A method for extrapolating the two-way propagation of train delays caused by inter-regional interference.

Abstract

This invention relates to a method for predicting the two-way propagation of train delays caused by inter-station interference, comprising: obtaining a first set of delays for trains arriving at the next station based on the type of interruption, information about the interruption section, and the railway network topology; performing backpropagation on trains within associated stations based on the emergency handling strategies of associated stations to obtain a second set of delays for trains at all associated stations; constructing a maximal algebraic discrete model with train departure, departure, and arrival at stations as events, and constraints based on the railway network timetable; the constraints include station capacity constraints; and solving the maximal algebraic discrete model using the MAPCP algorithm considering station capacity constraints based on the first and second delay sets to obtain the two-way propagation results. This method can accurately and comprehensively predict the global impact of train delay propagation caused by emergencies, providing technical support for the global optimization of scheduling decisions.

Description

Technical Field

[0001] This invention belongs to the field of train delay propagation technology in high-speed railway networks, and particularly relates to a method for deriving two-way propagation of train delays caused by inter-section interference. Background Technology

[0002] my country's high-speed railway network has evolved from a "four vertical and four horizontal" network to an "eight vertical and eight horizontal" network, characterized by high density, large scale, and a "networked" development pattern. On-time performance is a crucial indicator for evaluating railway operations and determining passenger service experience. High-speed trains typically operate on railway lines according to their scheduled arrival and departure times. However, due to the long operating routes, often spanning multiple provinces, high-speed trains face complex operating environments influenced by varying climates and terrains. Unexpected extreme weather, natural disasters, obstructions, and equipment malfunctions can all cause initial delays. The complex topology of the railway network and the high-speed operation of trains accelerate the dynamic propagation of delays, leading to widespread cascading delays. Large-scale delays can have irreversible negative effects on railway operations and passenger service. For example, large numbers of passengers stranded at stations may experience stampedes due to extreme congestion; simultaneously, a large number of ticket refunds can cause significant economic losses to the railway system.

[0003] To address this, existing technologies provide a method for predicting train delay propagation in high-speed railway networks. This method includes: acquiring train timetables and station track capacity information for all trains within the network to be predicted; establishing a directed weighted network at the physical track level based on the acquired train timetable information; establishing a directed weighted network at the planned timetable level based on the acquired train timetable information; establishing a discrete event dynamic network based on the established directed weighted networks at the physical track level and the planned timetable level, and representing the discrete event dynamic network as a mathematical model of delay propagation using the maximum algebra method; using an initial delay point as input, predicting train delay propagation in the high-speed railway network based on the mathematical model of delay propagation and with track capacity as a constraint. This method can predict the spatiotemporal range of delays across the entire network, providing an important reference for actual operation and maintenance.

[0004] However, the above methods only consider time adjustment as a scheduling means. In reality, the delay propagation process is constrained by factors such as interval operation restrictions, station track number restrictions, and station detention strategies adopted by the railway bureau for safety reasons. As a result, the existing prediction methods result in spatiotemporal inaccuracies and biases in the prediction results. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the aforementioned problems in the prior art, this invention provides a method for deriving the two-way propagation of train delays caused by inter-regional interference.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] This invention provides a method for extrapolating the two-way propagation of train delays caused by inter-regional interference, including:

[0010] S10. Based on the type of emergency interruption, the information on the interval of the emergency interruption, and the railway network topology, obtain the first set of delays for the arrival of the running train at the next station;

[0011] S20. Based on the emergency handling strategy of the associated stations, perform backpropagation simulation on the trains running in the associated stations to obtain the second set of delays for all trains running in the associated stations; the associated stations are all stations that are associated with the delays of the trains running in the first set of delays.

[0012] S30. Based on the timetable of the railway network, construct a maximal algebraic discrete model with train departure, departure and arrival at stations as events and constraints.

[0013] The constraints include station capacity constraints, dwell time constraints, departure interval time constraints, arrival interval time constraints, and interval travel time constraints.

[0014] S40. Based on the first delay set and the second delay set, the MAPCP algorithm, which takes into account station capacity constraints, is used to solve the maximum algebraic discrete model and obtain the bidirectional propagation derivation results.

[0015] Optionally, S10 includes:

[0016] Unexpected event interruption types include: emergency braking scenarios and temporary speed limit scenarios; interference types include: section interruption and temporary speed limit.

[0017] Information on the interruption period of a sudden event includes: the interval in which the sudden event occurred [S] i ,S i+1 The location of the interval where the emergency occurred [s] s g ,s e g The duration of the emergency Δt g =[t s g ,t e g Initial timetable X0

[0018] When φ = 0, it indicates that the interference type is an interval interruption; when φ = 1, it indicates that the interference type is a temporary speed limit.

[0019] Establish a linear correlation between the duration and interruption type of the emergency and the trains operating in the railway network topology to determine whether the emergency falls within the interference interval [S]. i ,S i+1 The first set of delays for trains arriving at the next station is P1;

[0020] S i Representing stations i and S i+1 Representing station i+1, s s g Indicates the location where the interference began; s e g Indicates the location where the interference ended; t s g Indicates the start time of the interference; t e g Indicates the start time of the interference; Δt g Indicates the duration of the interference.

[0021] Optionally, S20 includes:

[0022] For each associated station, based on the station's emergency response strategy, station capacity, predefined backpropagation range, and the duration of the emergency [t], s g ,t e g A linear relationship is established between [t] and station capacity, and [t] is used to determine the relationship between [t] and station capacity. s g ,t e g The N2 trains within the [] are used to perform station capacity detection to obtain the second delay subset of all delayed trains departing from that station; the second delay subsets of all stations in the associated stations are combined to form the second delay set P2;

[0023] t s g Indicates the start time of the interference; t e g Indicates the time when the interference started.

[0024] Optionally, S20 includes:

[0025] For each of the associated stations, based on the station's emergency response strategy, assuming there are k trains located in the interference zone [S] i ,S i+1 In the above formulas (2) to (4), the actual arrival time and initial delay of train j are calculated.

