Multi-dimensional dynamic elastic identification method and system for key coupling nodes of power distribution information physical system

Abstract

The invention relates to the technical field of intelligent power grids, in particular to a multi-dimensional dynamic elastic recognition method and system for key coupling nodes of a power distribution information physical system, and the system comprises a key node screening unit which constructs a unified CPDS model and preliminarily screens a candidate key node set based on structure controllability and structure observability; the fuzzy scene generation unit is used for constructing a dynamic fuzzy disaster scene set by utilizing a Markov chain Monte Carlo method and generating a set containing a large number of dynamic fuzzy disaster scenes; an elastic function construction unit; a node calculation output unit; according to the novel CPDS key coupling node accurate identification method, structure controllability, structure observability, dynamic fuzzy disaster scenes, reverse reinforcement learning and Shapley value comprehensive calculation are fused, so that the accuracy, fairness and adaptability of elastic analysis and decision making of a system are improved; and the rapid response and recovery capability of the power grid to disasters or attack disturbance is improved.

Description

Technical Field

[0001] This invention relates to the field of smart grid technology, and in particular to a multi-dimensional dynamic elastic identification method and system for key coupled nodes in a power distribution cyber-physical system. Background Technology

[0002] With the global energy transition and the rapid development of information technology, smart grids have become a core direction for the modernization of power systems. As an important component of smart grids, Cyber-Physical Distribution System (CPDS) achieves real-time monitoring, optimized scheduling, and rapid fault recovery of distribution systems through deep integration of power networks (physical layer) and communication networks (information layer). CPDS not only improves the operational efficiency of power systems but also enhances the system's adaptability to external disturbances through cyber-physical coupling. However, with the increasing frequency and intensity of extreme weather events (such as typhoons and snowstorms) and cyberattacks (such as malicious data injection and denial-of-service attacks), most existing CPDS key node identification methods are based on static topology or single indicators, making it difficult to accurately reflect the true importance of nodes in multi-type, uncertain disaster environments. Furthermore, traditional methods often neglect the impact of inter-node collaboration on the overall system resilience, leading to potentially incomplete and unfair identification results.

[0003] In CPDS (Content-Based Response System), the power network and communication network interact through coupled nodes. These coupled nodes (such as sensors, controllers, or communication routers) play a crucial role in system operation, responsible for transmitting status information, executing control commands, and coordinating the collaborative work of the physical and information layers. However, if a critical coupled node fails due to a fault or attack, it can lead to a significant decline in system performance and even trigger cascading failures, seriously threatening the stability and reliability of power supply. Therefore, accurately identifying critical coupled nodes is an important prerequisite for improving the resilience of CPDS.

[0004] This invention addresses the shortcomings of existing key node identification methods in Distribution Cyber-Physical Systems (CPDS) by disclosing a multi-dimensional dynamic resilience identification method for key coupled nodes. Current methods are mostly based on static topology or single indicators, which fail to accurately reflect the true importance of nodes under dynamic disaster environments and node synergy. To solve this problem, this invention, for the first time, integrates multi-dimensional structural analysis with data-driven expert experience weights, and innovatively uses the Shapley value from cooperative game theory to accurately identify key coupled nodes. This significantly improves the dynamism, accuracy, and decision-making fairness of system resilience assessment, demonstrating outstanding theoretical and engineering value. Summary of the Invention

[0005] This invention provides a multi-dimensional dynamic elastic identification method and system for key coupled nodes in a power distribution information physical system, which overcomes the shortcomings of the prior art. It can effectively solve the problem that existing node identification methods, which are based on dynamic topology or a single index, are difficult to accurately identify key coupled nodes.

[0006] To address the above problems, one of the technical solutions of this invention is achieved through the following method: a multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system, comprising the following steps: A unified CPDS model is constructed, and a preliminary set of candidate key nodes is selected based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. A set of dynamic fuzzy disaster scenarios is constructed using the Markov chain Monte Carlo method, generating a set containing a large number of dynamic fuzzy disaster scenarios; By using inverse reinforcement learning, the weights of each disaster scenario are adaptively learned and optimized from expert experience, and a dynamic weighted elasticity function is constructed. Based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, the weighted elasticity function of the fused scenario is calculated, the Shapley value of each candidate key node is calculated, and the nodes are sorted and output according to the Shapley value.

[0007] The above-mentioned construction of a unified CPDS model includes: The unified CPDS model is an interconnected network system consisting of power networks and communication networks; whereby the power network is the physical layer, defined as follows: In the formula, Represents the set of nodes in a power network. For edge sets in a power network, This refers to the power grid; the communication network, also known as the information layer, is defined as follows: , Represents the set of nodes in a communication network. For the edge set in the communication network, Indicates a communication network; Integrate power grids and communication networks into a unified coupled adjacency matrix. A CPDS The function is represented as follows: , In the formula, A PP For the internal connection matrix of the power network, A CC For the internal connection matrix of the communication network, A PC This represents the information flow dependency from the power grid to the communication network.A CP This represents the control flow dependency from the communication network to the power network; Wherein, if a CPDS contains N P Power network nodes and N C If there are 10 communication network nodes, then the set of candidate key nodes is... N=N P +N C .

