Cascade effect safety assessment method based on dynamic bayesian network and evidence theory

Abstract

The application provides a kind of cascade effect safety evaluation method based on dynamic bayesian network and evidence theory, belong to system safety evaluation technical field, it includes: obtaining the topological structure model of system, constructs dynamic bayesian network DBN structure;Using evidence theory to parameterize DBN structure, constructs condition belief table CBT for DBN structure, CBT defines the basic belief assignment BBA of the state of child node under the condition of given parent node state;Based on DBN structure and CBT, execute evidence-based dynamic timing reasoning, to dynamically calculate the belief of each component state in system, and output failure belief interval according to the belief of state, to evaluate the cascade effect safety of system.The application can improve the accuracy, robustness and information richness of evaluation result.

Description

Technical Field

[0001] This invention relates to the fields of computer technology and system security assessment technology, and in particular to a cascading effect security assessment method based on dynamic Bayesian networks and evidence theory for complex systems, such as power networks, transportation networks, and aerospace systems. Background Technology

[0002] The security of complex systems, such as critical infrastructure, is crucial to modern society. The components within such systems are highly coupled, and a failure in a single component can propagate through network dependencies, triggering a cascading effect that can lead to systemic collapse. Therefore, accurately assessing and predicting the risks of cascading effects is essential.

[0003] The existing security assessment methods have the following drawbacks: (1) Limitations of static or deterministic assessment: Traditional methods such as fault tree analysis (FTA) are usually static and difficult to capture the dynamic characteristics and path dependence of cascading effects over time.

[0004] (2) The state space explosion problem of dynamic models: When facing complex networks with many nodes, such as Markov chains, the state space of dynamic models will grow exponentially, making computation infeasible.

[0005] (3) Insufficient handling of uncertainty: The evolution of cascade effects is full of uncertainty. Existing methods mostly use probability theory for modeling, which is relatively mature in dealing with random uncertainty caused by physical randomness. However, traditional probability theory is difficult to effectively represent cognitive uncertainty caused by data sparsity, imprecise models, and fuzzy or conflicting expert knowledge. Forcibly defining fuzzy information as a precise probability value may lead to overconfidence or misleading assessments of system risk.

[0006] Therefore, there is an urgent need for a safety assessment method that can characterize the dynamic evolution of cascading effects within a unified framework, and effectively quantify and integrate random uncertainty and cognitive uncertainty. Summary of the Invention

[0007] The present invention aims to overcome the shortcomings of the prior art and provide a dynamic safety assessment system and method for complex systems with cascading effects that can simultaneously handle temporal dynamics and mixed uncertainties, so as to improve the accuracy, robustness and information richness of the assessment results.

[0008] To address the aforementioned technical problems, as one aspect of this invention, a cascade effect security assessment method based on dynamic Bayesian networks and evidence theory is disclosed. This method is executed by a computer program and includes the following steps: S1. Obtain the topology model of the system and construct a dynamic Bayesian network (DBN) structure based on the topology model. The components of the system are defined as state nodes in the DBN structure, and the dependencies between components are defined as the transition dependencies between different time slices of the DBN structure. S2. The DBN structure is parameterized using evidence theory, and a conditional confidence table (CBT) is constructed for the DBN structure. The CBT defines the basic confidence assignment (BBA) of the child node state given the parent node state. S3. Based on the DBN structure and CBT, perform evidence-based dynamic temporal reasoning to dynamically calculate the confidence level of each component state in the system, and output the confidence level of the state. Reliability interval [ , The system's cascading effect safety is assessed; among which, [ , [ ] represents the failure confidence interval of node i at time t. .

[0009] Furthermore, middle: ; ; in, and To preserve some of the impact of the node's historical state; and The impact of static reliability on the fusion of multi-source evidence; and Transmit influence to neighbors; As a historical inertia weight, For nodes exist Trust level at all times As the benchmark evidence weight, The baseline confidence level is calculated by CBT. The baseline likelihood is calculated by CBT. For topological coupling weights, For nodes exist Trust level at all times; For nodes exist The likelihood at time j is the number of nodes. The adjacent nodes that have an impact For nodes The set consisting of all adjacent nodes.

[0010] Furthermore, S2 includes: S21. For each node in the DBN structure, given the combination of its parent node states, obtain evidence of its next state from multiple heterogeneous information sources. S22. Using Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a Basic Reliability Assignment (BBA). The BBA is then used as an item in the Conditional Reliability Table (CBT) to construct the Conditional Reliability Table (CBT) for the DBN structure.

[0011] Furthermore, S22 includes: S221. Modeling and preprocessing of multiple heterogeneous information sources; S222. Based on Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a Basic Reliability Assignment (BBA). S223. The fused basic reliability assignment (BBA) is used as an item in the CBT to construct the conditional reliability table (CBT) for the DBN structure.

[0012] Furthermore, the evidence from multiple heterogeneous information sources in S22 includes physical model evidence, historical data evidence, and expert knowledge evidence.

[0013] Furthermore, S3 includes: S31. Obtain the initial perturbation event of the current time slice as initial observation evidence and convert it into a basic confidence assignment (BBA). S32. For each time step from t to t+1, the iterative inference alternately executes the prediction and update sub-steps. If new observational evidence is obtained in the next time slice, the prior state confidence is fused with the new observational evidence to obtain the posterior state confidence of the next time slice node. S33. The state confidence of each node at any given time is expressed as a confidence interval composed of the confidence function (Belief) and the likelihood function (Plausibility). , The output is presented in the form of ], thereby enabling dynamic assessment and prediction of the risk of cascading effect propagation.

[0014] Furthermore, S31 includes: S311. Obtain the initial disturbance event, which is an abnormal signal that deviates the system from the normal steady state; S312. Perform evidence mapping to transform quantitative data into qualitative reliability. Mapping methods include: Based on the membership function, the membership degree of the observed values ​​to each proposition is calculated, and evidence mapping is performed: a fuzzy membership function is constructed; based on the probability density distribution, the probability likelihood of the observed values ​​under each category condition is calculated and normalized, and evidence mapping is performed: using the probability density function PDF obtained from historical data statistics, the probability likelihood of the observed values ​​under each category condition is calculated and normalized; evidence mapping is performed based on direct correspondence with expert rules. S313. After the evidence mapping transformation is completed, output the BBA vector of the node at time t.

