An Airport Group System Resilience Assessment Method Based on Regional Control Capability

Abstract

The present invention relates to a method for evaluating the resilience of an airport group system based on regional control capabilities. The aim is to address the problems existing in the research on the combat support effectiveness of airports. Taking the airport group system as the research object, a network model is established. Further considering the main factors such as the maximum sortie rate of the airport group system, the mission execution time, and the importance of the mission area, and combining with the resource-limited recovery strategy, a method and process for evaluating the resilience of the airport group system based on regional control capabilities are established. A case study is carried out on the airport group system in a certain region to analyze the dynamic impact of different recovery strategies on the resilience of the airport group system, providing support for the planning, design, and combat application of the resilient airport group system.

Description

Technical Field

[0001] The present invention relates to the field of airport group system resilience assessment methods, and specifically, to an airport group system resilience assessment method based on regional control capabilities. Background Art

[0002] In the existing research on the combat support effectiveness of airports, most of them are qualitative studies based on the combat support effectiveness of individual airports. In the research on individual airports, usually a few high-value targets are protected with emphasis to improve the overall survival and support capabilities. However, in this way, the effectiveness will be restricted by many factors such as the total amount of system resources, the connection between nodes, network connectivity, and coordination relationships.

[0003] In reality, airports are not isolated fortresses, and system confrontation is the main mode of future wars. Therefore, qualitative and quantitative research on airport group systems is needed.

[0004] As a part of the battlefield facility system, the airport group system will inevitably be affected by events such as precision strikes, terrorist attacks, or internal equipment failures. When the system withstands a series of internal and external impacts, it is expected that the system can have the capabilities of buffering, recovery, and adaptation. Specifically, in the offensive and defensive confrontation, when the attacking party's capabilities are limited, if means such as flexible protection design and recovery resource backup can be adopted to enhance the resilience of the airport group system, the support capabilities of the system can be greatly improved. Therefore, in the analysis of combat support effectiveness, it is necessary to overall consider and select appropriate functional characteristic indicators based on the resilience of the airport group system to provide more scientific and reasonable support for the spatial layout of the airport group system, the update of protection means, and the configuration of recovery resources. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the purpose of the present invention is to propose a network model established based on the airport group system, comprehensively consider the main factors such as the maximum sortie of the airport group system, the mission execution time, and the importance degree of the mission area, and at the same time combine the resource-limited recovery strategy to establish an airport group system resilience assessment method and process based on regional control capabilities; and taking a regional airport system as an example, quantitatively analyze the impact of different recovery strategies on the resilience of the airport system, in order to provide a decision-making basis for the effective protection and rapid recovery of the airport group system.

[0006] The technical solution of the present invention is as follows:

[0007] An airport group system resilience assessment method based on regional control capabilities specifically includes the following steps:

[0008] Step 1: Determine the network structure of the airport group system and construct a one-way weighted network G=(N, E, W):

[0009] Step 2: Within the preset time interval Δt, the maximum number of sorties w of Airport i i ;

[0010] Step 3: Determine the regional control ability p of the airport group system G;

[0011] Step 4: Based on the regional control ability p of the airport group system G, calculate the importance of each airport i in turn Determine the airport recovery order;

[0012] Step 5: According to the interference or impact event occurring at time t, determine the failed airport as the damaged node after being externally interfered;

[0013] Step 6: Obtain the maximum regional control ability Z(t0, G) of the airport group system at time t;

[0014] Step 7: According to the damaged nodes of the airport group system after being externally interfered, determine the resource recovery strategy S, S = {s1, s2,... s i}; According to the importance of Airport i Sort the resource recovery strategies s in the resource recovery strategy S i to obtain the optimized resource recovery strategy set S';

[0015] Step 8: According to the optimized resource recovery strategy set S' in Step 7, perform recovery in turn;

[0016] Step 9: Determine whether there are unrepaired nodes;

[0017] Step 10: Construct an airport group system resilience analysis model based on regional control ability, and calculate the resilience value of the airport group system based on the target control ability according to Z(t, G).