[0008] The aforementioned structural controllability includes: The state equation for structural controllability is: , in, This represents the state vector of a power network node. u ( t ) represents the input control vector; A This is the adjacency matrix of the power network; B The input control matrix is ​​determined by the communication node. The state equation for structural controllability represents the rate of change of the state of a power network node over time. Maximum matching determines the minimum set of driving nodes. D min The formula is defined as: , in, N A set of candidate key nodes; This represents the maximum number of matched edges. The impact index of node failure is defined as follows: , in, C i For nodes i Failure impact indicators; For nodes i The number of uncontrollable nodes that increase after failure; Represents the set of nodes in a power network; N This is the set of candidate key nodes.

[0009] The above-mentioned structural observability includes: The observed system state satisfies the output model: , in, This represents the state vector of a power network node. C For measurement output matrix; To output the measurement vector; A minimum sensor placement method based on network topology is used to calculate the power network observation node set. O min Power network observation node set O min The following observability conditions must be met: , in, O For the set of measurement nodes; C For measurement output matrix; A This is the adjacency matrix of the power network; σ ( A ) is a matrix A The set of eigenvalues; For matrix A eigenvalues; I It is the identity matrix; N A set of candidate key nodes; The impact index of node failure observation is defined as follows: , in, O i For nodes i Failure observation impact indicators; For nodes i The number of unobservable nodes added after a failure; N A set of candidate key nodes; Represents the set of nodes in a power network; The overall importance index is defined as follows: , in, α、β These are the weighting coefficients; C i For nodes i Failure impact indicators; O i For nodes i Failure observation impact indicators; I i For nodes i The comprehensive importance indicator.

[0010] The above method uses Markov chain Monte Carlo to construct a set of dynamic fuzzy disaster scenarios, generating a set containing a large number of dynamic fuzzy disaster scenarios, including: Based on historical data and expert experience, the transition probabilities between different disaster types and their intensities are defined; where disaster types include natural disasters and man-made attacks; and where the intensity of each disaster type is defined as a continuous variable. x Define the generalized Gaussian intensity fuzzy membership function: , Where, x As for the intensity of the disaster, m The average intensity σ Standard deviation k For shape parameters; The initial disaster state is randomly sampled from the defined intensity fuzzy membership function using the MCMC method; Based on the transition probability and time step, a series of continuous disaster scenario sequences with fuzzy features are generated iteratively from the initial disaster state; For each generated disaster scenario, its comprehensive fuzzy membership degree across multiple dimensions is calculated, and its potential cascading effects are simulated; whereby, a disaster scenario set is defined. Each characteristic disaster scenario S j Expressed as: , Where, As a type of disaster, For intensity vectors, To the area / scope of impact, The potential cascading effects it may trigger; This represents the comprehensive fuzzy membership degree of the feature scene; Based on the comprehensive fuzzy membership degree, a set containing a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula: S dynamic ={ S j,t}, Where, S j,t Indicates time t The j One disaster scenario; S dynamic It is a collection containing a large number of dynamic and blurred disaster scenarios.

[0011] The above-mentioned method of adaptively learning and optimizing the weights of various disaster scenarios from expert experience through inverse reinforcement learning includes: Construct a trajectory database that includes the entire lifecycle operation status of CPDS, expert decisions, and system responses. The data structure within the trajectory database... Including status s n ,action a n ,award r n Among them, for each expert experience trajectory : The reward function is derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, where the reward function is as follows: , In the formula, f ( s,a ) is the feature vector corresponding to the state-action sequence; It is the weight vector that needs to be learned; T Transpose of a vector; turn up To ensure that the feature expectations of the expert trajectory match the feature expectations of all policies, a weight vector is calculated using an iterative algorithm. Simultaneously, the entropy of the policy is maximized, where the entropy of the policy is maximized as shown in the following formula: , in, In the reward function The probability of the trajectory below; D expert It is an expert trajectory database; It is a regularization parameter; It represents the expert trajectory database D expert A specific expert trajectory in the dataset; K is the total number of expert trajectories; L is the length or time steps of each trajectory; It represents the trajectory τ The prior probability distribution; max w This represents a maximization operation, which involves finding the weight vector that maximizes the objective function. ; Based on the learned reward function Assessment experts in characteristic disaster scenarios S j The expected reward for taking the optimal action: , In the formula, max a In the current characteristic disaster scenario S j Next, iterate through all possible actions a and calculate the expected reward value for each action a; V( S j () represents a characteristic disaster scenario S j Under these circumstances, the maximum expected reward that can be obtained by taking the optimal action; Extract weights related to disaster scenario characteristics from the reward function. : , In the formula, For each characteristic disaster scenario S j Extract its key features; use softmax normalization to ensure that the sum of all scene weights is 1; w T This represents the transpose of the weight vector w, which transposes the weight vector from a column vector to a row vector.

[0012] The above iterative algorithm includes the following iterative process: Strategy evaluation: for the current reward function Standard reinforcement learning algorithms are used to compute the optimal policy. ; Reward function update: The weight vector of the reward function is updated using the gradient ascent method. The gradient ascent method is shown in the following equation: , In the formula, η is the learning rate; For optimal strategy The resulting behavioral characteristics are expected; The expected actual behavioral characteristics in the expert experience database; Convergence criterion: Repeat the policy evaluation and reward function update steps until... Convergence or reaching the maximum number of iterations.

