Railway infrastructure protection resource allocation method based on traction power supply facility fault

Abstract

The invention discloses a railway infrastructure protection resource allocation method based on a traction power supply facility fault, belongs to the field of railway infrastructures, and researches a resource allocation method for railway infrastructure pre-disaster protection. The method comprises the following steps: firstly, synthesizing (structure-function) importance of a railway infrastructure site and a traction power supply facility as an attack preference possibly adopted by an attacker, and calculating to obtain an attack signal released by the attacker in an early stage; then, making a corresponding protection strategy by using an attack signal adopted by an attacking party, and calculating the railway transport capacity characteristic after the traction power supply facility is attacked by using the operation mechanism and distribution characteristics of the traction power supply facility and the railway infrastructure and taking the railway delay time as the railway transport capacity characteristic; then, attack resource input strategies and corresponding protection strategies in different stages are calculated by using a signal game technical method; and finally, obtaining the maximum benefit values of the attack and defense parties and the corresponding optimal resource configuration sets in different stages by using a maximum and minimum calculation method.

Description

Technical Field

[0001] Based on game theory techniques, the present invention studies a resource allocation method for pre-disaster protection of railway infrastructure. First, the comprehensive (structural-functional) importance of railway infrastructure stations and traction power supply facilities is used as the attack preference that the attacker may adopt to calculate the attack signals released by the attacker in the early stage. Then, using the attack signals taken by the attacker, corresponding protection strategies are formulated. By using the operation mechanism and distribution characteristics of traction power supply facilities and railway infrastructure, with the railway delay time as the railway transport capacity characteristic, the railway transport capacity characteristic after the traction power supply facilities are attacked is calculated. Then, using the signal game technique method, the attack resource input strategies and corresponding protection strategies in different stages are calculated. Finally, using the maximin calculation method, the maximum benefit values of both the attacker and the defender in different stages and the corresponding optimal resource allocation sets are obtained. The present invention belongs to the field of railway infrastructure, and specifically relates to technologies such as attack-defense game and resource optimization. Background Art

[0002] Traction power supply facilities play a crucial role in railway infrastructure, not only directly affecting the power source and efficiency of train operation, but also involving multiple aspects such as environmental protection, transportation safety, and economic benefits. With the continuous advancement of railway electrification, traction power supply facilities will further promote the modernization, high efficiency, and sustainability of railway transportation.

[0003] The allocation of protection resources is a key factor in ensuring the safety, stability, and disaster prevention of railway infrastructure. Resource allocation involves the reasonable distribution and use of resources such as human, material, financial, and technical resources to achieve the effective protection of infrastructure. Especially when facing threats such as terrorist attacks and cyber attacks, the effective and reasonable allocation of protection resources can maximize the protection ability of railway infrastructure and ensure the long-term stable operation of railway infrastructure. Therefore, it has important practical significance to rationally allocate protection resources before disasters to improve the disaster resistance ability of railway infrastructure.

[0004] Since deliberate attacks on traction power supply facilities are more subjective and strategic. In railway infrastructure, there are significant differences in the attack preferences of different decision-makers. Therefore, the reasonable allocation of protection resources will effectively reduce the impact caused by the attacker's multiple attacks on railway infrastructure.

[0005] Considering issues such as the current methods of deliberate attacks, their impacts, and the possibility of continuous damage, as well as the limited effectiveness of traditional single-stage resource allocation methods, the present invention proposes a method for allocating railway infrastructure protection resources under traction power supply facility failures. First, a resource allocation model based on game theory techniques is constructed. Then, the strategy sets and signal sets of both the attacker and the defender are constructed. Using the attack preferences commonly adopted by current attackers, the attacker's strategy set is obtained. Then, the belief decay factor is used to fit the attack strategy set to obtain the attack signals received by the defender and the corresponding protection strategies. Then, using the operating mechanisms and distribution characteristics of traction power supply facilities and railway infrastructure, with railway delay time as the railway transport capacity characteristic, the railway transport capacity characteristic after the traction power supply facility is attacked is calculated. Then, using signal game techniques, the attack resource input strategies and corresponding protection strategies at different stages are calculated. Finally, the maximum benefit values of both the attacker and the defender at different stages and the corresponding optimal resource allocation sets are obtained using the maximin calculation method. Summary of the Invention

[0006] Different from existing resource allocation methods, the present invention uses dynamic game techniques to propose a method for allocating railway infrastructure protection resources under traction power supply facility failures. To overcome the deficiencies in the prior art, the present invention models through signal game theory, defines the dynamic adjustment rules of the strategies of both the attacker and the defender, simulates the damage states of traction power supply facilities with different strike input amounts under the strike condition of 1000 - 5000 pounds of TNT equivalent, and obtains the optimal protection resource allocation for railway infrastructure.

