Train delay prediction method and device and storage medium

Abstract

The present disclosure relates to a train delay prediction method, device and storage medium. The method comprises: determining an initial railway network graph at a current time, wherein the nodes in the railway network graph comprise one or more of train nodes, station nodes and disturbance event nodes, and the edges in the railway network graph and the adjacency matrix corresponding to the edges are used to represent the interaction relationship between the nodes; inputting the initial railway network graph at the current time into a railway network delay evolution prediction model, and determining a train delay prediction result after a preset time interval based on the features of the nodes, the features of the edges and the initial adjacency matrix corresponding to the edges in the initial railway network graph. According to the embodiments of the present disclosure, the train delay prediction is realized in a prediction range-oriented manner, and the interaction relationship of the trains in the delay evolution process can be revealed, so that the explainability and accuracy of the delay evolution prediction can be coordinated.

Description

Technical Field

[0001] This disclosure relates to the field of artificial intelligence technology, and in particular to a method, apparatus and storage medium for predicting train delays. Background Technology

[0002] Accurate delay forecasting is a crucial component of railway operations management. Accurate forecasting estimates the potential impact of delays at the operational level, providing decision support for real-time adjustments to delayed trains. Simultaneously, understanding the intricate interactions between various factors during the evolution of delays is essential for tactical timetable development, helping to optimize the tactical allocation of redundant time in the timetable plan.

[0003] Current train delay prediction schemes struggle to balance interpretability and accuracy. Schemes emphasizing interpretability often rely on Markov properties such as Markov chains and Bayesian networks, or are built on overly simplistic models, which tend to exhibit relatively poor predictive performance. Conversely, schemes prioritizing prediction accuracy typically employ machine learning techniques; however, these schemes often treat the delay evolution process as a black box, failing to elucidate the specific mechanisms by which various influencing factors lead to delay propagation. Therefore, a train delay prediction method that combines accuracy and interpretability is urgently needed. Summary of the Invention

[0004] In view of this, this disclosure proposes a method, apparatus and storage medium for predicting train delays.

[0005] According to one aspect of this disclosure, a method for predicting train delays is provided. The method includes:

[0006] Determine the initial railway network graph at the current moment. The nodes in the railway network graph include one or more of the following: train nodes, station nodes, and interference event nodes. The edges in the railway network graph and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between the nodes.

[0007] The initial railway network diagram at the current moment is input into the railway network delay evolution prediction model. Based on the characteristics of the nodes and edges in the initial railway network diagram, as well as the initial adjacency matrix corresponding to the edges, the train delay prediction result after a preset time interval is determined.

[0008] In one possible implementation, the initial railway network graph at the current moment is input into the railway network delay evolution prediction model. Based on the characteristics of nodes and edges in the initial railway network graph, as well as the initial adjacency matrix corresponding to the edges, the train delay prediction results after a preset time interval are determined, including:

[0009] Based on the characteristics of train nodes in the initial railway network graph, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0010] Replace the adjacency matrix corresponding to the edge between train nodes in the initial adjacency matrix of the initial railway network graph with the updated adjacency matrix corresponding to the edge between train nodes to determine the updated railway network graph.

[0011] Based on the updated railway network map, the predicted train delays are determined after a preset time interval.

[0012] In one possible implementation, based on the characteristics of train nodes in the initial railway network graph, the adjacency matrix corresponding to the edges between updated train nodes is determined, including:

[0013] Feature extraction is performed on the features of train nodes in the initial railway network diagram to determine the first train node embedding corresponding to the train node.

[0014] Based on the first train node embedding, determine the first edge embedding corresponding to the edge between train nodes;

[0015] The embedding of the second train node is determined based on the embedding of the first edge;

[0016] Determine the second edge embedding based on the second train node embedding;

[0017] Based on the second edge embedding, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0018] In one possible implementation, based on the updated railway network map, the predicted train delays after a preset time interval are determined, including:

[0019] Based on the preset continuous distribution, the adjacency matrix corresponding to the edges between the updated train nodes is normalized to obtain a representation that conforms to the preset continuous distribution.

[0020] Based on the representation that conforms to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, the train delay prediction results after the preset time interval are determined.

[0021] In one possible implementation, based on a representation conforming to a preset continuous distribution, and the characteristics of nodes and edges in the updated railway network graph, the train delay prediction result after a preset time interval is determined, including:

[0022] Based on the representation that conforms to the preset continuous distribution, the third edge embedding is determined. The third edge embedding is used to indicate whether there is a connection between train nodes.

[0023] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the train nodes in the updated railway network graph are aggregated with other nodes to determine the features of the updated train nodes.

[0024] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the station nodes in the updated railway network graph are aggregated to determine the features of the updated station nodes.

[0025] Based on the third edge embedding, the features of the updated train node, the features of the updated station node, the features of the interference event node in the updated railway network graph, and the features of the edges, the features of the target train node are determined.

[0026] Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the train delay prediction results are determined after a preset time interval.

[0027] In one possible implementation, the characteristics of a train node include any one or more of the following: the train's delay time at the current moment, the time interval between the current and previous train nodes, the minimum running time of the train within a preset time interval, the planned running time of the train within a preset time interval, and the occurrence time of the most recent event before the current moment.

[0028] The characteristics of a station node include the number of arriving and departing tracks in the station;

[0029] The characteristics of the interference event node include the vectorized interference event.

[0030] In one possible implementation, the edge features include the features of the edges between station nodes and train nodes, as well as the features of the edges between station nodes. The features of the edges between station nodes and train nodes include the planned arrival / departure time of the train from the current time to the station, and the features of the edges between station nodes include the shortest travel time between stations.

[0031] In one possible implementation, the railway network delay evolution prediction model includes an encoder, a latent space, and a decoder. The encoder is used to determine the adjacency matrix corresponding to the edges between train nodes after the update. The latent space is used to determine the representation that conforms to a preset continuous distribution. The decoder is used to determine the train delay prediction result after a preset time interval.

[0032] In one possible implementation, the railway network delay evolution prediction model is a trained railway network delay evolution prediction model, and the method further includes:

[0033] Input historical railway network map sample data into the initial railway network delay evolution prediction model to obtain the predicted train delay results;

[0034] The value of the loss function is calculated based on the predicted train delay results;

[0035] The initial railway network delay evolution prediction model is trained based on the loss function value to obtain the trained railway network delay evolution prediction model.

[0036] In one possible implementation, the loss function includes a divergence component and a reconstruction component. The divergence component is determined based on the encoder output of the initial railway network delay evolution prediction model, while the reconstruction component is determined based on the decoder output of the initial railway network delay evolution prediction model and the label data corresponding to the historical railway network map sample data. The label data is used to represent the actual train delay prediction results.

[0037] According to another aspect of this disclosure, a train delay prediction device is provided. The device includes:

[0038] The first determining module is used to determine the initial railway network graph at the current time. The nodes in the railway network graph include one or more of train nodes, station nodes, and interference event nodes. The edges in the railway network graph and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between the nodes.

[0039] The second determining module is used to input the initial railway network map at the current time into the railway network delay evolution prediction model, and determine the train delay prediction result after a preset time interval based on the characteristics of the nodes, the characteristics of the edges, and the initial adjacency matrix corresponding to the edges in the initial railway network map.

[0040] In one possible implementation, the second determining module is used for:

[0041] Based on the characteristics of train nodes in the initial railway network graph, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0042] Replace the adjacency matrix corresponding to the edge between train nodes in the initial adjacency matrix of the initial railway network graph with the updated adjacency matrix corresponding to the edge between train nodes to determine the updated railway network graph.

[0043] Based on the updated railway network map, the predicted train delays are determined after a preset time interval.

[0044] In one possible implementation, based on the characteristics of train nodes in the initial railway network graph, the adjacency matrix corresponding to the edges between updated train nodes is determined, including:

[0045] Feature extraction is performed on the features of train nodes in the initial railway network diagram to determine the first train node embedding corresponding to the train node.

[0046] Based on the first train node embedding, determine the first edge embedding corresponding to the edge between train nodes;

[0047] The embedding of the second train node is determined based on the embedding of the first edge;

[0048] Determine the second edge embedding based on the second train node embedding;

[0049] Based on the second edge embedding, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0050] In one possible implementation, based on the updated railway network map, the predicted train delays after a preset time interval are determined, including:

[0051] Based on the preset continuous distribution, the adjacency matrix corresponding to the edges between the updated train nodes is normalized to obtain a representation that conforms to the preset continuous distribution.

