MDD-based adaptive competition failure modeling and analysis method for multi-stage task system

Abstract

The invention discloses an MDD-based multi-stage task system adaptive competitive failure modeling and analysis method, which comprises the following steps: dividing a system component set, constructing a dynamic fault tree model containing communication mode adaptive switching logic, separating global propagation fault events of non-probabilistic function dependent components, and establishing a multi-stage task system adaptive competitive failure model. Constructing a trigger component fault event space and a fault isolation event set, distinguishing failure competition results, simplifying the model, establishing an MDD model, finally calculating the overall failure probability of the system, and establishing a fault isolation event through a dynamic topology modeling mechanism, a probabilistic competition failure model and an MDD unified modeling structure. According to the method, the dynamic topological coupling and probabilistic competition failure modeling problem and the computational efficiency bottleneck are solved, efficient and accurate analysis of the system reliability under the dynamic task profile is achieved, and the method is suitable for multi-scene task reliability design.

Description

Technical Field

[0001] This invention relates to the field of multi-stage task system technology, and in particular to an adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD. Background Technology

[0002] Multi-stage task systems are complex systems that divide the overall task into multiple sequential execution stages. Each stage may differ in system configuration, operating environment, component states, and failure mechanisms. All stages must be completed sequentially to achieve the task objective; failure in any stage will lead to the overall task failure. In the reliability analysis of such systems, the core challenges lie in accurately describing the migration and coupling relationships of functional logic between different task stages, and characterizing the probabilistic competition behavior of failure isolation and propagation effects caused by the timing differences between local and globally propagated failures among dependent components. Multi-valued decision diagrams (MDDs), as an extension of binary decision diagrams, allow variables to take multiple values, naturally representing the various states of components at different stages. This effectively avoids the model size explosion problem caused by binary decision diagrams due to binary decomposition, making it an efficient tool for modeling multi-stage task systems.

[0003] The existing technology has significant drawbacks: First, the existing solutions are based on static communication topology assumptions and fail to consider the adaptive switching of communication modes driven by task processes. They assume that when the relay component is working normally, the dependent components always connect to the aggregation node through it, ignoring the dynamic changes in the distance between the dependent components and the aggregation node and the adaptive characteristics of the task scenario. This fails to truly reflect the actual working state of the system when it selects direct connection or relay mode based on real-time conditions under fault-free conditions. Second, the static topology assumptions lead to distorted competition failure modeling. In a dynamic topology environment, the competition relationship between local failures of relay components and global propagation failures of dependent components is not deterministic, but related to the probability of communication mode switching. Existing methods mistakenly classify this as a deterministic event, which leads to deviations in the estimation of system failure probability and results in reliability assessments that do not match reality. Summary of the Invention

[0004] To overcome the shortcomings and deficiencies of existing technologies, this invention provides an adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD.

[0005] The technical solution adopted in this invention is an adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD, comprising the following steps: S1, dividing system components into a set of probabilistic functionally dependent components and a set of non-probabilistic functionally dependent components, clarifying the occurrence characteristics of local failures and global propagation failures of each component and the task stage division; S2, constructing a dynamic fault tree model of the multi-stage task system, embedding adaptive switching logic for communication modes, and determining the switching rules between direct connection mode and relay mode based on the real-time topology relationship between components and task stage parameters; S3, separating global propagation failure events of non-probabilistic functionally dependent components, and defining the mutually exclusive event boundaries between normal system operation and global collapse; S4, constructing a fault event space for triggering components, including all mutually exclusive sub-events of triggering components experiencing local failures at each stage and those without local failures throughout the entire process; S5, defining a set of fault isolation events for different triggering component fault events, distinguishing the competitive results dominated by failure propagation effects and failure isolation effects, simplifying the dynamic fault tree model and establishing a corresponding multi-valued decision graph model; S6, calculating the occurrence probability and conditional failure probability of each event through the multi-valued decision graph model, and integrating them to obtain the overall failure probability of the multi-stage task system.

[0006] Furthermore, the probability that a globally propagated fault in a non-probabilistic function-dependent component has not occurred is calculated using the following formula: ,in, This represents a set of non-probabilistic, function-dependent components. Indicates components No global propagation failures occurred at any stage of the entire mission. Indicates the probability of an event occurring; component in the first... The probability of a local failure or a globally propagated failure occurring in a phase satisfies: ,in, Indicates components In the The probability of a local or global propagation failure occurring during a phase. Indicates the first The duration of the phase Indicates components The failure time probability density function for local faults or globally propagated faults. Indicates the first Phase system operational load intensity, Indicates the first Scale of the execution environment for the phased tasks This represents the functional relationship between the duration of a phase and the load intensity and environmental scale.