[0013] The above calculation of the weighted elasticity function of the fused scenario, based on each initially selected candidate key node and each dynamically fuzzy disaster scenario, includes: CPDS elasticity index E j Quantification: for each characteristic disaster scenario The elasticity of the system E j This can be obtained through simulation and measured using comprehensive indicators: , The elasticity of a physical system can be quantified as: , Among them, Lost Load( t )for t The amount of load loss at any given time, System recovery time; The normalized time base is used; Total Annual Load is the total electrical energy supplied or consumed by the system under normal operating conditions within one year. The resilience of a communication system can be quantified as follows: , Among them, Communication Interruption Rate ( t )for t The communication interruption rate at any given time; Total Communication Needs refers to the system's communication interruption rate at a given time reference. Within, the total amount of communication services required to ensure the normal operation of the power system; The impact of cyber-physical cascade failures is quantified by the amount of physical load loss caused by information failures or the amount of communication interruption caused by physical failures in the simulation. : These are weighting coefficients used to balance different elasticity dimensions; Weighted elasticity function for fusion scenarios v ( K ), defined as follows: , In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained from inverse reinforcement learning j The weight of each disaster scenario.

[0014] The above process calculates the Shapley value for each candidate key node, sorts the nodes based on their Shapley values, and outputs the results, including: Determine the set of nodes to be evaluated. N This refers to the initial set of candidate key nodes; Enumerate all possible node alliances K ; For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ; compute nodes i In each league K Marginal contribution ; According to the Shapley value formula, by weighted summing of all marginal contributions, the node value is obtained. i Shapley value Among them, nodes i Shapley value The calculation formula is: , in: N It is a set of candidate key nodes; n= | N | is a set N Total number of nodes in the alliance; K It refers to a set consisting of one or more nodes; | K | is an alliance K The number of nodes in; Represents a node i Join the Alliance K The marginal contribution it brings is the increment of the weighted elasticity function value of the overall system elasticity after the node is added; Based on the calculated nodes i Shapley value Sort all nodes in descending order and output the key coupled nodes after sorting.

[0015] The second technical solution of this invention is achieved through the following method: a multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system, wherein the multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system uses the aforementioned multi-dimensional dynamic resilience identification method for key coupled nodes in a power distribution cyber-physical system, comprising: The key node screening unit constructs a unified CPDS model and initially screens a set of candidate key nodes based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. The fuzzy scene generation unit uses the Markov chain Monte Carlo method to construct a dynamic fuzzy disaster scene set, generating a set containing a large number of dynamic fuzzy disaster scenes; The elasticity function construction unit adaptively learns and optimizes the weights of various disaster scenarios from expert experience through inverse reinforcement learning, and constructs a dynamically weighted elasticity function. The node calculation output unit calculates the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, calculates the Shapley value of each candidate key node, sorts the nodes according to the Shapley value, and outputs the results.

[0016] This invention proposes a novel method for accurately identifying key coupled nodes in CPDS (Conditional Process Detection and Resilience Analysis) by integrating structural controllability, structural observability, dynamic fuzzy disaster scenarios, inverse reinforcement learning, and Shapley value calculation. This method aims to improve the accuracy, fairness, and adaptability of system resilience analysis and decision-making, and enhance the power grid's rapid response and recovery capabilities to disasters or attack disturbances. Attached Figure Description

[0017] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0018] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention.

[0019] Figure 2 This is a schematic diagram of the CPDS unified network model in Embodiment 1 of the present invention.

[0020] Figure 3 This is a schematic diagram of the CPDS modeling and preliminary key node identification process in Embodiment 1 of the present invention.

[0021] Figure 4 This is a schematic diagram of the dynamic fuzzy disaster scenario construction and inverse reinforcement learning weight optimization process in Embodiment 1 of the present invention.

[0022] Figure 5 This is a schematic diagram of the calculation process of the weighted elasticity function and Shapley value in Embodiment 1 of the present invention.

[0023] Figure 6 This is a schematic diagram of the system structure framework of Embodiment 2 of the present invention. Detailed Implementation

[0024] The present invention is not limited to the following embodiments, and the specific implementation can be determined according to the technical solution of the present invention and the actual situation.

[0025] Example 1: As Figure 1 As shown in the figure, this invention discloses a multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system, comprising the following steps: Step S101: Construct a unified CPDS model and preliminarily screen the set of candidate key nodes based on structural controllability and structural observability; wherein, the unified CPDS model includes power networks and communication networks; thereby, by preliminarily screening out the set of key nodes that have a significant impact on the system's operating status, the candidate set of key nodes is narrowed down, thereby improving the accuracy of the preliminary screening.

[0026] Step S102: Construct a set of dynamic fuzzy disaster scenarios using the Markov chain Monte Carlo method to generate a set containing a large number of dynamic fuzzy disaster scenarios; thereby, by constructing a quantitative analysis model of dynamic fuzzy disaster scenarios, the uncertainty characteristics of actual disasters can be reflected.

[0027] Step S103 involves adaptively learning and optimizing the weights of each disaster scenario from expert experience through inverse reinforcement learning, and constructing a dynamic weighted elastic function. Thus, by using a disaster scenario weight dynamic optimization method based on inverse reinforcement learning, the accuracy of disaster scenario importance estimation is improved through a data-driven approach, solving the problem of difficulty in determining disaster scenarios due to insufficient fusion of multiple factors.

[0028] Step S104: Based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, calculate the weighted elasticity function of the fused scenario, calculate the Shapley value of each candidate key node, sort the nodes according to the Shapley value and output it; thus, by introducing the Shapley value analysis method in cooperative game theory, the marginal contribution of nodes under the collaborative action of multiple nodes is quantified fairly and accurately, and the limitations of node collaborative contribution are fully considered.