[0052] Based on the representation that conforms to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, the train delay prediction results after the preset time interval are determined.

[0053] In one possible implementation, based on a representation conforming to a preset continuous distribution, and the characteristics of nodes and edges in the updated railway network graph, the train delay prediction result after a preset time interval is determined, including:

[0054] Based on the representation that conforms to the preset continuous distribution, the third edge embedding is determined. The third edge embedding is used to indicate whether there is a connection between train nodes.

[0055] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the train nodes in the updated railway network graph are aggregated with other nodes to determine the features of the updated train nodes.

[0056] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the station nodes in the updated railway network graph are aggregated to determine the features of the updated station nodes.

[0057] Based on the third edge embedding, the features of the updated train node, the features of the updated station node, the features of the interference event node in the updated railway network graph, and the features of the edges, the features of the target train node are determined.

[0058] Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the train delay prediction results are determined after a preset time interval.

[0059] In one possible implementation, the characteristics of a train node include any one or more of the following: the train's delay time at the current moment, the time interval between the current and previous train nodes, the minimum running time of the train within a preset time interval, the planned running time of the train within a preset time interval, and the occurrence time of the most recent event before the current moment.

[0060] The characteristics of a station node include the number of arriving and departing tracks in the station;

[0061] The characteristics of the interference event node include the vectorized interference event.

[0062] In one possible implementation, the edge features include the features of the edges between station nodes and train nodes, as well as the features of the edges between station nodes. The features of the edges between station nodes and train nodes include the planned arrival / departure time of the train from the current time to the station, and the features of the edges between station nodes include the shortest travel time between stations.

[0063] In one possible implementation, the railway network delay evolution prediction model includes an encoder, a latent space, and a decoder. The encoder is used to determine the adjacency matrix corresponding to the edges between train nodes after the update. The latent space is used to determine the representation that conforms to a preset continuous distribution. The decoder is used to determine the train delay prediction result after a preset time interval.

[0064] In one possible implementation, the railway network delay evolution prediction model is a trained railway network delay evolution prediction model, and the device further includes:

[0065] The third determination module is used to input historical railway network map sample data into the initial railway network delay evolution prediction model to obtain the predicted train delay results;

[0066] The calculation module is used to calculate the value of the loss function based on the predicted train delay results;

[0067] The training module is used to train the initial railway network delay evolution prediction model based on the loss function value, so as to obtain the trained railway network delay evolution prediction model.

[0068] In one possible implementation, the loss function includes a divergence component and a reconstruction component. The divergence component is determined based on the encoder output of the initial railway network delay evolution prediction model, while the reconstruction component is determined based on the decoder output of the initial railway network delay evolution prediction model and the label data corresponding to the historical railway network map sample data. The label data is used to represent the actual train delay prediction results.

[0069] According to another aspect of this disclosure, a train delay prediction device is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0070] According to another aspect of this disclosure, a non-volatile computer-readable storage medium is provided that stores computer program instructions thereon, wherein the computer program instructions, when executed by a processor, implement the above-described method.

[0071] According to another aspect of this disclosure, a computer program product is provided, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0072] According to the embodiments of this application, by determining the initial railway network diagram at the current moment, wherein the nodes in the railway network diagram include one or more of train nodes, station nodes, and interference event nodes, and the edges in the railway network diagram and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between nodes, the importance of the interaction between various elements in the railway network in the delay evolution process and the sensitivity of the influencing features can be analyzed. By inputting the initial railway network diagram at the current moment into the railway network delay evolution prediction model, based on the characteristics of the nodes, the characteristics of the edges in the initial railway network diagram and the initial adjacency matrix corresponding to the edges, the train delay prediction result after a preset time interval is determined. This realizes train delay prediction guided by the prediction range, while considering multiple trains in the line, which is more holistic and systematic. At the same time, by considering the interaction relationships between multiple elements, the delay prediction accuracy is higher, and the interaction relationships of trains in the delay evolution process can be revealed, improving the interpretability of delay evolution, thereby coordinating the interpretability and accuracy of delay evolution prediction.

[0073] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0074] The accompanying drawings, which are included in and form part of this specification, illustrate exemplary embodiments, features, and aspects of this disclosure together with the specification and serve to explain the principles of this disclosure.

[0075] Figure 1 A schematic diagram illustrating an application scenario according to an embodiment of this application is shown.

[0076] Figure 2 A flowchart illustrating a train delay prediction method according to an embodiment of this application is shown.

[0077] Figure 3 A schematic diagram showing the current state of the railway network according to an embodiment of this application is provided.

[0078] Figure 4 This diagram illustrates a prediction task for the current state of a railway network according to an embodiment of this application.

[0079] Figure 5 A schematic diagram of a railway network according to an embodiment of this application is shown.

[0080] Figure 6 A schematic diagram of the structure of a railway network delay evolution prediction model according to an embodiment of this application is shown.

[0081] Figure 7 A flowchart illustrating a train delay prediction method according to an embodiment of this application is shown.

[0082] Figure 8 A flowchart illustrating a train delay prediction method according to an embodiment of this application is shown.

[0083] Figure 9 A schematic diagram illustrating the predictive performance of a railway network delay evolution prediction model according to an embodiment of this application is shown.

[0084] Figure 10 A structural diagram of a train delay prediction device according to an embodiment of this application is shown.

[0085] Figure 11 This is a block diagram illustrating an apparatus 1900 for predicting train delays according to an exemplary embodiment. Detailed Implementation

[0086] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0087] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0088] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0089] Accurate delay prediction is a crucial component of railway operations management. It provides decision support for real-time adjustments to delayed trains by estimating the potential impact of delays at the operational level. Simultaneously, understanding the intricate interactions between various factors during delay evolution is essential for tactical timetable development, helping to optimize the tactical allocation of redundant time in the timetable plan. Current train delay prediction schemes struggle to balance interpretability and accuracy. Schemes emphasizing interpretability often rely on Markov properties such as Markov chains and Bayesian networks, or are built on overly simplistic models, which tend to exhibit relatively poor predictive performance. Conversely, schemes prioritizing prediction accuracy typically employ machine learning techniques; however, these schemes often treat the delay evolution process as a black box, failing to elucidate the specific mechanisms by which various influencing factors lead to delay propagation. Therefore, a train delay prediction method that combines accuracy and interpretability is urgently needed.

[0090] In view of this, this application provides a train delay prediction method, apparatus, and storage medium. The method of this application determines an initial railway network diagram at the current time, wherein the nodes in the railway network diagram include one or more of train nodes, station nodes, and interference event nodes. The edges in the railway network diagram and their corresponding adjacency matrices are used to represent the interaction relationships between nodes. This allows analysis of the importance of the interactions between elements in the railway network during the delay evolution process, as well as the sensitivity of the influencing features. By inputting the initial railway network diagram at the current time into a railway network delay evolution prediction model, and based on the characteristics of the nodes, the characteristics of the edges, and the initial adjacency matrices corresponding to the edges in the initial railway network diagram, the train delay prediction result after a preset time interval is determined. This achieves train delay prediction guided by the prediction range, while considering multiple trains on the line, making it more holistic and systematic. Furthermore, by considering the interaction relationships between multiple elements, the accuracy of delay prediction is higher, and the interaction relationships between trains during the delay evolution process can be revealed, improving the interpretability of delay evolution. This allows for a balance between the interpretability and accuracy of delay evolution prediction.

[0091] Figure 1A schematic diagram illustrating an application scenario according to an embodiment of this application is shown. For example... Figure 1 As shown, the train delay prediction system of this application embodiment can be used in the scenario of predicting the delay of trains in the railway network. The train delay prediction system can obtain the railway network map at the current time and output the train delay set in the railway network map, that is, the train delay prediction result. The train delay set can include the delay duration of each train in the railway network map at its subsequent stations after a preset time interval at the current time.

[0092] In the application scenarios of this application embodiment, the train delay prediction results can be used to make real-time adjustments to train operation and provide support for train rescheduling at the operational level. The train delay prediction results also help to explain the interaction between various influencing factors (train, station, interference time) during the train evolution process, thereby supporting the allocation of redundant time in the tactical level train timetable planning, so that train operation can be restored under interference conditions.

