A flight zone aircraft-vehicle conflict risk field prediction method and system based on closed vehicle team conservation law and density over-limit probability

Abstract

The present application relates to a kind of flight area aircraft-vehicle conflict risk field prediction method and system based on closed vehicle team conservation law and density over-limit probability.The method obtains service road directed graph, conflict interface, initial vehicle density, initial state of reservoir and aircraft random process;Monte Carlo sampling is carried out to aircraft process, and the time-space capacity modulation field of each aircraft sample is constructed to service road edge;Closed random conservation law model is established on service road directed graph, vehicle density evolution is solved edge by edge, and boundary flux is provided at node by reservoir node solver;The edge density and node reservoir state of multiple samples are aggregated according to time barrel, the probability that edge density exceeds critical density and the probability that node reservoir quality exceeds critical value are calculated, and edge over-limit risk field and node over-limit risk field are obtained.The present application can provide time-dependent conflict risk prediction on edge and node level in future time period for flight area path planning and scheduling system.

Description

Technical Field

[0001] This invention relates to the fields of intelligent civil aviation operation support and intelligent transportation technology. Specifically, it relates to a method and system for predicting the risk field of aircraft-vehicle conflict in the flight area based on the closed vehicle fleet conservation law and the probability of density exceeding limits. Background Technology

[0002] Airport flight areas contain a large number of ground service vehicles, including baggage towing vehicles, refueling vehicles, catering vehicles, passenger boarding stairs, guidance vehicles, and cleaning vehicles. These vehicles operate on the service road network and interact with aircraft operations at taxiway-service road intersections, aircraft stand entrances and exits, and near support operation areas. The uncertainty inherent in aircraft arrivals, pushbacks, taxiing, holding, and crossings affects service road capacity and further influences vehicle density distribution and conflict risk.

[0003] Existing aircraft-vehicle conflict prediction technologies are mostly based on vehicle location, fixed rules, historical conflict hotspots, or data-driven models. Location- and rule-based methods typically only allow for current-state traffic control and struggle to predict the spatiotemporal distribution of risks over a future period. Methods based on historical conflict hotspots often create static risk zones, failing to reflect changes in aircraft operating times and taxiing disturbances. While deep learning-based prediction methods can utilize historical data, they generally lack constraints on fleet mass conservation, density non-negativity, and physical constraints on aircraft disturbance stability.

[0004] In airport operation management, route planning and scheduling systems not only need to know whether a conflict point is occupied by an aircraft, but also the probability of vehicle density congestion or node queue exceeding limits occurring at different edges and nodes of the service road in the future. Therefore, it is necessary to propose a method and system that can establish a macroscopic conservation model of vehicle groups on the service road map and transform the uncertainty of aircraft operation into a risk field of edge / node over-limit probability. Summary of the Invention

[0005] This invention aims to address the technical problems of existing airfield aircraft-vehicle conflict prediction methods, which lack macroscopic physical modeling of vehicle group density, make it difficult to transform aircraft operational uncertainties into time-related risk fields at the edge and node levels, and lack guarantees of mass conservation, density positivity, and disturbance stability in the prediction results.

[0006] To achieve the above objectives, this invention proposes a method for predicting the aircraft-vehicle conflict risk field in flight zones based on the conservation law of closed vehicle fleets and the probability of density exceeding limits, comprising: S1, obtain the directed graph of the service roads, the initial vehicle density distribution along each service road, and the initial vehicle mass of each node's reservoir, and obtain the set of conflict interfaces; S2, generate N aircraft process samples based on the distribution parameters of the aircraft operation process; S3, For each aircraft process sample, calculate the capacity modulation field along each service road based on the conflict interface location and aircraft event time; S4. At each service road, the vehicle density conservation equation is solved based on the capacity modulation field to obtain the density field under that sample. S5. At the service road node, calculate the node flux based on the boundary flux of the adjacent edge and the state of the node reservoir, and use the node flux as the boundary condition of the adjacent service road edge, while updating the vehicle mass of the node reservoir. S6, repeat S3 to S5 until all aircraft process samples have completed density evolution solutions; S7, aggregate the edge density and node water storage status of each sample according to the preset time bucket; S8, calculate the edge over-limit risk field and the node over-limit risk field based on the aggregation results; S9 outputs a spatiotemporal risk field consisting of the out-of-limit probabilities of all service roadsides and nodes across all time buckets.