[0029] like Figure 2 As shown, in step S101 above, constructing the unified CPDS model includes: The unified CPDS model is an interconnected network system consisting of a power network (busbars, substations) and a communication network (sensors, controllers, communication routers); the power network is the physical layer, defined as follows: In the formula, Represents the set of nodes in a power network. For edge sets in a power network, This refers to the power grid; the communication network, also known as the information layer, is defined as follows: , Represents the set of nodes in a communication network. For the edge set in the communication network, Indicates a communication network; Integrate power grids and communication networks into a unified coupled adjacency matrix. A CPDS The function is represented as follows: , In the formula, A PP For the internal connection matrix of the power network, A CC For the internal connection matrix of the communication network, A PC This represents the information flow dependency from the power grid to the communication network. A CP It represents the control flow dependency from the communication network to the power network; the matrix elements can represent weighted values ​​such as connection strength, bandwidth, and dependency degree. This deep coupling model can capture the cascading effects between information and physical faults. Wherein, if a CPDS contains N P Power network nodes and N C If there are 10 communication network nodes, then the set of candidate key nodes is... N=N P +N C .

[0030] like Figure 3 As shown, in step S101 above, structural controllability involves calculating the minimum set of driving nodes in the network based on the maximum matching Hopcroft-Karp algorithm to determine the minimum number of control input nodes required to achieve complete network controllability, and recording the degree of impact on the controllable state of the system when a node fails; wherein, structural controllability includes: The state equation for structural controllability is: , in, This represents the state vector of a power network node. u ( t ) represents the input control vector; A This is the adjacency matrix of the power network; B The input control matrix is ​​determined by the communication node. The state equation for structural controllability represents the rate of change of the state of a power network node over time. Maximum matching determines the minimum set of driving nodes. D min The formula is defined as: , in, N A set of candidate key nodes; This represents the maximum number of matched edges. The impact index of node failure is defined as follows: , in, C i For nodes i Failure impact indicators; For nodes i The number of uncontrollable nodes that increase after failure; Represents the set of nodes in a power network; N This is the set of candidate key nodes.

[0031] like Figure 3 As shown, in step S101 above, structural observability involves determining the minimum number of measurement nodes required for the network to achieve complete observation using a minimum sensor placement method based on network topology, and recording the degree of loss in network state observation performance due to node failure; wherein, structural observability includes: The observed system state satisfies the output model: , in, This represents the state vector of a power network node. C For measurement output matrix; To output the measurement vector; A minimum sensor placement method based on network topology is used to calculate the power network observation node set. O min Power network observation node set O min The following observability conditions must be met: , in, O For the set of measurement nodes; C For measurement output matrix; A This is the adjacency matrix of the power network; σ ( A ) is a matrix A The set of eigenvalues; For matrix A eigenvalues; I It is the identity matrix; N A set of candidate key nodes; The impact index of node failure observation is defined as follows: , in, O i For nodes i Failure observation impact indicators; For nodes i The number of unobservable nodes added after a failure; N A set of candidate key nodes; Represents the set of nodes in a power network; The overall importance index is defined as follows: , in, α、β These are the weighting coefficients; C i For nodes i Failure impact indicators; O i For nodes i Failure observation impact indicators; I i For nodes i The comprehensive importance indicator.

[0032] By combining the two structural indicators of structural controllability and structural observability, and analyzing the structural controllability (i.e., the importance of the node to the control of the entire system) and structural observability (i.e., the importance of the node to the monitoring of the entire system status) of a node, preliminary key nodes affecting system operation control and status observation are quickly screened out. After combining the two indicators to initially identify the key nodes that have the greatest impact on "system operation control" and "status observation", a dynamic fuzzy disaster scenario is established to consider the complex disaster characteristics in actual operation in order to further improve the accuracy of node analysis and scenario adaptability.

[0033] like Figure 4 As shown, in step S102 above, a set of dynamic fuzzy disaster scenarios is constructed using the Markov chain Monte Carlo method, generating a set containing a large number of dynamic fuzzy disaster scenarios, including: Based on historical data and expert experience, the transition probabilities between different disaster types and their intensities are defined; where disaster types include natural disasters and man-made attacks; and where the intensity of each disaster type is defined as a continuous variable. x Define the generalized Gaussian intensity fuzzy membership function: , In the formula, x For disaster intensity, m The average intensity σ Standard deviation, k For shape parameters; k The "fatness" of the membership function can be adjusted to more flexibly represent fuzzy boundaries of different intensity levels (e.g., when...). k When = 2, it is a Gaussian function; when... k When =1, it is an exponential function); The MCMC method is used to randomly sample initial disaster states from defined intensity fuzzy membership functions. Markov Chain Monte Carlo (MCMC) sampling combines intensity fuzzy membership functions and historical disaster occurrence frequencies to generate more representative dynamic fuzzy disaster scenarios. This not only considers the static characteristics of the scenario but also simulates the evolution of the disaster, such as gradually increasing wind speed or secondary disasters triggered by an earthquake. Based on the transition probability and time step, a series of continuous disaster scenario sequences with fuzzy features are generated iteratively from the initial disaster state; For each generated disaster scenario, its comprehensive fuzzy membership degree across multiple dimensions is calculated, and its potential cascading effects are simulated; whereby, a disaster scenario set is defined. Each characteristic disaster scenario S j Represented as: , In the formula, The type of disaster (e.g., windstorm). Intensity vector (e.g., wind speed) I j wind, duration I j (duration) To the area / scope of impact, The potential cascading effects it could trigger (such as icing of power lines and communication disruptions caused by typhoons); and The comprehensive fuzzy membership degree of this feature scene can be obtained from the membership degrees of each dimension (e.g., the intensity fuzzy membership function). It is obtained by multiplying the membership degrees of each dimension (by multiplying the membership degrees of each dimension) or by weighted average (by weighted average of the membership degrees of each dimension).