[0093] The train delay prediction system of this application embodiment can be used in terminal devices or servers. Terminal devices can be any one or more of the following: mobile phones, foldable electronic devices, tablets, desktop computers, laptops, handheld computers, ultra-mobile personal computers (UMPCs), netbooks, cellular phones, and in-vehicle equipment. This application embodiment does not impose special restrictions on the specific type of terminal device; it can have wired or wireless communication capabilities. Servers can be located locally or in the cloud, and can be physical devices or virtual devices, such as virtual machines or containers, with wireless communication capabilities. These wireless communication capabilities can be configured in the server's chip (system) or other components. Wireless communication capabilities can be implemented, for example, through 2G / 3G / 4G / 5G mobile communication technologies, as well as Wi-Fi, Bluetooth, frequency modulation (FM), data radio, satellite communication, etc. Wired connections can also be used for communication to enable interaction with other devices.

[0094] Figure 2 A flowchart illustrating a train delay prediction method according to an embodiment of this application is provided. This method can be used in the aforementioned train delay prediction system, such as... Figure 2 As shown, the method includes:

[0095] Step S201: Determine the initial railway network map at the current moment.

[0096] Because railway network diagrams are influenced by various factors, including trains, stations, and disruption events, the interaction between trains, especially train intervals, is a significant factor affecting the evolution of delays. Following trains are more susceptible to the effects of delays caused by preceding trains. Furthermore, stations also influence the evolution of train delays due to their different characteristics (e.g., different stations have different train schedules and arrival / departure times). In addition, disruption events such as extreme weather or vehicle malfunctions can have varying impacts on the evolution of delays. Therefore, these factors need to be considered when analyzing the evolution of train delays. For example, extreme weather may cause delays across multiple sections, while vehicle malfunctions may only affect one train at one station / section. Therefore, in this application, trains, stations, and disruption events can be considered as factors influencing the evolution of delays.

[0097] See Figure 3 This diagram illustrates the current state of the railway network according to an embodiment of this application. Figure 3 As shown, a railway network may include 7 stations (A-F and O in the figure), distributed on three different lines (A, B, O; O, D, C; and E, F, O). 7 trains (trains 1-7 in the figure) are heading towards station O on the railway network at time step t (i.e., time t). Trains 1 and 2 are affected by extreme weather, while train 4 experiences a vehicle failure at time t (in the figure, Vehicle Failure). Both extreme weather and vehicle failure can be considered interference events. At this time, if a train is in a certain section (e.g., between two stations) at time t, the delay duration of its previous arrival or departure events can be used as a known delay measurement. Based on this, the delay duration of arrival or departure events before time t+Δt can be predicted, where arrival events can be the train arriving at the corresponding station, and departure events can be the train leaving the corresponding station.

[0098] See Figure 4 This diagram illustrates a prediction task for the current state of a railway network according to an embodiment of this application. Figure 4 As shown, the blue labels represent known values, indicating the nearest train before time t (including Trains 1 through 7, corresponding to...). Figure 3 The diagram shows the delay durations of trains 1-7 at each station for arrival / departure events. Yellow labels represent unknown values, indicating the delay duration of trains' departure / arrival events at each station. Labels within red dashed boxes represent values ​​to be predicted, indicating the delay duration of the nearest departure / arrival event before time t+Δt. For example, train 1 runs between station A and station B at time t, and between station B and station 0 at time t+Δt. Therefore, the known delay duration for train 1 could be the delay duration of train 1's departure event at station A (i.e., the delay duration shown in the diagram). The predicted delay time for train 1 can be the delay time of train 1's departure event at station B (i.e., the delay time shown in the figure). ).

[0099] This application will Figure 3 and Figure 4 The railway network shown is constructed as the railway network diagram G at time t. t =(V t E t A t (This can include the node at time t) side The adjacency matrix corresponding to the edge

[0100] In the railway network diagram, nodes can include train nodes. Station Node Interference event nodes One or more of the following. Disruption events can include extreme weather, vehicle malfunctions, etc. Edges and their corresponding adjacency matrices in a railway network graph can be used to represent the interaction relationships between nodes.

[0101] Figure 5 A schematic diagram of a railway network according to an embodiment of this application is shown. Figure 5 As shown, blue nodes A-B and O can represent station nodes, yellow nodes 1-7 can represent train nodes, and red nodes 1-2 can represent interference event nodes.

[0102] The blue edges represent the edges between station nodes (i.e., station-to-station edges). The direction of the edges is determined by the direction of travel of the train on the track, pointing from the preceding station node to the following station node; black edges can represent the edges between station nodes and train nodes (i.e., station-train edges). The direction of the edges points from the preceding station node to the following train node; the red edges can represent the edges between the interfering event node and the train node (i.e., the interference-train edge). The direction of the edges is from the interference event node to the train node; the yellow edges can represent edges between train nodes (i.e., train-to-train edges). In the initial railway network graph, it can be assumed that the edges between train nodes are bidirectional edges.

[0103] The adjacency matrix includes Corresponding adjacency matrix Corresponding adjacency matrix The corresponding adjacency matrix and Corresponding adjacency matrix in, and Used to represent nodes and nodes The number of nodes, with subscripts m and n being the indexes of node types, and tr, st, and ds representing node types as train, station, and interference event, respectively. For the i-th node sender index, For the j-th node The receiver index, when the i-th With the j-th The edge between them is the i-th one. Pointing to the j-th hour, The value is 1, otherwise... The value is 0.

[0104] In the railway network graph of this application, nodes and edges include corresponding feature values. A node can be represented as... It can represent The kth node in the array.

[0105] The characteristics of a train node can include the train's delay time at the current moment. The time interval between the previous train node Minimum running time of the train within the preset time interval The planned running time of the train within the preset time interval The time of the most recent event before the current moment for the train. One or more of them.

[0106] Since the evolution of train delays can be viewed as an autocorrelation and cross-correlation process, this means that the delay of a train at time t+Δt is influenced by both its own delay and the delay of the train preceding it. Therefore, the delay time of the train at the current moment and the time interval between the train and the preceding train node can be used as features of the train node. The delay time of the train at the current moment is the current delay set of the train node, which can include the delay duration of each train node in the railway network diagram at the current moment; the time interval between the train and the preceding train node is the headway set of the train node, representing the time required for the train to reach the location of the preceding train, which can include the time interval between each train node at the current moment and its preceding train node. The time interval between the train and the preceding train node can be predetermined based on train timetables, etc.

[0107] Since a redundancy period is reserved in the train timetable to ensure that train operation can be restored in the event of interference, and this redundancy period is usually determined by the minimum running time and the planned running time, the minimum running time and the planned running time of the train within the preset time interval can be used as train node characteristics. The preset time interval is Δt as described above.

[0108] The minimum travel time of a train within a preset time interval can represent the minimum travel time for a train to travel from the nearest station before time t to the nearest station before time t+Δt. The planned travel time of a train within a preset time interval can represent the planned travel time for a train to travel from the nearest station before time t to the nearest station before time t+Δt. The minimum travel time and the planned travel time of a train within a preset time interval can be predetermined based on train timetables, etc.

[0109] Since trains cannot be guaranteed to stop at stations at times t and t+Δt, the aforementioned minimum running time and planned running time are not entirely accurate. Therefore, this application uses the occurrence time of the most recent event before the current time as a train node feature to reflect the actual redundancy time. The most recent event before the current time can be a departure or arrival event at the nearest station before the current time.

[0110] When trains are affected by disruptions, they may need to be reordered at stations (i.e., overtaken) to ensure the operation of high-priority trains or reduce the impact of delays. The number of arrival and departure tracks determines how many trains can be considered in the reordering plan; therefore, the characteristics of a station node can include the number of arrival and departure tracks in the station.

[0111] Since different interference events may lead to different delayed evolutions, this application treats interference events as nodes. Interference events can be recorded in text format, including the cause, impact, and location of the interference event. The text-recorded interference events can be vectorized to serve as features of the interference event nodes. Therefore, the features of interference event nodes can include the vectorized interference events. For example, the text corresponding to the interference event can be segmented into words to ensure the model can handle interference. Then, the word2vec technique can be used to convert the words into integer vectors, thus obtaining the vectorized interference events.