[0007] Furthermore, the overall failure probability of a multi-stage task system is calculated using the following formula: PMS failure PMS failure PMS failure , Where Pr(PMSfailure) represents the overall system failure probability. failure This represents the conditional probability of system failure when there is no globally propagated fault in a non-probabilistic function-dependent component. failure This represents the conditional probability of system failure when a globally propagated fault occurs in a non-probabilistic, function-dependent component. This indicates that no globally propagated failure has occurred in any of the non-probabilistic, function-dependent components. This indicates an event in which a globally propagated failure occurs in any non-probabilistic, function-dependent component.

[0008] Furthermore, the probability of conditional failure is calculated using the following formula: ,in, This represents the probability of system conditional failure when there is no globally propagated fault in a non-probabilistic function-dependent component. This indicates the total number of task phases. Indicates the triggering component in the first Sub-events in a phase where a partial fault occurs or where there is no partial fault throughout the entire process. Indicates an event The probability of occurrence Indicates an event The conditional probability of system failure when it occurs.

[0009] Furthermore, when the triggering component has no partial fault, the relevant probabilities satisfy: ,in, This indicates an event that triggers a component without any localized faults throughout its entire lifecycle. This indicates an event where the triggering component has no local faults and none of the probabilistically dependent components have globally propagated faults. This indicates an event in which the triggering component has no local faults and at least one probabilistic functionally dependent component experiences a globally propagated fault. This represents a set of probabilistically functionally dependent components.

[0010] Furthermore, the triggering component in the first When a local fault occurs during a phase, the probability of the fault isolation event and related calculations satisfy: ; ; in, Indicates the first The first stage when a component's partial failure is triggered A fault isolation event, This represents the set of probabilistically functionally dependent components that have been successfully isolated. Indicates triggering component isolation component The probability, This indicates the total number of probabilistically functionally dependent components. This indicates an event where the failure isolation effect is dominant. This indicates an event where the failure propagation effect is dominant. Indicates an event The conditional probability of system failure when it occurs.

[0011] Furthermore, S2 includes the following sub-steps: S21, sorting out the component configuration, operating environment and failure mechanism of each stage of the multi-stage task system, and clarifying the functional logic and reliability requirements of each stage; S22, analyzing the relative position change law of probabilistic functionally dependent components and convergence nodes, and determining the threshold conditions and triggering criteria for communication mode switching; S23, integrating adaptive switching logic into the dynamic fault tree model, and associating component failure paths under different communication modes through logic gates; S24, defining the variable value rules of the multi-value decision graph, and incorporating component status, communication mode, and stage identifier as multi-value variables into the modeling framework.

[0012] Further, S3 includes the following sub-steps: S31, identifying the global propagation fault characteristics of non-probabilistic functionally dependent components and clarifying the impact path of their failure on the overall system; S32, defining the event boundaries of the occurrence and non-occurrence of global propagation faults of non-probabilistic functionally dependent components, ensuring that the two types of events are mutually exclusive and exhaust all possibilities; S33, determining the probability that each non-probabilistic functionally dependent component has no global propagation fault at each stage based on the component failure time distribution and stage parameters; S34, integrating the probabilities of all non-probabilistic functionally dependent components having no global propagation faults through product operations to obtain the joint probability that the event did not occur.

[0013] Further, S4 includes the following sub-steps: S41, analyze the occurrence pattern of local faults of the triggering component, and clarify the probability of local faults occurring in each stage and the persistence of the failure state; S42, define the sub-events in which the triggering component has no local faults throughout the entire process, and the sub-events in which a local fault occurs for the first time in each stage; S43, verify the mutual exclusivity and exhaustiveness of all sub-events, and construct a complete fault event space for the triggering component; S44, calculate the probability of each sub-event occurring based on the failure parameters of the triggering component and the stage duration.

[0014] Further, S5 includes the following sub-steps: S51, for each triggering component failure sub-event, define all possible failure isolation events based on the isolation status of probabilistic functionally dependent components; S52, based on the failure occurrence sequence and topology reconstruction results, distinguish between the competing results dominated by failure propagation effect and failure isolation effect; S53, remove the probabilistic functionally dependent gates and triggering components from the dynamic fault tree model, and logically assign values ​​to the states of relevant components according to the isolation events to obtain a simplified fault tree model; S54, transform the simplified fault tree model into a multi-valued decision graph model, define node values ​​and edge probabilities, and construct a complete symbolic modeling structure.

