A rail transit cooperative energy-saving scheduling method and system based on analytical gradient guided Monte Carlo tree

Abstract

The application relates to the technical field of rail transit scheduling, in particular to a rail transit cooperative energy-saving scheduling method and system based on gradient analysis guided Monte Carlo tree, which comprises the following steps: demarcating a dynamic time window of a braking source train; determining a candidate train and an equivalent candidate train in the dynamic time window, and solving transmission efficiency; constructing a candidate load set, generating a time sequence scheduling action as a Monte Carlo tree search branch, and eliminating a search branch that does not pass a safety check; if the corresponding transmission efficiency is lower than a preset efficiency threshold, constructing a step constraint to extract an effective overlapping time segment, otherwise taking the dynamic time window as the segment; constructing an energy extreme value objective function for the effective overlapping time segment to solve a partial derivative, and taking an energy extreme value as an evaluation value; mapping corresponding continuous time variables into discrete values, updating the Monte Carlo tree according to the evaluation value, and outputting an instruction. The application can solve invalid energy matching caused by neglecting network loss, and improve actual energy recovery rate.

Description

Technical Field

[0001] This application relates to the technical field of rail transit scheduling, and in particular to a collaborative energy-saving scheduling method and system for rail transit based on analytical gradient-guided Monte Carlo trees. Background Technology

[0002] The coordinated operation of multiple trains in urban rail transit relies on timing dispatch instructions issued by the control center. The kinetic energy generated during the braking phase of a train is converted into regenerative braking energy and transmitted along the DC traction power supply network to other trains in traction mode within the same section. To improve the recovery and utilization rate of this energy, conventional train dispatching schemes fine-tune train dwell times and departure intervals to ensure that the operating times of braking and traction vehicles overlap. Such dispatching calculations are constrained by actual operating rules and must use the minimum safe following block distance between trains and the maximum delay tolerance time for the entire line as mandatory execution boundaries.

[0003] Chinese invention patent CN113065239B discloses an energy-saving optimization method for urban rail transit timetables based on an adaptive large neighborhood search algorithm. This scheme defines the traction and braking overlap time of adjacent trains based on departure density and establishes an integer programming model for the timetable. The model uses maximizing the total traction and braking overlap time as the single objective function, with train dwell time and departure interval as decision variables. The solution phase employs an adaptive large neighborhood search algorithm, configured with destructive operators such as random removal, associated node removal, and maximum impact removal, as well as repair operators such as random insertion and greedy insertion. The algorithm performs high-frequency destruction and reconstruction operations on some variables in the current timetable solution set, repeatedly sampling within constraints to search for the departure and dwell parameters with the maximum total overlap time.

[0004] When multiple braking events occur concurrently in a high-density road network, scheduling logic that absolutely equates the time-domain overlap of operating conditions to the actual energy recovery rate deviates from the underlying physical impedance mechanism of the power grid. In actual DC traction networks, power transmission efficiency continuously decreases with the increase of physical distance between trains. Limited by the pure time-dimensional optimization model, when the physical positions of the braking car and the traction car are too far apart, even if the system outputs a scheduling scheme with a very long overlap period, the feedback power will inevitably be largely dissipated as line heat loss during long-distance transmission. At the same time, facing a huge discrete state space, existing algorithms rely on a large amount of random sampling and discrete reconstruction to perform repeated deductions in the pure mathematical domain. Due to the lack of a mechanism to identify invalid high-impedance matching in the physical space and the direction guidance of the physical attenuation gradient, ineffective computing power is consumed, and the final output control command does not reach the optimal physical boundary of actual power grid transmission efficiency. Summary of the Invention

[0005] To address the issue of ineffective energy matching caused by ignoring network losses and improve the actual energy recovery rate, this application provides a collaborative energy-saving scheduling method and system for rail transit based on analytical gradient-guided Monte Carlo trees.

[0006] Firstly, this application provides a rail transit cooperative energy-saving scheduling method based on an analytical gradient-guided Monte Carlo tree, employing the following technical solution: A rail transit cooperative energy-saving scheduling method based on an analytical gradient-guided Monte Carlo tree, comprising:

[0007] Define the dynamic time window for customized dynamic trains;

[0008] The candidate trains within the dynamic time window and the equivalent candidate trains with static load attributes are determined. The physical displacement difference between the two trains and the braking source train is extracted as the evaluation electrical distance, and then the transmission efficiency is solved.

[0009] Those with transmission efficiency lower than a preset efficiency threshold are removed to construct a candidate load set, and their dynamic electrical distance and the relative speed parameters of the candidate trains are extracted;

[0010] Based on the candidate load set, a time-series scheduling action with discrete-time parameters is generated as a Monte Carlo tree search branch, and the search branch that fails the security check is removed;

[0011] When the search reaches the leaf node of the Monte Carlo tree, the discrete-time parameter is converted into a continuous-time variable;

[0012] The relative temporal displacement difference of the candidate trains and the absolute physical displacement difference of the equivalent candidate trains are deduced, and the maximum dynamic electrical distance is extracted by combining the relative speed parameter.

[0013] If the corresponding transmission efficiency is lower than the preset efficiency threshold, a step constraint is constructed to extract the effective overlapping time segment; otherwise, the dynamic time window is taken as the segment.

[0014] For the effective overlapping time segments, construct an energy extremum objective function, solve for the partial derivatives, and perform iterative search along the first-order gradient direction to obtain the energy extremum as the evaluation value;

[0015] The continuous-time variables are mapped to discrete values, the Monte Carlo tree is updated backtracking according to the evaluation value, and the instructions are output.

[0016] Optionally, the dynamic time window for defining the dynamic source train includes:

[0017] Real-time operating parameters are input into the kinematic model to perform forward simulation and extract a set of braking events with energy feedback characteristics;

[0018] The queue is constructed by sorting the events in ascending order of timestamps, and the train associated with the first event is designated as the braking source train.

[0019] The predicted braking start and end times are compensated based on a preset communication delay parameter, and the compensated time is used as the integration boundary to define the dynamic time window.