[0112] An edge can be represented as It can represent The k-th edge in It can represent an edge The number of train nodes. Since the features of the edges between train nodes are the parts to be predicted, it is not necessary to pre-assign features to this type of edge. As for the features of the edges between interference event nodes and train nodes, this application only considers whether the interference event node has an impact on the train node, without considering the degree of impact. Therefore, it is also not necessary to assign features to this type of edge.

[0113] The features of an edge can include the features of the edge between a station node and a train node, as well as the features of the edge between two station nodes.

[0114] Since the characteristics of the edges between station nodes and train nodes can reflect the influence of station nodes on train nodes, for example, the time required for a train to arrive at the next station from time t can determine the time for the next update of train delay information, the characteristics of the edges between station nodes and train nodes can include the planned arrival / departure time of the train from the current time to the station.

[0115] The characteristics of edges between station nodes can be used to represent the physical structure of a railway network, and can include the shortest travel time between stations. These characteristic values ​​can be obtained based on train timetables, etc.

[0116] Therefore, the initial railway network diagram at the current moment can be determined.

[0117] Step S202: Input the initial railway network map at the current time into the railway network delay evolution prediction model. Based on the characteristics of the nodes, the characteristics of the edges, and the initial adjacency matrix corresponding to the edges in the initial railway network map, determine the train delay prediction result after a preset time interval.

[0118] The train delay prediction results after the preset time interval include, for example, the delay duration of the nearest event (departure event / arrival event) before time t+Δt for each train in the railway network diagram at time t+Δt.

[0119] According to the embodiments of this application, by determining the initial railway network diagram at the current moment, wherein the nodes in the railway network diagram include one or more of train nodes, station nodes, and interference event nodes, and the edges in the railway network diagram and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between nodes, the importance of the interaction between various elements in the railway network in the delay evolution process and the sensitivity of the influencing features can be analyzed. By inputting the initial railway network diagram at the current moment into the railway network delay evolution prediction model, based on the characteristics of the nodes, the characteristics of the edges in the initial railway network diagram and the initial adjacency matrix corresponding to the edges, the train delay prediction result after a preset time interval is determined. This realizes train delay prediction guided by the prediction range, while considering multiple trains in the line, which is more holistic and systematic. At the same time, by considering the interaction relationships between multiple elements, the delay prediction accuracy is higher, and the interaction relationships of trains in the delay evolution process can be revealed, improving the interpretability of delay evolution, thereby coordinating the interpretability and accuracy of delay evolution prediction.

[0120] The following section first introduces the structure of the railway network delay evolution prediction model (which can be called NRI-GraphSAGE). See [link to relevant documentation]. Figure 6 This diagram illustrates the structure of a railway network delay evolution prediction model according to an embodiment of this application. Figure 6 As shown, the railway network delay evolution prediction model can include an encoder, a latent space, and a decoder.

[0121] The encoder can be used to determine the updated adjacency matrix based on the railway network graph, that is, to learn the interaction between trains. It can include the following modules in sequence: node embedding updates, node-to-edge, edge-to-node, node-to-edge, and edge probability output.

[0122] The latent space can be used to determine a representation that conforms to a preset continuous distribution, and the learned interactions between trains can be sampled from the latent space.

[0123] The decoder is used to determine the train delay prediction results after a preset time interval, and may include node-to-node, aggregation, node-to-node, and aggregation modules in sequence.

[0124] The above-mentioned railway network delay evolution prediction model is the trained railway network delay evolution prediction model. The following section first introduces the training process of the railway network delay evolution prediction model.

[0125] See Figure 7 The diagram illustrates a flowchart of a train delay prediction method according to an embodiment of this application. Figure 7 As shown, the method may include:

[0126] Step S701: Input the historical railway network map sample data into the initial railway network delay evolution prediction model to obtain the predicted train delay results.

[0127] Historical railway network map sample data can include railway network maps at historical points in time; see [link to sample data]. Figure 5 This is an illustration. In the initial output of the railway network delay evolution prediction model, it can be assumed that all trains in the railway network are interconnected, that is, the adjacency matrix corresponding to the edges between station nodes is all 1s.

[0128] The predicted train delays can be obtained after a preset event interval. The detailed process for obtaining the predicted train delays based on the railway network delay evolution prediction model will be discussed later. Figure 8 The introduction in the text.

[0129] Step S702: Calculate the value of the loss function based on the predicted train delay results.

[0130] The loss function can include a divergence component and a reconstruction component. The divergence component can be determined based on the encoder output of the initial railway network delay evolution prediction model, while the reconstruction component can be determined based on the decoder output of the initial railway network delay evolution prediction model and the label data corresponding to the historical railway network map sample data. The label data can be used to represent the actual train delay prediction results.

[0131] The formula for the loss function can be found in formula (1):

[0132]

[0133] Where l can represent the loss function. It can represent the reconstructed components. Indicates q φ (z|V tr ) Perform the expected value calculation. q φ (z|V tr The distribution can be determined based on the encoder output, and is a posterior distribution, p. θ (z) represents the prior distribution, and θ represents the model parameters; KL[q] φ (z|V tr ∥p θ (z)] can represent the divergence component.

[0134] Where, log p θ (V trThe calculation method for |z) can be found in formula (2):

[0135]

[0136] in, It can be used to represent the number of train nodes, where j is the quantity identifier. It can represent the j-th train node. The predicted train delay results It can represent the corresponding label data, and δ is a preset hyperparameter used to determine the degree of error penalty for negative log-likelihood.

[0137] The divergence component can be calculated using formula (3):

[0138]

[0139] Since the latent variable z is discrete, it may prevent backpropagation during sampling. To facilitate calculation and sampling, p θ (z) can be a pre-defined continuous distribution, that is, a continuous approximation of a discrete distribution.

[0140] Step S703: Train the initial railway network delay evolution prediction model based on the loss function value to obtain the trained railway network delay evolution prediction model.

[0141] The backpropagation algorithm can be used to train the initial railway network delay evolution prediction model. The model parameters can be updated based on the gradient of the approximate value (i.e., the value obtained by sampling a preset continuous distribution) (which can be determined by reparameterization, etc.), so as to obtain the trained railway network delay evolution prediction model.

[0142] The following describes the reasoning process for predicting train delays based on the railway network delay evolution prediction model.

[0143] See Figure 8 The diagram illustrates a flowchart of a train delay prediction method according to an embodiment of this application. Figure 8 As shown, step S202 may include:

[0144] Step S801: Based on the characteristics of train nodes in the initial railway network graph, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0145] The characteristics of train nodes can be found above. In the initial railway network graph, it can be assumed that all trains in the railway network are interconnected, that is, the adjacency matrix corresponding to the edges between train nodes in the initial railway network graph is set to all 1s, and the updated adjacency matrix corresponding to the edges between train nodes is determined based on the encoder in the railway network delay evolution prediction model.

[0146] In step S801, the following can be done:

[0147] Feature extraction is performed on the features of train nodes in the initial railway network diagram to determine the first train node embedding corresponding to the train node.

[0148] Based on the first train node embedding, determine the first edge embedding corresponding to the edge between train nodes;

[0149] The embedding of the second train node is determined based on the embedding of the first edge;

[0150] Determine the second edge embedding based on the second train node embedding;

[0151] Based on the second edge embedding, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0152] The first train node embedding can be a feature representation obtained by updating the features of the train node using a fully connected neural network. The first train node embedding corresponding to the train node can be determined using the node embedding updates module in the encoder described above, and the determination method can be found in formula (4):

[0153]

[0154] in, This can represent the j-th train node in the initial railway network graph. f can represent the embedding of the first train node corresponding to the j-th train node. emb (·) is determined based on a fully connected neural network (FCNN).

[0155] The first edge embedding can be a feature representation obtained by updating the feature of the first train node embedding of two interconnected train nodes using a fully connected neural network. The first edge embedding can be determined using the first node-to-edge module in the encoder described above, and the determination method can be found in formula (5):

[0156]

[0157] in, This can represent the first edge embedding corresponding to the edge between the i-th train node and the j-th train node. It can be determined based on FCNN.

[0158] The second train node embedding can be a feature representation obtained by updating the first edge embedding using a fully connected neural network. The second train node embedding can be determined using the edge-to-edge module in the encoder described above, as shown in formula (6):

[0159]

[0160] in, This can represent the embedding of the second train node of the j-th train node. It can be determined based on FCNN.