[0015] Beneficial Effects: This invention proposes an adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD (Multi-Dimensional Data Structure). By associating task stage runtime variables with component topology relationships, it achieves dynamic selection between direct connection and relay modes, realistically reflecting the reconfiguration behavior of communication links during the task process, and solving the reliability coupling problem of stage migration and topology switching. Addressing the distortion in probabilistic competitive failure modeling under dynamic topology, it constructs a time-series probabilistic model, incorporating communication mode switching probabilities and topology reconfiguration conditions into the reasoning framework. This accurately quantifies the competitive relationship between local faults in relay components and global propagation faults in dependent components, avoiding deterministic misjudgments of failure isolation and propagation effects. Facing the bottleneck of low computational efficiency in traditional methods, this method uses MDD as a unified modeling structure, directly embedding multi-state variables without binarization decomposition, reducing model size expansion and computational redundancy. Simultaneously, by simplifying the fault tree model and reusing isomorphic subgraphs, it significantly improves the efficiency of reliability analysis for complex multi-stage task systems, balancing modeling accuracy and engineering application timeliness, providing strong support for reliability design in multiple scenarios. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall steps of the method of the present invention; Figure 2 This is a flowchart of method step S2 of the present invention; Figure 3 This is a flowchart of method step S3 of the present invention; Figure 4 This is a flowchart of method step S4 of the present invention; Figure 5 This is a flowchart of step S5 of the method of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] like Figure 1As shown, the adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD begins with inputting key parameters of system components, including the occurrence time of local and globally propagated failures, failure propagation time, and isolation parameters. Based on this input data, the failure probability and probabilistic failure isolation probability of the components at each stage are calculated. The core processing stage then begins by separating globally propagated failure events of non-probabilistic functionally dependent components, clarifying the boundary between normal system operation and global collapse. Next, a fault event space for triggering components is constructed, including all mutually exclusive sub-events, covering all cases where the triggering component experiences local failures at each stage and no local failures throughout the entire process. Then, by determining whether the stage identifier corresponding to the triggering component failure event is zero, path-specific processing is performed: when the stage identifier is zero, the probability of the event and the corresponding system failure probability are calculated; when the stage identifier is non-zero (from 1 to H-1 and then to H), a failure isolation event is first constructed, then two types of events—those dominated by failure isolation effects and those dominated by failure propagation effects—are distinguished, and their relevant probabilities and conditional failure probabilities are calculated respectively, thus obtaining the contribution value of the triggering component failure event to the system failure probability. After calculating the contribution values ​​of all triggering component failure events, the system conditional failure probability is obtained by summing them up. Finally, combined with the event probability of non-probabilistic functionally dependent components having no globally propagated failures, the overall failure probability of the multi-stage task system is calculated. The process ends here, including the following steps: S1, divide the system components into a set of probabilistic function-dependent components and a set of non-probabilistic function-dependent components, and clarify the occurrence characteristics of local faults and global propagation faults of each component and the division of task stages; Specifically, step S1 categorizes and defines the system components and outlines their basic characteristics, providing clear analytical objects and data support for subsequent modeling. First, based on the functional dependencies of components within the system, all system components are strictly divided into a set of probabilistically dependent components and a set of non-probabilistically dependent components. This categorization process must consider whether a component has the potential to propagate a global fault through the isolation of other component failures. The classification result is determined by verifying the functional association attributes and fault impact range of each component. Second, the occurrence characteristics of local and globally propagated faults for each component are clarified. Key parameters such as the fault occurrence time distribution type, mean time between failures (MTBF), and fault repair characteristics (in this system, components are defined as unrepairable) need to be collected. Simultaneously, local faults are defined as fault types that only affect the component's own function, while globally propagated faults are fault types that can spread to other components and potentially cause system collapse. Finally, determining the task phase division requires considering factors such as the task execution process logic, environmental change nodes, and function switching requirements. It is necessary to clarify the number of task phases (usually set to 2 to 10 phases, adjusted according to the actual task complexity), the basis for dividing each phase, and the boundary conditions. At the same time, the preset duration range of each phase, the main task objectives and component operation requirements within the phase should be recorded to ensure that subsequent analysis can accurately match the system state at different phases.