[0018] Preferably, according to the number a of airports in the selected area and the number b of mission areas; determine that the number of nodes of the unidirectional weighted network G = (N, E, W) is a + b, and the maximum number of edges is a × b.

[0019] Preferably, within a certain time period Δt, the maximum number of sorties w of Airport i i can be expressed as:

[0020]

[0021] Preferably, the regional control ability p of the airport group system G is:

[0022]

[0023] η j is a constant, which represents the importance of mission area j, and 0 ≤ η j ≤ 1;

[0024] θ is the attenuation coefficient, representing the non-linear relationship between the regional control ability and the number of aircraft, and 0 < θ < 1:

[0025] t ij is the time for the aircraft taking off from airport i to perform tasks after arriving at mission area j;

[0026] w ij is the number of aircraft departures from each airport i to mission area j;

[0027] Among them, within the preset time interval Δt, the total number of aircraft departures from all airports ∑w ij .

[0028] Preferably, the time t for the aircraft taking off from airport i to perform tasks after arriving at mission area j ij is twice the ratio of the difference between the combat radius l of the aircraft of model k deployed at the airport k and the distance d between the airport and the mission area ij to the average speed v k .

[0029] Preferably, at time t1, a certain attack event occurs to the airport group system, causing some airport nodes to fail, and the maximum number of aircraft departures w of the failed airport i drops to 0.

[0030] Preferably, when t = t1, a certain attack event occurs to the airport group system, causing some airport nodes to fail, and the maximum number of aircraft departures w of the failed airport i drops to 0. At this time, the one-way network G of the airport group system has a structural adjustment; the number of nodes and the number of edges are recalculated; the number of aircraft departures between each airport and the corresponding mission area is readjusted, and the maximum regional control ability of the airport group system decreases, reaching a new maximum regional control ability Z(t1, G|N1).

[0031] Preferably, if an interference event occurs at time t1, and the set of failed nodes is represented as N1, then the maximum regional control ability of the system decreases to Z(t1, G|N1).

[0032] Preferably, at time t0, the maximum regional control ability Z(t0, G) of the airport group system can be expressed as:

[0033]

[0034] Preferably, at time t2 (t2 ≥ t1), the resilience R(t1→t2, s) of the airport group system based on the target control ability can be expressed as:

[0035]

[0036] Compared with the prior art, the advantages of the present invention are as follows: By analyzing the relevant concepts of the resilience of airport group systems, a unidirectional weighted network model describing the characteristics such as the tasks and functions of airport group systems is established, the differences of different configuration strategies under the condition of limited resources are analyzed, and a resilience evaluation method and process for airport group systems based on regional control ability are proposed, providing a basic theoretical support for the spatial layout and group operation of airport group systems. Through case studies, the feasibility and effectiveness of the resilience evaluation method for airport group systems based on regional control ability are verified, and the dynamic impacts of disasters and resource inputs on the regional control ability of airport group systems are analyzed, providing support for further research on resilience theories under different airport group configurations and changes in resource input strategies. Brief Description of the Drawings

[0037] The above and / or additional advantages of the present invention will become apparent and be readily understood from the description of the embodiments in conjunction with the following drawings, wherein:

[0038] Figure 1 is a flowchart of the resilience evaluation method for airport group systems based on regional control ability according to the present invention.

[0039] Figure 2 is a network diagram of the airport group system based on the maximum number of sorties according to the resilience evaluation method for airport group systems based on regional control ability of the present invention.

[0040] Figure 3 is a schematic diagram of the change in the resilience of the airport group system according to the resilience evaluation method for airport group systems based on regional control ability of the present invention.

[0041] Figure 4 is a schematic diagram of the change in the recovery resource input of the airport group system according to the resilience evaluation method for airport group systems based on regional control ability of the present invention.

[0042] Figure 5 is a result graph of the change in the maximum regional control ability of the airport group system with the recovery resource input according to the resilience evaluation method for airport group systems based on regional control ability of the present invention. Detailed Embodiments

[0043] The above and other technical features and advantages of the present invention will be described in more detail below in conjunction with the drawings.

