Toughness evaluation method based on railway infrastructure power supply system

Abstract

The invention discloses a toughness evaluation method based on a railway infrastructure power supply system, belongs to the field of railway infrastructures, and researches a method for stability and recovery capability of the railway infrastructure power supply system under the background of strategic attacks such as deliberate attacks. The method comprises the following steps: firstly, establishing a power supply system topology network structure chart by analyzing operation characteristics of a railway infrastructure power supply system; a power supply system performance response function is used to calculate a power supply system network node importance index under a strategic strike background; constructing an attack and defense game model by utilizing a game theory technical method, calculating to obtain a strategy set of attack and defense parties by adopting a Bayesian equilibrium strategy solving method, and obtaining a damage probability of each node of the power supply system network in combination with a risk assessment theory; and finally, according to the network damage state of the power supply system, calculating by using the proposed performance response function of the power supply system to obtain a quantitative evaluation result of the toughness of the power supply system under different protection resources and protection budget scenarios.

Description

Technical Field

[0001] Based on the performance response function method, the present invention studies a method for the stability and recovery capability of railway infrastructure under the background of strategic strikes such as deliberate attacks. First, by analyzing the operating characteristics of the power supply system of the railway infrastructure, a topological network structure diagram of the power supply system is established; then, the power supply system performance response function is used to calculate the importance index of the power supply system network node under the background of strategic strikes; then, the attack and defense game model is constructed using game theory technology, and the Bayesian equilibrium strategy solution method is used to calculate the strategy set of both the attack and defense parties, and the damage probability of each node in the power supply system network is obtained in combination with the risk assessment theory; finally, through the damage state of the power supply system network, and using the proposed power supply system performance response function to calculate the quantitative evaluation results of the power supply system resilience under different protection resources and protection budget scenarios, and the recovery resources and recovery budget can be reasonably allocated according to the calculated resilience value. The present invention belongs to the field of railway infrastructure, and specifically involves technologies such as attack and defense game, Monte Carlo simulation and risk assessment. Background Art

[0002] The railway infrastructure power supply system is an important part of the key infrastructure system and plays a vital role in maintaining the urban social and economic operation and residents' lives.

[0003] Resilience assessment can be widely used in many engineering fields such as protection, disaster reduction and public safety. In particular, when the railway power supply system faces the threat of deliberate human attacks, resilience assessment can help decision makers rationally allocate limited protection resources and budgets to ensure that the protection strategy covers all stages such as pre-disaster protection, emergency response during disasters and post-disaster recovery. This comprehensive optimization configuration can maintain the continuity and stability of the power supply system to the greatest extent, reduce the impact of deliberate attacks on the normal operation of the railway system, and improve the safety and reliability of railway transportation.

[0004] Taking into account the possibility of upgrading the means of attack and increasing the scope of destruction, and the limited effectiveness of traditional resilience assessment methods, this invention proposes a method for quantitatively assessing the resilience of the power supply system of railway infrastructure under the background of strategic attacks such as deliberate attacks. First, by analyzing the operating characteristics of the power supply system of railway infrastructure, a topological network structure diagram of the power supply system is established; then, the power supply system performance response function is used to calculate the importance index of the power supply system network node under the background of strategic attacks; then, the attack and defense game model is constructed using game theory technology, and the Bayesian equilibrium strategy solution method is used to calculate the strategy set of both the attack and defense parties, and the damage probability of each node of the power supply system network is obtained in combination with risk assessment theory; finally, the power supply system network damage state is calculated by using the proposed power supply system performance response function to obtain the quantitative assessment results of the resilience of the power supply system under different protection resources and protection budget scenarios. Summary of the invention

[0005] The present invention is different from the existing resilience assessment methods. It uses game theory and risk assessment technology to propose a resilience assessment method based on the railway infrastructure power supply system. In order to overcome the shortcomings of the prior art, the present invention defines the resilience assessment value of the railway infrastructure power supply system after damage under the background of deliberate attack through risk assessment theory, game theory technology and performance response function modeling, and obtains the resilience optimization strategy of the railway infrastructure power supply system.

