Rail transit communication security defense method based on Bayesian game

Abstract

The invention discloses a Bayesian game-based rail transit communication security defense method, which comprises the following steps of: establishing a combined communication architecture combining train-ground communication and train-train communication, and defining the state deviation of a train; defining an attack and defense strategy set of the attacker and the train according to the state deviation of the train; calculating a target revenue function of the train by integrating the attack and defense strategy set, the state deviation of the train and the communication quality parameters of the train; based on the target revenue function, constructing a multi-round dynamic Bayesian game model, and under different state transition conditions, according to the target revenue function, the attack and defense strategy and belief, calculating utility functions of attack and defense parties; and with maximization of a defender utility function as a target, an optimal defense strategy of the train is obtained by solving Nash equilibrium of the multi-round dynamic Bayesian game model. The problem that complex and changeable attack strategies are difficult to deal with in the prior art can be solved.

Description

Technical Field

[0001] This invention relates to the field of rail transit communication security technology, and specifically to a rail transit communication security defense method based on Bayesian game theory. Background Technology

[0002] In recent years, with the rapid development of rail transit systems towards intelligence and networking, vehicle-to-ground (T2G) and vehicle-to-vehicle (T2T) communication systems have become core supports for ensuring the safe and efficient operation of trains. However, these communication systems face unique operating environments and technical challenges.

[0003] Currently, rail transit communication systems face a variety of security threats, including but not limited to malicious attacks such as signal eavesdropping, data tampering, identity forgery, and denial-of-service attacks. These attacks may not only disrupt the integrity and availability of communication, but may even directly affect train control and operational safety.

[0004] However, traditional security defense mechanisms often assume a relatively stable network environment and a single attack method, making it difficult to cope with complex and ever-changing attack strategies. Especially when facing new types of coordinated attacks, existing technologies lack effective dynamic response and adaptive defense capabilities. Therefore, how to construct an adaptive defense method capable of real-time awareness of security status and dynamic adjustment of defense strategies in the resource-constrained and network-volatile rail transit communication environment is a technical problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a Bayesian game-based method for security defense of rail transit communication, in order to solve the problem that existing technologies are unable to cope with complex and ever-changing attack strategies.

[0006] A Bayesian game-based approach to security defense in rail transit communication includes: Step S1: Based on the communication-based train control system, a joint communication architecture combining vehicle-to-ground communication and vehicle-to-vehicle communication is established. In the joint communication architecture, the state deviation of the train is defined, which is used to reflect the degree of abnormality after the joint communication is disturbed or attacked. Step S2: Define the attack and defense strategy set for the attacker and the train based on the state deviation of the train. The attack and defense strategy set includes the action choices of the attacker and the train, and then define the state of the attacker and the train. Step S3: Calculate the train's objective payoff function by combining the set of offensive and defensive strategies, the train's state deviation, and the train's communication quality parameters. The obtained objective payoff function serves as the benchmark for evaluating the outcome of a single game. Step S4: Based on the objective payoff function, a multi-round dynamic Bayesian game model is constructed. The two sides dynamically adjust their attack and defense strategies based on historical information and beliefs, and then update their beliefs based on the attack and defense strategies. Different communication states are used as the state space. The state transition conditions are defined based on the interference threshold and attack intensity of state switching. Then, under different state transition conditions, the utility functions of the attacker and defender are calculated based on the objective payoff function, attack and defense strategies and beliefs. Step S5: With the goal of maximizing the defender's utility function, the optimal defense strategy for the train is obtained by solving the Nash equilibrium of the multi-round dynamic Bayesian game model.