[0007] In a first aspect, the present invention provides a method for allocating railway infrastructure protection resources under traction power supply facility failures, including:

[0008] First, using the comprehensive (structure - function) importance of railway infrastructure stations and traction power supply facilities as the attack preferences that the attacker may adopt, the attack signals released by the attacker in the early stage are calculated. Then, using the attack signals adopted by the attacker, the corresponding protection strategies are formulated. Using the operating mechanisms and distribution characteristics of traction power supply facilities and railway infrastructure, with railway delay time as the railway transport capacity characteristic, the railway transport capacity characteristic after the traction power supply facility is attacked is calculated. Then, using signal game techniques, the attack resource input strategies and corresponding protection strategies at different stages are calculated. Finally, the maximum benefit values of both the attacker and the defender at different stages and the corresponding optimal resource allocation sets are obtained using the maximin calculation method.

[0009] The present invention constructs a method for allocating railway infrastructure protection resources under traction power supply facility failures to guide the overall optimization process of the protection department during pre-disaster protection, and can provide theoretical guidance and decision-making support for the protection department. Brief Description of the Drawings

[0010] Figure 1 is the overall framework diagram of the protection resource allocation of railway infrastructure based on the traction power supply facility failure in the present invention;

[0011] Figure 2 is the relevant operation relationship of the traction power supply facility in the railway infrastructure in the present invention. Specific implementation manners

[0012] In order to more fully understand the technical content of the present invention, the technical solution of the present invention will be further introduced and described below in conjunction with specific embodiments, but not limited thereto.

[0013] Combined with Figure 1 The present invention aims at the railway infrastructure under the traction power supply facility failure. From the association between the traction power supply facility and the railway infrastructure, the sections affecting the railway infrastructure are clarified, the input amount of attack resources is determined, and the strategy sets of both the attacker and the defender are dynamically adjusted according to the signal game technical method to determine the optimal allocation scheme of the protection resources of the railway infrastructure under the traction power supply facility failure. The specific implementation steps include:

[0014] Step 1: Construction of the topological network of railway infrastructure based on geographical functions

[0015] Step 1.1: The adjacency matrix of railway infrastructure and the adjacency matrix of railway infrastructure and traction power supply facilities are subjected to geographical information matching according to the topological network structure of each station coordinate along the line, the distribution points of traction power supply facilities and the control area, the connection relationship of each station is determined, and the association set between the traction power supply facilities and each railway station is determined, and the adjacency matrix is generated through pajek software.

[0016] Step 1.2: Construction of the topological network of railway infrastructure covering traction power supply facilities

[0017] Input the world standard geographical coordinates (WGS-84) of each station along the national railway infrastructure and traction power supply facilities into any version of Gephi software, and then obtain the topological network of railway infrastructure covering traction power supply facilities through the generated adjacency matrix. The nodes in the figure represent stations and traction power supply facilities, and the edges represent track lines and key transmission lines of traction power supply facilities.

[0018] Step 2: Construction of the comprehensive importance evaluation model of railway infrastructure topological network stations and traction power supply facilities

[0019] Step 2.1: Construction of the importance evaluation model of railway infrastructure station network structure

[0020] The unit importance of the topological network of railway infrastructure constructed in Step 1 is evaluated by using the connectivity index in the complex network index.

[0021] The connectivity index formula is as follows:

[0022]

[0023] In the formula, C is the connectivity index. The larger the value, the stronger the overall connectivity of the network; d(i, j) represents the length of the shortest railway line between station i and station j; N represents the total number of stations in the network.

[0024] Step 2.2: Construct the performance index function of railway infrastructure

[0025] By quantifying each performance dimension of the railway infrastructure, a multi-dimensional comprehensive evaluation function is established to comprehensively evaluate the performance of the railway system. By selecting track density, station throughput, train passing capacity, and transport capacity indicators, and considering the cascading impact caused by traction power supply facility failures, the performance index function of the railway infrastructure is constructed. By standardizing the index data of each station and using the weighted average method or other adaptive weighting methods, the importance score of each station is calculated. The setting of weights can be optimized through expert evaluation or the analytic hierarchy process. The expert database for expert review can adopt the expert database in the field of protective engineering.