[0006] In a first aspect, the present invention provides a resilience assessment method based on a railway infrastructure power supply system, comprising:

[0007] Compared with the prior art, the present invention has the following advantages:

[0008] Firstly, by analyzing the operating characteristics of the power supply system of railway infrastructure, a topological network diagram of the power supply system is established; then, the power supply system performance response function is used to calculate the importance index of the power supply system network nodes under the background of strategic attack; then, the attack and defense game model is constructed using game theory technology, and the Bayesian equilibrium strategy solution method is adopted to calculate the strategy set of both the attack and defense parties, and the damage probability of each node in the power supply system network is obtained by combining the risk assessment theory; finally, the power supply system network damage state is calculated by using the proposed power supply system performance response function to obtain the quantitative evaluation results of the power supply system resilience under different protection resources and protection budget scenarios;

[0009] By constructing a method for quantitatively evaluating the resilience of the power supply system of railway infrastructure under the background of deliberate attacks and other strategic human strikes, it can guide the protection departments in optimizing the protection plans throughout the entire process of pre-disaster, during-disaster and post-disaster, and provide theoretical guidance and decision-making support for the protection departments. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is the overall framework diagram of the resilience assessment process of the railway infrastructure power supply system under the background of human strategic strikes such as deliberate attacks in the present invention. DETAILED DESCRIPTION

[0011] In order to more fully understand the technical content of the present invention, the technical solution of the present invention is further introduced and illustrated in conjunction with specific embodiments below, but is not limited thereto.

[0012] Combination Figure 1The present invention targets the railway infrastructure power supply system under the background of deliberate attacks and other strategic strikes, and carries out a quantitative assessment of the resilience of the railway infrastructure power supply system, from the importance assessment of the power supply system node units to the reasonable allocation of protection resources and protection budgets, and then combines Monte Carlo simulation and risk assessment technical methods, and can reasonably allocate recovery resources and recovery budgets according to the calculated resilience values. The specific implementation steps include:

[0013] Step 1: Establishment of performance response function of railway infrastructure power supply system

[0014] Step 1.1: Railway infrastructure power supply system topology network construction

[0015] According to the geographical layout of the railway infrastructure power supply system and the geographical coordinates of the load nodes and power generation nodes and the topology of the node units, a topological network of the railway infrastructure power supply system is generated, in which the edges represent the key transmission lines of the power supply facilities and the node units represent the load nodes and power generation nodes.

[0016] Step 1.2: Establishment of performance response function of railway infrastructure power supply system

[0017] In order to ensure that the performance response function of the railway infrastructure power supply system can represent the ability of the power supply network to perform its functions under normal operating conditions, and this ability is affected by the maximum power of electric energy transmission and the equivalent impedance between the "generation-load" node pairs. Therefore, the performance response function of the railway infrastructure power supply system is defined as:

[0018]

[0019] Among them, F(t) represents the value of the performance response at time t, and its relationship with time t is mainly reflected in the structural state change of the railway infrastructure power supply system network; M G Represents the number of power generation nodes; M D Indicates the number of load nodes; min(N Gi (t),N Dj (t)) is the smaller value of the active power of the power generation node i and the load node j at time t, representing the maximum power that the node unit pair can transmit; X eqij (t) represents the equivalent impedance of the node unit pair (i, j) at time t, that is, the electrical distance.

[0020] Step 2: Construction of comprehensive importance assessment model for railway infrastructure power supply system

[0021] Step 2.1: Construction of the self-value assessment model of the importance of node units in the railway infrastructure power supply system

[0022] The present invention adopts the hierarchical analysis method to evaluate the value of the railway infrastructure node unit itself. By comparing the load nodes, power generation nodes and balance nodes in pairs, and using the relative scale concept, the importance comparison result of node unit i and node unit j is c ij , and construct a judgment matrix based on the comparison results, and perform consistency check and random consistency check on the judgment matrix.

[0023]

[0024]

[0025]

[0026]

[0027] In the above formula, CI represents the consistency test index; RI represents the random consistency test index; n represents the order of the judgment matrix; λ represents the eigenvalue of the judgment matrix; CR represents the test coefficient. When CR is less than or equal to 0.1, it means that the judgment matrix is ​​established, otherwise it means that the judgment matrix is ​​not established. n An element representing a consistency check indicator.

[0028] The evaluation of i on j in the judgment matrix of Table 1 is made using the expert evaluation method.