[0161] The second edge embedding can be a feature representation obtained by updating the feature of the second train node embeddings of two interconnected train nodes using a fully connected neural network. The second edge embedding can be determined using the second node-to-edge module in the encoder described above, and the determination method can be found in formula (7):

[0162]

[0163] in, Let represent the second edge embedding corresponding to the edge between the i-th train node and the j-th train node. It can be determined based on FCNN.

[0164] The method for determining the adjacency matrix corresponding to the edges between the updated train nodes can be found in formula (8):

[0165]

[0166] in, The updated adjacency matrix can represent the edges between train nodes. Using formulas (4) to (8), the input data can be encoded into a latent two-dimensional representation. The updated adjacency matrix can represent the distribution of the input data in the latent space. p (·) can be determined based on FCNN.

[0167] Step S802: Replace the adjacency matrix corresponding to the edge between train nodes in the initial adjacency matrix of the initial railway network graph with the updated adjacency matrix corresponding to the edge between train nodes, and determine the updated railway network graph.

[0168] The method for determining the updated railway network map can be found in formula (9):

[0169]

[0170] in, It can represent an updated railway network map. This is the adjacency matrix corresponding to the edges between train nodes in the initial adjacency matrix.

[0171] Step S803: Based on the updated railway network map, determine the train delay prediction results after the preset time interval.

[0172] Among them, due to the formula (8) above, Since it conforms to a discrete distribution, we can first use the latent space in the above-mentioned railway network delay evolution prediction model to approximate the discrete distribution to obtain a representation that conforms to a continuous distribution, so that it can be processed in the subsequent input decoder.

[0173] In step S803, the following can be done:

[0174] Based on the preset continuous distribution, the adjacency matrix corresponding to the edges between the updated train nodes is normalized to obtain a representation that conforms to the preset continuous distribution.

[0175] Based on the representation that conforms to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, the train delay prediction results after the preset time interval are determined.

[0176] The default continuous distribution can be a Gumbel distribution. The normalization method for the adjacency matrix corresponding to the edges between the updated train nodes can be found in formula (10):

[0177]

[0178] Among them, z ij The continuous distribution after factorization is used to indicate train nodes. and The probability that there is an interaction relationship between them (including) Does it apply to as well as Does it apply to The value range is [0,1]. g represents a vector consisting of independent and identically distributed samples drawn from the Gumbel distribution. τ is a preset parameter used to control the smoothness of the samples.

[0179] The representation conforming to a preset continuous distribution, along with the features of nodes and edges in the updated railway network diagram, can be used as inputs to the decoder of the aforementioned railway network delay evolution prediction model to determine the train delay prediction result after a preset time interval. The decoder can be expressed as formula (11):

[0180]

[0181] Where, p θ (V tr |z) represents the probability distribution corresponding to the late prediction results obtained by the decoder. It can be expressed as given a latent variable z (based on z) ij (Obtained) and updated railway network map In the case of train node at the next time step (i.e., time t+Λt), The probability distribution corresponding to the delayed prediction results.

[0182] In the process of determining the train delay prediction results after a preset time interval based on a representation conforming to a preset continuous distribution, and the characteristics of nodes and edges in the updated railway network graph, the following can be done:

[0183] Based on the representation that conforms to the preset continuous distribution, the third edge embedding is determined. The third edge embedding is used to indicate whether there is a connection between train nodes.

[0184] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the train nodes in the updated railway network graph are aggregated with other nodes to determine the features of the updated train nodes.

[0185] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the station nodes in the updated railway network graph are aggregated to determine the features of the updated station nodes.

[0186] Based on the third edge embedding, the features of the updated train node, the features of the updated station node, the features of the interference event node in the updated railway network graph, and the features of the edges, the features of the target train node are determined.

[0187] Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the train delay prediction result after a preset time interval is determined.

[0188] The above process can be implemented based on a decoder, where the method for determining the third-side embedding can be found in formula (12):

[0189]

[0190] in, z can represent the third edge embedding of the edge between the i-th train node and the j-th train node. ijk z can be represented ij The value of the k-th element in the array. The third edge embedding can be determined based on FCNN. The resulting third edge embedding can be a binarized result with a value of 0 or 1. A value of 0 indicates that there is no connection between train nodes, while a value of 1 indicates that there is a connection between train nodes.

[0191] The updated train node features can be determined using the first Aggregation module in the decoder described above. The determination method can be found in formula (13):

[0192]

[0193] in, This can represent the updated features of the j-th train node, which is the result of aggregation. m is the node's category identifier, m∈(tr,st,ds). For the i-th node sender index, For the j-th train node Receiver index. This can be represented by a graph neural network, GraphSAGE (Graph Sample and Aggregation), which can be determined based on edge features in the updated railway network graph. The first node-to-node module in the decoder described above can be used for this determination. It can represent a node and train nodes There are connections between nodes, with the direction of the connection being the node. Pointing to the train node

[0194] The updated station node characteristics can also be determined using the first Aggregation module in the decoder described above. The determination method can be found in formula (14):

[0195]

[0196] in, It can represent the updated features of the j-th station node, which is the result of aggregation. For the i-th station node sender index, For the j-th station node Receiver index. This can represent GraphSAGE and can be determined based on edge features in the updated railway network graph. It can be determined using the first node-to-node module in the decoder described above. It can represent station nodes and station nodes There is a connection between them, and the direction of the connection is from the station node. Point to station node

[0197] The characteristics of the target train nodes can be determined using the second Aggregation module in the decoder described above. The determination method can be found in formula (15):

[0198]

[0199] in, The characteristics of the target at the j-th train node can be represented by the aggregated result. This can represent GraphSAGE, which can be determined based on edge features in the updated railway network graph. It can be determined using the second node-to-node module in the decoder described above.

[0200] Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the method for determining the train delay prediction result after a preset time interval can be found in formula (16):

[0201]

[0202] in, This represents the probability distribution of the predicted train delays after a preset time interval. The predicted train delays after the preset time interval follow a normal distribution N(μ). t+1 ,σ 2 I), where μ t+1 This represents the mean of a normal distribution. σ 2 Let I represent the variance of the normal distribution, and let I be the identity matrix. To express to Perform nonlinear transformations or neural network processing.

[0203] This application selects two local railway networks in China, namely the Guangzhou South Network (GZS-Net) and the Changsha South Network (CSS-Net), to validate the effectiveness of the railway network delay evolution prediction model. These two local networks play a crucial role in the overall Chinese high-speed rail network. They differ significantly in terms of station distances and traffic volume. The Guangzhou South Network is a large-scale and complex network, while the Changsha South Network is a smaller-scale network. We strategically selected 12 surrounding stations to represent the GZS-Net and selected 8 stations surrounding Changsha South (CSS) station to form the CSS-Net.

[0204] This application utilizes historical observation data from February to July 2018 for validation, including train operation data and interference event data. Only trains heading to GZS and CSS stations are considered. To accommodate different scheduling strategies, predicting train delays within different prediction intervals (Δt) is crucial. Therefore, we established three line-of-sight prediction models for railway network delay evolution, including Δt = 10 / 20 / 30 minutes, to meet both short-term and long-term prediction requirements. To ensure the effectiveness of the prediction models, we only considered the period from 8:00 to 23:00. This is because the number of trains in the network is significantly lower during early morning and evening hours. Furthermore, to ensure statistical significance, trains with delays exceeding 90 minutes were excluded. Thus, the datasets for Δt = 10 / 20 / 30 minutes in GZSNet and CSS-Net contain over 16,000 / 8,000 / 5,300 samples, respectively. Finally, we selected 50% of the historical observation data for training, 20% for validation, and the remaining 30% for testing.

[0205] Based on the above data, to assess the accuracy of the railway network delay evolution prediction model, we first verified its predictive performance. Subsequently, since the determination of these edges is based on a pre-analysis of delay evolution, we conducted node connectivity analysis through edge ablation experiments (i.e., evaluating the model by removing edges), verifying the rationality and effectiveness of the four types of edges in the railway network delay evolution prediction model. Train node features play a crucial role in the delay evolution process. Therefore, we conducted experiments to determine the feature sensitivity of train nodes by deleting corresponding train node features.