[0026]

[0027] In the formula, f transport represents the performance of the railway infrastructure. The larger the value, the stronger the overall performance of the network; t ij represents the fault-free passing time from station i to station j; w 1 , w 2 , w 3 , w 4 respectively represent the weight coefficients of track density E td , station throughput E st , train passing capacity E tc and transport capacity. w 1 , w 2 , w 3 can be set to 0.15 each, and w 4 is 0.55; N represents the total number of stations in the network; V represents the running speed of the train when it is fully loaded with goods; χ j represents the running speed when arriving at station j after a traction power supply facility failure; K i represents the running speed when departing from station i.

[0028] Step 2.3: Construction of the comprehensive importance evaluation model of railway infrastructure stations based on traction power supply failures This step is mainly used to construct the comprehensive importance evaluation model of railway infrastructure stations based on traction power supply failures. This step comprehensively considers the impact on track density E td, Site throughput E st , Train passing capacity E tc and the influence of multiple dimensions of transport capacity, a multi-index weighted comprehensive evaluation model is established to evaluate the comprehensive importance of each railway infrastructure site in the case of traction power supply failure.

[0029] Step 3: Construction of the set of attack and defense strategies and the set of signals

[0030] Step 3.1: Construction of the set of attack and defense strategies

[0031] Take the result of the comprehensive importance of the railway infrastructure network unit calculated in Step 2 as the set of strategies of the attacker in the initial stage. According to the identification results of the failure impact on the traction power supply facilities after the input of different TNT equivalents, construct the set of attack and defense strategies.

[0032] D line =(q 1 ,q 2 ,...,q n ) T (3)

[0033] D power =(d 1 ,d 2 ,...,d z ) T (4)

[0034] In the formula, D line and D power respectively represent the protection strategy types of the stations along the line and the traction power supply facilities; q n represents the protection resources allocated by the defender to railway station n, where the protection resources include the number of emergency repair professional teams, the recyclable materials required for emergency repair, and the emergency repair budget; d z represents the protection resources allocated by the defender to traction power supply facility z, where the protection resources include the number of emergency repair professional teams, the recyclable materials required for emergency repair, and the emergency repair budget; T represents the strategy in the T-th stage of the game.

[0035] A line =(a 1 ,a 2 ,...,a n ) T (5)

[0036] A power =(b 1 ,b 2 ,...,b z ) T (6)

[0037] In the formula, A line and Apower respectively represent the attack strategy types of the stations along the line and the traction power supply facilities; a n represents the attack resources allocated by the defender to railway station n, where the attack resources are the TNT input equivalent; b z represents the attack resources allocated by the defender to the traction power supply facility z, where the anti-attack resources are the TNT input equivalent, and T represents the strategy at the T-th stage of the game.

[0038] Step 3.2: Signal set construction

[0039] According to the attack strategy set obtained in Step 3.1, through normalization processing, the belief of the attacker's TNT input intensity for each railway station and each traction power supply facility is obtained, and it is fitted through the belief attenuation factor. Finally, the possible TNT equivalent input strategies of the attacker for each railway station and each traction power supply facility collected by the defender in the initial stage are obtained.

[0040] The expression of the belief attenuation factor is:

[0041]

[0042] In the formula, λ represents the attenuation constant, generally any value between 0 and 1 can be taken, depending on the needs of the user; x represents the ratio of the attacker's benefits in the previous stage and the next stage each time. In the first signal strategy, this value is taken as 1; k is the power, which determines the degree of belief attenuation as the ratio increases, generally any value between 0 and 1 can be taken, depending on the needs of the user.

[0043] The signal strategy set is:

[0044]

[0045] In the formula, S line and S power respectively represent the signal strategy sets of the stations along the line and the traction power supply facilities; and respectively represent the signal strategies of the n-th station and the z-th traction power supply facility of the attacker collected by the defender.

[0046] Step 4: Prediction of the protection resource allocation of railway infrastructure at each stage

[0047] Step 4.1: Construction of the dynamic game model between the attacker and the defender

[0048] This model is constructed on the basis of dynamic game, assuming that the decision-making behaviors of both sides are made at different time points, and the decisions of both sides will affect each other. Among them, the attacker can choose different attack strategies, and the defender can adjust the defense strategy according to the attacker's behavior, and solve by analyzing the strategy combinations of the attacker and the defender.