[0044] A resilience evaluation model for airport group systems based on regional control ability, which includes a parameter setting module for the resilience model of the airport group system, an external interference or impact module, a resource input and system ability recovery module, and a system resilience calculation module; wherein

[0045] The resilience model parameter setting module of the airport group system initializes recovery resources according to the network structure of the airport group system, solves the number of sorties of each airport, solves the maximum regional control ability of the airport group system, and then obtains the importance of each airport in the system; transfer to the external interference or impact module for subsequent processing;

[0046] Preferably, determine the number of airports included in the airport group system and the number of task areas to obtain a one-way weighted network G=(N, E, W) based on airports and task areas; where: N represents the set of nodes in network G, that is, the set of airport i and task area j; E represents the set of edges in network G, and any edge can be represented by (i, j); W represents the set of edge weight values w ij of, w ij represents the number of aircraft sorties of each airport i to the task area j.

[0047] Specifically, if the airport group system in a certain region covers 3 airports and 5 task areas, the relationship between airports and task areas is converted into a one-way weighted network G=(N, E, W) with 8 nodes and 8 edges.

[0048] Preferably, take the maximum number of sorties w i of airport i as the number of sorties of each airport.

[0049] Preferably, the number of aircraft sorties is mainly restricted by the maximum support capacity of the airport, the main performance and quantity of aircraft types, etc., and the maximum support capacity of the airport depends on the maximum load of the airport, the task preparation time and the task execution time, etc. However, from the perspective of ground preparation time and air flight time, considering the professional degree of personnel, facilities and equipment, the aircraft sortie cycle t ck of type k aircraft is generally relatively stable. Therefore, within a certain time period Δt, the maximum number of sorties w i of airport i can be expressed as:

[0050]

[0051] where, represents rounding down, t ck can be approximately expressed as:

[0052]

[0053] Preferably, the regional control ability p of the airport group system G can be expressed as:

[0054]

[0055] where: η j is a constant, representing the importance of task area j, and 0≤η j≤1; θ is the attenuation coefficient, representing the non-linear relationship between the regional control ability and the number of aircraft, and 0 < θ < 1; t ij is the time for the aircraft taking off from airport i to perform tasks after arriving at mission area j, which is mainly affected by the combat radius l k of the aircraft of type k deployed at the airport and the average speed v k , as well as the distance d ij between the airport and the mission area. It can be expressed as:

[0056] t ij = 2·(l k - d ij ) / v k

[0057] It can be seen from Equation that the regional control ability p of the airport group system is mainly affected by the number of aircraft departures w ij from airport i to mission area j and the time t ij for the aircraft to perform tasks after arriving at mission area j.

[0058] To construct an airport group system resilience analysis model based on the regional control ability p, in practical applications, if it is necessary to strengthen the control of the mission area to the greatest extent by the airport group system, then at time t0, the maximum regional control ability Z(t0, G) of the airport group system can be expressed as:

[0059]

[0060] where

[0061] Preferably, in order to reasonably select the airport group system recovery strategy and clarify the recovery order of each airport, the importance of the airport based on the regional control ability is used to determine the airport recovery order. Among them, the importance

[0062]

[0063] of airport i can be expressed as: where Z(t0, G|i) represents the regional control ability when airport i fails in network G. In the airport group system, once an airport is damaged and fails due to interference or impact,

[0064] the nodes with higher

[0065] Resource input and system capacity recovery module, configured to determine whether the recovery resource loss reaches the upper limit;

[0066] If the upper limit is reached, directly record the change curve of the regional control capacity of the airport group system; then transfer to the system resilience calculation module for subsequent processing;

[0067] If the recovery resource loss does not reach the upper limit, let t = t + Δt, allocate recovery resources according to the airport importance ranking, and determine whether there are un-repaired airports;

[0068] If there are un-repaired airports, transfer to the external interference or impact module, re-solve the maximum regional control capacity of the airport group system at the current time t, then transfer to the resource input and system capacity recovery module, record the change curve of the regional control capacity of the airport group system; determine whether the recovery resource loss reaches the upper limit, if the upper limit is reached, directly record the change curve of the regional control capacity of the airport group system, if the recovery resource loss does not reach, let t = t + Δt, allocate recovery resources according to the airport importance ranking, and re-determine whether there are un-repaired airports;

[0069] If there are no un-repaired airports, record the change curve of the regional control capacity of the airport group system; then transfer to the system resilience calculation module to solve the resilience value of the airport group system;

[0070] System resilience calculation module, configured to solve the resilience value of the airport group system.