[0007] Furthermore, the capacity modulation field is constructed in the following manner: For each conflicting interface, the event time of the aircraft passing through the interface is converted into a capacity attenuation coefficient on the service roadside using a spatial kernel function and a temporal kernel function. The attenuation coefficients of multiple conflicting interfaces associated with the same service roadside are superimposed and then clipped by upper and lower bounds to obtain the capacity modulation field.

[0008] Furthermore, the vehicle density conservation equation is:

[0009] in, To serve the vehicle density on roadside e, Let f be the edge flux function. For aircraft random processes, u is the scheduling control input; The edge flux function is:

[0010] in, Let velocity be the function. The capacity modulation factor is driven by the aircraft process.

[0011] Furthermore, the vehicle mass of the node water storage tank meets the following requirements:

[0012] in, Let the mass of the vehicle in the reservoir at node v be [the mass of the vehicle in the reservoir]. and Let V be the sets of edges that enter and leave node v, respectively. This is a state transition item for the node service.

[0013] Furthermore, the generation of the aircraft process sample includes: Based on historical operational data or real-time operational plans, a planned route is determined for each aircraft, and at least one of its pushback time, taxi speed, and waiting time is randomly sampled to obtain the event time of each aircraft passing through each conflict interface.

[0014] Furthermore, in step S4, the vehicle density conservation equation is spatially discretized using a monotonic finite volume scheme, and the time step is selected according to the CFL condition for numerical solution.

[0015] Furthermore, the edge over-limit risk field is calculated using the following formula:

[0016] in, The critical density threshold for the service road edge e; The Monte Carlo empirical estimate of the edge over-limit risk field is: .

[0017] Furthermore, the node over-limit risk field is calculated using the following formula:

[0018] in, Let V be the critical vehicle mass of the reservoir at node v.

[0019] Furthermore, it also includes a stability verification step, whereby the distance between the density field and the nodal reservoir state satisfies the following when the aircraft process is disturbed:

[0020] in, The distance between the two density-reservoir states under aircraft disturbance. For the distance of the aircraft's process state, is the disturbance stability constant.

[0021] On the other hand, to achieve the above objectives, this invention proposes a flight area aircraft-vehicle conflict risk field prediction system based on the closed vehicle convoy conservation law and density over-limit probability, comprising: The Service Road Network Abstraction Module is used to obtain the directed graph of service roads; The initial fleet status module is used to obtain the initial vehicle density distribution along each service road and the initial vehicle mass of each node's reservoir. The aircraft random process sampling module is used to generate N aircraft process samples based on the distribution parameters of the aircraft operation process; The capacity modulation field construction module is used to calculate the capacity modulation field along each service road for each aircraft process sample; A closed stochastic conservation law solution module is used to solve the vehicle density conservation equation along each service road to obtain the density field; The reservoir node solution module is used to calculate the node flux at the service road node and update the reservoir state at the node, while using the node flux as the boundary condition for the adjacent service road edge. The Monte Carlo density sample aggregation module is used to aggregate the edge density and node reservoir status of each sample by time bucket. The out-of-limit risk field calculation module is used to calculate the edge out-of-limit risk field and the node out-of-limit risk field; The risk field output module is used to output the spatiotemporal risk field, which consists of the out-of-limit probabilities of all service roadsides and nodes in all time buckets.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention models the ground service vehicle group as a closed conserved system on a directed graph of service roads, which can ensure the conservation of fleet mass and density positivity, and reduce non-physical prediction results; This invention treats the aircraft operation process as an exogenous stochastic process and influences the vehicle conservation law coefficients through a capacity modulation field, thereby establishing a coupling relationship between the aircraft process, the capacity field, the conservation law, and the risk field. This invention calculates the density exceedance probability and the node reservoir exceedance probability by Monte Carlo sample aggregation, and can output the edge / node risk field that changes over time, rather than a static conflict hotspot. The spatiotemporal risk field output by this invention can be used as input for risk perception path planning, vehicle scheduling, and operation control, improving the interpretability and usability of aircraft-vehicle conflict risk prediction in the flight area. Attached Figure Description