[0007] The rail transit communication security defense method based on Bayesian game theory provided by the present invention has the following beneficial effects: (1) This invention establishes a joint communication architecture combining T2G and T2T and uses the train control system to define state deviations such as train position intervals and speeds. These state deviations directly reflect the degree of abnormality of the joint communication system after it is disturbed or attacked, and can perceive the security status in real time. The joint communication architecture of the train control system itself is used as the basis for the game scenario and state definition. The state deviations can directly measure the security level of the joint architecture and provide quantifiable state inputs for subsequent games. (2) This invention defines the attack and defense strategy set of the attacker and the train based on the deviation of each state of the train, including the action selection of the attacker and the train, and then defines the state of the attacker and the train. The attack and defense strategy is related to the switching link and control action, constructing a real adversarial game scenario, introducing the attacker role with active attack capability, and upgrading the train safety from passive fault tolerance to active confrontation. The attacker strategy (such as interference against a specific link) and the train defense strategy (such as communication mode switching) are both directly derived from and act on the joint communication architecture. (3) The present invention integrates the set of offensive and defensive strategies and the deviation of each state of the train, as well as the communication quality parameters to calculate the target benefit function of the train. The obtained target benefit function is used as the benchmark for evaluating the result of a single game. It realizes the quantification of benefits with real-time physical state deviation and communication quality indicators as direct inputs. By directly mapping the train operation deviation and communication quality indicators to the immediate benefits of each party in the game, it realizes the real-time dynamic correlation between information security game and physical operation safety at the utility level. (4) Based on the objective payoff function, this invention constructs a multi-round dynamic Bayesian game model. Both sides of the game can dynamically adjust their attack and defense strategies based on historical information and beliefs, and then update their beliefs based on the attack and defense strategies. Using different communication states as the state space, the state transition conditions are defined based on the interference threshold and attack intensity of state switching. The system can switch autonomously between different states according to the real-time communication quality, thereby reflecting the changes in the network environment and the evolution of the attack situation, effectively responding to complex and ever-changing attack strategies, dynamically adjusting defense strategies, and then calculating the utility functions of both sides of the attack and defense based on the objective payoff function, attack and defense strategies and beliefs under different state transition conditions. This invention associates state transition with quantifiable attack intensity and channel interference threshold, so that the game model can dynamically reflect the random and nonlinear changes in the communication environment under the action of attack and defense. (5) This invention aims to maximize the defender's utility function. By solving the Nash equilibrium of a multi-round dynamic Bayesian game model, the optimal defense strategy for the train system is obtained, which effectively improves the security performance of the rail transit communication system, reduces the success rate of attacks, and enhances the utilization rate of communication resources and the resilience of the system. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating the rail transit communication security defense method based on Bayesian game theory provided by the present invention. Detailed Implementation

[0009] To facilitate understanding of the present invention, a more complete description will be given below with reference to various embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0010] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0011] Please see Figure 1 The embodiments of the present invention provide a rail transit communication security defense method based on Bayesian game theory, including steps S1-S5: Step S1: Based on the communication-based train control system, a joint communication architecture combining vehicle-to-ground communication and vehicle-to-vehicle communication is established. In the joint communication architecture, the state deviation of the train is defined, which is used to reflect the degree of abnormality after the joint communication is disturbed or attacked.

[0012] The joint communication architecture adds a T2T communication link to the train control system (CBTC), and the established joint communication architecture includes a regional controller, a vehicle-to-ground communication network, and a vehicle-to-vehicle communication network.

[0013] When using the vehicle-to-vehicle communication network for information transmission, the area controller calculates the updated mobility authorization; when using the vehicle-to-ground communication network for information transmission, the area controller is responsible for a remote node that retransmits information between all trains. At each time period, the area controller issues mobility authorization to each train.

[0014] Assuming there is a regional controller Each train has a delay-sensitive task and establishes communication links with other subsystems.

[0015] definition for The system status of the train at all times, including its position and speed, is monitored. At the beginning of each cycle, if the train-to-train communication network is selected for information transmission, the sensors on the train will... The data is transmitted directly to the controller on the following train via the vehicle-to-vehicle communication network; if a vehicle-to-ground communication network is used for information transmission, the sensors on the train transmit data to the controllers on other trains via the uplink and controller. .