[0071] The airport group system resilience evaluation method based on regional control capacity according to the present invention specifically includes the following steps:

[0072] Step 1: Determine the network structure of the airport group system, and construct a unidirectional weighted network G=(N, E, W):

[0073] Preferably, determine the number a of airports and the number b of mission areas within the selected area; convert the relationship between airports and mission areas according to the attack and defense relationship into a node set containing a + b nodes, and regard the mission area as a massless point with its geometric center as the node; if the geometric center of the mission area, that is, the node, is within the coverage range of the airport, then there is an edge between this airport and the mission area; for the unidirectional weighted network G=(N, E, W), the maximum number of edges is a + b; the minimum number of edges is 0, that is, all mission areas are outside the coverage range of the airport; where N represents the set of nodes in the unidirectional weighted network G, that is, the set of airport i and mission area j; E represents the set of edges in the unidirectional weighted network G, and any edge can be represented by (i, j); W represents the set of weight values w ij of;

[0074] Preferably, initializing the recovery resources means assigning values to the amount of recovery resources. For example, in the initial state, the recovery resources are set to the total amount C of the recovery resources of the airport group.

[0075] Step 2: Within a preset time interval Δt, the maximum number of sorties w of airport i i ;

[0076] Preferably, the number of sorties of an aircraft is mainly restricted by the maximum support capacity of the airport, the main performance and quantity of the aircraft type, etc. And the maximum support capacity of the airport depends on the maximum load of the airport, the mission preparation time and the mission execution time, etc. However, from the perspectives of the ground preparation time and the air flight time, considering the professional degree of personnel, facilities and equipment, the sortie cycle t of the aircraft of type k ck is generally relatively stable.

[0077] Preferably, within a certain time period Δt, the maximum number of sorties w of airport i i can be expressed as:

[0078]

[0079] Wherein, represents rounding down, and t ck can be approximately expressed as:

[0080]

[0081] Step 3: Determine the regional control ability p of the airport group system G;

[0082] Specifically, the regional control ability p of the airport group system G is:

[0083]

[0084] Where: η j is a constant, which represents the importance degree of mission area j, and 0 ≤ η j ≤ 1;

[0085] θ is the attenuation coefficient, which represents the non-linear relationship between the regional control ability and the number of aircraft, and 0 < θ < 1

[0086] t ij is the time for the aircraft taking off from airport i to perform the mission after arriving at mission area j;

[0087] w ij is the number of sorties of the aircraft of each airport i for mission area j;

[0088] Wherein, within the preset time interval Δt, the total number of sorties ∑w of the aircraft dispatched by all airports ij ;

[0089] According to the number of airports, the total number of aircraft w at each airport i i and the mission area j, the optimal w is obtained ij ; w ij can be obtained by methods such as nonlinear integer programming method, enumeration method, heuristic algorithm, etc. Preferably, the time t for the aircraft taking off from airport i to perform the mission after arriving at the mission area j ij is twice the ratio of the difference between the combat radius l of the aircraft of type k deployed at the airport k and the distance d between the airport and the mission area ij to the average speed v k .

[0090] The time t for performing the mission ij can be expressed as:

[0091] t ij = 2·(l k - d ij ) / v k ;

[0092] From the regional control ability of the airport group system G it can be seen that the regional control ability p of the airport group system is related to the number of aircraft sorties w of airport i to the mission area j ij and the time t for the aircraft to perform the mission after arriving at the mission area j ij .