[0023] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a flowchart illustrating the conflict risk field prediction method of the present invention. Figure 2 This is a schematic diagram illustrating the coupling relationship between the closed random conservation law and the reservoir node in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the relationship between the aircraft capacity modulation field and vehicle density evolution in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the Monte Carlo aggregation generation of an edge / node over-limit risk field in an embodiment of the present invention. Detailed Implementation

[0024] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] This embodiment provides a method and system for predicting the aircraft-vehicle conflict risk field in a flight area based on the closed platoon conservation law and the density exceedance probability. The system includes an aircraft stochastic process sampling module, a service road network abstraction module, an initial platoon state module, a capacity modulation field construction module, a closed stochastic conservation law solution module, a reservoir node solution module, a Monte Carlo density sample aggregation module, an exceedance risk field calculation module, and a risk field output module. The system executes the following... Figure 1 The steps shown are as follows: S1, obtain the directed graph of service roads through the service road network abstraction module. The initial vehicle density distribution along each service road is obtained through the initial fleet state module. and the initial vehicle mass of each node's reservoir and obtain the set of conflicting interfaces. ; S2 generates N aircraft process samples based on the distribution parameters of the aircraft operation process through the aircraft random process sampling module. ; S3, for the nth aircraft process sample The capacity modulation field of the service roadside e is calculated using the capacity modulation field construction module. ; in, It is the traffic capacity modulation factor of the service road edge e at time t and position x on the edge under the nth aircraft process sample. It is obtained by mapping the event time of the aircraft sample passing through or affecting the conflict interface to the service road edge through the spatial kernel function and the temporal kernel function.

[0026] The specific calculation process is as follows: (1) For the first A sample of aircraft processes Based on the aircraft taxiing path, pushback / crossing / waiting events, determine the conflict interface c that it affects and the corresponding event time. .

[0027] (2) For each service road edge e, read the set of conflict interfaces associated with it. .

[0028] (3) On the time grid and the spatial grid, for each Calculate the impact of each conflicting interface .

[0029] (4) Add up the impact items of multiple conflicting interfaces on the same service road to obtain the total capacity attenuation.

[0030] (5) Subtract the total capacity attenuation from 1 to obtain the remaining capacity ratio, and then multiply by the upper limit of capacity. Finally passed and Perform cropping to ensure that the capacity modulation factor is not negative and is not lower than the set lower bound.

[0031] S4, using a closed stochastic conservation law solution module, solves the vehicle density conservation equation on the service road edge e to obtain the density field under sample n. ; in, This represents the nth aircraft process sample. Below, the vehicle density at time t and position x on the service road edge e is the deterministic vehicle density evolution result corresponding to this sample. e represents a service road edge in the directed graph of the service road; n represents the nth Monte Carlo aircraft process sample; t represents the prediction time; and x represents the one-dimensional position coordinates along service road edge e. , Let e ​​be the length of edge e; Due to each aircraft sample This will result in different arrival, taxiing, waiting, or crossing times of the conflict interface for aircraft, thus leading to different capacity modulation fields. This leads to the determination of different vehicle density evolution results.

[0032] The initial conditions are:

[0033] The boundary flux conditions are provided by the reservoir node solution module. In other words, the inflow and outflow of vehicles at the beginning and end of the service road edge are jointly determined by the demand, supply, queuing status of adjacent nodes and aircraft capacity constraints, and serve as the boundary conditions for the edge density conservation equation.

[0034] S5, calculate the node flux at the service road node through the reservoir node solution module, and use the node flux as the boundary condition for the adjacent service road edge; S6, repeat S3 to S5 until all aircraft process samples have completed density evolution solutions; S7, through the Monte Carlo density sample aggregation module, by time bucket Aggregate the edge density and node reservoir status of each sample; S8, calculates the edge over-limit risk field through the over-limit risk field calculation module. and node over-limit risk field ; S9 outputs a spatiotemporal risk field through the risk field output module, which consists of the out-of-limit probabilities of all service roadsides and nodes in all time buckets.

[0035] In one implementation, the closed stochastic conservation law on the service road edge e is:

[0036] in, To serve the vehicle density on roadside e, Let f be the edge flux function. For aircraft random processes, u is the scheduling control input.

[0037] In one implementation, the edge flux function is:

[0038] in, Let velocity be the function. The capacity modulation factor is driven by the aircraft process.