[0019] S2, construct a dynamic fault tree model for a multi-stage task system, embed adaptive switching logic for communication modes, and determine the switching rules between direct connection mode and relay mode based on the real-time topology relationship between components and the parameters of the task stage. Specifically, step S2 involves constructing a dynamic fault tree model and embedding communication mode switching logic to achieve preliminary modeling of the system's dynamic behavior. When constructing the dynamic fault tree model for a multi-stage task system, it is necessary to first clarify the logical relationships between components, determining that the top event of the fault tree is overall system failure, intermediate events are combinations of failures in subsystems or key components, and bottom events are local failures of individual components or global propagation failures. Logic gates (such as OR gates, AND gates, and probabilistic functional dependency gates) are used to link these events, clarifying the triggering conditions for different fault paths. Subsequently, the adaptive communication mode switching logic is embedded. This requires setting core parameters for switching decisions, including distance thresholds between dependent components and the aggregation node (set according to the communication technology type; for example, wireless communication can be set to different threshold ranges from 100 meters to 5000 meters), channel quality assessment indicators (such as signal-to-noise ratio and critical values ​​for bit error rate), component remaining energy thresholds, etc., and establishing a switching decision rule base. When determining the switching rules between direct connection mode and relay mode based on the real-time topology relationship between components and the parameters of the task stage, it is necessary to collect dynamic parameters such as the relative distance between dependent components and the aggregation node, the channel fading coefficient, and the transmission delay in real time. Combined with parameters such as the load intensity and environmental scale of the current task stage, the optimal communication mode is determined through preset conditions in the rule base to ensure that the switching logic can respond to the dynamic changes in the topology during the task process, so that the model is close to the actual operating state of the system.

[0020] S3 separates the globally propagated fault events of non-probabilistic function-dependent components and defines the mutually exclusive event boundary between normal system operation and global crash. Specifically, step S3 isolates globally propagated fault events from non-probabilistic functionally dependent components, clarifying the core boundary conditions for system failure. First, it is necessary to accurately identify the characteristics of globally propagated faults in non-probabilistic functionally dependent components. A significant characteristic of these components is that their globally propagated faults cannot be isolated from local faults in other components. Once a globally propagated fault occurs, it will directly spread to the entire system, causing task interruption. Based on this characteristic, by analyzing the component's fault propagation path, simulating the scope of impact, and verifying the possibility of fault isolation, the triggering conditions, propagation speed, and degree of impact of globally propagated faults in non-probabilistic functionally dependent components are clarified. Subsequently, the mutually exclusive event boundaries between normal system operation and global crash are defined. A normal system operation event requires that no global propagation failure occurs in any non-probabilistic functional dependent component, and that the failure of other components does not form a fault chain leading to system failure. A global crash event is defined as any non-probabilistic functional dependent component experiencing a global propagation failure. The definition of this boundary must be rigorously verified to ensure that the two types of events are mutually exclusive and exhaust all possible system states, providing a clear basis for event division for subsequent probability calculations. At the same time, parameters such as the statistical range and historical data interval of the probability of global propagation failure of non-probabilistic functional dependent components must be recorded to provide data support for subsequent calculations.

[0021] S4, construct the fault event space of the triggering component, including all mutually exclusive sub-events of the triggering component when a partial fault occurs in each stage and when there is no partial fault throughout the entire process; Specifically, step S4 completes the construction of the fault event space for triggering components, comprehensively covering all possible fault states of the triggering components. First, the definition and selection criteria for triggering components are clarified. Triggering components are key components in the system that trigger the fault behavior of probabilistically functionally dependent components, typically relay components, control components, etc. The selection process needs to consider parameters such as the component's position in the functional dependency chain and the degree of impact of the fault on other components. Then, based on the task phase division results, a fault event space including H+1 mutually exclusive sub-events (H is the total number of task phases) is constructed. One sub-event occurs when the triggering component does not experience a local fault throughout the entire task. The remaining H sub-events correspond to the triggering component not experiencing a local fault in the first h-1 phases, and experiencing a local fault only in the h-th phase (h ranges from 1 to H), respectively. During the construction process, the time boundaries of each sub-event need to be clarified, i.e., the start and end times of each phase. Combining the local fault occurrence time distribution parameters of the triggering component and the phase duration, the logical definition and occurrence conditions of each sub-event are determined. At the same time, it is necessary to verify the mutual exclusivity and exhaustiveness of each sub-event to ensure that there is no overlap and that all possible local fault occurrences of the triggering component are covered. The description of each sub-event should include key information such as the stage of the fault occurrence and the initial state, so as to lay the foundation for subsequent analysis of system behavior under different fault scenarios. At the same time, parameters such as the local fault probability of the triggering component and the state persistence after the fault occur should be recorded.