[0093] Step 4: Based on the regional control ability p of the airport group system G, calculate the importance of each airport i in turn It can also be expressed as to determine the airport recovery order;

[0094] Preferably, in order to reasonably select the airport group system recovery strategy and clarify the recovery order of each airport. Among them, the importance of airport i can be expressed as:

[0095]

[0096] Among them, Z(t0, G|i) represents the regional control ability when airport i fails in network G. In the airport group system, once an airport is damaged and fails due to interference or impact, the node with a higher value has a dominant recovery time sequence until the airport is fully restored.

[0097] Step 5: According to the interference or impact event occurring at time t, determine the failed airport as the damaged node after being externally interfered;

[0098] Preferably, at time t1, the airport group system is attacked by a certain event, causing some airport nodes to fail. The maximum number of aircraft sorties w of the failed airport iDrop to 0;

[0099] Step 6: Obtain the maximum regional control ability Z(t0, G) of the airport group system at time t;

[0100] When t = t1, the airport group system suffers an attack event that causes some airport nodes to fail, and the maximum sortie w of the failed airport i Drops to 0. At this time, the one-way network G of the airport group system undergoes a structural adjustment.

[0101] Recalculate the number of nodes and the number of edges; readjust the number of aircraft sorties between each airport and the corresponding mission area. The maximum regional control ability of the airport group system decreases, reaching a new maximum regional control ability Z(t1, G|N1), and at the same time, use the recovery resources to accelerate the recovery and restoration of the maximum regional control ability; where t1≥t0 and t0 is the initial time;

[0102] In practical applications, it is necessary to strengthen the control of the mission area to the greatest extent by the airport group system, and construct a resilience analysis model of the airport group system based on the regional control ability p. At time t0, the maximum regional control ability Z(t0, G) of the airport group system can be expressed as:

[0103]

[0104] Where

[0105] Step 7: Determine the resource recovery strategy S according to the damaged nodes of the airport group system after being externally disturbed, S = {s1, s2,... s i}; According to the importance of airport i Sort the resource recovery strategies s in the resource recovery strategy S i To obtain the optimized resource recovery strategy set S′;

[0106] Step 8: Perform recovery in sequence according to the optimized resource recovery strategy set S′ in Step 7;

[0107] Preferably, considering that the total amount of recovery resources such as spare aircraft, emergency repair materials or personnel is usually limited, let the total amount of recovery resources C of the airport group be the upper limit;

[0108] During the recovery process, set the amount of used recovery resources as c(t), set the recovery resources invested within the preset time interval Δt as Δc, and judge whether the loss of recovery resources c(t)+Δc after the preset time interval Δt reaches the upper limit; at the initial moment, the amount of used recovery resources is zero, c(t) t＝0 = 0.

[0109] If the restored resources c(t) + Δc invested after Δt reach the upper limit, that is, c(t) + Δc > C, then let Δc = C - c(t), and record the change curve Z(t, G) of the regional control ability of the airport group system; go to Step Ten;

[0110] If the restored resources Δc invested after the preset time interval Δt do not exceed the upper limit, that is, c(t) + Δc ≤ C; then update t = t + Δt, c(t) = c(t) + Δc; go to Step Nine;

[0111] Among them, Δc preferentially satisfies airports with a higher importance until they are fully restored;

[0112] Preferably, at time t (the time before the preset time interval Δt), first judge whether the amount of restored resources c(t) used is ≤ C. If the amount of restored resources c(t) used at this time ≤ C, then judge whether the restored resources c(t) + Δc invested after the preset time interval Δt is ≤ C;

[0113] If c(t) + Δc is greater than C, record the change curve Z(t, G) of the regional control ability of the airport group system; if c(t) + Δc ≤ C, then update the amount of restored resources c(t) used to c(t + Δt) = c(t) + Δc, and update the time to t = t + Δt. Go to Step Nine;

[0114] Step Nine: Judge whether there are unrepaired nodes;

[0115] If there are unrepaired nodes, return to Step Six to recalculate the maximum regional control ability Z(t0, G) of the airport group system at time t;

[0116] If there are no unrepaired nodes, record the change curve Z(t, G) of the regional control ability of the airport group system;