[0015] Furthermore, the prediction sub-steps performed in S32 include: P1: Obtain the basic confidence assignment (BBA) for each node at time t; P2: Inject the basic confidence assignment (BBA) of each node at time t into the corresponding clique node of the CBT clique tree structure; perform evidence propagation and state update to obtain the posterior state confidence at time t; P3: Construct a time-invariant cluster tree structure; P4: Forward message passing and prediction based on cluster trees.

[0016] Furthermore, the update sub-step executed in S32 includes: if new observational evidence is obtained at time t+1, the Dempster synthesis rule is used to fuse the prior state confidence with the new observational evidence to obtain the posterior state confidence of the node at time t+1.

[0017] Furthermore, P4 includes: P41. The system extracts the marginal distribution of interface variables from the clique tree at time t. Interface variables are key variables connecting two time slices, and their state information needs to be passed to the next time slice. P42. Along the edge connecting time slice t and time slice t+1 in the clique tree, send the prepared message from the clique node at time t to the clique node at time t+1. P43. The clique node at time t+1 receives the message from time t and combines it with its own prior potential. Using the state transition probability defined in DBN, it realizes the state prediction from t to t+1 through the message passing mechanism. P44. Normalize the potential energy in the clique nodes at time t+1 to obtain the prior state confidence distribution of each node at that time.

[0018] As another aspect of this invention, it also provides a dynamic security assessment system for cascading effects of complex systems: a model building module for acquiring a topological model of the complex system and constructing a dynamic Bayesian network (DBN) structure based on it; a parameter learning module for parameterizing the DBN using evidence theory and constructing a conditional confidence table (CBT); a dynamic inference module for performing temporal inference based on the DBN structure and CBT to dynamically calculate the confidence of the states of each component in the system; and an evaluation output module for evaluating the security of the cascading effects of the system based on the confidence of the states and outputting the results.

[0019] The parameter learning module is configured to: acquire evidence from at least two heterogeneous information sources, including physical models, historical data, and expert knowledge; and fuse the evidence using Dempster's synthesis rules to generate a basic confidence assignment (BBA) defined in the CBT. The dynamic inference module is configured to iteratively perform prediction and update operations on consecutive time slices.

[0020] Compared with the prior art, the present invention has the following significant advantages: 1. This invention innovatively introduces evidence theory and conditional confidence scale (CBT), which can quantify and disseminate random uncertainty and cognitive uncertainty within a unified framework, effectively distinguishing between "uncertainty" and "ignorance". It is especially suitable for scenarios with sparse data and expert knowledge intervention, and enhances the ability to quantify uncertainty.

[0021] 2. This invention outputs a confidence interval [Bel, Pl] rather than a single probability value. This interval provides decision-makers with a lower limit (supported by direct evidence) and an upper limit (the possibility of no contradiction) for the risk, making the assessment results more conservative and robust. It avoids overconfidence or misjudgment caused by imposing precise probabilities, and improves the robustness and information richness of the assessment results.

[0022] 3. This invention combines the temporal reasoning capability of DBN to simulate the gradual evolution of cascading effects, dynamically update the risk status of each component in the system, and predict high-risk propagation paths in advance, thus gaining valuable time for taking preventive control measures and achieving true dynamic risk assessment and prediction.

[0023] 4. The framework of this invention is universal and can be applied to dynamic risk management and reliability analysis of various complex networked systems such as power systems, aviation flight control systems, communication networks, and financial systems, and has wide applicability. Attached Figure Description

[0024] Figure 1 This is a schematic diagram illustrating the workflow of the cascade effect security assessment method based on dynamic Bayesian networks and evidence theory of this invention. Figure 2 This is a schematic diagram of the hardware structure of a computer system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a 10-node network topology according to an embodiment of the present invention; Figure 4 This is a dynamic evolution comparison diagram of the failure probability of node 2 according to an embodiment of the present invention; Figure 5 This is a cascaded fault assessment process for an aviation flight control system according to an embodiment of the present invention; Figure 6 This is a detailed illustration of the CBT construction process according to an embodiment of the present invention. Detailed Implementation

[0025] The following is with reference to the appendix. Figures 1-6 The implementation method of the cascade effect security assessment method based on dynamic Bayesian networks and evidence theory of the present invention will be described.

[0026] The core idea of ​​this invention lies in constructing a hybrid evaluation framework that deeply integrates the temporal reasoning capabilities of Dynamic Bayesian Networks (DBNs) with the cognitive uncertainty handling capabilities of DS evidence theory. This method and system can be deployed on... Figure 2 The general-purpose computer system shown includes a processor, memory, input / output interfaces, etc. The memory stores a computer program that implements the method of the present invention.

[0027] As an example of an implementation of the present invention, see the appendix. Figure 1 As shown, this invention discloses a cascading effect security assessment method based on dynamic Bayesian networks and evidence theory. This method is executed by a computer program and includes the following steps: S1. Obtain the topology model of the complex system and construct a dynamic Bayesian network (DBN) structure based on the topology model, where the system components are defined as state nodes in the DBN structure.

[0028] System Modeling and DBN Structure Construction: This involves obtaining a physical topology model of a complex system and mapping this topology to a temporal structure of a Dynamic Bayesian Network (DBN). Each component of the system is defined as a state node in the DBN structure, and the dependencies between components are defined as transition dependencies between different time slices in the DBN structure. Specifically, the state of any node at time t+1 depends on its own state at time t and the states of its neighboring nodes at time t.

[0029] S2. The DBN structure is parameterized using evidence theory, and a conditional confidence table (CBT) is constructed for the DBN structure. The CBT defines the basic confidence assignment (BBA) of the child node state given the parent node state.

[0030] Parameter learning based on evidence theory: Using evidence theory, taking DS theory as an example, the DBN structure is parameterized to construct a Conditional Belief Table (CBT) to replace the Conditional Probability Table (CPT) in the traditional DBN structure. This includes the following steps: S21. For each node in the DBN structure, given the combination of its parent node states, obtain evidence of its next state from multiple heterogeneous information sources.