[0034] Based on the comprehensive fuzzy membership degree, a set containing a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula: S dynamic ={ S j,t}, In the formula, S j,t Indicates time t The j One disaster scenario; S dynamic It is a collection containing a large number of dynamic and blurred disaster scenarios.

[0035] Among them, natural disasters include wind disasters (wind speed, duration, and affected area), earthquakes (magnitude, intensity, and focal depth), floods (water level, flow rate, and inundated area), and snow and ice disasters (ice thickness and duration); human attacks include cyberattacks (attack traffic, attack targets, duration, and attack type), physical damage (damaged targets and extent of damage), and malware (infection range and disruptive functions).

[0036] As can be seen from the above, each characteristic disaster scenario Comprehensive fuzzy membership degree including disaster type T j Intensity vector comprehensive fuzzy membership degree I j Scope of influence, comprehensive fuzzy membership degree D j Potential cascade effect combined fuzzy membership degree C j and the comprehensive fuzzy membership degree of this feature scene. Therefore, the comprehensive fuzzy membership degree It describes each characteristic disaster scenario. An important component of its inherent characteristics; the final collection containing a large number of dynamically blurred disaster scenarios. S dynamic Based on comprehensive fuzzy membership This means that the fuzzy membership degree is generated. The value will be used as a generator and filter to add to the final set of disaster scenarios containing a large number of dynamically blurred disaster scenarios. S dynamic Based on this, the comprehensive fuzzy membership degree of each possible disaster scenario is first calculated. Then, based on these calculation results, a set containing a large number of dynamically blurred disaster scenarios is constructed. S dynamic .

[0037] Specifically, considering cascading failures means that when generating scenarios, not only the impact of a single disaster is considered, but also the potential cascading failure effects it may trigger. For example, when a windstorm reaches a certain intensity, it may cause physical breaks in power lines, leading to the interruption of related communication equipment and creating a vicious cycle of information and physical disruption. This cascading effect can be simulated using a pre-set rule base or a probabilistic model learned from historical data.

[0038] like Figure 4 As shown, in step S103 above, the weights of each disaster scenario are adaptively learned and optimized from expert experience through inverse reinforcement learning, including: Construct a trajectory database that includes the entire lifecycle operation status of CPDS, expert decisions, and system responses. The data structure within the trajectory database... Including status s n ,action a n ,award r n Among them, for each expert experience trajectory :in, n Representing the entire time span, it refers to a set or sequence that starts at time step t=0, passes through t=1, 2, ..., until the last time step t= n All states, actions, and rewards; The reward function is derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, where the reward function is as follows: , In the formula, f ( s,a) is the feature vector corresponding to the state-action (e.g., power outage load, communication interruption, number of damaged nodes, intensity of the current disaster scenario, etc.); It is the weight vector that needs to be learned; T This is the transpose of a vector; the feature vector here needs to contain information related to the disaster scenario so that the reward function can reflect the expert's preference for different disaster scenarios. turn up To ensure that the feature expectations of the expert trajectory match the feature expectations of all policies, a weight vector is calculated using an iterative algorithm. Simultaneously, the entropy of the policy is maximized, where the entropy of the policy is maximized as shown in the following formula: , in, In the reward function The probability of the trajectory below; D expert It is an expert trajectory database; It is a regularization parameter; It represents the expert trajectory database D expert A specific expert trajectory in the dataset; K is the total number of expert trajectories; L is the length or time steps of each trajectory; It represents the trajectory τ When using the maximum entropy principle, the prior probability distribution of a given probability is usually assumed to be uniform if there is no specific prior information; max w This represents a maximization operation, which involves finding the weight vector that maximizes the objective function. ; Based on the learned reward function Assessment experts in characteristic disaster scenarios S j The expected reward for taking the optimal action: , In the formula, max a In the current characteristic disaster scenario S j Next, iterate through all possible actions 'a', calculate the expected reward for each action 'a', and finally select the action that maximizes the expected reward from all these outcomes; V( S j () represents a characteristic disaster scenario S j Under these circumstances, the maximum expected reward that can be obtained by taking the optimal action; Extract weights related to disaster scenario characteristics from the reward function. : , In the formula, For each characteristic disaster scenario S j Key features were extracted (including information such as type, intensity, and scope of influence); softmax normalization was used to ensure that the sum of weights for all scenes was 1; w T This represents the transpose of the weight vector w, which transforms the weight vector from a column vector to a row vector so that it can be compared with the feature vector. Perform matrix multiplication. In this way, what is learned... It can directly map to the importance of each disaster scenario, thereby adaptively generating weights for the disaster scenario set. This means that disaster scenarios that experts perceive as leading to higher systemic risks and greater recovery difficulties will receive higher weight.