[0117] Step Ten: Construct a resilience analysis model of the airport group system based on the regional control ability, and calculate the resilience value of the airport group system based on the target control ability according to Z(t, G);

[0118] If an interference event occurs at time t1, and the set of failed nodes is represented as N1, then the maximum regional control ability of the system drops to Z(t1, G|N1). At the same time, the airport group system adopts strategy s i for recovery, and preferentially invests Δc restored resources in failed nodes with a higher importance every Δt time. Then at time t2 (t2 ≥ t1), the resilience R(t1 → t2, s) of the airport group system based on the target control ability can be expressed as:

[0119]

[0120] ​Among them, t1→t2 represents the time from t1 to t2; s represents any recovery strategy, and |N1 is the set of failed nodes after being attacked; Z(t1, G|N1, s) is the maximum regional control ability of the airport group system under any recovery strategy s when there exists the set of failed nodes |N1. It represents the integral of the maximum regional control ability of the airport group system from t1 to t2 with respect to time. By taking the ratio of it to Z(t0, G)(t2 - t1), R(t1→t2, s) is obtained.

[0121] R(t1→t2, s) represents the resilience value of the airport group system based on the target control ability under any recovery strategy s. The larger this value is, the higher the resilience ability of the airport group system is. That is to say, its recovery ability after being attacked is stronger.

[0122] The change in the resilience of the airport group system includes two aspects. On the one hand, it is the ability of the system to resist interference or impact, manifested as the decrease value (p1 - p2) of the regional control ability. On the other hand, it is the process of the system's adjustment and recovery. Under different strategies, the time for the regional control ability to recover is different. Preferably, when being interfered or impacted, some airports in the airport group system fail, and then the regional control ability p of the airport group system decreases. Among them, at t = t1, the airport group system is interfered or impacted, and the regional control ability of the airport group system decreases from p1 to p2. At this time, under different total resource conditions, different recovery measures can be taken to recover the regional control ability to different degrees.

[0123] If the strategy s1 with a large resource investment is adopted, the change of the regional control ability with time is shown as the curve p(t, s1), and the area A1 of the abc region represents the change magnitude of the regional control ability.

[0124] If the strategy s2 with a small resource investment is adopted, the change of the regional control ability with time is shown as the curve p(t, s2), and the area A2 of the abd region represents the change magnitude of the regional control ability.

[0125] Preferably, the total amount C of recovery resources such as standby aircraft, emergency repair materials or personnel is generally limited and difficult to be invested at the same moment. The process of its investment and recovery is continuous, dynamic and delayed.

[0126] Therefore, after the airport system is externally interfered, the input recovery resources within a certain time period Δt can be expressed as Δc. Different targets and times for the input of Δc correspond to different recovery effects of the system. Specifically, when the system is externally interfered and nodes 1 and 3 are damaged, considering the limited recoverable resources Δc available in each stage, three recovery strategies can be adopted: preferentially recovering node 3, simultaneously recovering nodes 1 and 3, and preferentially recovering node 1. Among them, preferentially recovering node 3 is taken as strategy s1; simultaneously recovering nodes 1 and 3 is taken as strategy s2; preferentially recovering node 1 is taken as strategy s3.

[0127] Taking Figure 2 the airport group system shown as an example, according to the locations of each airport, the attack and defense relationships form a weighted unidirectional network G of the airport group system, and an initial time t0, the total recovery resources C of the airport group, the recoverable resources Δc within the time period Δt, the types of aircraft stationed at each airport and the combat radius l k and speed v k of its aircraft type, the quantity n i and attenuation coefficient θ and other parameters are set. Calculate the maximum sortie w i of each airport and the mission execution time t ij , and respectively calculate the maximum regional control ability Z(t0, G) of the airport group system in the initial state and the airport importance

[0128] Conduct a case study and quantitatively analyze the resilience of the airport group system under interference or impact conditions. The distances between each node are shown in Table 1.

