the formula Indicator On site The value at

[0049] right After normalization, the results are shown in Table 2, Table 3, and Table 4.

[0050] Table 2 Normalized node values

[0051]

[0052] Table 3 Normalized position values

[0053]

[0054] Table 4 Normalized comprehensive passenger flow-time value

[0055]

[0056] S103: using different clustering methods to divide sites based on the obtained NPRT index, and selecting the clustering model with the best performance as the final site division method;

[0057] Specifically, the selection and application of the clustering method in this embodiment:

[0058] K-Means: A prototype-based clustering algorithm that partitions data by minimizing the distance within clusters.

[0059] AGNES (Agglomerative Hierarchical Clustering): A hierarchical clustering algorithm that builds a hierarchy by progressively merging similar clusters.

[0060] DBSCAN: A density-based clustering algorithm that can identify clusters of arbitrary shapes and handle noise points.

[0061] GMM (Gaussian Mixture Model): A probabilistic clustering model that assumes that the data comes from a mixture of multiple Gaussian distributions.

[0062] These clustering methods are applied to the data of subway station sites, dividing the sites according to information such as node value, location value and passenger flow at different times.

[0063] Clustering performance evaluation can be divided into two categories:

[0064] External indicators

[0065] For the dataset , assuming that the clusters given by clustering are divided into C, and the clusters given by the reference model are divided into . and Represents C and When comparing samples pairwise, the number of unique pairs is expressed as .

[0066] : Indicates that in C and The number of pairs of samples with the same label.

[0067] : Indicates that the labels are the same in C but The number of pairs of samples with different labels.

[0068] : Indicates that the labels are different in C but in The number of pairs of samples with the same label.

[0069] : Indicates that in C and The number of pairs of samples whose labels are different.

[0070] Jaccard coefficient (JC): , the result range is To evaluate the consistency between the clustering results and the reference model, the larger the value, the better.

[0071] Rand Index (RI) and Adjusted Rand Index (ARI): RI measures the similarity between the clustering results and the reference model. ARI adjusts RI by considering the possibility of random clustering results. The larger the value, the more consistent the clustering results are with the actual situation.

[0072] Internal indicators

[0073] The clustering results are directly evaluated without relying on a reference model.

[0074] Sum of Squared Error (SSE): Measures the sum of squared distances from data points to cluster centers and is the optimization objective of K-Means.

[0075] Silhouette coefficient (SC): evaluates the compactness of samples within a cluster and the separation of samples between clusters. The closer the value is to 1, the better the clustering effect.

[0076] Calinski-Harabasz index (CH): reflects the ratio of inter-cluster distance to intra-cluster distance. The higher the value, the better the clustering effect, the clearer the clusters and the higher the separation.

[0077] S104: predicting the passenger flow of each station by a fitting method;

[0078] Specifically, in this embodiment, the passenger flow of Chengdu subway station is predicted by using multiple linear regression (MLR), deep neural network (DNN) and k-nearest neighbor (KNN) regression methods, and the performance of different models is evaluated;

[0079] Multiple Linear Regression (MLR): The regression coefficients are estimated using the least squares method to establish the linear relationship between the dependent variable (passenger flow) and multiple independent variables (node ​​and location indicators).

[0080] Deep Neural Network (DNN): Build a neural network with input layer, hidden layer and output layer. Train the network to fit the data and predict passenger flow by selecting appropriate activation functions (such as ReLU and LeakyReLU) and optimization algorithms (such as stochastic gradient descent).

[0081] k-Nearest Neighbor (KNN) regression: finds the k nearest neighbors of each sample and predicts the passenger flow of the sample based on the passenger flow of these neighbors.

[0082] The dataset is divided into a training set and a test set, where the training set is used to train the model and the test set is used to evaluate the performance of the model.

[0083] Specifically, eight datasets of IT1-IT4 and OT1-OT4 were fitted. 10% of each dataset was reserved for testing and 90% was used for training. The MSE on the test set was used to evaluate the effectiveness of the model.