[0026]

[0027]

[0028]

[0029] Where, when φ=0, When φ = 1, The calculation is the actual arrival time of the j-th train, while formula (4) calculates the initial delay;

[0030] The trains whose actual arrival time varies and all trains with initial delays are grouped into a second delay set P2;

[0031] Train N2 is numbered S = {jk-1,jk-2,…,jk-N2}, and is at station S i The vehicle was previously in position, and when it stopped at station S... i The number of trains in the interval [S] i-1 ,S i The sum of the number of operations is greater than station S. i When the capacity is reached, station S i This will trigger the suspension policy;

[0032] During the duration of the disturbance, stop moving to interval [S] i ,S i+1 [Departure, for car jk-1, it departs from station S] i The time is t e g For subsequent trains, the departure time of the first batch of detained trains is calculated based on formula (5). for:

[0033]

[0034] Where Δk represents the order of trains stopped at the station, and η represents the order of stations. This process The process terminates at the designated time and updates P2.

[0035] Indicates the interval [S] i ,S i+1 The time taken for the j-th vehicle to run; This represents the time taken for the braking of the j-th vehicle. This represents the time spent by the j-th vehicle's traction component; This represents the time spent by the j-th vehicle during the cruise phase; This indicates the actual time when the j-th vehicle leaves station i; This represents the planned arrival time of the j-th vehicle at station i+1; Indicates arrival interval time constraints; Let represent the delay time of the j-th vehicle leaving the (i+1)-th station. This represents the time when the j-th vehicle actually leaves the (i+1)-th station. This represents the time when the j-th car is scheduled to leave the (i+1)-th station.

[0036] Optionally, S30 includes:

[0037] Based on the timetable and topology of the current railway network, a maximal algebraic discrete model is constructed, with train departure, arrival, and departure from the station as events.

[0038]

[0039] Where A is an n×n constraint matrix, and its element a pq Indicates event e p and e q There are constraint values ​​that exist, when e p and e q When there is a direct correlation, a pq It equals the specific constraint value; and when e p and e q When they are independent of each other, a pq =ε;T n×1 X represents the planned time of the event. n×1 P represents the actual time of the event. n×1 Let T represent the initial set of delays; T and P both represent matrices, and X is a matrix that is updated in real time.

[0040] The constraints include:

[0041] (1) Interval running time constraint: In the interval [S i ,S i+1 The train's travel time must be greater than the minimum interval travel time M. i,i+1 ,Right now:

[0042]

[0043] (2) Arrival interval time constraint: For two adjacent trains, for station S i If two or more routes have the same entry route, their arrival times at the station should not be less than the minimum arrival time. Right now:

[0044]

[0045] (3) Departure interval time constraint: For two adjacent trains, for station S iIf two routes have the same exit route, the interval between their departures from the station should not be less than the minimum arrival interval. Right now:

[0046]

[0047] (4) Dwell time constraint: For train j at station S i The stay time should be greater than the minimum permissible stay time, that is:

[0048]

[0049] (5) Station capacity constraint: Station capacity represents the number of trains that a station can accommodate. When a station's tracks are full, no other trains are allowed to enter. In reality, trains are not allowed to stop on the main tracks of a station. The station capacity is the total number of tracks minus one main track. Define the auxiliary variable χ. i (t) indicates that at time t, station S i The number of trains stopping, default χ i (t) = 0; when station S i After an arrival event occurs at time t, χ i (t) = 1; when station S i After a departure event occurs at time t, χ i (t) = -1; the station S at time t. i The number of trains is calculated as follows:

[0050] t' represents a time point between 0 and t;

[0051] Define c i Station S i If the number of tracks is given, then the following constraint holds:

[0052]

[0053] in, This represents the actual departure time of train j*, which is the first train to leave station i. This indicates the minimum safe time interval between train arrival and departure events due to the interlocking rules inherent within the station.

[0054] Optionally, S40 includes:

[0055] Using the first and second delay sets as inputs to a maximal algebraic discrete model, the MAPCP algorithm, which considers station capacity constraints, is used to solve for the associated delay values, including:

[0056] S41: Constructing the constraint matrix: The constraint matrix A is n e ×ne A matrix whose elements a p,q This represents the minimum time interval between events p and q;

[0057] S42: Construction of the predecessor matrix: The predecessor matrix B is also an n e ×n e The matrix, element b p,q For: b p,q =t q -t p +c p,q ;

[0058] Among them, t p and t q Let p and q represent the planned times for events p and q respectively; then B represents the idle time between the two events.

[0059] S43: Forward Graph Construction: C represents the adjacency matrix of the forward graph, and C is also an n e ×n e Let C be a matrix, and the elements of C are defined as follows: if nodes p and q are reachable from matrix B, then C... ij It is equal to the longest path length between nodes p and q in matrix B;

[0060] S44: Define P p =e d,k Indicates the initial delay t dk Given an initial set of delayed nodes, and then for node p, the actual time x p for:

[0061] S45: Capacity Constraint Check: Using the formula Check the capacity of each station; when the number of stopped trains exceeds the station capacity, the arrival time of the trains is delayed according to the station capacity constraint formula; then inject the new delay value into the discrete model based on maximal algebra to calculate the associated delay; if there are no events exceeding the station capacity, exit and obtain the two-way propagation derivation results.

[0062] Optionally, the method further includes:

[0063] The bidirectional propagation simulation results were verified based on model simulation.

[0064] Secondly, the present invention provides a device for predicting the two-way propagation of train delays caused by inter-regional interference, comprising:

[0065] The first acquisition unit is used to acquire the first set of delays for trains to arrive at the next station based on the type of emergency interruption, the information of the emergency interruption section, and the railway network topology.