[0039] In one implementation, such as Figure 2 As shown, the state of the node's reservoir satisfies:

[0040] in, Let the mass of the vehicle in the reservoir at node v be [the mass of the vehicle in the reservoir]. This is a state transition item for the node service.

[0041] In one implementation, the mass conservation condition for a closed convoy is:

[0042] In one implementation, for a subset of conflicting interfaces The capacity modulation field satisfies:

[0043] in, For the capacity attenuation intensity of the conflict interface, For spatial kernel functions, For time kernel function, The time of the event when the aircraft passes through the conflict interface c.

[0044] In one implementation, the edge over-limit risk field is:

[0045] in, The critical density threshold for the service road edge e.

[0046] In one implementation, the Monte Carlo empirical estimate of the edge over-limit risk field is:

[0047] In one implementation, the node over-limit risk field is:

[0048] in, Let V be the critical vehicle mass of the reservoir at node v.

[0049] Furthermore, when two aircraft processes and When a disturbance occurs, the distance between the density field and the state of the nodal reservoir satisfies:

[0050] in, The distance between the two density-reservoir states under aircraft disturbance. For the distance of the aircraft's process state, is the disturbance stability constant.

[0051] The steps and principles of the technical solution in this embodiment are explained in detail below: 1. Input data and initial state The system input includes a directed graph of service roads. Conflict Interface Set Side length Maximum edge density Boundary critical density threshold Critical vehicle mass of node reservoir Initial edge density and the initial node water tank vehicle mass .

[0052] In one embodiment, the service road network includes 30 service road nodes, 67 service road edges, 6 aircraft stands, 2 parking garages, and 19 aircraft-vehicle conflict interfaces. The initial total fleet mass is:

[0053] In practical implementation, the system can read the mapping relationships of service road topology, edge capacity modulation interface, node reservoir interface, and conflict interface from the dynamic road network construction system. For each service road edge, the system establishes a one-dimensional directed interval. The vehicle density on that side is interpreted as the vehicle mass per unit length. Vehicle mass can be measured by the number of vehicles or by standard vehicle equivalents; when there are significant differences in the length, turning radius, or safety interval of different vehicle models, large support vehicles can be converted to a standard vehicle equivalent greater than 1.

[0054] Initial edge density The density can be obtained from vehicle location data, scheduling task lists, or historical statistical distributions. If real-time vehicle location data exists, the system first matches the vehicle location map to the service roadside, then calculates the vehicle mass on each edge according to the spatial grid, and approximates the initial density distribution through kernel smoothing or piecewise constants. If real-time location data is lacking, the system can set the initial density for each edge based on the garage vehicle departure plan, machine station operation plan, and historical traffic flow ratio, and allocate the remaining vehicle mass to the reservoirs of garage nodes or waiting area nodes.

[0055] In one embodiment, the edge critical density threshold Based on the maximum edge density And the operating strategy is determined, for example, taking to For edges near aircraft conflict interfaces, aircraft stand pushback impact zones, or service road bottlenecks, a lower critical density can be set; for edges of ordinary service roads, a higher critical density can be set. Critical vehicle mass of node reservoirs. It can be determined based on the physical waiting space of the node, the number of vehicles allowed to queue, and the safety interval.

[0056] The system can also perform a quality consistency check during the initialization phase. Specifically, the system calculates the sum of the integrals of all edge densities and the vehicle masses of all node reservoirs, and compares this with the number of vehicles registered in the fleet or the number of active vehicles in the scheduling system. If the difference exceeds a preset threshold, the initial state is corrected through normalization, reassignment to garage nodes, or removal of vehicles with abnormal locations. This step ensures that subsequent evolution of the closed conservation law has a consistent initial mass.

[0057] 2. Aircraft Sample Generation The system generates N independent sample paths based on the distribution parameters of the aircraft's operation. Each sample path includes the aircraft's position status, event time, and operating mode. Event time can include moments such as arrival, pushback, taxiing holding, crossing a conflict point, or runway crossing.

[0058] In one embodiment, the system uses a Monte Carlo sample size of N=50, and the aircraft process is obtained by fitting historical ADS-B data, taxiing time distribution, and pushback time disturbance. For each sample, the system calculates the event time of the aircraft passing through each conflict interface. .