[0029] Table 1 Judgment matrix c ij Value

[0030]

[0031] Table 2 RI values

[0032]

[0033] Step 2.2: Construction of system value assessment model for node unit importance of railway infrastructure power supply system

[0034] Step 2.2.1: Railway infrastructure power supply system network performance change value

[0035] Since the failure of a node unit in the power supply system will lead to a decrease in system performance, the performance response function of the railway infrastructure power supply system proposed in step 1.2 is used as the consequence of the failure of the node unit. When a node unit i in the railway infrastructure power supply system is damaged, the unit is removed and the power flow calculation is performed again to obtain the performance function value F after the network is stable. i , and finally get the network performance change value:

[0036] ΔF i =F0-Fi (6)

[0037] F i represents the performance value of the network after the power flow calculation is performed again after the node unit i is damaged and fails; F0 represents the initial performance value of the power supply system network; ΔF i It indicates the change value of network performance. The greater the change, the greater the impact of node unit damage and failure on the power supply system network.

[0038] Step 2.2.2: Evaluation and solution of node unit importance of railway infrastructure power supply system

[0039] According to the network performance change value calculated in step 2.2.1, normalization is performed to obtain the importance of the node unit of the railway infrastructure power supply system:

[0040]

[0041] Where n represents the number of node units in the railway infrastructure power supply system.

[0042] Step 2.3: Construction of comprehensive value assessment model for node unit importance of railway infrastructure power supply system

[0043] The entropy weight method is used to quantitatively evaluate the weight of self-value and system value. First, an evaluation data matrix between each node unit is established. Secondly, each element in the matrix is ​​dimensionless processed to obtain standard indicators. Finally, the weight coefficient of self-value and system value is determined.

[0044] P i =ω1F i +ω2E i (8)

[0045] In the formula, ω1 represents the self-value weight coefficient; ω2 represents the system value weight coefficient; they can be set to 0.4 and 0.6 respectively.

[0046] Step 3: Construction of the strategic game model between the attacker and the defender

[0047] Step 3.1: Construction of attack and defense strategy set

[0048] For n power supply system node units, a strategy A of the attacker is expressed as:

[0049] A=(a1,a2,...,a n ) (9)

[0050] Where: A is the attacking strategy; a i (i=1,2,...,n) is the attack probability of power supply system node unit i, satisfying 0≤a1,a2,...,a n≤1 and a1+a2+...+a n =1; n is the total number of node units in the power supply facility system.

[0051] The attacker's strategy set SA is expressed as:

[0052]

[0053] Where: Represents any real number. For n power supply facility system node units, a strategy d of the defender can be expressed as:

[0054] D=(d1,d2,...,d n ) (11)

[0055] Where: D is the defense strategy; d i (i=1,2,...,n) is the protection investment proportion of power supply system node unit i, satisfying 0≤d1,d2,...,d n ≤d and d1+d2+...+d n =d, d is the total amount of protection resources, where protection resources represent recovery resources (number of professional teams, recyclable materials) and recovery budget; n is the total number of node units in the power supply facility system.

[0056] The defender’s strategy set SD is expressed as:

[0057]

[0058] D is the defense strategy; d i (i=1,2,...,n) is the protection investment proportion of power supply system node unit i, satisfying 0≤d1,d2,...,d n ≤d and d1+d2+...+d n =d, d is the total amount of protection resources, where protection resources represent recovery resources (number of professional teams, recyclable materials) and recovery budget.

[0059] Step 3.2: Calculate the benefits of both attackers and defenders

[0060] Combined with the risk assessment theory, the attack risk of node unit i in the railway infrastructure power supply system can be expressed as:

[0061] R i =a i ×V i (d i )×C i (13)

[0062] Where R i represents the comprehensive risk value of power supply system node unit i; Vi (d i ) indicates that node unit i is configuring protection resource d i The fragility after the number can be obtained through finite element simulation calculation; C i represents the consequence of node unit i being successfully hit, which can be determined according to the calculation result of step 2.3. i =P i .

[0063] Based on the comprehensive risk R i , attacker A k The income is:

[0064]

[0065] Where: The attacker A k of income; Attacker A k The value assessment of attacking node unit i of the power supply system is the profit after a successful attack; n is the total number of node units in the power supply system of railway infrastructure; k represents the kth type of attacker; represents the value assessment of the k-th attacker on the power supply system node unit i, which can be represented by the comprehensive importance calculated in step 2.