[0066] The second acquisition unit is used to perform backpropagation deduction on the running trains in the associated stations according to the emergency handling strategy of the associated stations, and to obtain the second delay set of running trains in all associated stations; the associated stations are all stations that are associated with the delay of running trains in the first delay set;

[0067] The construction unit is used to construct a maximal algebraic discrete model and its constraints based on the timetable of the railway network, with train departure, departure and arrival at stations as events.

[0068] The constraints include station capacity constraints, dwell time constraints, departure interval time constraints, arrival interval time constraints, and interval travel time constraints.

[0069] The result derivation unit is used to solve the maximal algebraic discrete model based on the first delay set and the second delay set, using the MAPCP algorithm that takes into account station capacity constraints, and obtain the bidirectional propagation derivation results.

[0070] Optionally, the types of sudden event interruptions include: emergency braking scenarios and temporary speed limit scenarios; the types of interference include: section interruptions and temporary speed limits.

[0071] Information on the interruption period of a sudden event includes: the interval in which the sudden event occurred [S] i ,S i+1 The location of the interval where the emergency occurred [s] s g ,s e g The duration of the emergency Δt g＝ [t s g ,t e g Initial timetable X0

[0072] When φ = 0, it indicates that the interference type is an interval interruption; when φ = 1, it indicates that the interference type is a temporary speed limit.

[0073] The first acquisition unit is specifically used to establish a linear correlation between the duration and interruption type of the emergency and the trains running in the railway network topology, and to determine whether the emergency falls within the interference interval [S] within the event range where the emergency occurred. i ,S i+1 The first set of delays for trains arriving at the next station is P1;

[0074] S i Representing stations i and S i+1 Representing station i+1, s s g Indicates the location where the interference began; s e gIndicates the location where the interference ended; t s g Indicates the start time of the interference; t e g Indicates the start time of the interference; Δt g Indicates the duration of the interference.

[0075] Thirdly, the present invention provides a computing device, comprising: a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program in the memory and performs the steps of the method for calculating the bidirectional propagation of inter-regional interference train delays as described in any of the first aspects above.

[0076] (III) Beneficial Effects

[0077] The present invention provides a method for deducing the two-way propagation mechanism of train delays under section interruption, which can accurately and comprehensively predict the global impact of train delay propagation caused by sudden events, providing technical support for the global optimization of scheduling decisions, and has important theoretical and practical application significance.

[0078] This invention addresses the problems of traditional train delay propagation methods, such as neglecting actual dynamic constraints, insufficient consideration of scheduling strategies, and spatiotemporal bias in prediction results. It proposes a method for deducing the two-way propagation mechanism of train delays under section interruption, which assists dispatchers and railway systems in formulating adjustment strategies, predicting stations and train numbers where delays will occur in advance, and notifying passengers to replan their trips in advance. This promotes the development of dispatching from reactive post-event response to proactive pre-event decision-making. Attached Figure Description

[0079] Figure 1A A flowchart illustrating a two-way propagation deduction method for inter-regional interference train delays provided by the present invention;

[0080] Figure 1B This is a diagram illustrating a train operation scenario under inter-section interference.

[0081] Figure 2 This is a diagram illustrating a train operation scenario under inter-section interference.

[0082] Figure 3A This is a diagram of the artificial railway network topology.

[0083] Figure 3B This is the timetable for trains S1 to S7;

[0084] Figure 3C This is the train timetable for S1 to S5;

[0085] Figure 4A , Figure 5A These are schematic diagrams illustrating the scenario of interval interruption;

[0086] Figure 4B , Figure 5B These are schematic diagrams of temporary speed limit scenarios;

[0087] Figure 6 A schematic diagram of the actual railway network of the Beijing-Tianjin-Hebei region;

[0088] Figure 7A This is a schematic diagram illustrating a 1-hour railway outage in the actual Beijing-Tianjin-Hebei railway network.

[0089] Figure 7B This is a schematic diagram of a temporary speed limit scenario for 2 hours in the actual railway network of the Beijing-Tianjin-Hebei region.

[0090] Figure 7C This is a schematic diagram illustrating a scenario of railway line disruption in the actual Beijing-Tianjin-Hebei railway network.

[0091] Figure 7D This is a schematic diagram of a temporary speed limit scenario in the actual railway network of the Beijing-Tianjin-Hebei region.

[0092] Figure 8A This is a schematic diagram of the deduction result of a part of the actual railway network of the "Beijing-Tianjin-Hebei" region.

[0093] Figure 8B This is a schematic diagram of the second deduction result based on a portion of the actual railway network of the Beijing-Tianjin-Hebei region;

[0094] Figure 9 This is a schematic diagram of some topological parameters of the actual railway network of the Beijing-Tianjin-Hebei region. Detailed Implementation

[0095] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0096] In the current railway network, when an initial delay occurs, the railway dispatching and command system will restore service immediately and prevent the widespread spread of cascading delays. However, considering the unpredictability, high intensity, and long duration of sudden interference, the multi-line crossover of train delays caused by section interruptions, and the limited number of tracks and manual adjustment strategies at stations, dispatchers find it difficult to quickly provide feasible and effective dispatching strategies to restore operations. Furthermore, the entire process from the generation of dispatching strategies to their dissemination to the railway site requires simultaneous coordination among multiple departments, resulting in a lag in the effectiveness of the strategies. Previously formulated dispatching strategies may even become unsuitable for the current situation during widespread delays. Moreover, in the case of large-scale delays, delayed trains and affected stations are distributed across different lines and railway bureaus nationwide. Therefore, accurately predicting the delayed train numbers and affected stations under large-scale delays can assist dispatchers at each station in developing timetable adjustment strategies from a national network perspective, promptly preventing potential delays, and promoting a shift in the dispatching system from passive response to proactive decision-making.