[0084] However, the results are not completely satisfactory, especially regarding OT3; in order to gain a deeper understanding, the data distribution in this particular case is observed. Subsequently, the distance between the independent and dependent variables for the two stations is calculated using the following method:

[0085] After calculating the above distances between each pair of stations, we can draw a distribution histogram (independent variables: N1-N8, P1-P9), such as Figure 2 shown.

[0086] Histograms were created to show the distances between pairs of data for each time span (IT1 to OT4). These histograms were then used to analyze the data for each time span. In OT3, the distances between the variables were in the range [0.50, 0.55]. Overall, the passenger flows between stations were generally similar, although the passenger flows of some stations showed significant differences despite having similar independent variables. To improve the fitting accuracy, stations with closely matched independent variables but significantly different passenger flows were excluded. This process was repeated for each group, and the counts of stations that were removed in each case were determined. After removing some stations, the data were fit using MLR, DNN, and KNN. The method with the best fitting effect was then selected as the final fitting method.

[0087] S105: By using different clustering methods and improving by adjusting hyperparameters and following the principles of clustering methods, cluster analysis is performed on the passenger flow of the station, and the clustering result with the best clustering effect is selected as the final clustering label to construct a labeled data set;

[0088] Specifically, in this embodiment, four clustering methods (K-Means, AGNES, DBSCAN, GMM) are used to label the data, and the internal indicators Silhouette Coefficient (SC) and Karlinski-Harabas Index (CH) are used to evaluate the effectiveness of clustering. The passenger flow is divided into 8 groups according to the time span (T), named IT1-OT4. The process of each group is the same. Take IT1 as an example:

[0089] The clustering results can be optimized by adjusting the hyperparameters of the clustering algorithm (e.g., for K-Means and GMM, adjust the number of clusters (k); for AGNES, determine the appropriate k value and distance definition method; for DBSCAN, modify the maximum neighborhood radius (eps) and the minimum number of samples within the radius (min_samples)).

[0090] From Table 5 and Figure 3-Figure 6 It can be seen that the evaluation index shows that the K-Means model with k=3 obtains the best clustering result for the data during IT1. Therefore, this clustering result can be used as the label of the data.

[0091] Table 5 Results of internal indicators corresponding to the models selected by clustering methods

[0092]

[0093] S2: Introduce partial differential equations to describe the changes in passenger flow in time and space in a continuous and dynamic way, and establish a PDE-NPRT model. Use a labeled data set to train the PDE-NPRT model, input the sites to be classified into the trained PDE-NPRT model, and output the site classification results.

[0094] Specifically, the coordination between nodes, locations and integrated passenger flow time values ​​in the NPRT model is studied by using the comprehensive application of the partial differential equation (PDE) heat equation. It is explored how the rail transit classification will change with the changes in the integrated passenger flow-time, node and location, and the passenger flow distribution at each time point is examined, and the PDE-NPRT model is established.

[0095] Concepts such as the second-order derivative in the PDE model are used to describe the speed and trend of passenger flow changes and how these changes are affected by surrounding nodes and locations.

[0096] Then the training set in S104 is used to train the PDE-NPRT model. The equation of the PDE-NPRT model is: , where is the position value, is the node value, is the passenger flow function, For time, is a proportionality constant; this equation describes the relationship between the first-order derivative of a multivariate function R with respect to a variable T and the second-order partial derivative of the function with respect to the other two variables N and P, where Representation function In keeping and Under the condition of no change, about the variable The first partial derivative of ; Representation function The second-order partial derivative with respect to N while keeping other variables unchanged; Representation function Keeping other variables unchanged, The second-order partial derivative of .

[0097] This embodiment also includes S201: solving, equating the PDE-NPRT equation to a heat equation; assuming that the solution of the PDE-NPRT equation is expressed as the sum of a series of sine waves or cosine waves, solving each sine wave component separately, and simplifying the calculation by using the second-order derivative properties of sine waves and cosine waves; selecting a suitable frequency according to the boundary conditions of the NPRT model, and adjusting the amplitude of each sine wave or cosine wave through initial conditions and boundary conditions; superimposing the solutions of all sine wave or cosine wave components to form a complete solution to the PDE-NPRT equation.