[0049] Step 4.1.1: Single - stage payoffs of the attacker and the defender

[0050] Set the payoff functions for each party under different strategy combinations. For the attacker, its payoff function usually depends on the probability of a successful attack, the losses caused by the attack, and the defensive capabilities of the defender; for the defender, its payoff function usually reflects factors such as the probability of a successful defense, the losses caused by the attack, and resource consumption, etc.

[0051] Among them, the expressions for the single - stage payoffs of the attacker and the defender are respectively:

[0052]

[0053] In the formula, U a represents the attacker's payoff, U d represents the defender's payoff, D p , D z , D m respectively represent the total amount of the emergency repair professional team, the recyclable materials required for emergency repair, and the total emergency repair budget.

[0054] Step 4.1.2: Total payoffs of the attacker and the defender

[0055] According to the discount by the decay factor, judge the ratio of the payoffs in the current stage to that in the previous stage, and determine whether to continue to update the defense strategy; if the ratio of the payoffs in the current stage to that in the previous stage is greater than 0.5, continue to update the defense strategy; if the ratio of the payoffs in the current stage to that in the previous stage is less than 0.5, terminate the update of the defense strategy, and output the corresponding defense strategy and the corresponding attack strategy.

[0056] The expressions for the total payoffs of the attacker and the defender are respectively:

[0057]

[0058] In the formula, U A represents the total attacker's payoff, U D represents the total defender's payoff, and T represents the game stage.

[0059] Step 4.2: Solving the optimal strategy combination

[0060] According to the dynamic game model of the attacker and the defender constructed in 4.1, apply the Nash equilibrium theory and use the method of finding the maximum - minimum value to solve for the optimal resource investment strategies at each stage.

[0061]

[0062] In the present invention, first, the comprehensive (structural - functional) importance degrees of railway infrastructure sites and traction power supply facilities are used as the attack preferences that the attacker may adopt to calculate the attack signals released by the attacker in the early stage; then, the corresponding protection strategies are formulated by using the attack signals adopted by the attacker, and the operation mechanism and distribution characteristics of the traction power supply facilities and railway infrastructure are utilized, with the railway delay time as the railway transport capacity characteristic, to calculate the railway transport capacity characteristic after the traction power supply facilities are attacked; then, the signal game technology method is used to calculate the attack resource input strategies and the corresponding protection strategies at different stages; finally, the max - min calculation method is used to obtain the maximum benefit values of both the attacker and the defender and the corresponding optimal resource allocation sets at different stages. The resource allocation method of the present invention defines the adjustment of the attack - defense strategies for the railway infrastructure under the failure of the traction power supply facilities, and provides a reasonable scheme for the protection resource allocation of railway facilities under different attack conditions of the traction power supply facilities.

[0063] Embodiments of the present application may be provided as a method, a system, or a computer program product. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may take the form of a computer program product implemented on one or more computer - usable storage media (including but not limited to disk memory, CD - ROM, optical memory, etc.) containing computer - usable program code.

[0064] Embodiments of the present application may be provided as a method, a system, or a computer program product. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may take the form of a computer program product implemented on one or more computer - usable storage media (including but not limited to disk memory, CD - ROM, optical memory, etc.) containing computer - usable program code.

[0065] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general - purpose computer, a special - purpose computer, an embedded processor, or other programmable data - processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data - processing devices generate means for realizing the functions specified in one Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0066] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the function specified in one or more of the flows Figure 1 one or more flows and / or blocks Figure 1 specified in the block or blocks.

[0067] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the function specified in one or more of the flows Figure 1 one or more flows and / or blocks Figure 1 specified in the block or blocks.