[0066] Facing different types of attackers, the defender’s benefits are calculated as follows:

[0067]

[0068] Where: U D represents the defender’s gain; L i is the destructive consequence of a successful attack on the power supply system node unit i, that is, the loss suffered by the defender, which can be calculated by formula (6); μ k It represents the probability of the k-th attacker appearing, and takes any value in [0,1].

[0069] Through the Harsanyi transformation method, it is determined that the optimal strategy combination of the attacker and defender at the Bayesian Nash equilibrium point must satisfy the following formula, and the probability of each power supply system node unit in the railway infrastructure power supply system being attacked by the attacker and the optimal protection resource configuration of the defender, that is, the Bayesian Nash equilibrium strategy of the attacker and defender, is obtained.

[0070]

[0071]

[0072] Where: Attacker A kThe probability of selecting the attack node unit i of the power supply system under the Bayesian Nash equilibrium strategy; SA k Attacker A k strategy set; It represents the number of protection resources allocated to the power supply system node unit i by the defender under the Bayesian Nash equilibrium strategy, and * represents the optimal value.

[0073] Step 4: Construction of a resilience assessment model for the railway infrastructure power supply system

[0074] Step 4.1: Calculation of damage probability of nodes in the railway infrastructure power supply system

[0075] According to the attack and defense strategy set calculated in step 3, the attack probability, allocated protection resources and vulnerability of each unit of the power supply system under the Bayesian Nash equilibrium state can be obtained, thereby determining the probability of damage to the nodes of the railway infrastructure power supply system under the background of deliberate attacks and other human strategy attacks.

[0076]

[0077] Step 4.2: Simulation of damage status of railway infrastructure power supply system

[0078] Generate a random number vector S=[S1,S2,...,S n ], where any element S i All obey random distribution, with S i ~U(0,1). The total number of elements in the vector n is equal to the total number of node units in the railway infrastructure power supply system, and the elements in the random number vector S generated in each random experiment are compared with In contrast, if If the node unit is damaged and loses its function, it will be removed from the network. Otherwise, it will be retained, and finally the damage form of the railway infrastructure power supply system under this random test will be formed. Repeat the above steps 5000 times, and average the results of 5000 times to obtain the final damage form of the railway infrastructure power supply system.

[0079] Step 4.3: Simulation of the restoration process of the railway infrastructure power supply system

[0080] According to the results obtained in step 3, step 4.1 and step 4.2, the railway infrastructure power supply system performance response function proposed in step 1 can be used to solve the railway infrastructure power supply system change curve over time.

[0081] Step 4.4: Quantitative assessment of the resilience of the railway infrastructure power supply system

[0082] According to the resilience change curve obtained in step 4.3, the time from the occurrence of intentional attacks and other strategic man-made disasters to the resilience control time is integrated, and the area enclosed by the y-axis is solved to obtain the resilience value of the railway infrastructure power supply system during this period, and the recovery resources and recovery budget can be reasonably allocated according to the calculated resilience value.

[0083] One is to allocate resources and budget to the system based on how resilient it is; or to allocate resources and budget to it based on the budget (fixed value) to obtain the optimal resilience, or to allocate resources and budget to it based on the resources (fixed value) to obtain the optimal resilience.

[0084] The present invention first establishes a topological network structure diagram of the power supply system by analyzing the operating characteristics of the railway infrastructure power supply system; then uses the power supply system performance response function to calculate the importance index of the power supply system network node under the background of strategic attack; then uses the game theory technical method to construct an attack and defense game model, and adopts the Bayesian equilibrium strategy solution method to calculate the strategy set of both the attack and defense parties, and combines the risk assessment theory to obtain the damage probability of each node in the power supply system network; finally, through the damage state of the power supply system network, and using the proposed power supply system performance response function to calculate the quantitative evaluation results of the power supply system resilience under different protection resources and protection budget scenarios. The present invention defines the resilience evaluation value of the railway infrastructure power supply system after being damaged under the background of intentional attack through risk assessment theory, game theory technical methods and performance response function modeling, and obtains the resilience optimization strategy of the railway infrastructure power supply system.