[0016] When the The train When receiving status information from the area controller or the previous train, the system combines the position and speed data obtained from the sensors to... The train Position interval of time and optimal value of position interval Deviation between , No. The train Speed ​​of time and optimal speed value Deviation between Defined as:

[0017]

[0018]

[0019] in, For the first Sensors on the train Location acquired in real time For the first Sensors on the train Location acquired in real time For the first Sensors on the train The speed at which real-time data is acquired.

[0020] It should be pointed out that, and It is calculated by the Automatic Train Protection (ATP) subsystem using a timetable and optimized guidance trajectory.

[0021] Thus, the first The train The deviation between the position interval at time and the optimal position interval , No. The train The deviation between the velocity at a given moment and the optimal velocity value for:

[0022]

[0023] in, For the first The train The deviation between the velocity at a given moment and the optimal velocity value. For the first The train acceleration at any moment For the first The train Acceleration at any moment; Furthermore, for the first train, since there are no trains running before it, the following formula is satisfied:

[0024]

[0025] in, For the first train in The deviation between the position interval at a given time and the optimal position interval. For the first train in The deviation between the position interval at a given time and the optimal position interval. For the first train in The deviation between the velocity at a given moment and the optimal velocity value. The sampling interval is... For the first train in acceleration at any moment For the first train in The deviation between the velocity at a given moment and the optimal velocity value.

[0026] Step S2: Define the attack and defense strategy set for the attacker and the train based on the state deviation of the train. The attack and defense strategy set includes the action choices of the attacker and the train, and then define the state of the attacker and the train.

[0027] Among them, the definition It is a set of offensive and defensive strategies for both the attacker and the train (i.e., the defender). , This is the attacker's attack strategy. As the train's defense strategy, in the subsequent game process, the attacker and the train, as the two sides, choose appropriate actions from the action set. The entire game process is divided into... Each round, of which any one round This represents a round of strategic interaction between the attacker and the train; the attacker in each round Select an attack action; action set The train's action set , The number of attack strategies. The number of defensive strategies. , , Rounds The first, second, and third in Each attack action, , , Rounds The first, second, and third in A defensive action, Indicates round The attacker does not launch an attack. Indicates round If the train does not defend, then the states of the attacking and defending sides are as follows:

[0028]

[0029] in, for Time for the first The state of the attacker who launched the attack on the train. for Time of the first The status of each train. This is the positional interval deviation threshold. This is the speed deviation threshold.

[0030] Step S3: Calculate the train's objective payoff function by combining the set of offensive and defensive strategies, the train's state deviation, and the train's communication quality parameters. The resulting objective payoff function serves as the benchmark for evaluating the outcome of a single game.

[0031] Among them, communication quality parameters include communication signal-to-noise ratio and data packet loss rate; No. Signal-to-noise ratio of individual trains during vehicle-to-ground communication for:

[0032] in, For vehicle-to-ground communication transmission power, For power gain in vehicle-to-ground communication, For noise power spectral density, For the first The train The bandwidth allocated to vehicle-to-ground communication at all times; No. Signal-to-noise ratio of individual trains during train-to-train communication for:

[0033] in, For vehicle-to-vehicle communication transmission power, For the power gain of vehicle-to-vehicle communication, These are the interference parameters for vehicle-to-vehicle communication. For the first The train The bandwidth allocated to vehicle-to-vehicle communication at all times; Data packet loss rate for:

[0034]

[0035]

[0036]

[0037] in, The bit error rate for joint communication is represented by minimizing the communication bit error rate. The number of bits in the data packet. The bit error rate for vehicle-to-ground communication. For vehicle-to-vehicle communication bit error rate, For safety weights, Represents the Gaussian Q-function. , As variables, Indicates through the Optimize to make the brackets The weighted bit error rate is the lowest within it.

[0038] Furthermore, to enhance communication robustness in adversarial environments, the train can dynamically switch between T2G, T2T, or joint communication modes. However, such switching is not instantaneous and will introduce communication switching delays. :

[0039] in, The switching delay constant, express The communication mode used at all times express The communication mode used at all times.