[0068] The above are only the preferred embodiments of the present invention. Without departing from the technical principles 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 method for configuring railway protection resources based on traction power supply facility failure, characterized in that: Firstly, the adjacency matrix is ​​extracted by using the connection relationship between the railway infrastructure and traction power supply facilities and the connection relationship between the sites, and the railway infrastructure and traction power supply facilities. The railway infrastructure topological network based on geographical functions is constructed through the coordinates of the sites and power supply facilities. Secondly, the importance evaluation model of the railway infrastructure topological network sites and traction power supply facilities is constructed by using the complex network theory and technical methods, and integrating the railway infrastructure functional indicators, including transportation volume and site capacity. The comprehensive (structure-function) importance of the railway infrastructure sites and traction power supply facilities is solved. Then, the target network parameters are input into the model, the initial attack preference type is calculated, and the corresponding attack strategy is obtained. The initial attack is obtained through the power belief attenuation factor. signal set of both sides; finally, the dynamic game theory technical method is first used to construct the attack and defense dynamic game model, and the proposed railway efficiency evaluation function is adopted. The maximum and minimum calculation method is used to obtain the optimal benefit value of both the attack and defense sides in the current stage, and the protection resource allocation strategy set of the current stage is extracted. Then, the attack strategy actually adopted by the attacker in the previous stage is used as the signal set obtained by the defender at the beginning of the current stage. The attack and defense dynamic game model is solved by the maximum and minimum calculation method to obtain the optimal benefit value and protection resource allocation strategy set in the non-first stage. When the ratio of the current stage benefit to the previous stage benefit is less than 0.5, the game link is terminated, and the protection resource set of each stage and the signal strategy set of each stage are output.

2. The method for configuring railway infrastructure protection resources based on traction power supply facility failure according to claim 1 is characterized in that: Step 1: Construction of railway infrastructure topology network based on geographical functions Step 1.1: Railway infrastructure adjacency matrix and railway infrastructure and traction power supply facility adjacency matrix According to the coordinate topological network structure of each station along the line, the distribution points of traction power supply facilities and the control area, geographic information matching is carried out to determine the connection relationship of each station and the association set between traction power supply facilities and each railway station, and the adjacency matrix is ​​generated through the Pajek software; Step 1.2: Construction of railway infrastructure topology network including traction power supply facilities Input the world standard geographic coordinates (WGS-84) of each station and traction power supply facility along the national railway infrastructure into any version of Gephi software, and then use the generated adjacency matrix to obtain the railway infrastructure topological network covering the traction power supply facilities, where the nodes in the graph represent stations and traction power supply facilities, and the edges represent the key transmission lines of the track lines and traction power supply facilities.

3. The method for configuring railway infrastructure protection resources based on traction power supply facility failure according to claim 1 is characterized in that: Step 2: Construction of comprehensive importance assessment model for railway infrastructure topology network sites and traction power supply facilities Step 2.1: Construction of railway infrastructure station network structure importance assessment model The connectivity index in the complex network index is used to evaluate the unit importance of the railway infrastructure topological network constructed in step 1; The connectivity index formula is: Where C is the connectivity index, the larger the value, the stronger the overall connectivity of the network; d(i, j) represents the shortest railway line length between station i and station j; N represents the total number of stations in the network; Step 2.2: Construct railway infrastructure performance index function Calculate the importance score of each site; Where f transport is the railway infrastructure performance, the larger the value, the stronger the overall network performance; ij represents the trouble-free travel time between station i and station j; w1, w2, w3, w4 represent the track density E td , site throughput E st , Train capacity E tc and the weight coefficient of transport capacity; N represents the total number of stations in the network; V represents the running speed of the train when it is fully loaded with goods; χ j K represents the running speed when the traction power supply facility reaches the station j after failure; i represents the running speed when starting from station i; Step 2.3: Construction of comprehensive importance assessment model for railway infrastructure sites under traction power supply failure By comprehensively considering the track density E after traction power supply failure td , site throughput E st , Train capacity E tc A multi-indicator weighted comprehensive evaluation model was established based on the impact of multiple dimensions of transportation capacity.

4. The method for configuring railway infrastructure protection resources based on traction power supply facility failure according to claim 1 is characterized in that: The detailed process of the comprehensive importance assessment model of railway infrastructure topology network sites and traction power supply facilities is as follows: 1) According to the importance of each component target in the unit, the analytic hierarchy process (AHP) is used to construct a pairwise comparison matrix of different targets and quantitatively analyze the track density E td , site throughput E st , Train capacity E tc and the weights of capacity indicators w1, w2, w3, w4; 2) Determine the trouble-free travel time between station i and station j; 3) Improve the network connectivity index function and convert the track density E td , site throughput E st , Train capacity E tc , capacity indicators and network structure value integration, and construct railway infrastructure performance indicator function under traction power supply facility failure; 4) Determine the degree of degradation of network performance caused by the failure of each unit after a traction power supply facility failure. 5) After normalizing the degree of network performance degradation of each unit, quantitatively evaluate the comprehensive importance of each unit.