[0020] Optionally, solving for transmission efficiency and extracting parameters includes:

[0021] Trains that include stops within the dynamic time window are extracted as candidate trains, and ground energy storage devices are mapped as equivalent candidate trains.

[0022] The transmission efficiency is solved by using the minimum displacement difference between the braking source train and the two as the input impedance model for evaluating electrical distance.

[0023] The time-series displacement difference of the candidate load set is calculated as the dynamic electrical distance, and the relative velocity parameter is extracted by differential calculation.

[0024] Optionally, after extracting the effective overlapping time segments, the method further includes:

[0025] If multiple braking or candidate trains are running concurrently in the same power supply section, the dynamic electrical distance of each node in the segment is extracted, and a multi-node equivalent circuit is constructed in the impedance model based on the dynamic electrical distance.

[0026] Based on Kirchhoff's laws, node merging is performed to extract parallel transmission paths. The shunt impedance loss is calculated along these paths, and the transmission efficiency is dynamically solved to incorporate the energy extremum objective function.

[0027] Optionally, the removal of search branches that fail the security check includes:

[0028] The tracking interval and cumulative delay time of the candidate trains after the superimposed scheduling actions are deduced, and the safety margin of the equivalent candidate train charging and discharging commands is verified.

[0029] If the running interval is less than the safe blocking distance, or the delay duration is greater than the delay tolerance time, or the safety margin is not met, the search branch is removed.

[0030] Optionally, the generation of timing scheduling actions includes:

[0031] The station dwell time of the candidate trains is extracted and combined with the discrete level position to determine the station dwell control boundary;

[0032] The available energy storage of the equivalent candidate train and the maximum scheduling time are extracted and combined with the discrete level to define the charging and discharging control boundary;

[0033] Within the corresponding boundary, a time-series adjustment amount is generated as the discrete-time parameter and extended downwards to construct the search branch.

[0034] Optionally, extracting the maximum dynamic electrical distance includes:

[0035] For the candidate train, the relative speed stationary point within the dynamic time window is extracted, and the dynamic electrical distance corresponding to the initial time and the end time of the dynamic time window is obtained respectively. The dynamic electrical distance is compared with the dynamic electrical distance corresponding to the relative speed stationary point, and the maximum value is selected as the maximum dynamic electrical distance.

[0036] For the equivalent candidate train, the maximum dynamic electrical distance corresponding to the beginning and end of the window is directly taken as the maximum dynamic electrical distance.

[0037] Optionally, the solution for transmission efficiency includes:

[0038] Acquire real-time temperature data of the overhead contact line;

[0039] A temperature coefficient is introduced into the impedance model, and the resistance value per unit length is corrected based on the temperature acquisition data. The transmission efficiency is then calculated based on the corrected model.

[0040] Optionally, obtaining energy extrema includes:

[0041] The partial derivatives are solved using Leibniz's integral rule to determine the direction of the first-order gradient.

[0042] The search is iteratively performed along this direction. If the energy gain is less than zero, the step size is reduced and the search is backtracked. If the gain is greater than or equal to a preset threshold, the variables are updated and the next round of iterative deduction is entered. If the gain is greater than or equal to zero and less than the threshold, convergence is determined and the energy value is extracted as the energy extreme value.

[0043] Secondly, this application provides a rail transit cooperative energy-saving scheduling system based on an analytical gradient-guided Monte Carlo tree, which adopts the following technical solution: A rail transit cooperative energy-saving scheduling system based on an analytical gradient-guided Monte Carlo tree, comprising:

[0044] The situation prediction module is used to define dynamic time windows for customized dynamic trains;

[0045] The candidate set construction module is used to determine the candidate trains and equivalent candidate trains with static load attributes within the dynamic time window, extract the physical displacement difference between the two and the braking source train as the evaluation electrical distance, and then solve the transmission efficiency. The transmission efficiency is eliminated to construct the candidate load set, and the dynamic electrical distance and the relative speed parameter of the candidate train are extracted.

[0046] The branch verification module is used to generate a time-series scheduling action with discrete time parameters as a Monte Carlo tree search branch based on the candidate load set, and to remove the search branch that fails the security verification.

[0047] The variable transformation module is used to convert the discrete-time parameters into continuous-time variables when the search reaches the leaf node of the Monte Carlo tree;

[0048] The gradient evaluation module is used to deduce the relative temporal displacement difference of the candidate train and the absolute physical displacement difference of the equivalent candidate train, and extract the maximum dynamic electrical distance by combining the relative speed parameter. If the corresponding transmission efficiency is lower than the preset efficiency threshold, a step constraint is constructed to extract the effective overlapping time segment. Otherwise, the dynamic time window is taken as the segment. An energy extremum objective function is constructed for the effective overlapping time segment, and the partial derivative is solved. An iterative search is performed along the first-order gradient direction to obtain the energy extremum as the evaluation value.

[0049] The backtracking update module is used to map the corresponding continuous-time variable to discrete values, backtrack and update the Monte Carlo tree according to the evaluation value, and output instructions.

[0050] In summary, this application includes the following beneficial technical effects:

[0051] 1. By extracting the physical displacement difference between the braking source train and candidate trains, as well as equivalent candidate trains, as the evaluation of the transmission efficiency of the electrical distance solution, and eliminating those with transmission efficiency below a preset efficiency threshold to construct a candidate load set, invalid matching objects that cause a large amount of energy dissipation as line heat loss due to high impedance in physical space are excluded. Furthermore, after converting discrete time parameters into continuous time variables at the leaf nodes of Monte Carlo trees, an energy extremum objective function is constructed for the effective overlapping time segments, and iterative search is performed along the first-order gradient direction to obtain the energy extremum as the evaluation value. This makes the search process directly guided by the physical transmission attenuation gradient, avoiding the waste of computing power caused by pure time dimension optimization and improving the actual energy recovery rate.

[0052] 2. By acquiring real-time temperature data of the overhead contact line, a temperature coefficient is introduced into the impedance model, and the resistance value per unit length is corrected based on the acquired data. Then, the transmission efficiency is solved based on the corrected model, which ensures the accuracy of the line impedance calculation under different ambient temperatures. This avoids the deviation in transmission efficiency calculation caused by temperature changes, which would lead to non-optimal scheduling actions. This effectively improves the adaptability and decision reliability of the scheduling system under complex working conditions.