[0097] Traditional methods for understanding delay propagation mechanisms often model delays using static time constraints based on periodic timetables, and only consider time adjustment as a scheduling method. In reality, delay propagation is constrained by limitations on inter-station operation, the number of tracks at stations, and station stopping strategies adopted by railway bureaus for safety reasons. Current research has not considered these factors, resulting in the current deduction of delay propagation mechanisms only being able to propagate in the direction of train movement. The backward propagation caused by stopping strategies has not been fully considered, leading to spatiotemporal inaccuracies and biases in the deduction results.

[0098] The present invention provides a method for deducing the two-way propagation mechanism of train delays under section interruption, which can accurately and comprehensively predict the global impact of train delay propagation caused by sudden events, and provide technical support for the global optimization of scheduling decisions, which has important theoretical and practical application significance.

[0099] Example 1

[0100] As shown in Figures 1 to 7, this invention provides a method for predicting the two-way propagation of train delays caused by inter-regional interference. The method is executed by a computing device and includes the following steps:

[0101] S10. Based on the type of emergency interruption, the information on the interval of the emergency interruption, and the railway network topology, obtain the first set of delays for the arrival of the running train at the next station;

[0102] In this embodiment, the types of sudden event interruptions include: emergency braking scenarios and temporary speed limit scenarios; the types of interference include: section interruptions and temporary speed limits.

[0103] Information on the interruption period of a sudden event includes: the interval in which the sudden event occurred [S] i ,S i+1 The location of the interval [s] s g ,s e g The duration of the event [t] s g ,t e g ] = Δtg, initial timetable X0, when φ = 0, it indicates that the interference type is interval interruption, when φ = 1, it indicates that the interference type is temporary speed limit;

[0104] A linear correlation is established between the duration and interruption type of the emergency and the initial delay of trains operating in the railway network topology to determine the affected interval [S] within the event range of the emergency. i ,S i+1 The first set of delays for trains arriving at the next station is P1.

[0105] S i Representing stations i and S i+1 Representing station i+1, s s g Indicates the location where the interference began; s e g Indicates the location where the interference ended; t s g Indicates the start time of the interference; t e g Indicates the time when the interference ends; Δt g Indicates the duration of the interference.

[0106] In this embodiment, the process of generating the initial delay can be described as obtaining the first delay set P1 and the second delay set P2.

[0107] S20. Based on the emergency handling strategy of the associated stations, perform backpropagation simulation on the trains running in the associated stations to obtain the second set of delays for all trains running in the associated stations; the associated stations are all stations that are associated with the delays of the trains running in the first set of delays.

[0108] In this embodiment, based on the emergency handling strategies of each associated station, and the linear relationship between station capacity, the scope of back propagation, the duration of the emergency, and station capacity, the duration [t] is determined. s g ,t e g The N2 trains within the station will perform station capacity detection, which will result in the second delay set P2 of the trains departing from the station via backpropagation.

[0109] The range of backpropagation can be roughly estimated in advance using delay propagation algorithms, such as locating North China. By narrowing the range, the computation time of the algorithm can be improved. Typically, train timetables specify the direction of train travel. Backpropagation works by moving the delay in the opposite direction specified in the timetable; specifically, if the station ahead is blocked, the train will be stuck inside the station along its intended direction of travel.

[0110] Further, S20 includes:

[0111] Assume there are k trains located in the affected section [S] i ,S i+1 In the above, based on the different strategies adopted by trains operating in the section before and after the interference, the actual arrival time and initial delay of train j are calculated;

[0112]

[0113]

[0114]

[0115] Where, when φ=0, When φ = 1,

[0116] Car N2 is numbered S = {jk-1,jk-2,…,jk-N2}. In S… i The train was running at its previous position when it stopped at station S. i The number of trains in the interval [S] i-1 ,S i The sum of the number of operations is greater than station S. i When the capacity is reached, station S i This will trigger a stop strategy, meaning that during the duration of the interference, movement into the interval [S] will be stopped. i ,S i+1 [Departure, for car jk-1, it departs from station S] i The time is t e g For subsequent trains, the departure time of the first batch of detained trains is calculated based on formula (5). for:

[0117]

[0118] Where Δk represents the order of trains stopped at the station, and η represents the order of stations.

[0119] This process The process terminates at that time and updates P2.

[0120] Indicates the interval [S] i ,S i+1 The time taken for the j-th vehicle to run; This represents the time taken for the braking of the j-th vehicle. This represents the time spent by the j-th vehicle's traction component; This represents the time spent by the j-th vehicle during the cruise phase; This indicates the actual time when the j-th vehicle leaves station i;

[0121] This represents the planned arrival time of the j-th vehicle at station i+1; Indicates arrival interval time constraints; Let represent the delay time of the j-th vehicle leaving the (i+1)-th station. This represents the time when the j-th vehicle actually leaves the (i+1)-th station. This represents the time when the j-th car is scheduled to leave the (i+1)-th station.

[0122] S30. Based on the timetable of the railway network, construct a maximal algebraic discrete model with train departure, departure and arrival at stations as events and constraints.

[0123] The constraints include station capacity constraints, dwell time constraints, departure interval time constraints, arrival interval time constraints, and interval travel time constraints.

[0124] S40. Based on the first delay set and the second delay set, the MAPCP algorithm, which takes into account station capacity constraints, is used to solve the maximum algebraic discrete model and obtain the bidirectional propagation derivation results.

[0125] This embodiment presents a method for deducing the two-way propagation mechanism of train delays under section interruption. It can accurately and comprehensively predict the global impact of train delay propagation caused by sudden events, providing technical support for the global optimization of scheduling decisions. It has important theoretical and practical application significance.

[0126] Example 2

[0127] Combination Figure 1B Figure 8 provides a detailed description of the method described in Embodiment 1.

[0128] Step 1: First, a detailed classification of the mechanisms by which sudden events occur in the railway section, causing initial delays for the lead train, is performed. Based on the emergency response strategy adopted by the first train encountering the event, the section interruption is divided into two scenarios: one where the train applies emergency braking, preventing the lead train from reaching the target station on time as scheduled (defined as the emergency braking scenario); and the other where the train operates at the speed stipulated by the temporary speed limit order, resulting in an initial delay that prevents it from reaching the target station on time (defined as the temporary speed limit scenario). The emergency response strategy adopted by the train also reflects the degree of impact of the sudden event on the railway network. Considering the complexity of sudden events, classifying them based on the emergency response strategy adopted by the train is more appropriate.