5. The method for configuring railway infrastructure protection resources based on traction power supply facility failure according to claim 1 is characterized in that: Step 3: Construction of attack and defense strategy set and signal set Step 3.1: Construction of attack and defense strategy set The result of the comprehensive importance of the railway infrastructure network unit calculated in step 2 is used as the strategy set of the attacker in the initial stage; based on the identification results of the impact of the failure on the traction power supply facilities after different TNT equivalent inputs, an attack and defense strategy set is constructed; D line =(q1,q2,...,q n ) T (3) D power =(d1,d2,...,d z ) T (4) Where D line and D power Respectively represent the protection strategy types of stations along the line and traction power supply facilities; q n represents the protection resources allocated by the defender to the railway station n, where the protection resources include the number of repair professional teams, the recyclable materials required for repair, and the repair budget; d z represents the protection resources allocated by the defender to the traction power supply facility z, where the protection resources include the number of repair professional teams, the recyclable materials required for repair, and the repair budget; T represents the strategy in the Tth stage of the game; <h2 style=";text-align:left;direction:ltr">A<h2 style=";text-align:left;direction:ltr"> line <h2 style=";text-align:left;direction:ltr"> (a1,a2,...,a)<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> )<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> (5) <h2 style=";text-align:left;direction:ltr">A<h2 style=";text-align:left;direction:ltr"> power <h2 style=";text-align:left;direction:ltr"> (b1,b2,...,b)<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> )<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> (6) In the formula, A line and A power Respectively represent the attack strategy types of stations along the line and traction power supply facilities; a n represents the attack resources allocated by the defender to railway station n, where the attack resources are equivalent to TNT input; b z represents the attack resources allocated by the defender to the traction power supply facility z, where the anti-attack resources are equivalent to TNT input, and T represents the strategy in the Tth stage of the game; Step 3.2: Signal set construction According to the attack strategy set obtained in step 3.1, the attacker's belief in the TNT investment intensity of each railway station and each traction power supply facility is obtained by normalization processing, and the belief attenuation factor is used for fitting, and finally the attacker's possible TNT equivalent investment strategy for each railway station and each traction power supply facility collected by the defender in the initial stage is obtained; The belief decay factor expression is: In the formula, λ represents the attenuation constant, which can be any value between 0 and 1, depending on the needs of the user; x represents the ratio of the previous and next stage gains of each attacker, and in the first signal strategy, this value is 1; k is the power, which determines the degree of belief attenuation as the ratio increases, and can be any value between 0 and 1, depending on the needs of the user; The signal strategy set is: In the formula, S line and S power They represent the signal strategy sets of stations along the line and traction power supply facilities respectively; and They respectively represent the signal strategies of the nth site and the zth traction power supply facility of the attacker collected by the defender.

6. The method for configuring railway infrastructure protection resources based on traction power supply facility failure according to claim 1 is characterized in that: Step 4: Forecast of railway infrastructure protection resource allocation at each stage Step 4.1: Construction of the dynamic game model between the attacker and the defender, as follows: Step 4.1.1: Single profit of both attacker and defender Assuming the payment function of each party under different strategy combinations, the expressions of the single benefits of the attacking and defending parties are: Where U a represents the attacker's profit, U d Denotes the benefit of the defender, D p , D z , D m They represent the total amount of emergency repair professional teams, recyclable materials needed for emergency repair, and emergency repair budget respectively; Step 4.1.2: Total benefits of both attackers and defenders According to the reduction of the attenuation factor, the profit ratio of the current stage to the previous stage is determined to determine whether to continue updating the protection strategy; if the profit ratio of the current stage to the previous stage is greater than 0.5, the protection strategy is continued to be updated; if the profit ratio of the current stage to the previous stage is less than 0.5, the protection strategy is terminated and the corresponding protection strategy and the corresponding attack strategy are output; The expressions of the total benefits of the attacker and the defender are: Where U A represents the total attack benefit, U D represents the total benefit of protection, T represents the game stage; Step 4.2: Finding the optimal strategy combination According to the dynamic game model between the attacker and the defender constructed in 4.1, the Nash equilibrium theory is applied and the maximum and minimum method is used to solve the optimal resource investment strategy for each stage;

Images