[0031] Evidence obtained from multiple heterogeneous information sources includes physical model evidence, historical data evidence, and expert knowledge evidence, and the obtained evidence from multiple heterogeneous information sources must include at least two of the above-mentioned heterogeneous information source evidence. Among them: Physical model evidence: refers to the basic confidence assignment (BBA) of the node failure probability calculated based on the physical operating mechanism of the system (such as the overload model of a complex power system).

[0032] Historical data evidence: refers to the basic confidence level assignment (BBA) of the probability of node failure obtained based on statistical analysis of historical operational data.

[0033] Expert knowledge evidence: refers to the basic confidence level assignment (BBA) of the probability of node failure based on the experience judgment of domain experts.

[0034] Basic Belief Assignment (BBA), also known as Basic Probability Assignment (BPA) or mass function, is one of the core concepts in DS evidence theory. It is a mathematical function used to represent and quantify the degree of confidence in a proposition, and is fundamental for handling uncertain information. BBA is a mathematical mapping, defined as follows: Let θ be the identification frame, 2... θ Let BBA be its power set (the set of all subsets). BBA is a power set of θ. θ The mapping function to the interval [0, 1], denoted as m, satisfies the following two conditions: For any of the following: The confidence level of the empty set is zero: m(∅)=0, which means that the confidence level for "an impossible event" is zero.

[0035] Condition 2: The total reliability is 1. , indicating that the sum of the confidence levels of all propositions is 1.

[0036] m(A) represents the degree of confidence in the evidence regarding proposition A. That is, there is m(A) of certainty that the truth lies within set A, but it is unknown which specific element of A it is. If m(A) > 0, then set A is called a focal element of BBA. A focal element is the fundamental proposition supported by the evidence. BBA differs from Bayesian probability, which must be assigned to single, mutually exclusive elements; BBA allows for uncertainty.

[0037] BBA is the cornerstone for building other important concepts: The belief function (Bel(A)) represents the total degree of belief that proposition A is true. It is the sum of the beliefs of all subsets that support A. The total support for proposition A represents the probability that "at least A is true". .

[0038] Here, B represents all subsets contained in set A. That is, if A = {overheating, normal}, and A is the universal set, then B may be a subset of {overheating}, {normal}, or {overheating, normal}.

[0039] The likelihood function (Pl(A)) represents the degree of confidence that proposition A is not false, i.e., the sum of the confidence of all subsets intersecting with A. It represents the non-rejection degree or latent probability of proposition A, indicating the likelihood that "it might be A". .

[0040] That is, the sum of the basic confidence assignments (m) of all non-empty subsets B that intersect with proposition A. It is the complement of A.

[0041] Assuming the identification framework is Θ={a,b}, the basic confidence assignment is as follows: m({a})=0.6, m({b})=0.2, m(Θ)=0.2; For the proposition A={a}: Trust function: Bel({a})=m({a})=0.6.

[0042] Likelihood function: The non-empty subsets that intersect with {a} are {a} and Θ. Therefore: Pl({a}) = m({a}) + m(Θ) = 0.6 + 0.2 = 0.8. Or, using the complementarity relation: Pl({a}) = 1 - Bel({b}) = 1 - 0.2 = 0.8.

[0043] The uncertainty interval [Bel(A), Pl(A)] constitutes the uncertainty interval of proposition A, also known as the confidence interval. It intuitively depicts the degree of confidence in A: Bel(A): Lower bound of trust level (definite support). Pl(A): Upper bound of trust level (maximum possible support).

[0044] Pl(A)-Bel(A): Uncertainty about A (i.e. the part that is "unknown").

[0045] The core value of Conditional Belief Tables (CBTs) lies in their role as the cornerstone of modeling uncertain information, playing a crucial role in practical applications. In scenarios such as multi-sensor data fusion and multi-expert opinion synthesis, each information source needs to transform its judgment into a CBT as input to the fusion algorithm. When faced with incomplete, ambiguous, or subjective expert judgments, CBTs effectively express this "don't know" or "uncertainty," which traditional probability theory struggles to handle directly. In systems like evidence networks and confidence rule bases, CBTs essentially define the dependencies between the BBTs of child node states under parent node states, thereby enabling uncertain reasoning.

[0046] The Basic Reliability Assignment (BBA) breaks through the limitations of traditional probability theory by allowing trust to be assigned to a set of propositions rather than a single hypothesis and providing a mechanism for directly expressing "I don't know," thus providing a powerful and flexible foundation for information fusion and decision reasoning in uncertain environments.

[0047] S22. Using Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a Basic Reliability Assignment (BBA). The BBA is then used as an item in the Conditional Reliability Table (CBT) to construct the Conditional Reliability Table (CBT) for the DBN structure.

[0048] Using Dempster's synthesis rule, evidence from multiple heterogeneous information sources is fused to obtain a unified Basic Reliability Assignment (BBA), which is then incorporated as a component of CBT. The BBA assigns reliability values ​​to the power set of the node state recognition framework, thereby quantifying cognitive uncertainty; for example, it assigns a portion of the reliability to the uncertain set of "normal or failed".

[0049] The core of this step lies in directly transforming the real-time fusion results of multi-source heterogeneous data into parameters in a dynamic Bayesian network (DBN) model, including the following steps: S221. Modeling and preprocessing of multiple heterogeneous information sources.

[0050] First, it is necessary to transform different types of information sources into a unified format that evidence theory can process—Basic Reliability Assignment (BBA).

[0051] Identification of multiple heterogeneous sources: Assume that the system has K information sources, such as physical model evidence, historical data evidence, and expert knowledge evidence.

[0052] Single-source BBA generation: For each information source, establish a mapping from the raw data to the recognition framework Θ.

[0053] Among them, the evidence for the physical model is quantitative data: evidence obtained from the physical model (such as residual T=20) ℃ The residuals need to be converted to a quality function before fusion. If the residuals are small and within the allowable error range, the evidence supports that the system is operating normally. Therefore, it can be converted to mS1({overheating}) = 0.1, mS1({normal}) = 0.9. If the residuals are large and exceed the model's prediction range, the evidence strongly supports that the system has malfunctioned (e.g., overheating). Therefore, it can be converted to mS1({overheating}) = 0.8, mS1({normal}) = 0.2.