[0039] Among them, state s n It includes physical status (node ​​voltage, line power flow, load, switch status, generator output, list of damaged equipment), information status (communication link bandwidth, latency, packet loss rate, communication equipment status), and dynamic fuzzy disaster scenario information (disaster type, intensity, scope of impact, cascading failure status).

[0040] action a n Experts or maintenance systems are in status s n The decisions made include, for example: physical side: line reconfiguration, load shedding, distributed power grid connection / disconnection, backup power supply activation, emergency repair team dispatch, and reinforcement measures; information side: communication route adjustment, redundant link switching, network topology reconfiguration, and bandwidth allocation optimization.

[0041] award r n Experts in action are in a state of readiness. s n The immediate reward brought about by the power outage is observable, but the underlying reward function is implicit; for example, the amount of reduction in power outage load, the amount of reduction in recovery time, and the degree of system function retention; for example, at a certain moment... t The reward can be defined as: , in, To restore power supply load, To reduce the amount of power outage time, To reduce communication loss, k 1 , k 2 , k3 These are the weighting coefficients.

[0042] like Figure 4 As shown, the above iterative algorithm includes the following iterative process: Strategy evaluation: for the current reward function Standard reinforcement learning algorithms (such as Q-learning, SARSA, or dynamic programming-based policy iteration) are used to compute the optimal policy. ; Reward function update: The weight vector of the reward function is updated using the gradient ascent method. The gradient ascent method is shown in the following equation: , Where, η The learning rate; For optimal strategy The resulting behavioral characteristics are expected; The expected behavior features in the expert experience database are used to reduce the gap between the model policy and the expert policy in terms of behavior features. The weights of the reward function are adjusted by gradient ascent so that the trajectory features generated by the model policy are closer to the features of the expert. Convergence criterion: Repeat the policy evaluation and reward function update steps until... Convergence or reaching the maximum number of iterations.

[0043] like Figure 5 As shown, in step S104 above, based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, the weighted elasticity function (system elasticity assessment) of the fused scenario is calculated. E j Both physical and information systems need to be considered in each characteristic disaster scenario. (The following functional loss and recovery ability), including: CPDS elasticity index E j Quantification: for each characteristic disaster scenario The elasticity of the system E j This can be obtained through simulation and measured using comprehensive indicators: , The elasticity of a physical system can be quantified as: , Among them, Lost Load( t )for t The amount of load loss at any given time, The system recovery time measures the power outage losses and recovery speed. As a normalized time reference, this is typically... Taking one year (i.e., 8760 hours), the denominator directly represents the total annual load or total annual communication demand; Total Annual Load is the total electrical energy supplied or consumed by the system in a year under normal operating conditions, and is a benchmark value for measuring the annual service scale of the system. The resilience of a communication system can be quantified as follows: , Among them, Communication Interruption Rate ( t )for t The communication interruption rate at any given time measures the availability and reliability of information transmission; Total Communication Needs refers to the system's communication needs at a normalized time reference. Within, the total amount of communication services required to ensure the normal operation of the power system; The impact of cyber-physical cascade failure is a negative indicator, representing the additional losses caused by the cascade effect. It can be quantified by the amount of physical load loss caused by information failure or the amount of communication interruption caused by physical failure in the simulation. : These are weighting coefficients used to balance different elasticity dimensions; Weighted elasticity function for fusion scenarios v ( K ), defined as follows: , In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained from inverse reinforcement learning j The weighting of each disaster scenario ensures that the resilience assessment fully considers the true importance of different disaster scenarios.

[0044] Among them, the alliance K A Coalition refers to a set of one or more nodes that work together to harden a system (e.g., simultaneously strengthening the nodes physically, adding redundancy, or deploying backup power). When a subset of nodes is hardened, its resilience under different disaster scenarios is assessed. Ej ( K This will improve.

[0045] like Figure 5 As shown, in step S104 above, the Shapley value of each candidate key node is calculated, the nodes are sorted according to the Shapley value and output, and thus the Shapley value is used to fairly allocate the contribution of each node to the overall system resilience. v (K) His contributions include: Determine the set of nodes to be evaluated. N This refers to the initial set of candidate key nodes; Enumerate all possible node alliances K For each consortium K, its nodes are assumed to have received some degree of protection or hardening. The performance of CPDS in consortium K after the nodes have been hardened is simulated under all dynamic fuzzy disaster scenarios, and its weighted resilience value is calculated. v ( K ); For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ; compute nodes i In each league K Marginal contribution ; According to the Shapley value formula, by weighted summing of all marginal contributions, the node value is obtained. i Shapley value Among them, nodes i Shapley value The calculation formula is: , in: N It is a set of candidate key nodes; n= | N | is a set N Total number of nodes in the alliance; K It refers to a set consisting of one or more nodes; | K | is an alliance K The number of nodes in; Represents a node i Join the Alliance K The marginal contribution it brings is the increment of the weighted elasticity function value of the overall system elasticity after the node is added; Based on the calculated nodes i Shapley value Sort all nodes in descending order and output the critical coupling nodes. Nodes with larger Shapley values ​​contribute more to the overall system resilience and are therefore identified as more critical coupling nodes. These nodes are the ones that should be prioritized for hardening or protection in the CPDS resilience enhancement strategy.

[0046] This also includes simulations of the reinforcement effects: assuming that the probability of the reinforced node failing in a disaster is reduced, or its recovery time is shortened, or its physical / communication capacity is improved, the specific effects can be quantified through preset models or historical data.