[0085] The embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0086] The embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0087] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0088] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0089] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0090] The above is only a preferred embodiment of the present invention. Without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A resilience assessment method based on a railway infrastructure power supply system, characterized in that The following steps are involved: Step 1: Establishment of performance response function of railway infrastructure power supply system Step 1.1: Railway infrastructure power supply system topology network construction According to the geographical layout of the railway infrastructure power supply system and the geographical coordinates of the load nodes and power generation nodes and the topology of the node units, a topological network of the railway infrastructure power supply system is generated, in which the edges represent the key transmission lines of the power supply facilities and the node units represent the load nodes and power generation nodes; Step 1.2: Establishment of performance response function of railway infrastructure power supply system The performance response function of the railway infrastructure power supply system is defined as: Where F(t) represents the value of the performance response at time t; M G Represents the number of power generation nodes; M D Indicates the number of load nodes; min(N Gi (t),N Dj (t)) is the smaller value of the active power of the power generation node i and the load node j at time t, representing the maximum power that the node unit pair can transmit; X eqij (t) represents the equivalent impedance of the node unit pair (i, j) at time t, that is, the electrical distance; Step 2: Construction of comprehensive importance assessment model for railway infrastructure power supply system Step 2.1: Construction of the self-value assessment model of the importance of node units in the railway infrastructure power supply system By comparing the load nodes, power generation nodes and balance nodes in pairs and using the concept of relative scale, the comparison result of the importance of node unit i and node unit j is c ij , and construct a judgment matrix based on the comparison results, and perform consistency test and random consistency test on the judgment matrix; In the above formula, CI represents the consistency test index; RI represents the random consistency test index; n represents the order of the judgment matrix; λ represents the eigenvalue of the judgment matrix; CR represents the test coefficient. When CR is less than or equal to 0.1, it means that the judgment matrix is ​​established, otherwise it means that the judgment matrix is ​​not established; CI n Elements representing consistency check indicators; The evaluation of i on j in the judgment matrix of Table 1 is evaluated by the expert evaluation method; Table 1 Judgment matrix c ij Value Table 2 RI values Step 2.2: Construction of system value assessment model for node unit importance of railway infrastructure power supply system Step 2.2.1: Railway infrastructure power supply system network performance change value The performance response function of the railway infrastructure power supply system proposed in step 1.2 is used as the consequence of the failure of the node unit. When a node unit i in the railway infrastructure power supply system is damaged, the unit is removed and the power flow calculation is performed again to obtain the performance function value F after the network is stable. i , and finally get the network performance change value: ΔF i =F0-F i (6) F i It indicates the performance value after the network is stabilized by recalculating the power flow after the node unit i is damaged and failed; F0 indicates the initial performance value of the power supply system network; Step 2.2.2: Evaluation and solution of node unit importance of railway infrastructure power supply system According to the network performance change value calculated in step 2.2.1, normalization is performed to obtain the importance of the node unit of the railway infrastructure power supply system: Where n represents the number of node units in the railway infrastructure power supply system; Step 2.3: Construction of comprehensive value assessment model for node unit importance of railway infrastructure power supply system The entropy weight method is used to quantitatively evaluate the weight of self-value and system value. First, the evaluation data matrix between each node unit is established. Then, each element in the matrix is ​​dimensionless processed to obtain the standard index. Finally, the weight coefficient of self-value and system value is determined. P i =ω1F i +ω2E i (8) Where ω1 represents the weight coefficient of its own value; ω2 represents the weight coefficient of system value; Step 3: Construction of the strategic game model between the attacker and the defender Step 3.1: Construction of attack and defense strategy set For n power supply system node units, a strategy A of the attacker is expressed as: <h2 style=";text-align:left;direction:ltr">A = (a1,a2,...,a)<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> ) (9) Where: A is the attacking strategy; a i is the attack probability of power supply system node unit i, i = 1, 2, ..., n; satisfying 0 ≤ a1, a2, ..., a n ≤1 and a1+a2+...