[0129] Define the interval in which the emergency occurs [S] i ,S i+1 The location of the interval [s] s g s e g The duration of the event [t] s g ,t e g The initial timetable X0 indicates that when φ = 0, the disturbance type is a section interruption; when φ = 1, the disturbance type is a temporary speed limit. A section interruption is the train's use of emergency braking. Specifically... Figure 1B As shown.

[0130] Step 2: Establish a linear relationship between the duration and type of the emergency and the initial delay process, that is, by knowing the duration Δt of the emergency. g And by using type φ, the initial delay time of the first train affected by the interference is estimated, and the affected section [S] within the event range of the sudden event is determined. i ,S i+1 The set of arrival delays P1 for trains in operation to reach the next station, such as... Figure 2 As shown.

[0131] Suppose there are k cars S = {j-1,j-2,…,jk} located in the interference interval [S i ,S i+1 The details are as follows, based on the different strategies adopted by trains operating in the sections before and after the disturbance. Figure 2 As shown, calculate the actual arrival time and initial delay of train j.

[0132]

[0133]

[0134]

[0135] Where, when φ=0, When φ = 1,

[0136] Step 3: Consider the impact of the station's train-stopping strategy in the face of an emergency. That is, when a train stops and slows down in a section, subsequent stations, for safety and passenger evacuation convenience, will stop the departure of subsequent trains, creating a reverse propagation. By considering station capacity, the scope of reverse propagation is linearly related to the duration of the emergency and the station capacity. This is achieved by considering the duration [t]. s g ,t e g The N2 cars within the station will have their station departure delay set P2 obtained through backpropagation when the station capacity is checked.

[0137] Train N2 is numbered S = {jk-1,jk-2,…,jk-N2}, where j represents the train number and k represents the nth station in the reverse direction. i The train was running at its previous position when it stopped at station S. i The number of trains in the interval [S] i ,S i+1 The sum of the number of operations is greater than station S. i When the capacity is reached, station S i This will trigger a stop strategy, meaning that during the duration of the interference, movement into the interval [S] will be stopped. i ,S i+1 Departure, for those in S i This also applies to stations preceding the station; therefore, for the (jk-1)th car, its departure time from station Si is t. e g For subsequent trains, the departure time for the first batch of detained trains is:

[0138]

[0139] Where Δk represents the order of trains stopped at the station, and η represents the order of stations. This process The process terminates at that time and updates P2.

[0140] Step 4: Based on the timetable and topology of the railway network under study, construct a maximal algebraic discrete system (i.e., a discrete model) with train departures, arrivals, and departures at stations as events. This discrete model also incorporates station capacity from the railway network topology. A refined model of the delay propagation process on the railway network under sudden events is then performed, yielding the system equations:

[0141]

[0142] Where A is an n×n constraint matrix, and its element a pq Indicates event e p and e q There are constraint values ​​that exist, when e p and e q When there is a direct correlation, a pq It equals the specific constraint value; and when e p and e q When they are independent of each other, a pq =ε;T n×1 X represents the planned time of the event. n×1 P represents the actual time of the event. n×1 This represents the initial set of delays, and the specific constraints mainly include five types, as follows:

[0143] (1) Interval running time constraint: The time requirement is that the time within the interval [S] is within the range of [S] i ,S i+1 The train's travel time must be greater than the minimum interval travel time M. i,i+1 ,Right now:

[0144]

[0145] (2) Arrival interval time constraint: For two adjacent trains, their arrival interval time with respect to station S i If two or more routes have the same entry route, their arrival times at the station should not be less than the minimum arrival time. Right now:

[0146]

[0147] (3) Departure interval time constraint: For two adjacent trains, their departure interval time for station S i If two routes have the same exit route, the interval between their departures from the station should not be less than the minimum arrival interval. Right now:

[0148]

[0149] (4) Dwell time constraint: For train j at station S i The stay time should be greater than the minimum permissible stay time, that is:

[0150]

[0151] (5) Station capacity constraint: Station capacity represents the number of trains that a station can accommodate. When a station's tracks are full, no other trains are allowed to enter. Considering that trains are not allowed to stop on the main tracks of an actual station, the station capacity is the total number of tracks minus one main track. An auxiliary variable χ is defined. i (t) indicates that at time t, station S i The number of trains stopping, default χ i (t) = 0; when station S i After an arrival event occurs at time t, χ i (t) = 1; when station S i After a departure event occurs at time t, χ i (t) = -1; therefore, the station S at time t is where the person is. i The number of trains can be calculated as follows:

[0152]

[0153] Define c i Station S i If the number of tracks is given, then the following constraint holds:

[0154]

[0155] in, This represents the actual departure time of train j*, which is the first train to leave station i. This indicates the minimum safe time interval between train arrival and departure events due to the interlocking rules inherent within the station.

[0156] Step 5: Merge the delay sets obtained in Step 2 and Step 3 to obtain the initial delay set P. Using the initial delay event as input, and based on the discrete model of delay propagation established in Step 4, the MAPCP algorithm considering station capacity constraints is used to solve for the associated delay value. The specific steps are as follows.

[0157] (51) Constructing the constraint matrix: The constraint matrix A is n e ×n e A matrix whose elements a p,q This represents the minimum time interval between events p and q.

[0158] (52) Construction of the predecessor matrix: The predecessor matrix B is also an n e ×n e A matrix whose elements b p,q The calculation can be performed as follows.

[0159] b p，q =t q -t p +cp，q

[0160] Among them, t p and t q Let A and B represent the planned times for events p and q, respectively; then B represents the idle time between the two events.