[0053] 3. When multiple braking or candidate trains are running concurrently in the same power supply section, a multi-node equivalent circuit is constructed and node merging is performed based on Kirchhoff's laws to extract the parallel transmission path and shunt impedance loss. The transmission efficiency is dynamically solved and incorporated into the energy extremum objective function. The Leibniz integral rule is called to solve the partial derivatives to determine the first-order gradient direction for iteration. This achieves accurate characterization and efficient optimization of energy flow in complex power supply networks with multiple trains running in parallel. While ensuring convergence stability, it avoids scheduling deviations caused by the lack of network loss shunt calculation in concurrent scenarios. Attached Figure Description

[0054] Figure 1 This is a logical flowchart of the scheduling method according to an embodiment of this application;

[0055] Figure 2 This is a schematic diagram illustrating the relationship between the dynamic time window and the timing changes in the evaluated electrical distance in an embodiment of this application;

[0056] Figure 3 This is a schematic diagram illustrating the dynamic electrical distance variation trend and maximum value extraction principle of an embodiment of this application;

[0057] Figure 4 This is a schematic diagram illustrating the principle of extracting the effective overlap time segment between feedback and power consumption in an embodiment of this application.

[0058] Figure 5 This is a schematic diagram illustrating the iterative derivation process of the energy extremum objective function along the analytical gradient in an embodiment of this application. Detailed Implementation

[0059] The following combination Figures 1-5 This application will be described in further detail.

[0060] The collaborative energy-saving scheduling method for rail transit based on analytical gradient-guided Monte Carlo trees disclosed in this specific embodiment is executed by the urban rail transit dispatch control center server. The dispatch control center server interacts in real time with the automatic train operation system of all trains on the entire line through the CBTC vehicle-to-ground communication system, collecting train operation data and issuing scheduling commands for adjusting station dwell times and controlling the charging and discharging of ground energy storage devices. All trains on the line are equipped with onboard positioning units and speed detection units, transmitting real-time data on train position, operating speed, operating status, and station dwell progress. The DC traction power supply system of the line is equipped with contact network parameter acquisition terminals, traction substations, and ground energy storage devices, uploading real-time measured data on contact network voltage, line impedance, and contact network temperature, and receiving and executing charging and discharging control commands.

[0061] The collaborative energy-saving scheduling system corresponding to this implementation is deployed on the scheduling and control center server and includes a situation prediction module, a candidate set construction module, a branch verification module, a variable transformation module, a gradient evaluation module, and a backtracking update module. The output of the situation prediction module is connected to the input of the candidate set construction module, the output of the candidate set construction module is connected to the input of the branch verification module, the output of the branch verification module is connected to the input of the variable transformation module, the output of the variable transformation module is connected to the input of the gradient evaluation module, the output of the gradient evaluation module is connected to the input of the backtracking update module, and the output of the backtracking update module is connected to the command issuance interface of the vehicle-to-ground communication system.

[0062] The system employs the IEEE 1588PTP precision time protocol to achieve full-line clock synchronization. Considering the tolerance boundaries of the dynamic electrical characteristics of high-speed trains, the synchronization accuracy is controlled to be no greater than 1ms. All timing data undergoes alignment processing under a unified benchmark using linear interpolation. Vehicle-to-ground communication is built upon the LTE-M network and the IEC 61375 standard. Command frames include device number, adjustment parameters, and execution timestamps, matching the minimum safety redundancy cycle of the CBTC (City Rail Transit Train Control System). The transmission cycle is set to 200ms, and timeout retransmission and CRC data verification mechanisms are configured. The system is configured with basic fault tolerance mechanisms: when the braking event set is empty, the current scheduling process is terminated, waiting for the next data acquisition cycle; when the candidate load set corresponding to a single braking source train is empty, the current scheduling for that braking source is terminated; when the Monte Carlo tree has no valid search branch or the iteration does not converge, a default scheduling command is output; if no device confirmation is received within 500ms after the command is issued, a retransmission is triggered; if three consecutive retransmissions fail, the adjustment action for the corresponding device is terminated.

[0063] The situation prediction module collects real-time operating parameters and preset train timetable data from the entire line via the CBTC vehicle-to-ground communication system at a fixed period of 200ms. This collection period matches the minimum data update interval of the urban rail transit train operation control system. Real-time operating parameters include train real-time location, speed, current operating conditions, duration of stops, and planned departure time. Combined with... Figure 1 The illustrated sequential logic shows that after acquiring the aforementioned real-time data, the system sequentially performs operations such as defining the dynamic time window for the braking source, eliminating inefficient candidate loads, generating scheduling branches, and performing safety checks. Upon reaching a leaf node, the system converts discrete parameters into continuous variables, calculates the displacement difference to determine transmission efficiency, constructs step constraints to extract effective overlapping segments, or directly takes a dynamic time window. It then constructs an energy extremum function for the defined time segment and extrapolates along the gradient, ultimately completing discretization and outputting MCTS commands. Specifically, the situation prediction module inputs the collected real-time operating parameters into a preset kinematic model and performs forward simulation.

[0064] The situation prediction module inputs the collected real-time operating parameters into a preset kinematic model and performs forward simulation. The preset kinematic model adopts the single-mass dynamic equation of the train and incorporates the traction and braking characteristic curves of the trains operating on the line, as well as the gradient and curve parameters obtained from the line's as-built measurements. To balance the real-time computing power of the control center with the fidelity of the forward prediction, the simulation step size is set to 100ms, covering the train's operation process over the next 120 seconds. The simulation process uses the train's real-time operating parameters as initial conditions and the line speed limit and platform stopping position as boundary conditions, simultaneously taking into account the additional resistance from gradients, additional resistance from curves, and basic operating resistance.

[0065] The situation prediction module extracts braking processes with energy feedback characteristics from the simulation output of the train's full-time operating condition time-series data, generating a set of braking events. A braking process with energy feedback characteristics refers to a braking process in which the train is in electric braking mode, the traction motor is operating in generator mode, and the duration of the feedback power is not less than 2 seconds. Each braking event includes the associated train number, predicted braking start time, predicted braking end time, braking process position time-series data, and feedback power time-series data.