[0022] S5. For different triggering component failure events, define a set of failure isolation events, distinguish between the competing results dominated by failure propagation effect and failure isolation effect, simplify the dynamic fault tree model and establish a corresponding multi-value decision graph model. Specifically, step S5 handles competing failure behaviors under different triggering component failure events, completing model simplification and multi-valued decision graph construction. For each triggering component failure sub-event, a set of failure isolation events is defined based on the difference in the triggering component's isolation capability for each probabilistic functionally dependent component. Each isolation event corresponds to a specific combination of probabilistic functionally dependent components being isolated, and the number of isolation events is 2 to the power of N (N is the total number of probabilistic functionally dependent components). During the definition process, parameters such as the set of isolated components and the probability of successful isolation for each isolation event must be clearly defined. Subsequently, based on the temporal relationship of the failure occurrence and the topology reconstruction result, the competitive outcome of failure propagation effect and failure isolation effect is distinguished. The judgment criteria are the order of occurrence of the local failure of the triggering component and the global propagation failure of the probabilistic functionally dependent component, the success probability of topology reconstruction, and the feasibility of communication mode switching of dependent components. When the propagation failure occurs first or the topology reconstruction fails, the failure propagation effect dominates; when the local failure occurs first and the topology reconstruction is successful, the failure isolation effect dominates. Next, the dynamic fault tree model is simplified by removing probabilistic functional dependency gates and triggering components. Variables of isolated components at corresponding stages are logically assigned values, resulting in a simplified fault tree model. Finally, a multi-valued decision graph method is used to model the simplified model. Component states, stage identifiers, and communication modes are embedded as multi-valued variables at the decision layer level. Node value rules and edge probability weights are defined to construct a symbolic model structure that can uniformly express stage states, topology switching, and competition failure results. During modeling, it is necessary to ensure that the layer order of the multi-valued decision graph is consistent with the task stage progress, supporting dynamic expansion and parameter adjustment of the model.

[0023] S6 calculates the probability of occurrence of each event and the probability of failure of each condition through a multi-valued decision graph model, and integrates them to obtain the overall failure probability of the multi-stage task system.

[0024] Specifically, step S6 uses a multi-valued decision graph model to perform various probability calculations, ultimately obtaining the overall system failure probability. This is the final and output stage of the entire analysis process. First, the probability of each event is calculated, including the probability of no globally propagated failure in non-probabilistic functionally dependent components, the probability of each triggering component failure sub-event, and the probability of each fault isolation event. This calculation requires accessing previously compiled component failure probability parameters, stage duration parameters, topology switching probabilities, and other data. Combining the structural characteristics of the multi-valued decision graph, the probability values ​​for each event are obtained through path traversal, probability multiplication, and summation. Care must be taken to ensure the correctness of the logical relationships and the consistency of the data during the calculation process. Second, the probability of conditional failure is calculated, i.e., the probability of system failure under specific event conditions. This requires traversing all paths leading to system failure based on a simplified multi-valued decision graph model, summing the edge probability products on the paths, and obtaining the conditional failure probabilities under different scenarios. Simultaneously, the reasonableness of the calculation results must be verified, and errors should be corrected by referring to historical data and simulation results. Finally, all calculation results are integrated, and the conditional failure probability is weighted and summed with the corresponding event occurrence probability according to the logical relationship of the events and the probability formula to obtain the overall failure probability of the multi-stage task system. During the integration process, the weight allocation and logical relationship of each probability parameter must be clearly defined. The final output of the overall failure probability should be accompanied by information such as the error range of the calculation process and the data source description to ensure the reliability and engineering applicability of the results. At the same time, failure probability decomposition results under different stages and different failure scenarios can be output as needed to provide more detailed reference for system optimization.

[0025] Preferably, the probability that a global propagation fault in a non-probabilistic function-dependent component has not occurred is calculated using the following formula: ,in, This represents a set of non-probabilistic, function-dependent components. Indicates components No global propagation failures occurred at any stage of the entire mission. Indicates the probability of an event occurring; component in the first... The probability of a local failure or a globally propagated failure occurring in a phase satisfies: ,in, Indicates components In the The probability of a local or global propagation failure occurring during a phase. Indicates the first The duration of the phase Indicates components The failure time probability density function for local faults or globally propagated faults. Indicates the first Phase system operational load intensity, Indicates the first Scale of the execution environment for the phased tasks This represents the functional relationship between the duration of a phase and the load intensity and environmental scale.