[0161] (53) Forward graph construction: C represents the adjacency matrix of the forward graph, and C is also an n e ×n e Let C be a matrix, and the elements of C are defined as follows: if nodes p and q are reachable from matrix B, then C... ij It is equal to the longest path length between nodes p and q in matrix B.

[0162] (54) Define P p =e d,k Indicates the initial delay t dk Given an initial set of delayed nodes, and then for node p, the actual time x p It can be calculated using the following formula.

[0163]

[0164] (55) Capacity constraint check: Use the formula Check the capacity of each station; when the number of stopped trains exceeds the station capacity, the arrival time of the trains is delayed according to the station capacity constraint formula. Then, inject the new delay value into the discrete system based on maximal algebra and proceed to step 5 to calculate the associated delay; if there are no events exceeding the station capacity, exit the algorithm.

[0165] The above embodiments are based on model design and simulation. For the inter-section interruption scenario, the relationship between the interference duration, initial delay, and total delay is studied; for the temporary speed limit scenario, the relationship between the speed limit value, initial delay, and total delay is studied.

[0166] This embodiment can accurately and comprehensively predict the global impact of train delays caused by emergencies, providing technical support for the global optimization of scheduling decisions. For example, it can assist dispatchers and railway systems in formulating adjustment strategies, predicting in advance the stations and trains where delays will occur, and notifying passengers to replan their trips in advance, thus promoting the development of scheduling from reactive post-event response to proactive pre-event decision-making.

[0167] The technical solution of this application will be further explained below with reference to specific railway network embodiments. To illustrate the effectiveness of the prediction model, it is verified through the design of an artificial railway network and an actual railway network. The first part selects an artificial railway network, with the railway topology as follows: Figures 3A to 3CAs shown, the timetable includes two lines, 7 stations, and 6 sections, with a total of 45 trains. For ease of calculation, the length of all sections is set to 150km. The second part selects the "Beijing-Tianjin-Hebei" railway network, which has 35 ordinary stations and 5 hub stations. The timetable is crawled from the 12306 website on February 20, 2022, which records 258 trains running on the railway network.

[0168] (1) Artificial railway network:

[0169] Let v1 = 280 km / h, v2 = 320 km / h, vlim = 350 km / h, for such Figure 2 The train running curve shown makes the first traction increase

[0170] The speed is 0.9 m / s 2 The first and second braking accelerations are 1 m / s². 2 The second traction acceleration is 1.2 m / s². 2 The interference occurs in the [S2, S3] section, with the train running in the [S1, S3] direction. For the section interruption scenario, assuming the first train experiences a equipment failure between 9:30 and 10:30, triggering emergency braking, two trains will be stranded in the section, incurring delays at locations of 96.475km and 73.141km, with initial delays of 102 and 100 minutes respectively. For the temporary speed limit scenario, assuming the interference occurs in the [S2, S3] section... Strong winds occurred between 60km and 95km, lasting from 9:35 to 12:30. Assuming the temporary speed limit was 80km / h, we can see that during the duration of the strong winds, a total of 5 trains were running on the section, and 3 trains were delayed. When the strong winds began, the temporary speed limit was applied at 76.425km, 47.252km, and 18.148km, with delays of 3, 20, and 37 minutes, respectively. The other two trains were not delayed because they had already left the wind zone when the strong winds began. The initial delays were injected into the discrete system, and the MAPCP algorithm was used to solve for the nodes with associated delays and separate the delay time. The results are shown in the figure. The black solid line represents the arrival event of the station, and the black dashed line represents the arrival event of the station. Through analysis, it can be seen that for both scenarios, the number of stations affected by the delay is 7. For the section interruption scenario, the number of trains affected by the delay is 8. For the temporary speed limit scenario, the number of trains affected by the delay is 9. It can also be seen that even if the interference occurs in [S2,S3] and the train runs from S1 to S2, the delay will propagate along the station S1 in the opposite direction of the train's run.

[0171] (2) The Beijing-Tianjin-Hebei railway network:

[0172] The relevant parameter settings for the "Beijing-Tianjin-Hebei" railway network topology are as follows: Figure 9 Table 1 shows that the main parameters include the section length, minimum running time, and stop time in the railway network topology. Taking the train delay incident at Beijing South Railway Station during the May Day holiday in 2021 as an example, a simulation was designed. The interference occurred at 9:30 AM in the Beijing-Zhuozhou section. For the scenarios of section interruption and temporary speed limit, the duration of the interference was designed to be 1 hour and 2 hours for delay prediction. For the temporary speed limit scenario, the speed limit was 80 km / h, and the interference location occurred at half the section length. The simulation results are as follows. Figure 8A and Figure 8B As shown; simultaneously, statistics on the delay results are compiled, including the number of stations affected, the number of trains affected, the initial delay time, and the associated delay time, etc. Figure 9 As shown in Table 2.

[0173] Example 3

[0174] In addition, this embodiment of the invention also provides a device for predicting the two-way propagation of train delays caused by inter-regional interference. This device can be a device in any computing device. The device in this embodiment includes:

[0175] The first acquisition unit is used to acquire the first set of delays for trains to arrive at the next station based on the type of emergency interruption, the information of the emergency interruption section, and the railway network topology.

[0176] The second acquisition unit is used to perform backpropagation deduction on the running trains in the associated stations according to the emergency handling strategy of the associated stations, and to obtain the second delay set of running trains in all associated stations; the associated stations are all stations that are associated with the delay of running trains in the first delay set;

[0177] The construction unit is used to construct a maximal algebraic discrete model and its constraints based on the timetable of the railway network, with train departure, departure and arrival at stations as events.

[0178] The constraints include station capacity constraints, dwell time constraints, departure interval time constraints, arrival interval time constraints, and interval travel time constraints.

[0179] The result derivation unit is used to solve the maximal algebraic discrete model based on the first delay set and the second delay set, using the MAPCP algorithm that takes into account station capacity constraints, and obtain the bidirectional propagation derivation results.