[0066] The situation prediction module sorts all events within the braking event set in ascending order of timestamps to construct a braking event queue. The train associated with the first event in the queue is identified as the braking source train. Based on a preset vehicle-to-ground communication delay parameter, the module performs timing compensation on the predicted braking start and end times of the braking source train. The compensation duration is equal to the preset vehicle-to-ground communication delay parameter. The preset vehicle-to-ground communication delay parameter is set to 50ms, matching the maximum end-to-end one-way transmission delay of the urban rail transit LTE-M vehicle-to-ground communication system. The situation prediction module uses the compensated braking start and end times as integration boundaries to define a dynamic time window corresponding to the braking source train.

[0067] Trains with braking sources within the queue are processed sequentially in ascending order of timestamps. A single-braking-source train represents the basic scenario where the queue contains only a single element, while a multi-braking-source train represents an extended scenario where the queue contains multiple elements. In the multi-braking-source train scenario, scheduling conflict handling prioritizes braking event timestamps in ascending order as the first priority, followed by the peak feedback power as the second priority.

[0068] The candidate set construction module determines candidate trains within a dynamic time window and equivalent candidate trains with static load attributes. Specifically, the candidate set construction module extracts operating trains within the dynamic time window that include planned stop phases as candidate trains, and maps ground energy storage devices in the rail transit line to equivalent candidate trains with static load attributes.

[0069] The candidate set construction module extracts the physical displacement difference between the braking source train and the candidate train, as well as the equivalent candidate train, as the evaluation electrical distance. Specifically, it obtains the predicted position time series data of the braking source train within the dynamic time window, as well as the predicted position data of each candidate train within the dynamic time window, and extracts the minimum physical displacement difference between the candidate train and the braking source train within the dynamic time window as the evaluation electrical distance corresponding to the candidate train.

[0070] Simultaneously, the physical displacement difference between the fixed point where the equivalent candidate train connects to the traction power supply network and the predicted spatial position of the braking source train within the dynamic time window is calculated and used as the evaluation electrical distance corresponding to the equivalent candidate train. For example... Figure 2 As shown in the dynamic temporal distribution, the spatial position trajectories of the braking source train and the candidate train in operation fluctuate nonlinearly over time. The aforementioned minimum physical displacement difference is the minimum vertical distance between the two running trajectory lines in the dynamic time window interval. The fixed access point of the equivalent candidate train is represented as a fixed horizontal baseline in the distance-time coordinate system, and its corresponding physical displacement difference is intuitively reflected as the real-time vertical distance between the fluctuating trajectory of the braking source train and the horizontal baseline.

[0071] The candidate set construction module calculates the transmission efficiency between the braking source train and candidate trains, as well as equivalent candidate trains, based on the evaluated electrical distance. Specifically, it inputs each evaluated electrical distance into a preset line impedance model to calculate the expected maximum transmission efficiency from the braking source train to the corresponding candidate train and equivalent candidate train. The candidate set construction module then eliminates trains with transmission efficiencies below a preset efficiency threshold to construct a candidate load set. This preset efficiency threshold is determined by inversely calculating the equivalent impedance based on the minimum allowable voltage at the end of the traction power supply arm, and in this embodiment, it is set to 70%. In other words, candidate trains and equivalent candidate trains with expected maximum transmission efficiencies below the preset efficiency threshold are eliminated, and the remaining candidate trains are aggregated with their equivalent counterparts to generate the candidate load set.

[0072] For the generated candidate load set, the candidate set construction module extracts the dynamic electrical distance of the candidate load set and extracts the relative speed parameter for the candidate trains within the candidate load set. Specifically, it calculates the time-series physical displacement difference of the candidate load set within the dynamic time window as the dynamic electrical distance, and extracts the relative speed parameter for the candidate trains within the candidate load set with dynamic operating attributes based on the predicted position time-series data through differential calculation.

[0073] In scenarios where at least two braking trains, including the braking source train, or at least two candidate trains coexist within the same power supply section, the candidate set construction module constructs a multi-node equivalent circuit in a preset line impedance model based on the dynamic electrical distance corresponding to each train. It then performs node merging on the multi-node equivalent circuit based on Kirchhoff's current law to extract parallel transmission paths. The module calculates the shunt impedance loss from the braking source train to each candidate train along these parallel transmission paths and solves for the corresponding transmission efficiency based on the shunt impedance loss. The power supply section is divided by the power supply arm of the traction substation. The candidate set construction module acquires real-time temperature data of the overhead contact line, introduces the contact line temperature coefficient into the preset line impedance model, and corrects the unit length resistance value based on the real-time temperature data. It then solves for the corresponding transmission efficiency based on the corrected preset line impedance model to improve the accuracy of transmission efficiency calculations under different ambient temperatures.

[0074] The branch verification module initializes the root node of the Monte Carlo tree based on the candidate load set. The root node corresponds to the current operating status of all trains on the line and the working status of the ground energy storage device. The system generates time-series scheduling actions with discrete-time parameters based on the candidate load set as search branches of the Monte Carlo tree. Specifically, for candidate trains in operation, the time-series scheduling action is physically instantiated as a stop time adjustment; for equivalent candidate trains with static load attributes, the time-series scheduling action is physically instantiated as a charging and discharging timing adjustment. The child nodes of the root node correspond to the time-series scheduling actions of each candidate train and equivalent candidate train within the candidate load set. In the multi-branch train extension scenario, the branch verification module initializes an independent root node for each braking source train in the queue, constructing a multi-branch Monte Carlo tree.