[0206] In the experimental design, we tuned the relevant hyperparameters. In the encoder module, consecutive FCNNs were used to acquire information related to train-to-train connections. The key parameter of the FCNN architecture is the number of neurons. For f... emb , and This parameter is configured to 64. It is worth noting that for f, which is responsible for learning the connections between train nodes... pThe number of neurons is specified as 2 (i.e., connected or not connected). For the decoder, we use the GraphSAGE method to update the node information in the node-to-node component. We use two GraphSAGE components, and two GraphSAGE layers (i.e., the node-to-node module in the decoder above) are configured with 64 and 32 neurons respectively. That is, in order to update the nodes on different edges, the first layer... and The number of neurons in the first layer is set to 64, while the second layer... The corresponding values ​​are 32. The aggregation techniques for node information include summation.

[0207] This application employs the adaptive optimizer Adam during training, which dynamically adjusts the local learning rate to avoid local optima. The initial learning rate is fixed at 0.001, which is the default value for the Adam optimizer. Furthermore, a technique for dynamically adjusting the learning rate (ReduceLROnPlateau) is used to enhance the model's robustness. When performance on the validation dataset does not show significant improvement within 20 time intervals, the global learning rate can be dynamically reduced by 10%. The maximum number of epochs is set to 300. However, if the performance degradation on the validation dataset is less than 0.01 within 50 epochs, an early stopping technique is activated to halt training, enhancing the model's resistance to overfitting. The data loader size used during training is 32.

[0208] Figure 9 This diagram illustrates the predictive performance of a railway network delay evolution prediction model according to an embodiment of this application. Rsquared(Rsquared) is used in this application. 2 The indicators validated the predictive accuracy of the proposed model, such as... Figure 9 As shown, R varies across different prediction ranges. 2 The value consistently exceeds 0.93. This indicates that the railway network delay evolution prediction model captures most of the variations in train delays well. Furthermore, the violin plot of the residual distribution shows that the residuals are concentrated near zero, indicating a high degree of consistency between the predicted and actual values. As the prediction ranges of both networks decrease, the residual distribution becomes more concentrated, suggesting an enhanced ability to predict delays over more recent timeframes. Therefore, we believe that the high predictive accuracy of the railway network delay evolution prediction model lays a solid foundation for subsequent explanations of delay evolution.

[0209] The decoder used in this application uses a model based on GraphSAGE from the Railway Network Delay Evolution Prediction Model (NRI-GraphSAGE). To demonstrate the importance of GraphSAGE, several baselines are designed in this application, applying different GNNs to the decoder to replace GraphSAGE, and experiments are conducted to further determine the advantages of the model in this application. Furthermore, the encoder is used to acquire knowledge of the adjacency matrix corresponding to the edges between trains and train nodes. The following baselines are constructed:

[0210] Decoder (GraphSAGE): This model removes the encoder component from NRI-GraphSAGE. Thus, in the adjacency matrix corresponding to the edges between train nodes, only the first column of the preceding train points to the following train (i.e., train-to-train interactions are determined by domain knowledge referencing previous research). Node updates are handled by the GraphSAGE neural network.

[0211] Decoder (GAT): Similar to the decoder (GraphSAGE) model described above, this model does not use an encoder; GraphSAGE is replaced by a GAT neural network.

[0212] NRI-GAT: In this model, the GraphSAGE in the NRI-GraphSAGE decoder is replaced by the GAT neural network.

[0213] Decoder (GCN): In this model, we do not use an encoder. GraphSAGE is replaced by GCN when updating node information via edges between station nodes and train nodes, and between train nodes themselves; other components are the same as the decoder (GraphSAGE).

[0214] NRI-GCN: In this model, when updating node information through the edges between station nodes and train nodes and between train nodes, the GraphSAGE in the NRI-GraphSAGE decoder is replaced by the GCN neural network, while the rest is the same as NRI-GraphSAGE.

[0215] The purpose of comparing NRI-GAT and its decoder (GAT), NRI-GraphSAGE and its decoder (GAT), and NRIGCN and its decoder (GCN) is to determine whether adding the encoder to learn the edge adjacency matrix between train nodes helps improve the accuracy of late departure evolution prediction. The purpose of comparing NRI-GraphSAGE, NRI-GAT, and NRI-GCN is to verify whether choosing the GraphSAGE algorithm in the decoder yields the best prediction performance.

[0216] The baselines described above used the same parameters and training techniques as NRI-GraphSAGE. The results are shown in Table 1.

[0217] Table 1

[0218]

[0219] Table 1 shows the superior prediction accuracy of NRI-GraphSAGE compared to various baseline models across different prediction ranges. NRI-GraphSAGE achieves higher accuracy compared to the decoder (GraphSAGE), thanks to the inclusion of the encoder, which facilitates the learning of the training-training adjacency matrix. The superior prediction performance of NRI-GAT (GAT) and NRI-GCN (GCN) further emphasizes the power of the encoder. Furthermore, NRI-GraphSAGE also outperforms NRI-GAT and NRI-GCN in prediction accuracy, highlighting the advantages of using GraphSAGE in the decoder. In addition, NRI-GraphSAGE exhibits lower mean absolute error (MAE) and root mean square error (RMSE) across the three different prediction ranges, indicating that it more closely approximates the actual late-point evolution.

[0220] The NRI-GraphSAGE model contains various nodes connected by different edges. To validate the rationale for edges between different types of nodes in the railway network graph, edge ablation analysis was performed in this application. The learned adjacency matrix in the NRI-GraphSAGE encoder can analyze the importance of train-to-train edges in the evolution of delays. Therefore, edge ablation experiments were conducted in this application to further investigate the importance of the other three edge types. We removed the other three edge types from the NRI-GraphSAGE model and compared the prediction accuracy of these modified models with that of the full NRI-GraphSAGE model. Through comparison, this application confirms the rationale for considering these edges and assesses their importance in influencing the evolution of delays.

[0221] By removing the corresponding edges in NRI-GraphSAGE, we can obtain the following models: interference event-train ablation, station-train ablation, and station-station ablation. For example, in the NRI-GraphSAGE decoder, the train embedding is not updated based on the edge between the interference event node and the train node, thus resulting in the interference-train ablation model. In other words, this model does not consider the interaction between interference events and train nodes during the delay evolution process. The results are shown in Table 2:

[0222] Table 2

[0223]

[0224] Table 2 shows that, compared to NRI-GraphSAGE, all baseline models obtained after edge removal have lower prediction accuracy across the entire prediction range. This demonstrates the effectiveness of these edges in delay evolution prediction. Furthermore, the prediction model obtained by removing station-train edges has the lowest accuracy, highlighting the significant impact of station-train edges on delay evolution compared to the other two types of edges. Station-train edges contain planned travel time information for trains to the next station, which is crucial for updating train delay information and recovering from delays. Additionally, when NRI-GraphSAGE updates train information via station-train edges, station capacity information (number of arrival-departure tracks) is also transmitted to the train. Station capacity affects train overtaking, which explains why station-station edges also influence delay evolution. Different disturbance events can lead to different delay evolution patterns. Therefore, considering specific disturbance events in NRIGraphSAGE provides more accurate information for delay evolution prediction compared to "disturbance-train ablation," thereby improving prediction accuracy.

[0225] To verify the rationality and effectiveness of train node features, this application conducted experiments to verify whether including these features helps improve the prediction accuracy of NRI-GraphSAGE. This included comparing the prediction accuracy of NRI-GraphSAGE with that of a model that excluded specific train node features. The decrease in prediction accuracy indicated the importance of the ignored features. Subsequently, the experiments also compared the prediction accuracy of models with different features removed. In these models, features with lower prediction accuracy were considered more important.

[0226] By systematically eliminating various features of train nodes in NRI-GraphSAGE, different models can be generated, namely Delay Ablation, Headway Ablation, Min-Run Ablation, Sch-Run Ablation, and Real-SupAblation. For example, the difference between NRI-GraphSAGE and Delay Ablation is that the latter does not consider the feature corresponding to the train's delay time at the current moment in the train node. Similarly, the other models mentioned are the results of deleting the corresponding train node features (node ​​features can be found above). The predictive performance of train node feature ablation obtained through experiments is shown in Table 3:

[0227] Table 3

[0228]

[0229] Table 3 shows that NRI-GraphSAGE outperforms the model that eliminates the corresponding train node features in terms of prediction accuracy, confirming the rationality of the train node features considered in this study. Among the ablated features, the model excluding the current delay time (Delay Ablation) has the lowest prediction accuracy, highlighting the most significant importance of the feature corresponding to the current delay time in delay evolution compared to other features. This is because the current delay is the basis for future delays. Furthermore, as the prediction range decreases, excluding the current delay time leads to a more significant drop in prediction performance. This is because as the prediction range becomes closer (i.e., short-term prediction), the impact of the current delay on future delays becomes more pronounced. For longer prediction ranges, other factors may significantly influence delay evolution, thereby reducing the importance of the current delay at that time.