[0026] Specifically, the accurate calculation of the probability of no global propagation failure of non-probabilistic functionally dependent components and the probability of component stage failure provides fundamental data support for the overall system reliability analysis. When calculating the probability of no global propagation failure of non-probabilistic functionally dependent components, it is necessary to first clarify the specific composition of this type of component set, confirm the state in which each component has not experienced a global propagation failure in any stage throughout the entire task, and multiply the probabilities of all components satisfying this state to ensure coverage of the failure states of all non-probabilistic functionally dependent components. When calculating the probability of local or global propagation failure of a component in a specific stage, the stage duration is derived from the system operational load intensity and task execution environment scale of the corresponding stage through a preset functional relationship. The load intensity can be set to a quantization range of 0 to 100 based on the task's busyness and data processing volume, while the environment scale is set to a quantization standard of 1 to 50 based on the task's coverage area and the number of subsystems involved. Subsequently, based on the failure time probability density function of the component's local or global propagation failure, the probability of the corresponding failure of the component in this stage is solved by integral operation. The failure time probability density function is determined in combination with the component design parameters, material properties, and historical data of the operating environment. For example, the mean time between failures of the component is set to the range of 1,000 hours to 10,000 hours to ensure that the calculation results accurately reflect the failure risk of the component in a specific stage.

[0027] Preferably, the overall failure probability of a multi-stage task system is calculated using the following formula: PMS failure PMS failure PMS failure , Where Pr(PMSfailure) represents the overall system failure probability. failure This represents the conditional probability of system failure when there is no globally propagated fault in a non-probabilistic function-dependent component. failure This represents the conditional probability of system failure when a globally propagated fault occurs in a non-probabilistic, function-dependent component. This indicates that no globally propagated failure has occurred in any of the non-probabilistic, function-dependent components. This indicates an event in which a globally propagated failure occurs in any non-probabilistic, function-dependent component.

[0028] Specifically, the calculation logic for the overall failure probability of a multi-stage task system integrates the system failure probabilities under different states of non-probabilistic functionally dependent components to form a complete and reliable reliability assessment result. During the calculation, a strict distinction is first made between two mutually exclusive events: none of the non-probabilistic functionally dependent components experienced a global propagation failure, and any component experienced a global propagation failure. This ensures that both types of events exhaust all failure states of that type of component, guaranteeing the completeness and rigor of the calculation logic. For the event where any non-probabilistic functionally dependent component experiences a global propagation failure, since no other component's local failure can isolate its global propagation failure, its occurrence will directly lead to the overall system collapse; therefore, the system failure conditional probability for this event is fixed at 1. For the event where none of the non-probabilistic functionally dependent components experienced a global propagation failure, the system failure conditional probability needs to be calculated by considering factors such as the failure states of other components, communication mode switching, and competition failure results. This probability ranges from 0 to 1, and the specific value is derived comprehensively based on parameters such as component failure probability, topology switching probability, and isolation success probability. Finally, the failure probabilities and occurrence probabilities of the two types of events are integrated by weighted summation, where the weights are the occurrence probabilities of each type of event, to obtain the overall failure probability of the system. The value ranges from 0 to 1, and the closer the value is to 0, the higher the system reliability.

[0029] Preferably, the conditional failure probability is calculated using the following formula: ,in, This represents the probability of system conditional failure when there is no globally propagated fault in a non-probabilistic function-dependent component. This indicates the total number of task phases. Indicates the triggering component in the first Sub-events in a phase where a partial fault occurs or where there is no partial fault throughout the entire process. Indicates an event The probability of occurrence Indicates an event The conditional probability of system failure when it occurs.