[0075] The branch verification module extracts the planned stopping time of candidate trains from the candidate load set and defines the stopping control boundary based on the preset discrete level. Simultaneously, it extracts the available energy storage capacity and maximum scheduling time of equivalent candidate trains in the candidate load set. Based on the current state of charge of the ground energy storage device, its available energy storage capacity, and the maximum scheduling time allowed by the power grid, it derives and calculates the actual allowable time axis offset boundary, and defines the charging and discharging timing control boundary based on the preset discrete level. The preset discrete level matches the time control accuracy of the train automatic driving system and the energy storage control system, with a value of 1 second. The lower limit of the stopping control boundary is 60% of the planned stopping time, and the upper limit is 140% of the planned stopping time. The boundary values ​​are determined based on the shortest time required for passengers to board and alight and the maximum buffer time preset in the entire line's timetable. The 60% lower limit corresponds to the minimum passenger boarding and alighting time of 18 seconds as stipulated in the "Urban Rail Transit Operation Management Specifications".

[0076] The branch verification module generates timing adjustment quantities that match preset discrete levels within the corresponding stop control boundary and charging / discharging timing control boundary. Specifically, it generates stop time adjustment quantities within the stop control boundary and charging / discharging timing adjustment quantities within the charging / discharging timing control boundary. The stop time adjustment quantity is the increase or decrease of the candidate train relative to the planned stop time, covering all discrete values ​​within the stop control boundary with a step size of 1 second; the charging / discharging timing adjustment quantity is the offset value of the equivalent candidate train relative to the rated charging / discharging timing, covering all discrete values ​​within the charging / discharging timing control boundary with a step size of 1 second. The branch verification module uses each timing adjustment quantity as a discrete time parameter and extends downwards from the current node of the Monte Carlo tree to construct the corresponding search branch.

[0077] The branch verification module performs a safety check on each search branch simultaneously, generating the corresponding search branch and calculating the tracking interval and cumulative delay time of the candidate train after the timing scheduling action. For branches of equivalent candidate trains, it checks the safety margin and over-limit status of the charging and discharging commands of the equivalent candidate train after the timing scheduling action. The tracking interval refers to the minimum spatial distance between the candidate train and the preceding train, and the cumulative delay time refers to the maximum delay time of the candidate train relative to the scheduled departure time in the timetable. If the calculated tracking interval is less than the preset safe block distance, or the cumulative delay time is greater than the preset delay tolerance time, or the charging and discharging command does not meet the safety margin, the branch verification module directly removes the corresponding search branch that fails the safety and delay checks and does not include it in the subsequent search process. The preset safe block distance is determined based on the safety protection standards for train tracking operation on the line and the emergency braking distance at the maximum operating speed, and the preset delay tolerance time is determined based on the maximum buffer time of a single station in the entire timetable, with a value of 30 seconds.

[0078] The Monte Carlo tree performs a search along the remaining search branches. When the search reaches a leaf node in the Monte Carlo tree where no next-level action has been generated, the variable transformation module obtains the discrete-time parameter corresponding to that leaf node. The discrete-time parameter is either the stop time adjustment or the charging / discharging timing adjustment corresponding to that branch. The variable transformation module converts the discrete-time parameter into a continuous-time variable, relaxing the range of values ​​for the timing adjustment from the discrete integer domain to the continuous real number domain.

[0079] This scheme uses continuous domain analytical gradient line search to replace the traditional Monte Carlo tree's full-time-domain derivation process at leaf nodes, directly solving for the node evaluation value. The gradient evaluation module obtains the predicted position time-series data, predicted speed time-series data, and feedback power time-series data of the braking source train within the dynamic time window, as well as the predicted position time-series data and predicted speed time-series data of each candidate train and its equivalent candidate train within the candidate load set within the dynamic time window.

[0080] During the deduction process of the current continuous-time variable node, the system performs decoupled deduction based on the physical properties of the target object: if the target is a candidate train with dynamic operating properties, the gradient evaluation module deduces the relative temporal displacement difference between the braking source train and the candidate train within the dynamic time window, and extracts possible relative speed stationary points (i.e., extreme points where the relative speed is zero) in combination with the relative speed parameter; for example Figure 3 As shown, the dynamic electrical distance exhibits a nonlinear continuous distribution trend with stagnation point peaks in the time domain. The dynamic electrical distances corresponding to the initial and final moments of the dynamic time window are obtained and compared with the dynamic electrical distances corresponding to the relative velocity stagnation points. The maximum value is selected as the maximum dynamic electrical distance corresponding to the candidate train. If the target is an equivalent candidate train with static load attributes, the gradient evaluation module deduces the absolute physical displacement difference of the equivalent candidate train. The system does not perform relative velocity stagnation point extraction and directly takes the maximum dynamic electrical distance corresponding to the initial and final moments of the dynamic time window as the maximum dynamic electrical distance corresponding to the equivalent candidate train.

[0081] If the transmission efficiency corresponding to the maximum dynamic electrical distance is lower than a preset efficiency threshold, the preset efficiency threshold is constructed as a dynamic step constraint. Under the current continuous time variable node, the physical position change is extrapolated along the physical time axis corresponding to the dynamic time window, and the instantaneous transmission efficiency is compared synchronously to pre-extract effective overlapping time segments that meet the transmission efficiency standard. For example... Figure 4 As shown in the waveform mapping relationship, both the braking regenerative power and the candidate load power consumption exhibit trapezoidal temporal fluctuations with the time axis. This effective overlapping time segment is the orthogonal projection intersection region where the two trapezoidal power waveforms are in a non-zero state on the time axis. Otherwise, the dynamic time window is used as the effective overlapping time segment.

[0082] For the pre-extracted effective overlapping time segments, the gradient evaluation module performs dynamic impedance verification of the multi-vehicle parallel network: if at least two braking trains, including the braking source train, or at least two candidate trains coexist in the same power supply section, the dynamic electrical distance of each node in the segment is extracted, and a multi-node equivalent circuit is constructed in the preset line impedance model based on the dynamic electrical distance. Based on Kirchhoff's current law, node merging is performed on the multi-node equivalent circuit to extract the parallel transmission path. The shunt impedance loss from the braking source train to each candidate train is calculated along the parallel transmission path, and the corresponding instantaneous transmission efficiency is dynamically solved. Subsequently, for the effective overlapping time segments, an energy extremum objective function containing instantaneous transmission efficiency and power waveform time-domain overlap characteristics is constructed, and the partial derivatives are solved.