+a n =1; n is the total number of node units in the power supply facility system; The attacker's strategy set SA is expressed as: Where: represents any real number; for n power supply facility system node units, a strategy d of the defender is expressed as: D=(d1,d2,...,d n ) (11) Where: D is the defense strategy; d i (i=1,2,...,n) is the protection investment proportion of power supply system node unit i, satisfying 0≤d1,d2,...,d n ≤d and d1+d2+...+d n = d, d is the total amount of protection resources, where protection resources represent recovery resources and recovery budget; recovery resources include the number of professional teams and recyclable materials; n is the total number of node units in the power supply facility system; The defender’s strategy set SD is expressed as: D is the defense strategy; d i (i=1,2,...,n) is the protection investment proportion of power supply system node unit i, satisfying 0≤d1,d2,...,d n ≤d and d1+d2+...+d n = d, d is the total amount of protection resources, where protection resources refer to recovery resources and recovery budget; recovery resources include the number of professional teams and recyclable materials; Step 3.2: Calculate the benefits of both attackers and defenders Combined with the risk assessment theory, the attack risk of node unit i in the railway infrastructure power supply system is expressed as: R i =a i ×V i (d i )×C i (13) Where R i represents the comprehensive risk value of power supply system node unit i; V i (d i ) indicates that node unit i is configuring protection resource d i The fragility after the number is calculated based on finite element simulation; C i represents the consequence of node unit i being successfully hit, which is determined according to the calculation result of step 2.3; where C i =P i ; Based on the comprehensive risk R i , attacker A k The income is: Where: The attacker A k of income; The attacker A k The value assessment of attacking power supply system node unit i, that is, the profit after a successful attack; n is the total number of node units in the railway infrastructure power supply system; k represents the kth type of attacker; represents the value assessment of the k-th attacker on the power supply system node unit i; Facing different types of attackers, the defender’s benefits are calculated as follows: Where: U D represents the defender’s gain; L i is the destructive consequence of a successful attack on power supply system node unit i, that is, the loss suffered by the defender, calculated by formula (6); μ k represents the probability of the k-th attacker appearing, which can be any value in [0,1]; Through the Harsanyi transformation method, the optimal strategy combination of the attacker and defender at the Bayesian Nash equilibrium point is determined to satisfy the following formula, and the probability of each power supply system node unit in the railway infrastructure power supply system being attacked by the attacker and the optimal protection resource configuration of the defender are obtained, that is, the Bayesian Nash equilibrium strategy of the attacker and defender; Where: The attacker A k The probability of selecting the attack node unit i of the power supply system under the Bayesian Nash equilibrium strategy; SA k The attacker A k strategy set; represents the number of protection resources allocated to the power supply system node unit i by the defender under the Bayesian Nash equilibrium strategy, and * represents the optimal value; Step 4: Construction of a railway infrastructure power supply system resilience assessment model Step 4.1: Calculation of damage probability of nodes in the railway infrastructure power supply system According to the attack and defense strategy set calculated in step 3, the attack probability, allocated protection resources and vulnerability of each unit of the power supply system under the Bayesian Nash equilibrium state are obtained, so as to determine the probability of damage to the nodes of the power supply system of the railway infrastructure under the background of deliberate attack strategy. Step 4.2: Simulation of damage status of railway infrastructure power supply system Generate a random number vector S=[S1,S2,...,S n ], where any element S i All obey random distribution, with S i ~U(0,1); the total number of elements in the vector n is equal to the total number of node units in the railway infrastructure power supply system, and the elements in the random number vector S generated in each random experiment are compared with In contrast, if If the node unit is damaged and loses its function, it will be removed from the network. Otherwise, it will be retained, and finally the damage form of the railway infrastructure power supply system under this random test will be formed. Repeat the above steps for more than 5000 times, and average the results of more than 5000 times to obtain the final damage form of the railway infrastructure power supply system. Step 4.3: Simulation of the restoration process of the railway infrastructure power supply system According to the results obtained in step 3, step 4.1 and step 4.2, the railway infrastructure power supply system performance response function proposed in step 1 is used to solve the time variation curve of the railway infrastructure power supply system; Step 4.4: Quantitative assessment of the resilience of the railway infrastructure power supply system According to the resilience change curve obtained in step 4.3, the time from the occurrence of these strategic strike disasters to the resilience control time is integrated, and the area enclosed by the y-axis is solved to obtain the resilience value of the railway infrastructure power supply system in this period, and the recovery resources and recovery budget are allocated according to the calculated resilience value.

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