[0129] Table 1 Distances between Airports and Mission Areas

[0130]

[0131] In this case, the aircraft types stationed at airports 1, 3, and 6 are type A, with corresponding quantities of 50, 40, and 60 respectively. The regional importance levels of nodes 2, 4, 5, 7, and 8 are set to 1, 0.5, 0.9, 0.7, and 0.4 respectively. At the same time, when t1 = 1, the airport system is attacked, and the aircraft at nodes 1 and 3 are completely damaged, and the node airports fail. The maximum sortie w i of the failed airport drops to 0. At this time, the weighted unidirectional network G of the airport group system undergoes a structural adjustment, and the sortie of each airport and the corresponding mission area will be readjusted. The maximum regional control ability of the airport group system decreases and reaches a new maximum regional control ability Z(t1, G|N1), and at the same time, the recovery resources are used to accelerate the recovery and restoration of the maximum regional control ability.

[0132] In addition, personnel are not considered for the recovery resources for the time being. The total resource quantity C is set to 90 type A aircraft, the available resources Δc per day is 10 aircraft, and the details of the settings of the mission area importance and other relevant parameters are shown in Table 2.

[0133] Table 2 Relevant parameter settings for case settings

[0134]

[0135] At time t (t ≥ t0), first, it is judged whether the amount of restored resources c(t) already used is less than or equal to C. If c(t) > C, the change curve Z(t, G) of the regional control ability of the airport group system is recorded. If c(t) ≤ C, the amount of restored resources c(t) already used is updated to c(t + Δt) = c(t) + Δc, and the time is updated to t = t + Δt. Among them, Δc first satisfies the airports with higher importance until they are fully restored, and then it is judged in the next step whether there are unrepaired airports. If not, Z(t, G) is recorded. If so, the maximum control ability of the calculation area is returned.

[0136] The maximum sortie w within Δt time for nodes 1, 3, and 6 is calculated i to be 153, 122, and 184 respectively; at the same time, the mission execution time t of the aircraft after taking off from node i and arriving at area j ij is shown in Table 3.

[0137] Table 3 Calculation results e of mission execution time

[0138]

[0139] Calculate the maximum sortie w from each airport node i to area j ij , and the results are shown in Table 4. Under this sortie plan, the value result corresponding to the maximum regional control ability Z(t0, G) of the airport group system is 9.4864.

[0140] Table 4 Calculation results of maximum sortie

[0141]

[0142] At this time, calculate the maximum regional control ability and importance of the three states of the failure of node 1, node 3, and node 6 of the airport group system respectively to determine the node recovery order. The calculation results are shown in Table 5. Among them, compared with the initial state of the airport group system, the decline rate of the maximum regional control ability is the largest when node 3 fails, indicating that Airport 2 is the most important among the three airports. According to the importance ranking, the priority supply order of the restoration resources is nodes 3, 6, and 1 respectively.

[0143] Table 5 Calculation results of different node damage cases

[0144]

[0145] According to the case setting, when the airport system is affected by disasters at t1 = 1, nodes 1 and 3 are completely damaged. According to the calculation process of the resilience of the airport group system, in this case, the order of restoring resource input should first satisfy node 3 (restoration order 3 → 1, strategy S 31 ), but to compare the impact of the order of resource input and verify the effectiveness of inputting resources according to the importance ranking, a control group is set (restoration order 1 → 3, strategy S 13 ). The change curve of the maximum regional control ability of its airport group system over time is as shown in Figure 5 .

[0146] It can be seen from the figure that the restoration resource input strategy based on the importance ranking can effectively improve the resilience level of the airport group system. Under the condition that the daily available restoration resources are limited to 10 F-16 fighter jets, the airport group system returns to the pre-disaster level at t2 = 10. Using strategy S 13 (restoration order 1 → 3), the calculated result of the resilience value R(t1 → t2, S 13 ) of the airport group system is 0.6423. While using strategy S 31 (restoration order 3 → 1), the calculated result of the resilience value R(t1 → t2, S 31 ) of the airport group system is 0.7039. Under the conditions of the same total amount of resources and time limit, compared with the restoration strategy S 13 , using the strategy S 31 based on the importance ranking increases the resilience value of the airport group system by nearly 10%.