[0054] Historical data evidence S2 is also quantitative data: Historical data cannot be directly used as evidence input; it must be mapped from "quantitative historical statistical values" to "qualitative basic probability distributions" through a mathematical model. Example of the conversion process: Suppose that historical data statistics show that the average temperature of a certain device during normal operation is 60℃, with a standard deviation of 5℃. Historical data evidence (quantitative): The current temperature is 80℃, but in the historical statistical distribution, 80℃ falls outside 3σ, representing an extremely low probability event. Conversion model (qualitative): Based on the normal distribution model, calculate the probability area of ​​80℃ belonging to the "abnormal" region. Suppose the calculated probability of being abnormal is 0.9. Fusion input (qualitative): mhistory({overheating}) = 0.9, mhistory({normal}) = 0.1.

[0055] Expert knowledge evidence S3 is qualitative data: directly assigned reliability. For example, if an expert believes that "fault is very likely," then mS3({fault}) = 0.9.

[0056] S222. Based on Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a basic confidence assignment (BBA).

[0057] The purpose of this step is to merge multiple independent BBAs into a single global BBA, thereby reducing the uncertainty of single-source information. Evidence fusion based on Dempster's synthesis rule, when there are k evidence sources, uses the orthogonal sum rule to iteratively combine the probability quality functions of multiple pieces of evidence. The method is pairwise sequential fusion: first, the first and second pieces of evidence are fused, and the result is then fused with the third piece of evidence, and so on, until all k pieces of evidence have been fused.

[0058] Let's take the fusion of two evidence sources as an example: Assume there are two evidence sources m1 and m2, and the identification frame is Θ. The Dempster synthesis rule is m = m1 ⊕ m2.

[0059] The definition is as follows: ; Where A, B, and C are all subsets (focal elements) of Θ. K is the conflict factor, calculated using the following formula: 1 / (1-K) is a normalization factor, which is used to remove the influence of conflicting evidence.

[0060] Calculation example: Assume the identification framework Θ = {Normal (N), Faulty (F)}.

[0061] Information Source 1 (Physical Model Evidence): m1({N})=0.6, m1({F})=0.3, m1({N,F})=0.1; Information source 2 (historical data evidence): m2({N})=0.2, m2({F})=0.7, m2({N,F})=0.1; Fusion result m fused : m fused ({N})∝0.6×0.2+0.6×0.1+0.1×0.2=0.2(before normalization); m fused ({F})∝0.3×0.7+0.3×0.1+0.1×0.7=0.31(before normalization).

[0062] Finally, the fused BBA is obtained through normalization. The result is then fused with the third piece of expert knowledge evidence, and so on, until all k pieces of evidence are fused.

[0063] S223. The fused basic reliability assignment (BBA) is used as an item in the CBT to construct the conditional reliability table (CBT) for the DBN structure.

[0064] This step is crucial for integrating a data-driven approach into the model structure. The merged BBA is then incorporated into CBT, including: The fused BBA is directly used as the state prior within the time slice: if the node is the root node or an input node, the fused BBA is directly used as the initial CBT value for that node at the current time t. That is: CBT Input (X t )=m fused (X t ).

[0065] Complete DBN Conditional Belief Table (CBT) Construction: Combining the above fusion results, a complete DBN node X's CBT consists of two parts: CBTtotal = {CBT...} Temporal， CBT Observation}

[0066] Timing transfer section CBT Temporal This describes the physical evolution of the state Xt from time t to time t+1. For example: m(Xt+1|Xt). This part is usually constructed based on system mechanisms or historical statistics.

[0067] Observation Fusion Part CBT Observation This is the output required for this step. It describes the mapping from the hidden state Xt to the observed evidence Et. Construction method: m(Et|Xt) = Dempster synthesis(mS1, mS2, ...). Through this method, this step is actually building a system that combines data-driven and model-driven approaches. Data-driven: Dempster synthesis refines chaotic, heterogeneous data into definitive evidence (BBA).

[0068] Model-driven: The extracted evidence is embedded into the DBN as part of the CBT, and the temporal reasoning capability of the DBN is used to handle dynamic processes.

[0069] S3. Based on the DBN structure and CBT, perform evidence-based dynamic temporal reasoning to dynamically calculate the reliability of the states of each component in the system, and output the reliability interval based on the reliability of the states. , The safety of the cascading effects of the system is assessed.

[0070] The results of the safety assessment of the cascading effects of the system are presented in confidence intervals. , The output is in the form of [], where Bel is the confidence function value and Pl is the likelihood function value. The width of this interval represents the degree of uncertainty of the evaluation result. The process includes the following steps: S31. Obtain the initial perturbation event of the current time slice as initial observation evidence and convert it into a basic confidence assignment (BBA).

[0071] The system acquires operational status data of the monitored object at the current time slice (time t) through a data acquisition interface; identifies abnormal patterns in the operational status data and marks them as initial disturbance events; it then calls a preset evidence mapping model to map the quantitative feature values ​​of the initial disturbance events to qualitative proposition support under the identification framework, generating the basic confidence allocation function (BBA) for each node, thus completing the transformation from the observation space to the evidence space. Specifically, this includes: S311. Obtain the initial disturbance event. The "disturbance event" usually refers to an abnormal signal that causes the system to deviate from its normal steady state.

[0072] Data source: real-time sensor readings (such as temperature, pressure, vibration), system log alarm codes, or characteristic parameters output by the previous module.

[0073] The identification logic includes: setting a threshold for judgment: when the observed value exceeds the normal threshold range, it is judged as a disturbance event. Alternatively, calculating the residual (the difference between the actual value and the predicted value), when the residual is significantly non-zero, it is confirmed as a disturbance.

[0074] S312. Perform evidence mapping to transform "quantitative data" into "qualitative reliability." Mapping methods include: Based on membership functions, the membership degree of each proposition is calculated, and evidence mapping is performed: fuzzy membership functions are constructed. For example, for the temperature node, two trapezoidal membership functions are constructed: "normal" and "overheated". Calculation process: Substitute the observed temperature value (e.g., 85℃) into the function to calculate its membership degree for each proposition. m({normal})=μ 正常 (85), m({overheating})=μ 过热 (85).