[0098] Specifically, the heat equation is: , where is the proportionality constant, is the temperature, For time.

[0099] The heat equation describes the temperature change on a rod over time, i.e., the temperature changes as we move from one point to another. With respect to the interpretation of the heat equation, we can apply N, P, R, and T to study the coordination relationship between the NPRT values ​​in the three-dimensional PDE. There is a derivative with respect to the node value N, which represents the rate at which the passenger flow R changes as we move along N. This can be interpreted as the slope of the surface as we mesh along the N axis in small steps, and the resulting small change in R gives the ratio between R and N. In addition, there is a rate of change related to time T, which can be interpreted as the slope of the surface as we mesh along the T axis. Each of these derivatives can only tell part of the story of the change in the R function. Therefore, we can call them partial derivatives of the NPRT model. Equation (3) refers to the small change in passenger flow R after a small change in time T, while equation (4) represents the change in R after a small step in the node value N.

[0100] A small change in passenger flow R after a small change in time T:

[0101] Changes in passenger flow R after a small step at node N:

[0102] According to equation (5), the function R changes with time (T), namely , depends on how it changes with the number of nodes (N), i.e. . More specifically, it is proportional to the second-order partial derivative with respect to (N). The general PDE-NPRT function is applicable to objects of any dimension, which means that the input of the PDE-NPRT function will be more, as shown in Equation (6).

[0103]

[0104] Consider the heat flow on a rod with the center as the cold point and two adjacent points with higher temperatures on either side of the center point. The temperature of the center point will tend to approach the average of the temperatures of its adjacent points and heat up. The greater the temperature difference, the faster the heating rate. Similarly, if the value of the center point is higher than the other two side points and the rate is proportional to the difference, this process is also valid for the three points on the (N) axis, where the node value of the center point is lower than the other points. If the average node value of the two adjacent points is higher or lower, the passenger flow at the center point will increase or decrease accordingly. Equation (7) shows that the derivative of point R2 with respect to time (T) is proportional to this difference, the average of its adjacent points, and its own value. is the proportionality constant. To write this equation in a way that will ultimately account for the second-order derivative in the PDE-NPRT model, let us rearrange the right side of equation (7) as a function of the difference between R1 and R2 and the difference between R2 and R3, as shown in equation (8). A simple calculation shows that equations (7) and (8) are identical, where .

[0105]

[0106] Next, we can consider the difference of differences .if and The average values ​​of R1 and R3 are the same as R2. Therefore, R2 will not change. Greater than , that is, the difference of the differences is positive; the average of R1 and R3 is greater than R2, so R2 tends to increase. Similarly, if the difference of the differences is negative, that is Less than , it means that the average value of these adjacent points is less than R2. If the sign is compressed, The entire term is written as , or the second-order difference, describes how different R2 is from the average of its neighboring points. As a result, the rate of change of traffic at a point is proportional to the second-order difference of its surroundings:

[0107] Mode ,Mode Japanese style middle, , is the passenger flow of the central point among the three points, They are the passenger flow of the three points. For time.

[0108] As we move from this finite case to the infinite continuous case, the analogue of the second-order difference is the second-order derivative. In calculus, we are concerned with the rate of change of traffic per unit distance, rather than the absolute difference tending to zero. With respect to the two independent rates of change, N and T, it is necessary to consider how traffic changes over time and as we move along the node axis. The core intuition is the same as in the discrete case. To know how a point differs from its neighbors, it is necessary to find out how the rate of change itself changes, as shown in equation (10): Equation (10) is the second-order partial derivative of R with respect to another variable N, which gives a measure of the difference between a value and the average of its neighboring points. The PDE-NPRT equation represents a system of equations for each node, location, passenger flow, and time axis point. It includes second-order derivatives with respect to other spatial directions, and the sum of these second-order derivatives is called the Laplace operator , which measures the difference between a point and the average of its neighboring points.