[0083] Based on a pre-defined dynamic step constraint triggering mechanism, the integral boundary is defined as a parameterized hard-truncation boundary directly controlled by continuous-time variables (time-series shifts). To this end, the system uses Leibniz's integral rule to solve the analytical partial derivatives of the energy extremum objective function to determine the first-order gradient direction. The system strongly correlates these analytical partial derivatives with objective physical engineering quantities: the analytical expression is deconstructed into a truncation term for abrupt changes in the physical power waveform caused by variations in the integration limit, and a dynamic impedance attenuation partial derivative term within the integration interval caused by changes in physical displacement differences. Thus, under the premise of conforming to objective causality, the first-order gradient direction in the continuous-time variable domain is determined.

[0084] The gradient evaluation module iteratively searches along the first-order gradient direction within the corresponding continuous-time variable domain with a preset initial step size, and calculates the energy gain generated by the overlap of power waveforms between the braking source train, candidate trains, and equivalent candidate trains with static load attributes at the current iteration step size. The preset initial step size is set to 0.1s to match the time accuracy of train operation control, and the energy gain is the difference between the available feedback energy at the current iteration step size and the energy at the previous iteration step size. Figure 5 As can be seen from the function evolution trajectory, the energy extremum objective function generally exhibits a zigzag upward trend as the continuous time variable moves to the right, with the first-order gradient direction serving as a directional guide for the positive nodes. During the iteration process, if a single-step deduction falls into a local trough as shown in the figure (i.e., the energy gain is less than zero), the gradient evaluation module reduces the current iteration step size by a preset ratio, moving backward out of the descent interval to perform a backtracking search. The backtracking search refers to retracing back to the previous iteration node and re-deducing along the new step size after the step size reduction. If the energy gain is greater than or equal to the preset threshold, the variables are updated and the next round of iteration deduction begins. If the energy gain is greater than or equal to zero and less than the preset threshold, it is determined that the search has reached the gentle highest point on the right side of the figure and satisfies the preset convergence boundary, the iteration stops, and the corresponding energy value at this time is extracted as the energy extremum. The energy gain calculated during the iteration process covers the power waveform overlap contribution of the braking source train and all candidate trains and equivalent candidate trains within the candidate load set. The preset threshold is set to 0.005 kWh, and the step size reduction ratio of 0.5 can quickly reduce the step size to the optimal interval while ensuring convergence stability. The preset convergence boundaries also include: the iteration step size is reduced to less than 0.01s, or the energy gain change is less than 0.01kWh for three consecutive iterations.

[0085] The gradient evaluation module obtains the energy extrema as the evaluation value; simultaneously, it maps the continuous-time variables corresponding to the obtained energy extrema to discrete values ​​based on a preset discrete level, replacing the discrete-time parameters of the original search branch, thus completing the closed-loop correction. In some embodiments, the iterative solution process can also use the Armijo line search criterion instead of the fixed step size reduction ratio to adaptively adjust the iteration step size and further improve the convergence speed. In the multi-braking-source train extended scenario, the gradient evaluation module performs joint situation determination and energy extrema solution for multi-braking-source trains, calculates the time-domain superposition value and joint absorption amount of the braking energy of multiple vehicles, and completes the evaluation value assignment of the corresponding leaf nodes.

[0086] The backtracking update module obtains the evaluation value corresponding to each leaf node. Based on the upper confidence bound (UCB1) criterion of the Monte Carlo tree, it performs backtracking updates on all parent nodes on the path from the leaf node to the root node, synchronously correcting the cumulative visit count and cumulative value of each node. The calculation formula for the UCB1 criterion is: In the formula, The average value of the nodes. The coefficient is used for exploration, and its value is [value missing]. , This represents the total number of visits to the parent node. This represents the number of times the current node has been visited. The formula calculation process balances the exploration and utilization weights of the Monte Carlo tree, avoiding the search process from getting trapped in local optima and ensuring the convergence stability of the algorithm.

[0087] The backtracking update module pre-sets the Monte Carlo tree search termination condition, with an iteration threshold of 1000 iterations and a maximum search depth matching the number of elements in the candidate load set. The search stops when either condition is met. The 1000 iterations match the millisecond-level real-time requirements of urban rail transit scheduling systems, and the maximum search depth matching the number of elements in the candidate load set ensures that all feasible station time adjustment combinations are fully covered. In some embodiments, the search termination condition can also be replaced by no node with a higher cumulative value appearing for 50 consecutive iterations, to further reduce the system's computational load while maintaining optimization effectiveness.

[0088] After the search stops, the backtracking update module extracts the timing scheduling action corresponding to the child node with the highest accumulated value under the root node as the target timing scheduling action. Based on this action, a scheduling instruction conforming to the CBTC communication protocol standard is generated and sent to the train automatic driving system of the corresponding candidate train and the local controller of the ground energy storage device through the vehicle-to-ground communication system. The scheduling instruction corresponding to the candidate train is the stop time adjustment instruction, which is achieved by adjusting the stop door opening duration. The equivalent scheduling instruction corresponding to the candidate train is the charging and discharging timing control instruction. In the multi-braking source train extended scenario, the backtracking update module completes the search and backtracking update of the Monte Carlo tree corresponding to each braking source train according to the timestamp order of the braking event queue. It integrates the target timing scheduling actions corresponding to all braking source trains, eliminates adjustment items with timing conflicts and safety boundary violations, and generates a globally optimal set of timing scheduling actions and corresponding scheduling instructions.

[0089] The rail transit collaborative energy-saving dispatching system based on analytical gradient-guided Monte Carlo trees disclosed in this embodiment is deployed on the urban rail transit dispatching and control center server. The dispatching and control center server is bidirectionally coupled to the train automatic driving system, on-board positioning unit, and speed detection unit of all trains on the entire line via the CBTC vehicle-to-ground communication system, and bidirectionally coupled to the contact network parameter acquisition terminal and the local controller of the ground energy storage device of the DC traction power supply system of the line.