[0059] In practice, the aircraft sample generation module can first read the list of arriving, departing, and towed aircraft within the future predicted time window from the operation plan, and determine the planned route for each aircraft. For departing aircraft, random variables may include pushback start time disturbance, pushback duration, taxi speed disturbance, and waiting time disturbance; for arriving aircraft, random variables may include runway departure time disturbance, taxi speed disturbance, and waiting disturbance near the gate. These random variables can be fitted to a normal distribution, log-normal distribution, empirical distribution, or piecewise empirical distribution based on historical operation data.

[0060] For the nth sample, the system accumulates the running time segment by segment along the aircraft's planned route to obtain the sample path of the aircraft on the directed graph of the taxiway. Subsequently, the system uses the conflict interface set... Locate the conflict interfaces that the aircraft's path passes through or affects, and calculate the corresponding event times. When an aircraft is waiting near a conflict interface, the system can extend the event time of that interface into an occupancy time interval; in a capacity modulation field, the center of the interval can be used as... And it covers the entire occupancy process by using a larger time kernel support radius.

[0061] In another embodiment, the system can use real-time aircraft processes as a sample mean and generate disturbance samples around the real-time state. If the aircraft's current position, speed, and planned route are already determined, the system only samples future taxiing times, waiting times, and conflict interface release times. This preserves the real-time operational state while also representing the uncertainties of future aircraft processes.

[0062] Optionally, the system can also employ stratified sampling or Latin hypercube sampling to reduce the number of samples required. During peak operating periods or times of significant aircraft disturbance, the Monte Carlo sample size can be increased; during stable operating periods, the sample size can be reduced to improve online computation speed. The sample size N is not limited to 50 and can be configured to 20, 100, or other values ​​depending on the prediction window length, airport size, and computational resources.

[0063] 3. Calculation of Capacity Modulation Field For each aircraft sample, the system calculates a capacity modulation field based on the conflict interface location and the aircraft event time. The capacity modulation field transforms the discrete occupancy events of the aircraft at the conflict point into continuous capacity attenuation coefficients along the service roadside.

[0064] In one embodiment, the spatial kernel function is a truncated Gaussian kernel, the temporal kernel function is a triangular kernel, and the capacity decay intensity is... The value is set to 0.8. If multiple conflicting interfaces are associated with the same service road, the capacity impact of the multiple conflicting interfaces is superimposed, and the capacity modulation factor is kept within the set range by upper and lower bound pruning.

[0065] In practical implementation, the system reads the associated conflict interface subset for each sample n and each service road edge e. For each conflict interface c, the system obtains the event time based on the aircraft sample path. And computed on the edge spatial grid and temporal grid. If the same side is affected by multiple conflicting interfaces at the same time, the system will add up the multiple influencing factors before performing lower and upper bound pruning.

[0066] For example, service roadside The system is associated with two conflicting interfaces, C1 and C2. C1 corresponds to an inbound aircraft crossing the line at 08:30:20, and C2 corresponds to a departing aircraft pushing back at 08:30:50. The system calculates the impact of these two interfaces within a time window from 08:30 to 08:32. The capacity attenuation is calculated, and the superimposed capacity modulation factor is output as... If the summation result is below the minimum capacity lower bound, then take... This avoids the flux function from having negative capacity that does not conform to the set rules.

[0067] Previous text e It is a universal number for any service roadside. It is along a specific service road, therefore That is, the service roadside under the nth aircraft process sample. The capacity modulation field. This quantity still represents the capacity modulation factor caused by the aircraft conflict interface at time t and edge position x.

[0068] In one embodiment, the capacity modulation field can also be converted into a velocity correction term in the side flux function. That is, given the vehicle density r and the control input... Under the condition of velocity function It decreases as the capacity modulation factor decreases. When When the speed approaches 1, vehicle speed is mainly affected by density and speed limit constraints; when As the threshold approaches, vehicle speed and traffic capacity decrease significantly, indicating the impact of aircraft processes on the traffic capacity of service roads.

[0069] 4. Solving the closed-loop conservation law The system solves the vehicle density conservation equation along each service road. A monotone finite volume scheme, such as a Godunov-type scheme, can be used to spatially discretize the edge intervals and select the time step based on the CFL condition. For the nth aircraft sample, the capacity modulation factor in the conservation law is... Therefore, each sample corresponds to a deterministic density evolution problem.