[0109] because The value of is unknown. This embodiment uses actual data and an optimization method to determine ; Also includes S202: optimizing the equations of the PDE-NPRT model.

[0110] Specifically, yes Integrate and compare it with the actual data to obtain different The subway station operates from 6:00 am to 23:00 pm. The optimization objective function is expressed as follows: In the formula, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period; N is the node value, P is the position value, R is the passenger flow function, and T is the time;

[0111] In the formula, express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express Theoretical passenger flow during this period; N is the node value, P is the position value, R is the passenger flow function, and T is time;

[0112] In order to minimize these objective functions to ensure that the theoretical passenger flow closely matches the actual passenger flow. All objective functions are minimized iteratively through the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which is an iterative optimization method for solving unconstrained nonlinear problems. It belongs to the quasi-Newton method and aims to minimize functions without using derivatives. BFGS determines the search direction for each iteration by approximating the inverse Hessian matrix of the objective function. This approximation is iteratively updated through the gradient of the objective function, allowing BFGS to converge to the optimal solution efficiently.

[0113] The optimization iteration results are shown in Table 6:

[0114] Table 6 Optimization Performance

[0115]

[0116] The parameters for the number of passengers entering and leaving the station show similar trends over time. This similarity is because subway travel time is usually short and passengers tend to enter and exit the station at the same time. In addition, each model only needs 3 to 5 iterations to optimize the parameters. This higher solution efficiency significantly reduces the training time of the model compared to other machine learning models.

[0117] The minimum objective of the optimization model is integrated and compared with the mean square error (MSE) between the actual passenger flow and the theoretical passenger flow.

[0118] In addition, this embodiment also compares the actual passenger flow with the passenger flow simulated by partial differential equations (PDEs) using the data of each data group. Figure 7-Figure 14 As shown in the figure. This figure shows the consistent trend between the actual passenger flow and the simulated passenger flow. Many simulated data points are closely consistent with the actual data points, which shows the effectiveness of the model proposed in this scheme. By observing the figure, it can be found that the change trend of the actual passenger flow and the simulated passenger flow is consistent, and many simulated data points are very close to the actual data points, which also shows that the model proposed in this scheme is reasonable.

[0119] This embodiment also includes S3: data analysis, performing descriptive statistics on different passenger flow characteristics to understand the distribution and variability of passenger flow in different periods; calculating the minimum and maximum values ​​of each period to describe the range of observed passenger flow levels; calculating the mean value as a central measure of the passenger flow distribution; calculating the standard deviation to quantify the dispersion or variability of the passenger flow level in each time period.

[0120] Specifically, detailed descriptive statistical analysis was conducted on the passenger flow data of different time periods, including minimum, maximum, average, standard deviation and coefficient of variation (CV). These statistics help researchers gain a deeper understanding of the distribution characteristics, average level, variability and dispersion of passenger flow in each time period.

[0121] By comparing the statistics of different time periods, we can identify the similarities and differences in passenger flow in different periods, and then analyze the factors that affect the changes in passenger flow.

[0122] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. A dynamic classification and prediction method for rail transit stations based on PDE and machine learning, characterized in that: The following steps are involved: S1: obtaining NPRT indicators and preprocessing the obtained NPRT indicators, wherein the NPRT indicators include node indicators, location indicators, passenger flow and time; S101: Select node indicators and location indicators, and evaluate the comprehensive transportation value and location value of the station; S102: using information entropy weighting, and integrating the node index and the position index into a node value N and a position value P respectively; S103: using different clustering methods to divide sites based on the obtained NPRT index, and selecting the clustering model with the best performance as the final site division method; S104: predicting the passenger flow of each station by a fitting method; S105: By using different clustering methods and improving by adjusting hyperparameters and following the principles of clustering methods, cluster analysis is performed on the passenger flow of the station, and the clustering result with the best clustering effect is selected as the final clustering label to construct a labeled data set; S2: Introduce partial differential equations to describe the changes in passenger flow in time and space in a continuous and dynamic way, and establish a PDE-NPRT model. Use a labeled data set to train the PDE-NPRT model, input the site to be classified into the trained PDE-NPRT model, and output the site classification result; the equation of the PDE-NPRT model is: , where N is the node value, P is the location value, R is the passenger flow function, and T is the time. is the proportionality constant.

2. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 1 is characterized in that: It also includes S201: solving, equating the PDE-NPRT equation to a heat equation; assuming that the solution of the PDE-NPRT equation is expressed as the sum of a series of sine waves or cosine waves, solving each sine wave component separately, and simplifying the calculation by using the second-order derivative properties of sine waves and cosine waves; selecting the frequency according to the boundary conditions of the NPRT model, and adjusting the amplitude of each sine wave or cosine wave through initial conditions and boundary conditions; superimposing the solutions of all sine wave or cosine wave components to form a complete solution to the PDE-NPRT equation.

3. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 2 is characterized in that: It also includes S3: Data Analysis, which performs descriptive statistics on different passenger flow characteristics to understand the distribution and variability of passenger flow in different periods; calculates the minimum and maximum values ​​for each period to describe the range of observed passenger flow levels; Calculate the mean as a central measure of the traffic distribution; Calculate the standard deviation to quantify the dispersion or variability of foot traffic levels within each time period.

4. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 3 is characterized in that: In S101, the node indicators include the number of entrances and exits of each subway station N1, the number of subway stations that a station can reach within 20 minutes N2, the first central business district N3, the second central business district N4, the distance from the first central business district N5, the distance from the second central business district N6, the degree centrality N7, and the near centrality N8; the location indicators include the average price of office land within a 1000m radius catchment area P1, the number of offices within a 1000m radius P2, the average price of commercial land within a 1000m radius catchment area P3, the number of stores within a 1000m radius P4, the average price of residential land within a 1000m radius catchment area P5, the number of residences within a 1000m radius P6, the number of public facilities within a 1000m radius catchment area P7, the number of parking lots within a 500m radius catchment area P8, and the number of bus stops within a 500m radius catchment area P9; The N7 is measured by the number of chains connected to the station, as shown in the following formula: , where Indicates the station and another station The connection relationship between Representing a collection Total number of stations in; The N8 is determined by the inverse sum of the shortest transit distances from the station to all other stations, as shown in the following formula: , where Indicates the station and another station The shortest distance between.

5. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 4 is characterized in that: In the above 105, the clustering methods used include K-Means, AGNES, DBSCAN, and GMM, and are improved respectively; for K-Means and GMM, the number of clusters k is adjusted; for AGNES, the k value and the distance definition method are determined; for DBSCAN, the maximum neighborhood radius eps and the minimum number of samples min_samples within the radius are modified.

6. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 5 is characterized in that: In S201, the small change in passenger flow after a small change in time is expressed by the following formula: ； The change in passenger flow after a small step in a node is expressed by the following formula: , where N is the node value, R is the passenger flow function, and T is the time.

7. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 6 is characterized in that: In S201, the passenger flow rate change rate per unit distance is expressed by the following formula: , where N is the node value and R is the passenger flow function.

8. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 7 is characterized in that: The heat equation is: , where is the proportionality constant, is the temperature, For time.

9. The method for dynamic classification and prediction of rail transit stations based on PDE and machine learning according to claim 8, characterized in that: The process also includes S202: optimizing the equations of the PDE-NPRT model, and expressing the optimized objective function as follows: In the formula, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period, express The actual passenger flow during this period, is the node value, is the position value, is the passenger flow function, For time; In the formula, The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is express The theoretical passenger flow during this period is is the node value, is the position value, is the passenger flow function, For time; Then, all objective functions are minimized iteratively through the BFGS algorithm, and the minimum objective of the optimization model is integrated and compared with the mean square error (MSE) between the actual passenger flow and the theoretical passenger flow.

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