[0040] The calculation of the train's target revenue function specifically includes: Calculate the payoff function based on state deviation and the revenue function based on communication quality parameters. :

[0041]

[0042] in, , , , , It is a constant. For the overall communication signal-to-noise ratio. The threshold for signal-to-noise ratio. For communication handover delay; Calculate the first The train Total payoff function at time step for:

[0043] in, , It is a constant. For rounds The first in A defensive action, For rounds The first in One attack action; Calculate the train's target revenue function for:

[0044] in, This represents the calculation of mathematical expectation. Total time The total number of trains. for The state of the attacker who launched the attack on the first train at any given moment. for Time for the first The state of the attacker who launched the attack on the train. for The status of the first train at any given time. for Time of the first The status of each train.

[0045] Step S4: Based on the objective payoff function, a multi-round dynamic Bayesian game model is constructed. The two sides dynamically adjust their attack and defense strategies based on historical information and beliefs, and then update their beliefs based on the attack and defense strategies. Different communication states are used as the state space. The state transition conditions are defined based on the interference threshold and attack intensity of state switching. Then, under different state transition conditions, the utility functions of the attacker and defender are calculated based on the objective payoff function, attack and defense strategies and beliefs.

[0046] In this game, both sides dynamically adjust their offensive and defensive strategies based on historical information and beliefs, and then update their beliefs based on these strategies. Specifically, this includes: In the initial stage of the game, the attacker's initial beliefs and the train's initial beliefs are defined as follows: and In the round At that time, the attacker takes an attack action. The train initiated defensive actions. As the game progresses, the attacker assesses the train's potential decisions based on their current beliefs and selects new attack actions. The train generates new defensive actions based on historical information and beliefs. ,definition The belief set representing an offensive and defensive game includes the attacker's belief set. The belief of the train ,in, This indicates that the attacker chose the first attack actions The probability, Indicates the train selection number A defensive action The probability, This indicates that the attacker targeted the train on the 1st. Wheel takes defensive action The belief, This indicates that the train was attacked in the first... Wheel takes attack action The belief.

[0047] Since the participants' strategies are influenced not only by the choices made in the current round, but also by historical information and updated beliefs, the strategies of the attacker and the train are updated in the _____. Wheel is represented as:

[0048]

[0049] in, It is a utility function that depends on each player's game role and the strategy choices of all players; In the first The probability of the train choosing the current action. For the first The historical information sequence of the rounds is used to describe the decision records of the previous stages; In the first The probability that the attacker will choose the current action; Based on the defensive actions chosen by the train and historical information, the attacker will update their beliefs and adjust the probability of choosing an attack strategy. Therefore, the attacker's beliefs in the next round will change. for:

[0050] in, Indicates a given attack action At that time, the train was at Choose defensive action The probability of; The train updates its beliefs based on the attacker's attack actions and historical information, adjusting the probability of choosing a defense strategy. Therefore, the train's beliefs for the next round... for:

[0051] in, Indicates a given defensive action At that time, the attacker was at the Choose attack action The probability of.

[0052] State transition conditions are defined based on the interference threshold and attack strength of state switching, specifically including: Set up state space , , This indicates a state where vehicle-to-vehicle communication is the primary mode of operation, and the area controller is responsible for global coordination rather than real-time calculation. This indicates the operating status, which primarily uses vehicle-to-ground communication as the communication mode. Real-time status synchronization is achieved through vehicle-to-vehicle communication. This indicates a communication state that simultaneously relies on vehicle-to-vehicle communication and vehicle-to-ground communication; [Definition] Indicates from Transferred to The probability depends on the severity of the attack on T2T communication. For communication status index, , for The corresponding communication status, for The corresponding communication status.