[0070] The boundary flux is given by the reservoir node solvers of adjacent nodes. The node solvers calculate the feasible flux vector based on the input demand, output supply, aircraft capacity constraints, and reservoir state, and ensure that the flux is non-negative, the reservoir state is non-negative, and the demand and supply boundaries are satisfied.

[0071] In practical implementation, the system can divide each service road into several finite volume units, with the average density of the units denoted as... , where j is the spatial cell number and m is the time step number. The system calculates the numerical flux between adjacent cells at each time step and updates the density according to a conservation scheme. Time step size. Based on maximum vehicle speed and spatial step size The selection of CFL conditions ensures that the propagation of vehicle mass between adjacent cells remains stable.

[0072] In one embodiment, such as Figure 3 As shown, the flux function can be a triangular basic diagram of capacity modulation or a velocity-density function. For example, when the vehicle density is below the critical density, the flux increases with increasing density; when the vehicle density is above the critical density, the flux is limited by both congestion and capacity modulation. Capacity modulation factor. It can be multiplied by free-flow velocity, maximum flux, or supply function to express the decrease in throughput caused by aircraft processes.

[0073] The nodal boundary conditions are provided through the reservoir node solver. For a given node v, the system reads the end element density of all input edges, the start element density of all output edges, and the reservoir mass of the node. The system calculates input demand, output supply, and aircraft capacity constraints, and then obtains the boundary fluxes for entering and leaving nodes. These boundary fluxes are used as boundary terms in the finite volume scheme of adjacent service road edges, thereby coupling edge density evolution with node queuing states.

[0074] To ensure the mass conservation of the closed-loop vehicle fleet, the system performs a mass check at each time step. This involves calculating the sum of the masses of all edge cell vehicles and all node reservoir vehicles, and then comparing this sum with the initial mass. Comparison. If the service state transition item satisfies... Furthermore, since the boundary flux is used in pairs between adjacent edges and nodes, the total mass remains unchanged in theory. Small errors generated in numerical calculations can be corrected by node reservoirs or normalized and limited to the preset tolerance.

[0075] In another embodiment, if the scheduling control input u intervenes in vehicle release, waiting, or speed limiting, the system uses this control input as parameters for the flux function and the node solver. For example, the operation control module can reduce the release ratio of specific edges within certain time buckets, or control the vehicle release rate at garage nodes. The aforementioned control input does not violate the conservation law structure, but rather alters the vehicle density evolution trajectory through the flux function and node boundary conditions.

[0076] 5. Risk Field Aggregation The system records the average density of each sample along each service road within each time bucket, as well as the vehicle mass in the reservoir at each node. For edge risk, the system calculates the time-space proportion of density exceeding the critical density threshold; for node risk, the system calculates the time proportion of node reservoir vehicle mass exceeding the critical value. Then, the average is calculated across all Monte Carlo samples to obtain the edge over-limit risk field and the node over-limit risk field, as follows: Figure 4 As shown.

[0077] In one embodiment, the time bucket width is 30 seconds, and the critical density threshold is... The system outputs the probability of each edge and each node exceeding the limit in each time bucket. For example, the node exceeding the limit risk of a conflict node in the time bucket from 08:30 to 08:31 is 0.35, which means that about 17 out of 50 samples will exceed the limit in that time bucket.

[0078] In practical implementation, the system can directly accumulate the overlimit indicator function during the conservation law solution process, without needing to save the complete density history of all time steps and spatial cells. This applies to edge e and time buckets. The system counts all time steps and spatial units falling into the time bucket in each sample, and calculates the density of those units exceeding a certain threshold. The time-space proportion. For node v, the system statistics show that the node's reservoir mass exceeds [a certain threshold]. The time percentage is calculated. After completing all samples, the average of the sample percentages is calculated to obtain the risk field estimate.

[0079] In this embodiment, a certain service roadside The length is 120 meters, divided into 12 spatial units, and a certain time bucket contains 6 numerical time steps. If there are 18 unit-time combinations in the nth sample that satisfy... Then, the percentage of edges exceeding the limit in this time bucket under this sample is: If the average proportion of the above-mentioned percentages among the 50 samples is 0.31, then the system outputs... .