[0030] Specifically, calculating the system conditional failure probability when no globally propagated failure occurs in non-probabilistic functionally dependent components provides key intermediate parameters for deriving the overall system failure probability. The calculation process first clarifies the total number of task stages, setting it to 2 to 10 stages based on actual task complexity. The division of each stage is determined according to the task execution flow, environmental change nodes, and functional switching requirements. Subsequently, a triggering component failure event space is constructed, including the total number of stages plus one mutually exclusive sub-event. This includes all cases where the triggering component does not experience a local failure throughout the entire task, and cases where no local failure occurs in the first few stages but only in specific stages. The probability of each sub-event is derived from the failure parameters of the triggering component. The probability of a local failure of the triggering component is calculated based on parameters such as its failure time distribution and stage duration. For example, the probability of a local failure of the triggering component in a single stage is set to the range of 0.01 to 0.1. The system failure conditional probability corresponding to each sub-event needs to be determined by considering factors such as the system topology, component failure state, and competitive failure results at the time of the sub-event, with a value ranging from 0 to 1. Finally, by performing a weighted summation operation, the probability of occurrence of each triggering component failure sub-event is multiplied by the corresponding system failure condition probability and then summed to obtain the system's conditional failure probability, which ranges from 0.1 to 0.5. This probability accurately reflects the risk level of system failure due to other factors when there is no globally propagated failure in non-probabilistic functionally dependent components.

[0031] Preferably, when the triggering component has no partial fault, the relevant probability satisfies: ,in, This indicates an event that triggers a component without any localized faults throughout its entire lifecycle. This indicates an event where the triggering component has no local faults and none of the probabilistically dependent components have globally propagated faults. This indicates an event in which the triggering component has no local faults and at least one probabilistic functionally dependent component experiences a globally propagated fault. This represents a set of probabilistically functionally dependent components.

[0032] Specifically, the probability calculations for triggering components without local faults are clearly defined, providing support for the accurate derivation of system conditional failure probabilities. When calculating the event probability of a triggering component without local faults and all probabilistically dependent components without global propagation faults, the event probability of the triggering component having no local faults throughout the entire task is first obtained. This probability is calculated based on parameters such as the failure time distribution of the triggering component and the total task duration. Then, the probability of each probabilistically dependent component not experiencing a global propagation fault in any stage of the entire task is confirmed. This probability is derived based on factors such as component failure parameters, stage duration, and topology switching, with the probability value for each component ranging from 0.6 to 0.99. The event probability of the triggering component having no local faults throughout the entire task is multiplied by the probability of all probabilistically dependent components having no global propagation faults, yielding the event probability of both the triggering component and probabilistically dependent components having no global propagation faults. The event probability of a triggering component having no local faults and at least one probabilistically dependent component experiencing a global propagation fault is obtained by subtracting the above product result from the event probability of the triggering component having no local faults throughout the entire task; this probability ranges from 0 to 0.4. Meanwhile, the system failure condition probability corresponding to an event in which the triggering component has no local faults and at least one probabilistically functionally dependent component experiences a globally propagated fault is fixed at 1. However, the system failure condition probability corresponding to an event in which the triggering component has no local faults and none of the probabilistically functionally dependent components experience a globally propagated fault needs to be derived by simplifying the fault tree model and establishing a multi-valued decision graph model, with a value range between 0 and 1.

[0033] Preferably, the triggering component is in the first When a local fault occurs during a phase, the probability of the fault isolation event and related calculations satisfy: ; ; in, Indicates the first The first stage when a component's partial failure is triggered A fault isolation event, This represents the set of probabilistically functionally dependent components that have been successfully isolated. Indicates triggering component isolation component The probability, This indicates the total number of probabilistically functionally dependent components. This indicates an event where the failure isolation effect is dominant. This indicates an event where the failure propagation effect is dominant. Indicates an event The conditional probability of system failure when it occurs.

[0034] Specifically, the calculation logic for the relevant probability when a triggering component experiences a partial failure at a specific stage provides a guarantee for the comprehensive derivation of the system condition failure probability. When calculating the probability of a fault isolation event, the total number of probabilistically functionally dependent components is first defined, set to 2 to 8. The isolation probability of each component is determined based on factors such as the isolation capability of the triggering component, topology conditions, and communication mode, with a value ranging from 0.1 to 0.9. Based on the isolation combinations of probabilistically functionally dependent components, 2 to the power of the total number of components are constructed as mutually exclusive fault isolation events, each event corresponding to a specific component isolation combination. The probability of each fault isolation event is obtained by multiplying the isolation probability of the isolated component by the non-isolation probability of the unisolated component, ensuring an accurate reflection of the likelihood of different isolation combinations occurring. When calculating the system failure probability contribution value when a triggering component failure event occurs, it is necessary to distinguish between two mutually exclusive sub-events dominated by failure propagation effect and failure isolation effect for each fault isolation event. The system failure conditional probability corresponding to the sub-event dominated by failure propagation effect is fixed at 1, while the system failure conditional probability corresponding to the sub-event dominated by failure isolation effect is derived by simplifying the fault tree model and establishing a multi-valued decision graph model, with a value ranging from 0 to 1. Finally, by summing the products of the two types of sub-event probabilities and the corresponding failure conditional probability for each fault isolation event, the system failure probability contribution value when the triggering component experiences a local failure at that stage is obtained. This value accurately reflects the degree of influence of this fault scenario on the overall system failure probability.