[0090] This system includes a situation prediction module, a candidate set construction module, a branch verification module, a variable transformation module, a gradient evaluation module, and a backtracking update module. The output of the situation prediction module is communicatively coupled to the input of the candidate set construction module; the output of the candidate set construction module is communicatively coupled to the input of the branch verification module; the output of the branch verification module is communicatively coupled to the input of the variable transformation module; the output of the variable transformation module is communicatively coupled to the input of the gradient evaluation module; the output of the gradient evaluation module is communicatively coupled to the input of the backtracking update module; and the output of the backtracking update module connects to the command issuance interface of the CBTC vehicle-to-ground communication system.

[0091] The situation prediction module is primarily used to define the dynamic time window for system scheduling. This module collects real-time operating parameters of all trains along the entire line and preset train timetable data at fixed intervals, and inputs this data into a preset kinematic model to perform forward simulation. Through forward simulation, the module extracts a set of braking events with energy feedback characteristics, constructs a braking event queue in ascending order of timestamps, and designates the train associated with the first event as the braking source train. Finally, the module performs timing compensation on the predicted braking start and end times based on preset vehicle-to-ground communication delay parameters, and uses the compensated time as the integration boundary to define the dynamic time window corresponding to the braking source train.

[0092] The candidate set construction module is responsible for screening high-transmission-efficiency load targets and constructing a candidate load set. The module first extracts candidate trains within a dynamic time window that include station stops, as well as equivalent candidate trains (ground energy storage devices) with static load attributes. It calculates the minimum displacement difference between these trains and the braking source train as the evaluation electrical distance. This distance is input into a preset line impedance model that can be combined with real-time temperature correction to solve for the expected highest transmission efficiency. Trains with efficiencies below a threshold (e.g., 70%) are removed to generate the candidate load set. For this set, the module extracts the time-series physical displacement difference as the dynamic electrical distance and extracts the relative speed parameter through differential calculation. If multiple trains run concurrently in the same section, it also combines multi-node equivalent circuits based on Kirchhoff's laws and dynamically calculates the parallel shunt impedance and transmission efficiency.

[0093] The branch verification module is responsible for generating the search branches of the Monte Carlo tree and strictly performing safety verification. This module extracts the planned stopping time of candidate trains, the available energy storage of equivalent candidate trains, and the maximum scheduling time, and defines the stopping and charging / discharging control boundaries based on preset discrete levels. Within these boundaries, it generates timing adjustment quantities matching the discrete levels as discrete time parameters, extending downwards to construct search branches. Simultaneously, the module performs safety simulations on the branches based on preset block distances and delay tolerance times. Search branches with excessively short tracking intervals, accumulated delays exceeding time limits, or charging / discharging commands not meeting safety margins are directly eliminated after simulation, ensuring the safety of the scheduling scheme.

[0094] The variable transformation module acts as a data bridge and relaxation mechanism between the discrete and continuous domains. During the Monte Carlo tree's downward search along the valid search branches that haven't been eliminated, this module is triggered when it encounters a leaf node that hasn't yet generated a next-level action. Its core function is to obtain the discrete-time parameter corresponding to that leaf node and convert it into a continuous-time variable. Through this transformation, the module relaxes the range of time-series adjustment values ​​from the discrete integer domain to the continuous real number domain, thus enabling subsequent modules to abandon full-time domain derivation and instead use continuous-domain analytical gradient line search to solve for extrema.

[0095] The gradient evaluation module performs iterative deduction within a continuous variable domain to evaluate node value. Based on predicted time-series data, this module deduces the relative / absolute displacement difference between targets and extracts the maximum dynamic electrical distance. If the corresponding transmission efficiency is too low, a dynamic step constraint is introduced to extract effective overlapping time segments; otherwise, the complete dynamic time window is used. The module constructs an energy extremum objective function for this segment, incorporating power overlap characteristics, and uses analytical partial derivatives to determine the first-order gradient direction to perform iterative deduction and calculate the energy gain. If the energy gain is less than zero, the step size is reduced and the search is backtracked; if the energy gain is greater than or equal to zero and less than a preset threshold, convergence is determined and iteration stops. The module extracts the energy value at convergence as the energy extremum, which serves as the evaluation value of the leaf node.

[0096] The backtracking update module is used to complete the value backtracking of the Monte Carlo tree and the generation and issuance of the final scheduling instruction. After obtaining the evaluated value of the leaf node, this module performs a backtracking update on all parent nodes on the path from that node to the root node based on the upper confidence bound (UCB1) criterion, synchronously correcting the cumulative visit count and cumulative value of the node. When the preset search termination condition is met, the module extracts the timing scheduling action corresponding to the child node with the highest cumulative value under the root node as the optimal target action. Finally, based on this action, a scheduling instruction conforming to the CBTC communication protocol standard is generated and issued to the corresponding train's automatic driving system and ground energy storage local controller for execution via the vehicle-to-ground communication system.

[0097] In this embodiment, the situation prediction module, candidate set construction module, branch verification module, variable transformation module, gradient evaluation module, and backtracking update module are all logical functional units. Their functions rely on the processor, memory, and system communication bus of the scheduling and control center server. The memory stores computer programs used to implement the corresponding functions of each module. The processor retrieves and executes the computer programs in the memory to complete the various data processing and control command generation operations in this embodiment.

[0098] The micro-level details of the specific data processing and control logic executed by each module in this embodiment have been described in detail in the foregoing method embodiments, and will not be repeated here.

[0099] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A collaborative energy-saving scheduling method for rail transit based on analytical gradient-guided Monte Carlo trees, characterized in that, include: Define the dynamic time window for customized dynamic trains; The candidate trains within the dynamic time window and the equivalent candidate trains with static load attributes are determined. The physical displacement difference between the two trains and the braking source train is extracted as the evaluation electrical distance, and then the transmission efficiency is solved. Those with transmission efficiency lower than a preset efficiency threshold are removed to construct a candidate load set, and their dynamic electrical distance and the relative speed parameters of the candidate trains are extracted; Based on the candidate load set, a time-series scheduling action with discrete-time parameters is generated as a Monte Carlo tree search branch, and the search branch that fails the security check is removed; When the search reaches the leaf node of the Monte Carlo tree, the discrete-time parameter is converted into a continuous-time variable; The relative temporal displacement difference of the candidate trains and the absolute physical displacement difference of the equivalent candidate trains are deduced, and the maximum dynamic electrical distance is extracted by combining the relative speed parameter. If the corresponding transmission efficiency is lower than the preset efficiency threshold, a step constraint is constructed to extract the effective overlapping time segment; otherwise, the dynamic time window is taken as the segment. For the effective overlapping time segments, construct an energy extremum objective function, solve for the partial derivatives, and perform iterative search along the first-order gradient direction to obtain the energy extremum as the evaluation value; The continuous-time variables are mapped to discrete values, the Monte Carlo tree is updated backtracking according to the evaluation value, and the instructions are output.