[0080] Among them This indicates the condition for determining if the density exceeds the limit. `This is the nth aircraft process sample, serving the roadside` Vehicle density at time t and location x; This is the critical density threshold for that side. When both satisfy the greater than relationship, it indicates that the vehicle density within that time and space unit exceeds the critical level allowed by safety or operational efficiency, and the unit-time combination is counted as an over-limit.

[0081] In this embodiment, the service roadside Divided into 12 spatial units, with each time bucket containing 6 numerical time steps, therefore there are a total of Unit-time combinations. If 18 of these combinations satisfy:

[0082] This indicates that in the nth sample, there are 18 spatiotemporal grid locations within this time bucket where the density exceeds the limit. The corresponding percentage of edge exceedances for this sample is:

[0083] Regarding node risk, if a certain node The critical reservoir vehicle mass is 3 standard vehicle equivalents. A sample was in this state for 20 seconds within the time bucket from 08:30 to 08:31. If the sample node exceeds the limit, then the proportion of nodes exceeding the limit is 20 / 60 = 0.333. If the average of 50 samples is 0.35, it means that there is a high probability that nodes in that time bucket are queuing or waiting beyond the limit.

[0084] Optionally, the system can also output the confidence interval or sample variance of the risk field to indicate the uncertainty of risk estimation. For edges or nodes with large sample variance, the system can automatically increase the number of Monte Carlo samples or increase the risk weight in downstream path planning. For ordinary edges with long-term risks close to zero, the system can use sparse storage to save only risk time buckets that are non-zero or exceed the threshold, in order to reduce storage and transmission overhead.

[0085] 6. Output and Stability Verification The system outputs a complete spatiotemporal risk field, including the edge over-limit risk field. Node over-limit risk field The system includes Monte Carlo sample size, time bucket width, and optional perturbation stability verification results. The spatiotemporal risk field can be provided to downstream path planning systems, enabling path planning to avoid service roadsides or nodes with higher future risks.

[0086] In one embodiment, when an aircraft process occurs During level disturbances, the change in the risk field is controlled by a stability constant. This property is used to explain the robustness of the risk field to aircraft operational deviations.

[0087] In practical implementation, the risk field output module can organize the output data by edge, node, and time bucket. For each service road edge, the system outputs the edge identifier, time bucket start and end times, edge over-limit risk value, critical density threshold, number of samples, and an optional average density or peak density summary; for each node, the system outputs the node identifier, time bucket start and end times, node over-limit risk value, critical reservoir vehicle mass, number of samples, and an optional average reservoir mass or peak reservoir mass summary.

[0088] In one embodiment, the output data can be used as soft cost input in the path planning system. The path planning system reads the corresponding time bucket when a vehicle occupies an edge or node. or The risk value is multiplied by the vehicle occupancy time and risk weight and added to the path cost. The output data can also be used as an alarm input for the operation control system; when the node over-limit risk of certain conflict nodes exceeds the preset threshold, the system can prompt the driver to slow down the exit from the garage in advance, adjust the parking position to ensure the arrival time of the vehicle, or temporarily close some service road directions.

[0089] Stability verification can be achieved through perturbation comparison experiments. The system selects a baseline set of aircraft process samples and constructs sets of aircraft processes after time perturbation, velocity perturbation, or waiting perturbation, calculating two sets of risk fields respectively. If the perturbation distance between the two sets of aircraft processes is small, the differences in the edge density field, nodal reservoir state, and out-of-limit risk field should be controlled by stability constants. This result can be used to demonstrate that the method does not simply rely on discrete judgments of individual samples, but rather forms continuous and interpretable risk predictions through conservation laws and probability aggregation.