[0230] The Real-Sup Ablation model eliminates the feature corresponding to the occurrence time of the most recent event before the current time, representing the true redundancy time of a train within the prediction range. This feature aims to address the inaccuracy of redundancy time caused by only updating station delay information. The decrease in accuracy compared to NRI-GraphSAGE supports the rationale for this feature design. Furthermore, the Real-Sup Ablation model has the second lowest prediction accuracy, further emphasizing the effectiveness and importance of this feature in capturing true redundancy time. Additionally, in Min-Run Ablation and Sch-Run Ablation, removing the feature corresponding to the minimum run time and planned run time within the prediction range causes the model to fail to accurately capture the planned redundancy time during that period. The decreased prediction accuracy observed in Headway Ablation compared to NRI-GraphSAGE can be attributed to the neglect of interactions between adjacent trains.

[0231] To improve the interpretability of the railway network delay evolution prediction model, this application further investigates the adjacency matrices corresponding to the edges between train nodes learned within the encoder. This includes a detailed study of the interactions between two (and three) adjacent trains on the same railway line and the interactions between trains on different railway lines. Based on the learned adjacency matrices, we provide explanations for the emergence of these train interactions from the perspectives of train operation rules and domain knowledge. Some findings regarding train interactions are summarized below:

[0232] Interactions between trains are not common. For example, when the train-tracking interval is large, the probability of the preceding train affecting the following train is relatively low. However, the possibility of the preceding train affecting the following train is high, especially when both trains are experiencing severe delays, or when the train-tracking interval is short and the preceding train is facing severe delays.

[0233] Regarding changes in train delays, if the preceding train's delay is significant or the train-to-train interval is short, and the delay change is an increase in delay, the probability of the preceding train affecting the following train is significant. However, when the following train is recovering from a delay, the delay of the preceding train usually does not affect the following train.

[0234] Train interactions extend beyond the interaction between adjacent trains; there is also potential interaction between the second train in front and the train behind (i.e., between three adjacent trains). Furthermore, these interactions are reciprocal, meaning that not only does the train in front affect the train behind, but the train behind may also affect the train in front.

[0235] In the absence of potential route conflicts, the probability of train interactions on different railways is relatively low. Nevertheless, the NRI-GraphSAGE model in this application demonstrates a powerful ability to capture the mutual influence of potentially conflicting trains on different railway lines.

[0236] Figure 10 A structural diagram of a train delay prediction device according to an embodiment of this application is shown. Figure 10 As shown, the device includes:

[0237] The first determining module 101 is used to determine the initial railway network diagram at the current time. The nodes in the railway network diagram include one or more of train nodes, station nodes, and interference event nodes. The edges in the railway network diagram and the adjacency matrix corresponding to the edges are used to represent the interaction relationship between the nodes.

[0238] The second determining module 102 is used to input the initial railway network map at the current time into the railway network delay evolution prediction model, and determine the train delay prediction result after a preset time interval based on the characteristics of the nodes, the characteristics of the edges, and the initial adjacency matrix corresponding to the edges in the initial railway network map.

[0239] In one possible implementation, the second determining module 102 is used for:

[0240] Based on the characteristics of train nodes in the initial railway network graph, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0241] Replace the adjacency matrix corresponding to the edge between train nodes in the initial adjacency matrix of the initial railway network graph with the updated adjacency matrix corresponding to the edge between train nodes to determine the updated railway network graph.

[0242] Based on the updated railway network map, the predicted train delays are determined after a preset time interval.

[0243] In one possible implementation, based on the characteristics of train nodes in the initial railway network graph, the adjacency matrix corresponding to the edges between updated train nodes is determined, including:

[0244] Feature extraction is performed on the features of train nodes in the initial railway network diagram to determine the first train node embedding corresponding to the train node.

[0245] Based on the first train node embedding, determine the first edge embedding corresponding to the edge between train nodes;

[0246] The embedding of the second train node is determined based on the embedding of the first edge;

[0247] Determine the second edge embedding based on the second train node embedding;

[0248] Based on the second edge embedding, determine the adjacency matrix corresponding to the edges between the updated train nodes.

[0249] In one possible implementation, based on the updated railway network map, the predicted train delays after a preset time interval are determined, including:

[0250] Based on the preset continuous distribution, the adjacency matrix corresponding to the edges between the updated train nodes is normalized to obtain a representation that conforms to the preset continuous distribution.

[0251] Based on the representation that conforms to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, the train delay prediction results after the preset time interval are determined.

[0252] In one possible implementation, based on a representation conforming to a preset continuous distribution, and the characteristics of nodes and edges in the updated railway network graph, the train delay prediction result after a preset time interval is determined, including:

[0253] Based on the representation that conforms to the preset continuous distribution, the third edge embedding is determined. The third edge embedding is used to indicate whether there is a connection between train nodes.

[0254] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the train nodes in the updated railway network graph are aggregated with other nodes to determine the features of the updated train nodes.

[0255] Based on the features of nodes and edges in the updated railway network graph with third-edge embedding, the station nodes in the updated railway network graph are aggregated to determine the features of the updated station nodes.

[0256] Based on the third edge embedding, the features of the updated train node, the features of the updated station node, the features of the interference event node in the updated railway network graph, and the features of the edges, the features of the target train node are determined.

[0257] Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the train delay prediction results are determined after a preset time interval.

[0258] In one possible implementation, the characteristics of a train node include any one or more of the following: the train's delay time at the current moment, the time interval between the current and previous train nodes, the minimum running time of the train within a preset time interval, the planned running time of the train within a preset time interval, and the occurrence time of the most recent event before the current moment.

[0259] The characteristics of a station node include the number of arriving and departing tracks in the station;

[0260] The characteristics of the interference event node include the vectorized interference event.

[0261] In one possible implementation, the edge features include the features of the edges between station nodes and train nodes, as well as the features of the edges between station nodes. The features of the edges between station nodes and train nodes include the planned arrival / departure time of the train from the current time to the station, and the features of the edges between station nodes include the shortest travel time between stations.

[0262] In one possible implementation, the railway network delay evolution prediction model includes an encoder, a latent space, and a decoder. The encoder is used to determine the adjacency matrix corresponding to the edges between train nodes after the update. The latent space is used to determine the representation that conforms to a preset continuous distribution. The decoder is used to determine the train delay prediction result after a preset time interval.

[0263] In one possible implementation, the railway network delay evolution prediction model is a trained railway network delay evolution prediction model, and the device further includes:

[0264] The third determination module is used to input historical railway network map sample data into the initial railway network delay evolution prediction model to obtain the predicted train delay results;

[0265] The calculation module is used to calculate the value of the loss function based on the predicted train delay results;

[0266] The training module is used to train the initial railway network delay evolution prediction model based on the loss function value, so as to obtain the trained railway network delay evolution prediction model.

[0267] In one possible implementation, the loss function includes a divergence component and a reconstruction component. The divergence component is determined based on the encoder output of the initial railway network delay evolution prediction model, while the reconstruction component is determined based on the decoder output of the initial railway network delay evolution prediction model and the label data corresponding to the historical railway network map sample data. The label data is used to represent the actual train delay prediction results.

[0268] According to the embodiments of this application, by determining the initial railway network diagram at the current moment, wherein the nodes in the railway network diagram include one or more of train nodes, station nodes, and interference event nodes, and the edges in the railway network diagram and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between nodes, the importance of the interaction between various elements in the railway network in the delay evolution process and the sensitivity of the influencing features can be analyzed. By inputting the initial railway network diagram at the current moment into the railway network delay evolution prediction model, based on the characteristics of the nodes, the characteristics of the edges in the initial railway network diagram and the initial adjacency matrix corresponding to the edges, the train delay prediction result after a preset time interval is determined. This realizes train delay prediction guided by the prediction range, while considering multiple trains in the line, which is more holistic and systematic. At the same time, by considering the interaction relationships between multiple elements, the delay prediction accuracy is higher, and the interaction relationships of trains in the delay evolution process can be revealed, improving the interpretability of delay evolution, thereby coordinating the interpretability and accuracy of delay evolution prediction.