[0047] In summary, this invention proposes a novel method for accurately identifying key coupled nodes in CPDS that integrates structural controllability, structural observability, dynamic fuzzy disaster scenarios, inverse reinforcement learning, and Shapley value calculation. This method aims to improve the accuracy, fairness, and adaptability of system resilience analysis and decision-making, and enhance the power grid's rapid response and recovery capabilities to disasters or attack disturbances.

[0048] Example 2: Figure 6 As shown, this invention discloses a multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system. The system utilizes a multi-dimensional dynamic resilience identification method for key coupled nodes in a power distribution cyber-physical system, comprising: The key node screening unit constructs a unified CPDS model and initially screens a set of candidate key nodes based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. The fuzzy scene generation unit uses the Markov chain Monte Carlo method to construct a dynamic fuzzy disaster scene set, generating a set containing a large number of dynamic fuzzy disaster scenes; The elasticity function construction unit adaptively learns and optimizes the weights of various disaster scenarios from expert experience through inverse reinforcement learning, and constructs a dynamically weighted elasticity function. The node calculation output unit calculates the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, calculates the Shapley value of each candidate key node, sorts the nodes according to the Shapley value, and outputs the results.

Claims

1. A multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system, characterized in that, Includes the following steps: A unified CPDS model is constructed, and a preliminary set of candidate key nodes is selected based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. A set of dynamic fuzzy disaster scenarios is constructed using the Markov chain Monte Carlo method, generating a set containing a large number of dynamic fuzzy disaster scenarios; By using inverse reinforcement learning, the weights of each disaster scenario are adaptively learned and optimized from expert experience, and a dynamic weighted elasticity function is constructed. Based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, the weighted elasticity function of the fused scenario is calculated, the Shapley value of each candidate key node is calculated, and the nodes are sorted and output according to the Shapley value.

2. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The construction of the unified CPDS model includes: The unified CPDS model is an interconnected network system consisting of power networks and communication networks; whereby the power network is the physical layer, defined as follows: In the formula, Represents the set of nodes in a power network. For edge sets in a power network, This refers to the power grid; the communication network, also known as the information layer, is defined as follows: , Represents the set of nodes in a communication network. For the edge set in the communication network, Indicates a communication network; Integrate power grids and communication networks into a unified coupled adjacency matrix. A CPDS The function is represented as follows: ， Where, A PP For the internal connection matrix of the power network, A CC For the internal connection matrix of the communication network, A PC This represents the information flow dependency from the power grid to the communication network. A CP This represents the control flow dependency from the communication network to the power network; Wherein, if a CPDS contains N P Power network nodes and N C If there are 10 communication network nodes, then the set of candidate key nodes is... N=N P +N C .

3. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The structural controllability includes: The state equation for structural controllability is: ， in, This represents the state vector of a power network node. u ( t ) represents the input control vector; A This is the adjacency matrix of the power network; B The input control matrix is ​​determined by the communication node. The state equation for structural controllability represents the rate of change of the state of a power network node over time. Maximum matching determines the minimum set of driving nodes. D min The formula is defined as: ， in, N A set of candidate key nodes; This represents the maximum number of matched edges. The impact index of node failure is defined as follows: ， in, C i For nodes i Failure impact indicators; For nodes i The number of uncontrollable nodes that increase after failure; Represents the set of nodes in a power network; N This is the set of candidate key nodes.

4. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 2 or 3, characterized in that, The structural observability includes: The observed system state satisfies the output model: ， in, This represents the state vector of a power network node. C For measurement output matrix; To output the measurement vector; A minimum sensor placement method based on network topology is used to calculate the power network observation node set. O min Power network observation node set O min The following observability conditions must be met: ， in, O For the set of measurement nodes; C For measurement output matrix; A This is the adjacency matrix of the power network; σ ( A ) is a matrix A The set of eigenvalues; For matrix A eigenvalues; I It is the identity matrix; N A set of candidate key nodes; The impact index of node failure observation is defined as follows: ， in, O i For nodes i Failure observation impact indicators; For nodes i The number of unobservable nodes added after a failure; N A set of candidate key nodes; Represents the set of nodes in a power network; The overall importance index is defined as follows: ， in, α、β These are the weighting coefficients; C i For nodes i Failure impact indicators; O i For nodes i Failure observation impact indicators; I i For nodes i The comprehensive importance indicator.

5. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The method of using Markov chain Monte Carlo to construct a set of dynamic fuzzy disaster scenarios generates a set containing a large number of dynamic fuzzy disaster scenarios, including: Based on historical data and expert experience, the transition probabilities between different disaster types and their intensities are defined; where disaster types include natural disasters and man-made attacks; and where the intensity of each disaster type is defined as a continuous variable. x Define the generalized Gaussian intensity fuzzy membership function: ， Where, x As for the intensity of the disaster, m The average intensity σ Standard deviation k For shape parameters; The initial disaster state is randomly sampled from the defined intensity fuzzy membership function using the MCMC method; Based on the transition probability and time step, a series of continuous disaster scenario sequences with fuzzy features are generated iteratively from the initial disaster state; For each generated disaster scenario, its comprehensive fuzzy membership degree across multiple dimensions is calculated, and its potential cascading effects are simulated; whereby, a disaster scenario set is defined. Each characteristic disaster scenario S j Expressed as: ， In the formula, As a type of disaster, For intensity vectors, To the area / scope of impact, The potential cascading effects it may trigger; This represents the comprehensive fuzzy membership degree of the feature scene; Based on the comprehensive fuzzy membership degree, a set containing a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula: S dynamic ={ S j,t}， Where, S j,t Indicates time t The j One disaster scenario; S dynamic It is a collection containing a large number of dynamic and blurred disaster scenarios.

6. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The method of adaptively learning and optimizing the weights of each disaster scenario from expert experience through inverse reinforcement learning includes: Construct a trajectory database that includes the entire lifecycle operation status of CPDS, expert decisions, and system responses. The data structure within the trajectory database... Including status s n ,action a n ,award r n Among them, for each expert experience trajectory : The reward function is derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, where the reward function is as follows: ， Where, f ( s,a ) is the feature vector corresponding to the state-action sequence; It is the weight vector that needs to be learned; T Transpose of a vector; turn up To ensure that the feature expectations of the expert trajectory match the feature expectations of all policies, a weight vector is calculated using an iterative algorithm. Simultaneously, the entropy of the policy is maximized, where the entropy of the policy is maximized as shown in the following formula: ， in, In the reward function The probability of the trajectory below; D expert It is an expert trajectory database; It is a regularization parameter; It represents the expert trajectory database D expert A specific expert trajectory in the dataset; K is the total number of expert trajectories; L is the length or time steps of each trajectory; It represents the trajectory τ The prior probability distribution; max w This represents a maximization operation, which involves finding the weight vector that maximizes the objective function. ; Based on the learned reward function Assessment experts in characteristic disaster scenarios S j The expected reward for taking the optimal action: ， In the formula, max a In the current characteristic disaster scenario S j Next, iterate through all possible actions a and calculate the expected reward value for each action a; V( S j () represents a characteristic disaster scenario S j Under these circumstances, the maximum expected reward that can be obtained by taking the optimal action; Extract weights related to disaster scenario characteristics from the reward function. : ， Where, For each characteristic disaster scenario S j Extract its key features; use softmax normalization to ensure that the sum of all scene weights is 1; w T This represents the transpose of the weight vector w, which transposes the weight vector from a column vector to a row vector.

7. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 6, characterized in that, The iterative algorithm includes the following iterative process: Strategy evaluation: for the current reward function Standard reinforcement learning algorithms are used to compute the optimal policy. ; Reward function update: The weight vector of the reward function is updated using the gradient ascent method. The gradient ascent method is shown in the following equation: ， In the formula, η is the learning rate; For optimal strategy The resulting behavioral characteristics are expected; The expected actual behavioral characteristics in the expert experience database; Convergence criterion: Repeat the policy evaluation and reward function update steps until... Convergence or reaching the maximum number of iterations.

8. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The step of calculating the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamically fuzzy disaster scenario includes: CPDS elasticity index E j Quantification: for each characteristic disaster scenario The elasticity of the system E j This can be obtained through simulation and measured using comprehensive indicators: ， The elasticity of a physical system can be quantified as: ， Among them, Lost Load( t )for t The amount of load loss at any given time, System recovery time; The normalized time base is used; Total Annual Load is the total electrical energy supplied or consumed by the system under normal operating conditions within one year. The resilience of a communication system can be quantified as follows: ， Among them, Communication Interruption Rate ( t )for t The communication interruption rate at any given time; Total Communication Needs refers to the system's communication interruption rate at a given time reference. Within, the total amount of communication services required to ensure the normal operation of the power system; The impact of cyber-physical cascade failures is quantified by the amount of physical load loss caused by information failures or the amount of communication interruption caused by physical failures in the simulation. : These are weighting coefficients used to balance different elasticity dimensions; Weighted elasticity function for fusion scenarios v ( K ), defined as follows: ， In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained by inverse reinforcement learning j The weight of each disaster scenario.

9. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 8, characterized in that, The process of calculating the Shapley value for each candidate key node, sorting the nodes based on the Shapley values, and outputting the results includes: Determine the set of nodes to be evaluated. N This refers to the initial set of candidate key nodes; Enumerate all possible node alliances K ; For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ; Compute nodes i In each league K Marginal contribution ; According to the Shapley value formula, by weighted summing of all marginal contributions, the node values ​​are obtained. i Shapley value Among them, nodes i Shapley value The calculation formula is: ， in: N It is a set of candidate key nodes; n= | N | is a set N Total number of nodes in the alliance; K It refers to a set consisting of one or more nodes; | K | is an alliance K The number of nodes in; Represents a node i Join the alliance K The marginal contribution it brings is the increment of the weighted elasticity function value of the overall system elasticity after the node is added; Based on the calculated nodes i Shapley value Sort all nodes in descending order and output the key coupled nodes after sorting.

10. A multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system, wherein the multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system uses the multi-dimensional dynamic resilience identification method for key coupled nodes in a power distribution cyber-physical system as described in any one of claims 1 to 9, characterized in that, include: The key node screening unit constructs a unified CPDS model and initially screens a set of candidate key nodes based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. The fuzzy scene generation unit uses the Markov chain Monte Carlo method to construct a dynamic fuzzy disaster scene set, generating a set containing a large number of dynamic fuzzy disaster scenes; The elasticity function construction unit adaptively learns and optimizes the weights of various disaster scenarios from expert experience through inverse reinforcement learning, and constructs a dynamically weighted elasticity function. The node calculation output unit calculates the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, calculates the Shapley value of each candidate key node, sorts the nodes according to the Shapley value, and outputs the results.

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