2. The rail transit collaborative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 1, characterized in that, The dynamic time window for the customized dynamic source train includes: Real-time operating parameters are input into the kinematic model to perform forward simulation and extract a set of braking events with energy feedback characteristics; The queue is constructed by sorting the events in ascending order of timestamps, and the train associated with the first event is designated as the braking source train. The predicted braking start and end times are compensated based on a preset communication delay parameter, and the compensated time is used as the integration boundary to define the dynamic time window.

3. The rail transit collaborative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 1, characterized in that, Solving for transmission efficiency and extracting parameters includes: Trains that include stops within the dynamic time window are extracted as candidate trains, and ground energy storage devices are mapped as equivalent candidate trains. The transmission efficiency is solved by using the minimum displacement difference between the braking source train and the two as the input impedance model for evaluating electrical distance. The time-series displacement difference of the candidate load set is calculated as the dynamic electrical distance, and the relative velocity parameter is extracted by differential calculation.

4. The rail transit cooperative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 3, characterized in that, After extracting the effective overlapping time segments, the method further includes: If multiple braking or candidate trains are running concurrently in the same power supply section, the dynamic electrical distance of each node in the segment is extracted, and a multi-node equivalent circuit is constructed in the impedance model based on the dynamic electrical distance. Based on Kirchhoff's laws, node merging is performed to extract parallel transmission paths. The shunt impedance loss is calculated along these paths, and the transmission efficiency is dynamically solved to incorporate the energy extremum objective function.

5. The rail transit collaborative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 1, characterized in that, The process of removing search branches that fail security checks includes: The tracking interval and cumulative delay time of the candidate trains after the superimposed scheduling actions are deduced, and the safety margin of the equivalent candidate train charging and discharging commands is verified. If the running interval is less than the safe blocking distance, or the delay duration is greater than the delay tolerance time, or the safety margin is not met, the search branch is removed.

6. The rail transit collaborative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 1, characterized in that, The generation of time-series scheduling actions includes: The station dwell time of the candidate trains is extracted and combined with the discrete level position to determine the station dwell control boundary; The available energy storage of the equivalent candidate train and the maximum scheduling time are extracted and combined with the discrete level to define the charging and discharging control boundary; Within the corresponding boundary, a time-series adjustment amount is generated as the discrete-time parameter and extended downwards to construct the search branch.

7. The rail transit cooperative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 1, characterized in that, Extracting the maximum dynamic electrical distance includes: For the candidate train, the relative speed stationary point within the dynamic time window is extracted, and the dynamic electrical distance corresponding to the initial time and the end time of the dynamic time window is obtained respectively. The dynamic electrical distance is compared with the dynamic electrical distance corresponding to the relative speed stationary point, and the maximum value is selected as the maximum dynamic electrical distance. For the equivalent candidate train, the maximum dynamic electrical distance corresponding to the beginning and end of the window is directly taken as the maximum dynamic electrical distance.

8. The rail transit cooperative energy-saving scheduling method based on analytical gradient-guided Monte Carlo trees according to claim 3, characterized in that, The solution for transmission efficiency includes: Acquire real-time temperature data of the overhead contact line; A temperature coefficient is introduced into the impedance model, and the resistance value per unit length is corrected based on the temperature acquisition data. The transmission efficiency is then calculated based on the corrected model.

9. A collaborative energy-saving scheduling method for rail transit based on an analytical gradient-guided Monte Carlo tree as described in claim 1, characterized in that, Reaching energy extreme values ​​includes: The partial derivatives are solved using Leibniz's integral rule to determine the direction of the first-order gradient. The search is iteratively performed along this direction. If the energy gain is less than zero, the step size is reduced and the search is backtracked. If the gain is greater than or equal to a preset threshold, the variables are updated and the next round of iterative deduction is entered. If the gain is greater than or equal to zero and less than the threshold, convergence is determined and the energy value is extracted as the energy extreme value.

10. A rail transit cooperative energy-saving scheduling system based on an analytical gradient-guided Monte Carlo tree, used to implement the rail transit cooperative energy-saving scheduling method based on an analytical gradient-guided Monte Carlo tree as described in any one of claims 1-9, characterized in that, The system includes: The situation prediction module is used to define dynamic time windows for customized dynamic trains; The candidate set construction module is used to determine the candidate trains and equivalent candidate trains with static load attributes within the dynamic time window, extract the physical displacement difference between the two and the braking source train as the evaluation electrical distance, and then solve the transmission efficiency. The transmission efficiency is eliminated to construct the candidate load set, and the dynamic electrical distance and the relative speed parameter of the candidate train are extracted. The branch verification module is used to generate a time-series scheduling action with discrete time parameters as a Monte Carlo tree search branch based on the candidate load set, and to remove the search branch that fails the security verification. The variable transformation module is used to convert the discrete-time parameters into continuous-time variables when the search reaches the leaf node of the Monte Carlo tree; The gradient evaluation module is used to deduce the relative temporal displacement difference of the candidate train and the absolute physical displacement difference of the equivalent candidate train, and extract the maximum dynamic electrical distance by combining the relative speed parameter. If the corresponding transmission efficiency is lower than the preset efficiency threshold, a step constraint is constructed to extract the effective overlapping time segment. Otherwise, the dynamic time window is taken as the segment. An energy extremum objective function is constructed for the effective overlapping time segment, and the partial derivative is solved. An iterative search is performed along the first-order gradient direction to obtain the energy extremum as the evaluation value. The backtracking update module is used to map the corresponding continuous-time variable to discrete values, backtrack and update the Monte Carlo tree according to the evaluation value, and output instructions.

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