[0269] In some embodiments, the functions or modules of the apparatus provided in this disclosure can be used to perform the methods described in the above method embodiments. The specific implementation can be referred to the description of the above method embodiments, and for the sake of brevity, it will not be repeated here.

[0270] This disclosure also proposes a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the above-described method. The computer-readable storage medium can be volatile or non-volatile.

[0271] This disclosure also proposes a train delay prediction device, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0272] This disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0273] Figure 11This is a block diagram illustrating an apparatus 1900 for predicting train delays according to an exemplary embodiment. For example, apparatus 1900 may be provided as a server or terminal device. (Refer to...) Figure 11 The apparatus 1900 includes a processing component 1922, which further includes one or more processors, and memory resources represented by memory 1932 for storing instructions, such as application programs, that can be executed by the processing component 1922. The application programs stored in memory 1932 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 1922 is configured to execute instructions to perform the methods described above.

[0274] Device 1900 may also include a power supply component 1926 configured to perform power management of device 1900, a wired or wireless network interface 1950 configured to connect device 1900 to a network, and an input / output interface 1958 (I / O interface). Device 1900 can operate on an operating system, such as Windows Server, stored in memory 1932. TM macOS X TM Unix TM Linux TM FreeBSD TM Or similar.

[0275] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by a processing component 1922 of the device 1900 to perform the above-described method.

[0276] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0277] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0278] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0279] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions to implement various aspects of this disclosure.

[0280] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0281] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0282] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0283] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0284] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for predicting train delays, characterized in that, The method includes: Determine the initial railway network graph at the current moment. The nodes in the initial railway network graph include train nodes, station nodes, and interference event nodes. The edges in the initial railway network graph and the adjacency matrix corresponding to the edges are used to represent the interaction relationships between the nodes. The initial railway network diagram at the current moment is input into the railway network delay evolution prediction model. Based on the characteristics of the nodes and edges in the initial railway network diagram and the initial adjacency matrix corresponding to the edges, the train delay prediction result after a preset time interval is determined. The characteristics of the train node include any one or more of the following: the train's delay time at the current moment, the time interval between the train and the previous train node, the minimum running time of the train within a preset time interval, the planned running time of the train within a preset time interval, and the occurrence time of the most recent event before the current moment. The characteristics of the station node include the number of arrival tracks and departure tracks in the station; The characteristics of the interference event node include the vectorized interference event; The features of the edges include the features of the edges between station nodes and train nodes, and the features of the edges between station nodes. The features of the edges between station nodes and train nodes include the planned arrival / departure time of the train from the current time to the station. The features of the edges between station nodes include the shortest travel time between stations. The railway network delay evolution prediction model includes an encoder, a latent space, and a decoder. The encoder is used to determine the adjacency matrix corresponding to the edges between train nodes after the update. The latent space is used to determine the representation that conforms to a preset continuous distribution. The decoder is used to determine the train delay prediction result after a preset time interval. The adjacency matrix corresponding to the edges between train nodes after the update is determined based on the characteristics of train nodes in the initial railway network graph.

2. The method according to claim 1, characterized in that, The process involves inputting the initial railway network map at the current moment into the railway network delay evolution prediction model, and determining the train delay prediction result after a preset time interval based on the characteristics of the nodes and edges in the initial railway network map and the initial adjacency matrix corresponding to the edges. This includes: Based on the characteristics of train nodes in the initial railway network graph, determine the adjacency matrix corresponding to the edges between the updated train nodes. Replace the adjacency matrix corresponding to the edge between train nodes in the initial adjacency matrix of the initial railway network graph with the updated adjacency matrix corresponding to the edge between train nodes to determine the updated railway network graph. Based on the updated railway network map, the predicted train delays are determined after a preset time interval.

3. The method according to claim 2, characterized in that, The process of determining the adjacency matrix corresponding to the edges between train nodes based on the characteristics of train nodes in the initial railway network graph includes: Feature extraction is performed on the features of train nodes in the initial railway network diagram to determine the first train node embedding corresponding to the train node. Based on the first train node embedding, determine the first edge embedding corresponding to the edge between the train nodes; Based on the first edge embedding, the second train node embedding is determined; The second edge embedding is determined based on the second train node embedding; Based on the second edge embedding, the adjacency matrix corresponding to the edges between the updated train nodes is determined.

4. The method according to claim 3, characterized in that, The train delay prediction results determined based on the updated railway network map after a preset time interval include: The adjacency matrix corresponding to the edges between the updated train nodes is normalized based on the preset continuous distribution to obtain a representation that conforms to the preset continuous distribution. Based on the representation conforming to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, the train delay prediction result after the preset time interval is determined.

5. The method according to claim 4, characterized in that, The step of determining the train delay prediction result after a preset time interval based on the representation conforming to the preset continuous distribution, and the characteristics of the nodes and edges in the updated railway network graph, includes: Based on the representation that conforms to the preset continuous distribution, a third edge embedding is determined, which is used to indicate whether there is a connection between train nodes; Based on the third edge embedding, the features of the nodes and the features of the edges in the updated railway network graph, the train nodes in the updated railway network graph are aggregated with other nodes to determine the features of the updated train nodes. Based on the third edge embedding, the features of the nodes and edges in the updated railway network graph, the station nodes in the updated railway network graph are aggregated to determine the features of the updated station nodes. Based on the third edge embedding, the characteristics of the updated train node, the characteristics of the updated station node, the characteristics of the interference event node in the updated railway network graph, and the characteristics of the edges, the characteristics of the target train node are determined. Based on the characteristics of train nodes in the updated railway network diagram and the characteristics of the target train node, the train delay prediction result after a preset time interval is determined.

6. The method according to claim 1, characterized in that, The railway network delay evolution prediction model is a trained railway network delay evolution prediction model, and the method further includes: Input historical railway network map sample data into the initial railway network delay evolution prediction model to obtain the predicted train delay results; The loss function value is calculated based on the predicted train delay results. The initial railway network delay evolution prediction model is trained based on the loss function value to obtain the trained railway network delay evolution prediction model.

7. The method according to claim 6, characterized in that, The loss function includes a divergence component and a reconstruction component. The divergence component is determined based on the encoder output of the initial railway network delay evolution prediction model, and the reconstruction component is determined based on the decoder output of the initial railway network delay evolution prediction model and the label data corresponding to the historical railway network map sample data. The label data is used to represent the actual train delay prediction results.

8. A train delay prediction device, characterized in that, The device includes: The first determining module is used to determine the initial railway network graph at the current time. The nodes in the initial railway network graph include train nodes, station nodes, and interference event nodes. The edges and their corresponding adjacency matrices in the initial railway network graph are used to represent the interaction relationships between the nodes. The second determining module is used to input the initial railway network map at the current time into the railway network delay evolution prediction model, and determine the train delay prediction result after a preset time interval based on the characteristics of the nodes and edges in the initial railway network map and the initial adjacency matrix corresponding to the edges. The characteristics of the train node include any one or more of the following: the train's delay time at the current moment, the time interval between the train and the previous train node, the minimum running time of the train within a preset time interval, the planned running time of the train within a preset time interval, and the occurrence time of the most recent event before the current moment. The characteristics of the station node include the number of arrival tracks and departure tracks in the station; The characteristics of the interference event node include the vectorized interference event; The features of the edges include the features of the edges between station nodes and train nodes, and the features of the edges between station nodes. The features of the edges between station nodes and train nodes include the planned arrival / departure time of the train from the current time to the station. The features of the edges between station nodes include the shortest travel time between stations. The railway network delay evolution prediction model includes an encoder, a latent space, and a decoder. The encoder is used to determine the adjacency matrix corresponding to the edges between train nodes after the update. The latent space is used to determine the representation that conforms to a preset continuous distribution. The decoder is used to determine the train delay prediction result after a preset time interval. The adjacency matrix corresponding to the edges between train nodes after the update is determined based on the characteristics of train nodes in the initial railway network graph.

9. A train delay prediction device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to implement the method of any one of claims 1 to 7 when executing instructions stored in the memory.

10. A non-volatile computer-readable storage medium storing computer program instructions thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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