[0053] The communication state transition shall be performed under the following conditions: (1) From arrive Transfer conditions: The intensity of interference from the attacker to vehicle-to-vehicle communication Greater than or equal to the critical value ; (2) From arrive Transfer conditions: Vehicle-to-vehicle communication returns to normal or the interference intensity of vehicle-to-ground communication decreases. Greater than or equal to the critical value ; (3) From arrive or arrive Transfer conditions: or , This indicates the maximum interference threshold. In this case, single communication is insufficient to maintain security, and the defense strategy automatically enables two communication modes to work together. (4) From arrive or arrive Transfer conditions: When vehicle-to-ground communication and vehicle-to-vehicle communication are working simultaneously, one of the communication links fails or recovers.

[0054] Under different state transition conditions, the utility functions of both the attacker and defender are calculated based on the objective payoff function, attack and defense strategies, and beliefs. Specifically, this includes: when At that time, the attacker's utility function is 0. The train's utility function under different states is as follows:

[0055]

[0056]

[0057] in, , , They are respectively In state, In state, The train utility function under the given state. For the train's revenue, For the cost of the train, For the revenue discount rate, ; when At that time, the utility function is calculated according to different states: (1) Communication status is At that time, if Then there is no need to switch states, and defense can proceed directly. This indicates that the current state cannot fully defend against attacks, and a switch to a different state is required. or At this point, the utility functions for the attacker and the train are:

[0058]

[0059] in, for The attacker's utility function in the state. For the attacker's benefit, For the cost of attackers, Indicates from Transferred to The probability, Indicates from Transferred to The probability of; (2) Communication status is At that time, the utility functions for the attacker and the train are:

[0060]

[0061] in, for The attacker's utility function in the state. Indicates from Transferred to The probability, Indicates from Transferred to The probability of; (3) Communication status is At that time, the utility functions for the attacker and the train are:

[0062]

[0063] in, for The attacker's utility function in the state.

[0064] Step S5: With the goal of maximizing the defender's utility function, the optimal defense strategy for the train is obtained by solving the Nash equilibrium of the multi-round dynamic Bayesian game model.

[0065] The optimal defense strategy for the train system is the strategy that maximizes the defender's utility function under game theory. This strategy is obtained by solving for the Nash equilibrium, ensuring that the defender's gain is maximized assuming the attacker also takes the optimal action. A higher gain indicates that the train's spacing, speed, and communication are all within specified limits. A negative gain indicates that at least one of these parameters exceeds a threshold, thus determining that the train has been attacked. Furthermore, this gain varies depending on the strategies of both sides.

[0066] The optimal defense strategy for a joint communication system requires maximizing the defender's expected utility function and selecting the optimal defense action. , making The attacker's goal is to maximize their utility function and choose the optimal attack action. , making ,in, For corresponding The utility function of the train, For corresponding The attacker's utility function.

[0067] Nash equilibrium is defined as a train's optimal defense strategy described by a multi-stage dynamic Bayesian game model. In Nash equilibrium, the optimal outcome of the game is that, given that other players have already chosen their strategies, neither side can gain an advantage by unilaterally changing their strategy. In Bayesian games, both sides aim to maximize their own payoff. In this model, we assume... The optimal strategy is... This indicates that when both the attacker and defender choose... The utility function at time. For any policy In other words, when either party changes its strategy, the utility function becomes... The Nash equilibrium is a pair of optimal strategies for both the attacker and the train. Therefore, when the multi-round dynamic Bayesian game model reaches Nash equilibrium, the following condition is satisfied:

[0068]

[0069] in, This is the optimal attack action; This is the optimal defensive action; Choose for attackers And train selection At that time, the attacker's utility function; Choose for attackers And train selection At that time, the utility function of the train; Selecting a train At that time, the attacker's utility function; Choose for attackers At that time, the utility function of the train.