[0180] In this embodiment, the types of sudden event interruptions include: emergency braking scenarios and temporary speed limit scenarios; the types of interference include: section interruption and temporary speed limit.

[0181] Information on the interruption period of a sudden event includes: the interval in which the sudden event occurred [S] i ,Si+1 The location of the interval where the emergency occurred [s] s g ,s e g The duration of the emergency Δt g＝ [t s g ,t e g Initial timetable X0

[0182] When φ = 0, it indicates that the interference type is an interval interruption; when φ = 1, it indicates that the interference type is a temporary speed limit.

[0183] At this point, the first acquisition unit mentioned above can be specifically used to establish a linear correlation between the duration and interruption type of the emergency and the trains running in the railway network topology, and to determine whether the emergency falls within the interference interval [S] within the event range where the emergency occurred. i ,S i+1 The first set of delays for trains arriving at the next station is P1;

[0184] S i Representing stations i and S i+1 Representing station i+1, s s g Indicates the location where the interference began; s e g Indicates the location where the interference ended; t s g Indicates the start time of the interference; t e g Indicates the start time of the interference; Δt g Indicates the duration of the interference.

[0185] According to another aspect of the present invention, embodiments of the present invention also provide a computing device, including: a memory and a processor, wherein the memory stores a computer program, the processor executes the computer program in the memory, and performs the steps of the method for calculating the bidirectional propagation of inter-regional interference train delays as described in Embodiment 1 or Embodiment 2 above.

[0186] In the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0187] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for deducing train delay bidirectional propagation under section interference, characterized in that, Comprise: S10, according to the emergency interruption type, the emergency interruption interval information and the railway network topology, obtain the first delay set of the running train arriving at the next station; The emergency interruption type includes: emergency braking scene, temporary speed limit scene; S20, according to the emergency processing strategy of the associated station, the running train in the associated station is carried out reverse propagation deduction, and the second delay set of the running train of all associated stations is obtained; Associated station is all stations associated with the delay of the running train in the first delay set; S20 comprises: for each station of the associated stations, according to the emergency handling strategy of the station, the station capacity, the pre-defined range of the back propagation, the time duration of the emergency and the station capacity, linearly associating, and performing the station capacity detection on N2 trains in the station to obtain a second delay subset of all delayed trains when departing from the station; grouping the second delay subsets of all stations in the associated stations to form a second delay set P2; S20 comprises: for each station of the associated stations, according to the emergency handling strategy of the station, the station capacity, the pre-defined range of the back propagation, the time duration of the emergency and the station capacity, linearly associating, and performing the station capacity detection on N2 trains in the station to obtain a second delay subset of all delayed trains when departing from the station; grouping the second delay subsets of all stations in the associated stations to form a second delay set P2; S20 comprises: for each station of the associated stations, according to the emergency handling strategy of the station, the station capacity, the pre-defined range of the back propagation, the time duration of the a time at which the occurrence of the interference starts; a time at which the occurrence of the interference ends; The range of reverse propagation is the range deduced in advance by the delay propagation algorithm, S30, according to the timetable of the railway network, a max-plus algebra discrete model and constraint condition are constructed with train departure, leaving and arriving station as events; The constraint condition includes station capacity constraint, stay time constraint, leaving interval time constraint, arrival interval time constraint and interval running time constraint; S40, according to the first delay set and the second delay set, the max-plus algebra discrete model is solved by using the MAPCP algorithm considering the station capacity constraint, and the bidirectional propagation deduction result is obtained; The station capacity represents the number of trains that the station can accommodate, and the station capacity is the number of all tracks of the station minus a main track.

2. The method of claim 1, wherein, The S10 comprises: The interference type includes: interval interruption and temporary speed limit; The emergency interruption section information includes: a section where the emergency occurs a position of the section where the emergency occurs a duration of the emergency an initial schedule X0, When , indicates that the interference type is an interval interruption, when , indicates that the interference type is a temporary speed limit; linearly associating the duration of the incident, the type of interruption and the trains running in the railway network topology, determining the first set of delays P1 of the trains running in the railway network topology that reach the next station within the range of events of the incident the first set of delays P1 of the trains running in the railway network topology that reach the next station within the range of events of the incident denotes a station i, denotes a station i+1, denotes a position where the disturbance occurrence starts; denotes a position where the disturbance occurrence ends; denotes a time when the disturbance occurrence starts; denotes a time when the disturbance occurrence starts; denotes a time duration of the disturbance.

3. The method of claim 1, wherein, The S20 comprises: For each station in the associated stations, based on the station's incident handling strategy, assume that there are k trains located in the interference section In this case, the actual arrival time and initial delay of the jth train are calculated according to the following equations (2) to (4); (2) (3) (4) wherein when , , ; when , ; The second delay set P2 is composed of the train with time change and all trains with initial delay; Train N2 is numbered as follows At the station Previously in position, when stopped at the station The number of trains in the section and in the interval The sum of the number of operations is greater than the number of stations. When the station has the capacity, This will trigger the suspension policy; During the duration of the disturbance, stop sending intervals to the section The departure time of the first train is The departure time of the first train is For the subsequent trains, the departure time of the first batch of trains that are stopped is calculated based on formula (5) : （5） wherein, denotes the order of trains that are coupled at the station, and denotes the order of stations, the process terminates when P2 is updated. Indicates the interval The time taken for the j-th vehicle to run; This represents the time taken for the braking of the j-th vehicle. This represents the time spent by the j-th vehicle's traction component; This represents the time spent by the j-th vehicle during the cruise phase; This indicates the actual time when the j-th vehicle leaves station i; This represents the planned arrival time of the j-th vehicle at station i+1; Indicates arrival interval time constraints; Let represent the delay time of the j-th vehicle leaving the (i+1)-th station. This indicates that the j-th car actually left the j-th car. Time at each station This indicates that the j-th car plans to leave the j-th car. The time for each station.