[0090] In another embodiment, the system can operate within a rolling prediction framework. Whenever a new aircraft position, pushback plan, or vehicle initial state enters the system, the risk field prediction module regenerates the risk field for several future time buckets starting from the current moment, and overwrites or merges the new risk field into the original output. In this way, the downstream path planning and vehicle scheduling modules can continuously obtain conflict risk prediction results that are updated with changes in aircraft processes and vehicle density states.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the risk field of aircraft-vehicle conflict in a flight area based on the conservation law of a closed vehicle fleet and the probability of density exceeding limits, characterized in that, include: S1, obtain the directed graph of the service roads, the initial vehicle density distribution along each service road, and the initial vehicle mass of each node's reservoir, and obtain the set of conflict interfaces; S2, generate N aircraft process samples based on the distribution parameters of the aircraft operation process; S3, For each aircraft process sample, calculate the capacity modulation field along each service road based on the conflict interface location and aircraft event time; S4. At each service road, the vehicle density conservation equation is solved based on the capacity modulation field to obtain the density field under that sample. S5, at the service road node, calculate the node flux based on the boundary flux of the adjacent edge and the state of the node reservoir, and use the node flux as the boundary condition of the adjacent service road edge, while updating the vehicle mass of the node reservoir. S6, repeat S3 to S5 until all aircraft process samples have completed density evolution solutions; S7, aggregate the edge density and node water storage status of each sample according to the preset time bucket; S8, calculate the edge over-limit risk field and the node over-limit risk field based on the aggregation results; S9 outputs a spatiotemporal risk field consisting of the out-of-limit probabilities of all service roadsides and nodes across all time buckets.

2. The method according to claim 1, characterized in that, The capacity modulation field is constructed in the following manner: For each conflicting interface, the event time of the aircraft passing through the interface is converted into a capacity attenuation coefficient on the service roadside using a spatial kernel function and a temporal kernel function. The attenuation coefficients of multiple conflicting interfaces associated with the same service roadside are superimposed and then clipped by upper and lower bounds to obtain the capacity modulation field.

3. The method according to claim 1, characterized in that, The vehicle density conservation equation is: ， in, To serve the vehicle density on roadside e, Let f be the edge flux function. For aircraft random processes, u is the scheduling control input; The edge flux function is: ， in, Let velocity be the function. The capacity modulation factor is driven by the aircraft process.

4. The method according to claim 1, characterized in that, The vehicle mass requirement for the node's water storage tank is: ， in, Let the mass of the vehicle in the reservoir at node v be [the mass of the vehicle in the reservoir]. and Let V be the sets of edges that enter and leave node v, respectively. This is a state transition item for node services.

5. The method according to claim 1, characterized in that, The generation of the aircraft process sample includes: Based on historical operational data or real-time operational plans, a planned route is determined for each aircraft, and at least one of its pushback time, taxi speed, and waiting time is randomly sampled to obtain the event time of each aircraft passing through each conflict interface.

6. The method according to claim 1, characterized in that, In step S4, the vehicle density conservation equation is spatially discretized using a monotonic finite volume scheme, and the time step is selected according to the CFL condition for numerical solution.

7. The method according to claim 1, characterized in that, The edge over-limit risk field is calculated using the following formula: ， in, The critical density threshold for the service road edge e; The Monte Carlo empirical estimate of the edge over-limit risk field is: 。 8. The method according to claim 1, characterized in that, The node over-limit risk field is calculated using the following formula: ， in, Let V be the critical vehicle mass of the reservoir at node v.

9. The method according to claim 1, characterized in that, It also includes a stability verification step, whereby the distance between the density field and the nodal reservoir state satisfies the following when the aircraft process is disturbed: ， in, The distance between the two density-reservoir states under aircraft disturbance. For the distance of the aircraft's process state, is the disturbance stability constant.

10. A prediction system for aircraft-vehicle conflict risk field in flight zones based on the conservation law of closed vehicle fleets and the probability of density exceeding limits, characterized in that, include: The Service Road Network Abstraction Module is used to obtain the directed graph of service roads; The initial fleet status module is used to obtain the initial vehicle density distribution along each service road and the initial vehicle mass of each node's reservoir. The aircraft random process sampling module is used to generate N aircraft process samples based on the distribution parameters of the aircraft operation process; The capacity modulation field construction module is used to calculate the capacity modulation field along each service road for each aircraft process sample; A closed stochastic conservation law solution module is used to solve the vehicle density conservation equation along each service road to obtain the density field; The reservoir node solution module is used to calculate the node flux at the service road node and update the reservoir state at the node, while using the node flux as the boundary condition for the adjacent service road edge. The Monte Carlo density sample aggregation module is used to aggregate the edge density and node reservoir status of each sample by time bucket. The out-of-limit risk field calculation module is used to calculate the edge out-of-limit risk field and the node out-of-limit risk field; The risk field output module is used to output the spatiotemporal risk field, which consists of the out-of-limit probabilities of all service roadsides and nodes in all time buckets.

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