[0075] Based on the probability density distribution, the probability likelihood values ​​of the observed values ​​under each category condition are calculated and normalized. Evidence mapping is then performed: using the probability density function (PDF) obtained from historical data statistics, the probability likelihood values ​​of the observed values ​​under each category condition are calculated and normalized.

[0076] Based on direct correspondence of expert rules, evidence mapping is performed: for example: sensor alarm signal ON->m({fault})=0.9,m({uncertain})=0.1.

[0077] S313. After the evidence mapping transformation is completed, output the BBA vector of the node at time t.

[0078] Example: Node: Device Temperature Status X t； Identification framework: Θ={Normal(N), Fault(F)}; Input disturbance: Temperature rises sharply to 90℃.

[0079] Transformation Output (BBA): m t({Normal}) = 0.1, indicating a very low reliability in supporting the normal outcome; m t ({fault}) = 0.8, indicating a high confidence level in supporting the fault; m t ({Normal, Fault}) = 0.1 indicates uncertainty due to factors such as sensor accuracy.

[0080] The generated BBA will be used as input parameters into the CBT clique tree structure for subsequent calculation of the posterior confidence at time t and the prior confidence at time t+1. This solves the problem of how the system knows what is happening now and transforms perturbations in the physical world into mathematical evidence (BBA).

[0081] S32. For each time step from t to t+1, iterative inference alternates between prediction and update sub-steps. If new observational evidence is obtained in the next time slice (time t+1), the prior state confidence is fused with the new observational evidence to obtain the posterior state confidence of the next time slice node.

[0082] Preferably, the following prediction and update sub-steps are performed alternately in step S32: Prediction sub-step: Based on the basic confidence assignments (BBA) and CBT for all nodes at time t, the prior state confidence of each node at time t+1 is calculated using the evidence propagation algorithm, specifically including: P1: Obtain the basic confidence assignment (BBA) for each node at time t.

[0083] P2: Inject the basic confidence assignment (BBA) of each node at time t into the corresponding clique node of the CBT clique tree structure; perform evidence propagation and state update to obtain the posterior state confidence at time t.

[0084] The CBT clique tree structure is invoked, and the Basic Confidence Assignment (BBA) of each node at time t is injected into the corresponding clique node. The clique tree propagation algorithm is executed to fuse, update, and normalize the potential energy of each node at time t, outputting the posterior state confidence distribution of each hidden node at time t. The clique tree propagation algorithm includes: Injection Phase: The BBA value obtained in step S1 is used as likelihood evidence and multiplied into the potential function of the corresponding leaf node or interface node in the clique tree structure. Propagation Phase: Within the clique tree at time t, nodes exchange messages. Each node receives messages from its neighbors and, combined with its own potential, eliminates redundant dependencies between variables. Posterior Calculation: Through the processes of message collection and distribution, the system calculates a joint distribution incorporating the current evidence. After marginalization, the posterior state confidence Bel of each target node at time t is obtained. t (X).

[0085] When using CBT (Cluster Tree) instead of the traditional Conditional Probability Table (CPT) for inference, the specific implementations of subsequent steps P3 and P4 will differ. The CBT algorithm performs state transitions and predictions through message passing on the cluster tree structure. Its core lies in utilizing pre-compiled tree templates and interface concepts to achieve efficient dynamic inference. The following are the specific implementation steps based on the CBT algorithm: Step P3: Construct a time-invariant cluster tree structure; Unlike dynamically expanding the entire DBN, the CBT algorithm pre-compiles a time-invariant clique tree template, which is reused repeatedly during inference.

[0086] Implementation details: The system constructs a clique tree spanning two adjacent time slices based on the DBN's transition network. This clique tree contains the variables at time t and t+1, as well as the interfaces connecting them (i.e., variables connected between time slices). This structure remains static during inference, avoiding the high overhead of repeatedly constructing the tree structure at each time step.

[0087] Step P4: Forward message passing and prediction based on the clique tree.

[0088] The state transition is no longer matrix multiplication, but rather a message-passing process on the clique tree. This includes: P41. The system extracts the marginal distribution of interface variables from the clique tree at time t. Interface variables are key variables connecting two time slices, and their state information needs to be passed to the next time slice.

[0089] P42. Along the edge connecting time slice t and time slice t+1 in the clique tree, send the prepared message from the clique node at time t to the clique node at time t+1.

[0090] P43. The clique node at time t+1 receives the message from time t and combines it with its prior potential (usually from the model definition). This process essentially utilizes the state transition probabilities defined in DBN to achieve state prediction from t to t+1 through a message passing mechanism.

[0091] P44. Normalize the potential energy in the clique nodes at time t+1 to obtain the prior state confidence distribution of each node at that time, i.e., P(Xt+1|E1:t).

[0092] The key difference in this step is that, with CPT, state transitions are explicit matrix operations, while with CBT, state transitions are implicitly encoded in the message passing process of the clique tree. The CBT algorithm is more suitable for complex network structures because it decomposes the reasoning problem into local message passing on the tree structure, resulting in higher computational efficiency. Therefore, the CBT algorithm achieves efficient prediction of the state of dynamic Bayesian networks by constructing time-invariant clique tree templates and using an interface-based message passing mechanism.

[0093] Update sub-step: If new observational evidence is obtained at time t+1, the Dempster synthesis rule is used to fuse the prior state confidence with the new observational evidence (the fusion method is discussed above) to obtain the posterior state confidence of the node at time t+1.

[0094] S33. The state confidence of each node at any given time is expressed as a confidence interval composed of the confidence function (Belief) and the likelihood function (Plausibility). , The output is presented in the form of a confidence interval, enabling dynamic assessment and prediction of the risk of cascading effects. The width of this confidence interval characterizes the degree of cognitive uncertainty in the assessment results.