4. The method of claim 3, wherein, The S30 comprises: Based on the timetable and the railway network topology of the current railway network, a max-plus algebra discrete model is constructed with train departure, leaving and arriving station as events, ； where A is a constraint matrix whose elements represent the constraint values existing between events and , when there is a direct correlation between and , equals a specific constraint value; and when and are independent of each other, ; represents the scheduled time of an event, represents the actual time of an event, represents an initial set of delays; T and P each represent a matrix, and X is a matrix that is updated in real time; The constraint condition includes: (1) Interval running time constraint: the running time of a train in an interval must be greater than the minimum interval running time The running time of a train must be greater than the minimum interval running time i.e.: ； (2) Arrival interval constraint: for two adjacent trains, for a station There are the same inbound route, their arrival interval at the station should not be less than the minimum arrival interval That is: ； (3) Departure interval constraint: for two adjacent trains, for a station There are the same outgoing routes, their departure interval from the station should not be less than the minimum arrival interval i.e.: ； (4) dwell time constraint: the dwell time of train j at station i should be greater than the minimum allowed dwell time, i.e.: ​ ； (5) Station capacity constraints: Station capacity represents the number of trains a station can accommodate. When a station's tracks are full, no other trains are allowed to enter. In reality, trains are not allowed to stop on the main tracks of a station. The station capacity is the total number of tracks minus one main track. Define auxiliary variables. Indicates the station at time t. The number of trains stopping (default) When the station After an arrival event occurs at time t When the station After a departure event occurs at time t The station where t is located at time t The number of trains is calculated as follows: ； Definitions represents the number of tracks of a station, the following constraints hold: ； wherein, denotes the first departure time of train j from station i, denotes the actual departure time of train j from station i, denotes the minimum safety time interval between the arrival and departure events of train j at station i due to the interlocking rules embedded in the station.

5. The method of claim 4, wherein, The S40 comprises: The first delay set and the second delay set are used as the input of the max-plus algebra discrete model, and the dependent delay value is solved by using the MAPCP algorithm considering the station capacity constraint, including: S41: Constructing the constraint matrix: the constraint matrix A is a matrix whose elements represent the minimum time interval between events p and q; S42: Precursor matrix construction: The precursor matrix B is also a matrix with elements : ; wherein, and respectively represent the scheduled time of event p and event q; B represents the free time between the respective two events; S43: Forward graph construction: C represents the adjacency matrix of the precedence graph, then C is also a matrix, and the elements of C are defined as follows, i.e. if node p and node q are reachable in matrix B, then equals the longest path length between node p and node q in matrix B; S44: define the initial delay node set , then for node p, the actual time is: ; S45: Capacity constraint check: use the formula Check the capacity of each station; when the number of stopped trains is greater than the station capacity, the arrival time of the train is delayed according to the station capacity constraint formula; then inject the new delay value into the discrete model based on the max-plus algebra to calculate the cascading delay; if there is no event exceeding the station capacity, exit and obtain the bidirectional propagation deduction result.

6. The method of claim 5, wherein, The method further comprises: Based on model simulation, the bidirectional propagation deduction result is verified.

7. A device for deducing train delay bidirectional propagation under section interference, characterized in that, Comprise: The first acquisition unit is used for obtaining the first delay set of the running train arriving at the next station according to the emergency interruption type, the emergency interruption interval information and the railway network topology; The emergency interruption type includes: emergency braking scene, temporary speed limit scene; The second acquisition unit is used for obtaining the second delay set of the running train of all associated stations by carrying out reverse propagation deduction on the running train in the associated station according to the emergency processing strategy of the associated station; Associated station is all stations associated with the delay of the running train in the first delay set; S20 comprises: for each station of the associated stations, according to the emergency handling strategy of the station, the station capacity, the pre-defined range of the back propagation, the time duration of the emergency and the station capacity, linearly associating, and obtaining a second delay subset of all delayed trains departing from the station by detecting the station capacity of N2 trains in the station The second delay subset belonging to all stations in the associated stations is grouped to form a second delay set P2. a time at which the occurrence of the interference starts; a time at which the occurrence of the interference ends; The range of reverse propagation is the range deduced in advance by the delay propagation algorithm, The construction unit is used for constructing a max-plus algebra discrete model and constraint condition with train departure, leaving and arriving station as events according to the timetable of the railway network; The constraint condition includes station capacity constraint, stay time constraint, leaving interval time constraint, arrival interval time constraint and interval running time constraint; The result deduction unit is used for obtaining the bidirectional propagation deduction result by solving the max-plus algebra discrete model by using the MAPCP algorithm considering the station capacity constraint according to the first delay set and the second delay set. The station capacity represents the number of trains that the station can accommodate, and is the total number of tracks of the station minus one main track.

8. The apparatus of claim 7, wherein, The emergency interruption type includes an emergency braking scene and a temporary speed limit scene, and the interference type includes an interval interruption and a temporary speed limit. The emergency interruption section information includes: a section where the emergency occurs , a position of the emergency occurrence section , a duration of the emergency , an initial schedule X0, When , indicates that the interference type is an interval interruption, when , indicates that the interference type is a temporary speed limit; The first acquisition unit is specifically configured to linearly associate the duration of the emergency event, the interruption type, and the trains running in the railway network topology, determine the trains running in the interference interval within the emergency event occurrence range, and determine the first delay set P1 of the trains running in the interference interval reaching the next station. The first delay set P1 of the trains running in the interference interval reaching the next station. denotes a station i, denotes a station i+1, denotes a position where the disturbance occurrence starts; denotes a position where the disturbance occurrence ends; denotes a time when the disturbance occurrence starts; denotes a time when the disturbance occurrence starts; denotes a time duration of the disturbance.

9. A computing device, comprising: Comprise: A memory and a processor, the memory stores a computer program, the processor executes the computer program in the memory, and executes the steps of the train delay bidirectional propagation deduction method under the interval interference according to any one of claims 1 to 6.

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