[0070] In summary, the Bayesian game-based approach to rail transit communication security defense offers the following advantages: (1) This invention establishes a joint communication architecture combining T2G and T2T and uses the train control system to define state deviations such as train position intervals and speeds. These state deviations directly reflect the degree of abnormality of the joint communication system after it is disturbed or attacked, and can perceive the security status in real time. The joint communication architecture of the train control system itself is used as the basis for the game scenario and state definition. The state deviations can directly measure the security level of the joint architecture and provide quantifiable state inputs for subsequent games. (2) This invention defines the attack and defense strategy set of the attacker and the train based on the deviation of each state of the train, including the action selection of the attacker and the train, and then defines the state of the attacker and the train. The attack and defense strategy is related to the switching link and control action, constructing a real adversarial game scenario, introducing the attacker role with active attack capability, and upgrading the train safety from passive fault tolerance to active confrontation. The attacker strategy (such as interference against a specific link) and the train defense strategy (such as communication mode switching) are both directly derived from and act on the joint communication architecture. (3) The present invention integrates the set of offensive and defensive strategies and the deviation of each state of the train, as well as the communication quality parameters to calculate the target benefit function of the train. The obtained target benefit function is used as the benchmark for evaluating the result of a single game. It realizes the quantification of benefits with real-time physical state deviation and communication quality indicators as direct inputs. By directly mapping the train operation deviation and communication quality indicators to the immediate benefits of each party in the game, it realizes the real-time dynamic correlation between information security game and physical operation safety at the utility level. (4) Based on the objective payoff function, this invention constructs a multi-round dynamic Bayesian game model. Both sides of the game can dynamically adjust their attack and defense strategies based on historical information and beliefs, and then update their beliefs based on the attack and defense strategies. Using different communication states as the state space, the state transition conditions are defined based on the interference threshold and attack intensity of state switching. The system can switch autonomously between different states according to the real-time communication quality, thereby reflecting the changes in the network environment and the evolution of the attack situation, effectively responding to complex and ever-changing attack strategies, dynamically adjusting defense strategies, and then calculating the utility functions of both sides of the attack and defense based on the objective payoff function, attack and defense strategies and beliefs under different state transition conditions. This invention associates state transition with quantifiable attack intensity and channel interference threshold, so that the game model can dynamically reflect the random and nonlinear changes in the communication environment under the action of attack and defense. (5) This invention aims to maximize the defender's utility function. By solving the Nash equilibrium of a multi-round dynamic Bayesian game model, the optimal defense strategy for the train system is obtained, which effectively improves the security performance of the rail transit communication system, reduces the success rate of attacks, and enhances the utilization rate of communication resources and the resilience of the system.

Claims

1. A method for rail transit communication security defense based on Bayesian game, characterized in that, Comprise: Step S1, based on the communication train control system, the establishment of train-ground communication and train-train communication combined joint communication architecture, define the state deviation of the train in the joint communication architecture, the state deviation is used to reflect the abnormal degree after the joint communication is disturbed or attacked; Step S2, according to the state deviation of the train, the attack and defense strategy set of the attacker and the train is defined, the attack and defense strategy set contains the action selection of the attacker and the train, and then the state of the attacker and the train is defined; Step S3, the target profit function of the train is calculated by comprehensively considering the attack and defense strategy set and the state deviation of the train, and the communication quality parameter of the train, and the target profit function obtained is used as the benchmark for single game result evaluation; Step S4, based on the target profit function, a multi-round dynamic Bayesian game model is constructed, both sides of the game dynamically adjust the attack and defense strategy according to the historical information and belief, and then the belief is updated by the attack and defense strategy, wherein, different communication states are used as state space, the state transition condition is defined based on the interference threshold and the attack strength of state switching, and then the utility function of both sides of attack and defense is calculated according to the target profit function, the attack and defense strategy and the belief under different state transition conditions; Step S5, taking maximizing the utility function of the defender as the target, the best defense strategy of the train is obtained by solving the Nash equilibrium of the multi-round dynamic Bayesian game model.

2. The Bayesian game-based rail transit communication security defense method according to claim 1, characterized in that, In step S1, the joint communication architecture established includes a regional controller, a train-ground communication network and a train-train communication network, when using the train-train communication network to transmit information, the regional controller will calculate and update the mobile authorization; When using the train-ground communication network to transmit information, the regional controller is responsible for a remote node, and the information is retransmitted between all trains, and the regional controller issues a mobile authorization for each train at each time stage.