[0095] In the above clustered tree reasoning and state update process, the node The specific confidence distribution at time t is dynamically calculated by integrating its own historical state, static baseline evidence, and cascading impacts from neighboring nodes in the network topology. The specific state evolution analytical model is as follows: [ ; ; ; in, and To preserve some of the impact of the node's historical state; and The impact of static reliability on the fusion of multi-source evidence; and To spread influence to neighbors. As a historical inertia weight, For nodes At the previous moment ( Trust level at any given moment As the benchmark evidence weight, The baseline (static) confidence level is calculated using the Conditional Reliability Scale (CBT). The baseline (static) likelihood is calculated using the Conditional Reliability Test (CBT). For topological coupling weights, For nodes At the previous moment ( Trust level (at any time); For nodes At the previous moment ( The likelihood of the target node at time (j) is given by the value of j. The adjacent nodes that have an impact For the target node The set consisting of all adjacent nodes, For the target node currently undergoing state assessment, This refers to the current discrete time step or the current cascade evolution stage.

[0096] As an embodiment of the present invention: Numerical Verification Based on a 10-Node Network: This embodiment aims to illustrate the specific execution flow and effectiveness of the method proposed in this invention through a standard 10-node network topology. Furthermore, to better demonstrate the propagation of cascading effects, it is assumed that nodes have extremely high reliability under normal conditions, and their own failure probability can be ignored, meaning they may only fail when affected by disturbances from other adjacent parent nodes.

[0097] S1. Obtain the topology model of the complex system and construct a dynamic Bayesian network (DBN) structure based on the topology model, where the system components are defined as state nodes in the DBN.

[0098] The complex system described here uses a system with 10 components as an example for system modeling and DBN structure construction: S11. Perform physical topology mapping of complex systems; obtain, for example... Figure 3 The diagram shows a 10-node network topology for a 10-component system, where each component of the system is defined as a state node in the DBN, and each node in the network (numbered 1-10) is defined as a state node in the DBN.

[0099] S12. Define the state space and set the state recognition framework for each node as follows. ={Normal, Ineffective}.

[0100] S13. Define dependencies and construct the time-slice transition structure of DBN. Specifically, define it as: the state of any node i in the network at time t+1. Its parent node set includes the state of the node itself at time t. And the set of states of all its adjacent nodes at time t.

[0101] S2. The DBN structure is parameterized using evidence theory, and a conditional confidence table (CBT) is constructed for the DBN structure. The CBT defines the basic confidence assignment (BBA) of the child node state given the parent node state. For each node in the network topology, given the combination of parent node states, evidence of the node's state at the next time step is obtained from multiple heterogeneous information sources. The Dempster synthesis rule formula is used to merge the BBAs from multiple heterogeneous information sources into a unified BBA, and then fill it into the corresponding item of the conditional confidence table (CBT) of node 2.

[0102] Parameter learning based on evidence theory: This step constructs a Conditional Belief Table (CBT) to replace the traditional CPT. Taking node 2 in the network as an example, assume its parent node is... If a node is in a specific combination of states (e.g., node 1 fails, and the other parent nodes are normal), then the presence of node 2 is determined by fusing the following three types of heterogeneous evidence. BBA in real-time status: S21. For each node, given the combination of its parent node states, obtain evidence of its next state from at least two heterogeneous information sources.

[0103] Heterogeneous information sources include physical model evidence, historical data evidence, and expert knowledge evidence, among which: Physical model evidence: Based on the physical mechanism of network flow, the overload probability caused by the redistribution of load to node 2 after node 1 fails is calculated. This physical failure probability is mapped to a Basic Confidence Assignment (BBA) using the Sigmoid function, denoted as... .

[0104] For example: (Note: 0.3 is reserved for the entire series.) This indicates that there is uncertainty in the physical model parameters.

[0105] Historical data evidence: Based on historical statistical data, assuming similar operating conditions in the observation records, convert them to BBA, denoted as... .

[0106] For example: .

[0107] Expert knowledge evidence: Based on domain experts' empirical judgments on the robustness of node 2 itself (e.g., believing that the node is relatively fragile), a subjective reliability assessment is given, denoted as . .

[0108] For example: .

[0109] S22. Evidence Fusion: Using Dempster's rules of synthesis. The BBAs from the three sources mentioned above are merged into a unified BBA, and then filled into the corresponding item of the Conditional Trust Table (CBT) in node 2.

[0110] S3. Based on the DBN structure and CBT, perform time-series inference to dynamically calculate the reliability of the states of each component in the system, and evaluate the safety of the cascading effects of the system based on the reliability of the states. The evaluation result of the safety of the cascading effects of the system is output in the form of a reliability interval [Bel, Pl], where Bel is the reliability function value, Pl is the likelihood function value, and the width of the interval represents the degree of uncertainty of the evaluation result.

[0111] Step S3 of performing temporal inference includes iteratively executing the following sub-steps over consecutive time slices: Evidence-based dynamic reasoning and security assessment include: S31. Initialization: This refers to the initial evidence acquisition. The initial disturbance event is set as... Time node 1 failed (as shown in the attached document) Figure 3 (As shown). Transform this deterministic observation into an initial BBA: .

[0112] S32, Iterative Reasoning: This includes prediction and updating, encompassing: S321, Prediction at time t=1: Based on the failure evidence of node 1 at time t=0, and combined with the constructed CBT, the prior state confidence of its neighboring nodes (such as node 2 and node 3) at time t=1 is calculated using the evidence reasoning algorithm.

[0113] S322, Update at time t=1: Assuming there is no new external observation data at time t=1, the posterior reliability is directly adopted from the predicted prior reliability.

[0114] S33. Evaluation output and comparative analysis, including: S331, Output of Failure Reliability Interval: As attached Figure 4 As shown, after calculation, the failure risk of node 2 at time t=1 is output in the form of a confidence interval, based on... Figure 2 As shown in the module, [Bel, Pl] = [41.2%, 42.3%].

[0115] S332, Uncertainty Analysis: Compared to the single probability value provided by traditional DBN methods, the confidence interval output by this invention clearly demonstrates cognitive uncertainty (interval width 42.3% - 41.2% = 1.1%). Although the overall failure risk of node 2 is low, the existence of the confidence interval suggests that decision-makers may still be affected by minor fluctuations and should pay attention to this in the safety assessment.

[0116] Evolutionary trend: Over time (t=2, 3, ... Repeat the above steps. As shown in the table below, the method of this invention generates a dynamic risk "confidence channel". Compared with the single curve of traditional methods, this channel can cover the most optimistic and most pessimistic scenarios of risk evolution, providing decision-makers with a more inclusive safety assessment boundary. See Table 1 below for details.