[0147] In addition, there are many specific implementation methods and ways for the present invention. The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the existing technology.

Claims

1. An airport group system resilience assessment method based on regional control capabilities, characterized in that, Specifically, it includes the following steps: Step 1: Determine the network structure of the airport group system, and construct a one-way weighted network G = (N, E, W); Step 2: The maximum number of sorties w of airport i within a preset time interval Δt i ; Step 3: Determine the regional control ability p of the airport group system G; The regional control ability p of the airport group system G is: η j is a constant, which represents the importance level of task area j, and 0 ≤ η j ≤ 1; θ is the attenuation coefficient, representing the non-linear relationship between the regional control ability and the number of aircraft, and 0 < θ < 1; t ij is the time for the aircraft taking off from airport i to perform tasks after arriving at mission area j; w ij The number of aircraft sorties from each airport i to mission area j; Among them, within a preset time interval Δt, the total number of sorties ∑w of aircraft dispatched by all airports ij ; Step 4: Calculate the importance of each airport i based on the regional control ability p of the airport group system G in turn Determine the airport recovery order; Step 5: According to the interference or shock event occurring at time t, determine the failed airport as the damaged node after being externally interfered; Step 6: Obtain the maximum regional control ability Z(t0, G) of the airport group system at time t; at time t0, the maximum regional control ability Z(t0, G) of the airport group system can be expressed as: Step 7: Determine the resource recovery strategy S based on the damaged nodes in the airport group system after being externally disturbed, where S = {s1, s1,... s i}; According to the importance of airport i Sort the resource recovery strategies s i in the resource recovery strategy S to obtain the optimized resource recovery strategy set S'; Step 8: According to the optimized resource recovery strategy set S' in Step 7, perform recovery in sequence; Step 9: Determine whether there are un-repaired nodes; Step 10: Construct a resilience analysis model of the airport group system based on the regional control ability, and calculate the resilience value of the airport group system based on the target control ability according to Z(t, G); At time t2 (t2 ≥ t1), the resilience R(t1→t2, s) of the airport group system based on the target control ability can be expressed as: Among them, Z(t1, G|N1) is to readjust the number of aircraft flights between each airport and the corresponding task area, and the maximum regional control ability of the airport group system decreases to reach a new maximum regional control ability.

2. The method for evaluating the resilience of an airport group system based on regional control capabilities according to claim 1, wherein According to the number a of airports in the selected area and the number b of task areas; determine that the number of nodes of the one-way weighted network G = (N, E, W) is a + b, and the maximum number of edges is a × b.

3. The method for evaluating the resilience of an airport group system based on regional control capabilities as claimed in claim 2, wherein Within a certain time period Δt, the maximum number of sorties w of airport i i can be expressed as:

4. The method for evaluating the resilience of an airport group system based on regional control capabilities according to claim 3, wherein The time t for an aircraft taking off from airport i to perform a mission after arriving at mission area j ij Is based on the combat radius l of an aircraft of model k deployed at the airport k And the distance d between the airport and the mission area ij The difference between them and the average speed v k Twice the ratio 5. The method for evaluating the resilience of an airport group system based on regional control capabilities according to claim 4, characterized in that, At time t1, a certain attack event causes some airport nodes in the airport group system to fail, and the maximum sortie w of the failed airport i drops to 0.

6. The method for evaluating the resilience of an airport cluster system based on regional control capabilities according to claim 5, wherein, When \(t = t_1\), a certain attack event occurs in the airport group system, causing some airport nodes to fail, and the maximum sortie \(w\) of the failed airports i drops to 0. At this time, the one-way network \(G\) of the airport group system has a structural adjustment; recalculate the number of nodes and the number of edges; Readjust the number of aircraft flights between each airport and the corresponding task area, and the maximum regional control ability of the airport group system decreases to reach a new maximum regional control ability Z(t1, G|N1).

7. The method for evaluating the resilience of an airport group system based on regional control capabilities according to claim 6, wherein If an interference event occurs at time t1, represent the set of failed nodes as N1, then the maximum regional control ability of the system decreases to Z(t1, G|N1).

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