3. The method of claim 2, wherein the method further comprises: In step S1, define For The system state of the train at the moment, including train position and speed, at the initial stage of each cycle, if the train-to-train communication network is selected for information transmission, the sensors on the train will Directly transmit to the controller on the rear train through the train-to-train communication network; if the train-to-ground communication network is used for information transmission, the sensors on the train will transmit Through the uplink and the controller to the controller on the other train; When the The train When receiving status information from the area controller or the previous train, the system combines the position and speed data obtained from the sensors to... The train Position interval of time and optimal value of position interval Deviation between , No. The train Speed ​​of time and optimal speed value Deviation between Defined as: wherein, is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time is the position of the sensor on the first train at time Thus, the first The train The deviation between the position interval at time and the optimal position interval , No. The train The deviation between the velocity at a given moment and the optimal velocity value for: wherein, is the deviation between the speed of the nth train at the time instant and the optimal speed value, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant, is the acceleration of the nth train at the time instant. In addition, for the first train, the following formula is satisfied: wherein, the deviation between the position interval of the first train at the optimal value of the position interval, the deviation between the position interval of the first train at the optimal value of the position interval, the deviation between the speed of the first train at the optimal value of the speed, is a sampling interval, is an acceleration of the first train at the optimal value of the speed, is an acceleration of the first train at the optimal value of the speed.

4. The method of claim 3, wherein the method further comprises: In step S2, define This is a set of attack and defense strategies for both attackers and trains. , This is the attacker's attack strategy. As the train's defense strategy, in the subsequent game process, the attacker and the train, as the two sides, choose appropriate actions from the action set. The entire game process is divided into... Each round, of which any one round This represents a round of strategic interaction between the attacker and the train; the attacker in each round Select an attack action; action set The train's action set , The number of attack strategies. The number of defense strategies. , , Rounds The first, second, and third in Each attack action, , , Rounds The first, second, and third in A defensive action, Indicates round The attacker does not launch an attack. Indicates round If the train does not defend, then the states of the attacking and defending sides are as follows: wherein, is the state of the attacker that attacks the train at the moment, is the state of the train at the moment, is a position interval deviation threshold value, is a speed deviation threshold value.

5. The rail transit communication security defense method based on Bayesian game according to claim 4, characterized in that, In step S3, the communication quality parameters include communication signal-to-noise ratio and data packet loss rate; The signal-to-noise ratio of the first train during train-ground communication is: wherein, is a transmission power for the train-ground communication, is a power gain for the train-ground communication, is a noise power spectral density, is a bandwidth allocated to the train-ground communication for the train at the time instant; No. Signal-to-noise ratio of individual trains during train-to-train communication for: wherein, a transmission power for car-to-car communication, a power gain for car-to-car communication, an interference parameter for car-to-car communication, a bandwidth allocated to car-to-car communication for the train at the time instant; Data packet loss rate Is: wherein, is the bit error rate for the joint communication, is the number of bits of the data packet, is the bit error rate for the vehicle-to-ground communication, is the bit error rate for the vehicle-to-vehicle communication, is the safety weight, denotes the Gaussian Q-function.

6. The Bayesian game-based rail transit communication security defense method according to claim 5, characterized in that, In step S3, the target profit function of the train is calculated, which specifically includes: Computing a state bias based reward function , and a communication quality parameter based reward function : wherein , , , , is a constant, is an overall communication signal-to-noise ratio, is a threshold value for the signal-to-noise ratio, is a communication switching latency; The total revenue function of the nth train at the mth time point is calculated as follows: ​​​ in, , It is a constant. For rounds The first in A defensive action, For rounds The first in One attack action; Computing a target revenue function for a train is: wherein, denotes a mathematical expectation calculation, is the total time, is the total number of trains, is the state of the attacker who attacks the 1st train at the time, is the state of the attacker who attacks the 1st train at the time, is the state of the 1st train at the time, is the state of the 1st train at the time.