[0117] Table 1. Changes in the confidence interval of each node over time.

[0118] As an embodiment of the present invention: As attached Figure 5 As shown, this embodiment is applied to the critical area of ​​aviation safety, specifically to conduct a cascade failure risk assessment of the fly-by-wire flight control system of a certain type of aircraft.

[0119] S1. System Modeling and DBN Structure Construction: S11, Physical Topology Mapping: Obtain the physical connection topology of the flight control system and map it to a DBN structure.

[0120] Based on the characteristics of the aircraft's operating conditions and flight control system, the network topology or CBT parameters are dynamically adjusted according to the flight envelope (such as angle of attack and Mach number). Specifically: Variable-structure DBN: For example, during high angle-of-attack maneuvers, strongly coupled fault propagation paths are activated; during cruise, these connections are weakened or a simpler model is used. This involves setting "gating conditions" for certain causal edges.

[0121] For example: Sensor drift → [Gating: Activated only in M3 (approach)] → PIO (Pilot-Induced Oscillation) Because sensor noise can easily trigger PIO during approach and landing; however, the path is broken during cruise. In the DBN inference engine, the weights in the adjacency matrix are dynamically adjusted (set to 0 or 1) based on the current Flight_Mode.

[0122] CBT parameter dynamic switching: Keep the topology unchanged, but the conditional confidence table (CBT) of the node is a function of the flight state.

[0123] For example: a decrease in hydraulic pressure leads to a delay in servo motor response; M1 (cruising) CBT: P (delay | voltage drop) = 0.2 (weak correlation); M2 (high angle of attack) CBT:BBA (latency | voltage drop) = {m (severe latency) = 0.8, m (stuck) = 0.2} (strong correlation); Implementation method: Create a lookup table or parameterized function for CBT=f(Flight_Mode).

[0124] The core characteristic of fly-by-wire flight control systems is that the control law and system redundancy management strategy change in real time according to the flight envelope. Therefore, the same fault can have drastically different consequences at different stages.

[0125] During the cruise phase (envelope center): aerodynamic linearity is good, rudder effectiveness is ample, and the control law primarily prioritizes comfort and economy. At this stage, a single sensor failure may be handled solely by the redundancy system, without creating a cascading effect.

[0126] High angle of attack / edge maneuvers (edge ​​of the envelope): airflow separation, reduced rudder effectiveness, control law switches to stability augmentation mode, and servo motors are prone to saturation. At this time, even minute sensor drifts are amplified by erroneous control laws, which may cause violent servo motor oscillations, thereby inducing structural resonance or pilot-induced oscillation (PIO), forming a fatal cascade.

[0127] Therefore, only by allowing the DBN topology / CBT parameters to switch synchronously with the flight status can this condition-dependent fault propagation be accurately characterized.

[0128] S12, Node Definition: Define the Inertial Reference Unit (IRU), Flight Control Computer (FCC), and Actuator Control Electronic Module (ACE) as state nodes of the DBN.

[0129] S13. Dependency definition: For example, define the timing dependency based on the signal flow (IRU→FCC→ACE). The state of FCC at time t+1 depends on its own state at time t and the input state of its upstream node IRU at time t.

[0130] S2. Construction of CBT based on evidence theory: For different node characteristics, heterogeneous information sources are collected, and a conditional confidence table (CBT) is constructed using Dempster's composition rules, as shown in the appendix. Figure 6 As shown: S21. For FCC nodes (integrating expert and physical evidence): Considering the complex Fault Detection and Isolation (FDI) logic within the FCC, expert knowledge evidence is primarily used. Engineers provide a Basic Confidence Assignment (BBA) for the success rate of FDI logic judgments, quantifying the cognitive uncertainty regarding "incomplete software logic coverage".

[0131] S22. For ACE nodes (fusion data evidence): Historical data evidence is used to derive BBA based on statistical analysis of hardware-in-the-loop (HIL) test data from a limited sample, in order to compensate for the scarcity of actual flight failure data.

[0132] Furthermore, a large number of "virtual fault injection experiments" are conducted using a high-fidelity flight control digital twin model to automatically learn and calibrate CBT parameters, addressing the problem of scarce actual fault data. This also verifies whether the propagation paths under different modes meet expectations.

[0133] S23, Fuzzy-Evidence Hybrid Modeling; Innovation: In CBT construction or BBA generation, fuzzy logic can be combined to handle continuous and fuzzy states such as performance degradation ("servo efficiency drops by 30%), rather than just handling discrete faults.

[0134] S24. Parameterization: The evidence from heterogeneous sources is fused to generate CBT for each node. At this point, the values ​​in the table are no longer single probabilities, but rather confidence assignments that include a set of uncertainties (such as θ).

[0135] First, a system-level recognition framework is defined as the "common language" for all fuzzy and discrete evidence, mapping all fuzzy and discrete evidence into common language evidence. Then, an independent BBA is generated for each evidence source and fused using Dempster's combination rules.

[0136] Furthermore, when fusing the evidence from heterogeneous sources, an adaptive evidence combination rule can be adopted. That is, when there is serious conflict in the sensor evidence (such as one saying "normal" and another saying "faulty"), the Dempster rule is not used blindly. Instead, the weights of each sensor are dynamically adjusted. Specifically, the credibility of the sensor is calculated based on historical accuracy or real-time consistency, and a weighted combination strategy such as PCR5 and Murphy averaging rule is used.

[0137] S3. Evidence-based dynamic reasoning and security assessment: S31. Initialization (Initial Evidence Acquisition): The scenario is set as a soft fault where the IRU experiences intermittent data "jumps". Due to sensor noise interference, the initial observations have high uncertainty. The system converts this initial disturbance into the following Basic Confidence Assignment (BBA): ; Note: A confidence level of 0.3 is reserved for the entire set θ here, which accurately expresses the cognitive uncertainty that "the current evidence is insufficient to fully confirm the state".

[0138] S32, Iterative Reasoning and Evaluation Output (Time t=1): S321, Process: Failure risk propagates from IRU1 to the downstream FCC. Evidence propagation prediction is performed based on FCC's CBT.