7. The Bayesian game-based rail transit communication security defense method according to claim 6, characterized in that, In step S4, both sides of the game dynamically adjust the attack and defense strategy according to the historical information and belief, and then the belief is updated by the attack and defense strategy, which specifically includes: At the initial stage of the game, the initial belief of the attacker and the initial belief of the train are defined as and At round , the attacker generates an attack action , the train generates a defense action , as the game rounds increase, the attacker evaluates the possible decisions of the train according to the current belief, selects a new attack action , the train generates a new defense action according to the historical information and the belief , define to represent the belief set of the attack-defense game, including the belief set of the attacker and the belief set of the train , wherein represents the probability of the attacker selecting the th attack action , and represents the probability of the train selecting the th defense action ; The strategy updates of the attacker and the train are in the first The wheel is represented as: in, For utility function, In the first The probability that the train will choose the current action. For the first The historical information sequence of the wheel, In the first The probability that the attacker will choose the current action; Based on the defense action and historical information of train selection, the attacker will update the belief and adjust the probability of selecting the attack strategy, and then the belief of the next round of attacker is: wherein, represents the probability of the train choosing a defense action at time when a given attack action is performed .​ The train updates the belief based on the attack action and historical information of the attacker, adjusts the probability of selecting the defense strategy, and then the belief of the next round of the train is: in, Indicates a given defensive action At that time, the attacker was at the Choose attack action The probability of.

8. The Bayesian game-based rail transit communication security defense method according to claim 7, characterized in that, In step S4, the state transition condition is defined based on the interference threshold and the attack strength of state switching, which specifically includes: Setting state space , , denotes a state running in a car-to-car communication as the main mode, the zone controller is responsible for global coordination rather than real-time calculation; denotes a state running in a car-to-ground communication as the main communication mode, real-time state synchronization is realized through car-to-car communication; denotes a communication state relying on both car-to-car communication and car-to-ground communication; The transfer of communication state is performed according to the following conditions: (1) From to transfer condition: the interference intensity of the attacker to the vehicle-to-vehicle communication is greater than or equal to a critical value ; (2) From to transfer condition: vehicle-to-vehicle communication returns to normal or the interference strength of vehicle-to-ground communication is greater than or equal to a threshold ; (3) from to or to transfer condition: or , denotes the maximum interference threshold value; (4) From to or to Transfer condition: when one of the communication links fails or recovers while both V2C and V2V are working.

9. The Bayesian game-based rail transit communication security defense method according to claim 8, characterized in that, In step S4, the utility function of both sides of attack and defense is calculated according to the target profit function, the attack and defense strategy and the belief under different state transition conditions, which specifically includes: When the attacker utility function is 0, and the train utility function in different states is: wherein, , , are respectively under the state of under the state of under the state of the revenue of the train, the cost of the train, the revenue discount rate; When the utility function is calculated according to different states: (1) If the communication state is , if , then no state switching is needed, and the defense is directly performed. If , then the current state cannot completely defend against the attack, and the state needs to be switched to or . At this time, the utility functions of the attacker and the train are as follows: wherein, is the attacker's utility function in state is the attacker's payoff, is the attacker's cost, denotes the probability of transitioning from to denotes the probability of transitioning from to denotes the probability of transitioning from to (2) the communication state is When the communication state is the utility function of the attacker and the train is wherein, is the utility function of the attacker in state represents the probability of transition from to represents the probability of transition from to to​ (3) the communication state is When the attacker and the train have utility functions of: wherein, is the attacker's utility function in state 10. The Bayesian game-based rail transit communication security defense method according to claim 9, characterized in that, In step S5, when the multi-round dynamic Bayesian game model reaches Nash equilibrium, the following conditional formula is satisfied: wherein, is the optimal attack action; is the optimal defense action; is the attacker's utility function when the attacker chooses and the train chooses is the attacker's utility function when the attacker chooses and the train chooses is the train's utility function when the attacker chooses and the train chooses is the attacker's utility function when the attacker chooses and the train chooses is the train's utility function when the attacker chooses and the train chooses

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