[0139] S322, Output: The calculated fault confidence interval for FCC at time t=1 is [Bel, Pl]=[0.08, 0.35].

[0140] Analysis: This interval indicates that although the lower bound for certainty of failure (Bel) is only 0.08, its upper bound for likelihood (Pl) is as high as 0.35. This accurately captures the system state of "high potential risk despite weak direct evidence." In contrast, traditional probabilistic methods may only give an averaged low probability value (such as 0.071), leading to missed risks.

[0141] S33, Iterative Reasoning and Evaluation Output (at time t=2): S331, Process: Uncertainty propagates further to the end-effector ACE.

[0142] S332, Output: The confidence interval for ACE failure calculated by this invention is [Bel, Pl] = [0.01, 0.15].

[0143] Beneficial effects: Even with a very low lower confidence limit (0.01), the plausibility upper limit of 0.15 provides effective early warning based on the "worst-case" scenario for safety-critical systems. The interval width (0.15-0.01=0.14) intuitively characterizes the accumulation of cognitive uncertainty in system state assessment as the cascade depth increases, suggesting the need to introduce more external observations to reduce uncertainty.

[0144] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A cascade effect security assessment method based on dynamic Bayesian networks and evidence theory, characterized in that, It includes the following steps: S1. Obtain the topology model of the system and construct a dynamic Bayesian network (DBN) structure based on the topology model. The components of the system are defined as state nodes in the DBN structure, and the dependencies between components are defined as the transition dependencies between different time slices of the DBN structure. S2. The DBN structure is parameterized using evidence theory, and a conditional confidence table (CBT) is constructed for the DBN structure. The CBT defines the basic confidence assignment (BBA) of the child node state given the parent node state. S3. Based on the DBN structure and CBT, perform evidence-based dynamic temporal reasoning to dynamically calculate the confidence level of each component state in the system, and output the confidence level of the state. Reliability interval [ , The system's cascading effect safety is assessed; among which, [ , [ ] represents the failure confidence interval of node i at time t. .

2. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 1, characterized in that, middle: ； ； in, and To preserve some of the impact of the node's historical state; and The impact of static reliability on the fusion of multi-source evidence; and Transmit influence to neighbors; As a historical inertia weight, For nodes exist Trust level at all times As the benchmark evidence weight, The baseline confidence level is calculated by CBT. The baseline likelihood is calculated by CBT. For topological coupling weights, For nodes exist Trust level at all times; For nodes exist The likelihood at time j is the number of nodes. The adjacent nodes that have an impact For nodes The set consisting of all adjacent nodes.

3. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 1, characterized in that, S2 include: S21. For each node in the DBN structure, given the combination of its parent node states, obtain evidence of its next state from multiple heterogeneous information sources. S22. Using Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a Basic Reliability Assignment (BBA). The BBA is then used as an item in the Conditional Reliability Table (CBT) to construct the Conditional Reliability Table (CBT) for the DBN structure.

4. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 3, characterized in that, S22 includes: S221. Modeling and preprocessing of multiple heterogeneous information sources; S222. Based on Dempster's synthesis rules, evidence from multiple heterogeneous information sources is fused to generate a Basic Reliability Assignment (BBA). S223. The fused basic reliability assignment (BBA) is used as an item in the CBT to construct the conditional reliability table (CBT) for the DBN structure.

5. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 4, characterized in that, The evidence in S22 comes from multiple heterogeneous sources, including physical model evidence, historical data evidence, and expert knowledge evidence.

6. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 1, characterized in that, S3 include: S31. Obtain the initial perturbation event of the current time slice as initial observation evidence and convert it into a basic confidence assignment (BBA). S32. For each time step from t to t+1, the iterative inference alternately executes the prediction and update sub-steps. If new observational evidence is obtained in the next time slice, the prior state confidence is fused with the new observational evidence to obtain the posterior state confidence of the next time slice node. S33. The state confidence of each node at any given time is expressed as a confidence interval composed of the confidence function (Belief) and the likelihood function (Plausibility). , The output is presented in the form of [], thereby enabling dynamic assessment and prediction of the risk of cascading effect propagation.

7. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 6, characterized in that, S31 includes: S311. Obtain the initial disturbance event, which is an abnormal signal that deviates from the normal steady state of the system; S312. Perform evidence mapping to transform quantitative data into qualitative reliability. Mapping methods include: Based on the membership function, the membership degree of the observed values ​​to each proposition is calculated, and evidence mapping is performed: a fuzzy membership function is constructed; based on the probability density distribution, the probability likelihood of the observed values ​​under each category condition is calculated and normalized, and evidence mapping is performed: using the probability density function PDF obtained from historical data statistics, the probability likelihood of the observed values ​​under each category condition is calculated and normalized; evidence mapping is performed based on direct correspondence with expert rules. S313. After the evidence mapping transformation is completed, output the BBA vector of the node at time t.

8. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 6, characterized in that, The prediction sub-steps performed in S32 include: P1: Obtain the basic confidence assignment (BBA) for each node at time t; P2: Inject the basic confidence assignment (BBA) of each node at time t into the corresponding clique node of the CBT clique tree structure; perform evidence propagation and state update to obtain the posterior state confidence at time t; P3: Construct a time-invariant cluster tree structure; P4: Forward message passing and prediction based on cluster trees.

9. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 6, characterized in that, The update sub-steps executed in S32 include: if new observational evidence is obtained at time t+1, the Dempster synthesis rule is used to fuse the prior state confidence with the new observational evidence to obtain the posterior state confidence of the node at time t+1.

10. The cascade effect security assessment method based on dynamic Bayesian networks and evidence theory according to claim 8, characterized in that, P4 includes: P41. The system extracts the marginal distribution of the interface variable from the clique tree at time t; the interface variable is the key variable connecting the two time slices, and its state information is passed to the next time slice. P42. Along the edge connecting time slice t and time slice t+1 in the clique tree, send the prepared message from the clique node at time t to the clique node at time t+1. P43. The clique node at time t+1 receives the message from time t and combines it with its own prior potential. Using the state transition probability defined in DBN, it realizes the state prediction from t to t+1 through the message passing mechanism. P44. Normalize the potential energy in the clique nodes at time t+1 to obtain the prior state confidence distribution of each node at that time.

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