[0035] Preferred, such as Figure 2 As shown, S2 includes the following sub-steps: S21, sorting out the component configuration, operating environment and failure mechanism of each stage of the multi-stage task system, and clarifying the functional logic and reliability requirements of each stage; S22, analyzing the relative position change law of probabilistic functionally dependent components and convergence nodes, and determining the threshold conditions and triggering criteria for communication mode switching; S23, integrating adaptive switching logic into the dynamic fault tree model, and associating component failure paths under different communication modes through logic gates; S24, defining the variable value rules of the multi-value decision graph, and incorporating component status, communication mode, and stage identifier as multi-value variables into the modeling framework.

[0036] Specifically, step S2 includes four sub-steps, comprehensively covering the implementation process of dynamic fault tree model construction and communication mode switching logic embedding. S21, when reviewing component configuration, operating environment, and failure mechanisms at each stage, requires clarifying that the number of components in each stage ranges from 5 to 20, determining the operating parameter thresholds for each component, such as controlling the operating temperature between -20℃ and 60℃, and ensuring that the operating voltage fluctuation does not exceed ±5%. Simultaneously, it records the differences in failure mechanisms between different stages, such as stage one being primarily due to mechanical wear, and stage two being primarily due to electronic component aging. S22, when analyzing the relative positional changes between probabilistic functionally dependent components and the aggregation node, sets distance thresholds based on the communication technology type. In the channel quality assessment indicators, the signal-to-noise ratio critical value is set to 15 dB, the bit error rate critical value is set to 10⁻⁵, and the component remaining energy threshold is set to 20% of the total energy. Based on these parameters, a switching decision rule base including 10 to 20 rules is established. When constructing the dynamic fault tree model in S23, the overall system failure is taken as the top event. Intermediate events are divided into 3 to 5 categories according to subsystems, and the bottom events clearly define the two types of failures of individual components. Logic gates are used to associate each event, with probabilistic functional dependency gates used to characterize the relationship between dependent components and relay components. In defining the variable value rules for the multi-valued decision graph in S24, component states are divided into three categories: normal, local fault, and globally propagated fault. Communication modes are divided into two categories: direct connection and relay. Stage identifiers are numbered according to the task stage sequence, ensuring that variable values ​​can comprehensively cover all types of system operation states, providing a complete variable system for subsequent modeling.

[0037] Preferred, such as Figure 3 As shown, S3 includes the following sub-steps: S31, identifying the global propagation fault characteristics of non-probabilistic functionally dependent components and clarifying the impact path of their failure on the overall system; S32, defining the event boundary between the occurrence and non-occurrence of global propagation faults of non-probabilistic functionally dependent components, ensuring that the two types of events are mutually exclusive and exhaust all possibilities; S33, determining the probability that each non-probabilistic functionally dependent component has no global propagation fault at each stage based on the component failure time distribution and stage parameters; S34, integrating the probabilities of all non-probabilistic functionally dependent components having no global propagation faults through product operations to obtain the joint probability that the event did not occur.

[0038] Specifically, step S3 has four sub-steps, clarifying the separation process and boundary definition criteria for global propagation fault events of non-probabilistic functionally dependent components. S31, when identifying the characteristics of global propagation faults in non-probabilistic functionally dependent components, simulates the fault propagation path to determine the fault propagation speed range as 1 to 10 milliseconds. The impact level is divided into 100% based on the proportion of system components affected (i.e., the entire system is affected). Simultaneously, the possibility of fault isolation is verified, confirming that such components have no isolation pathways. The triggering conditions for their global propagation faults are recorded, such as voltage surges exceeding 10% or temperature exceeding a critical value for 5 seconds. S32, when defining the mutually exclusive event boundary between normal system operation and global collapse, clarifies that normal system operation requires that all non-probabilistic functionally dependent components have not experienced global propagation faults, and that faults in other components have not formed failure paths. A global collapse event is triggered by a global propagation fault in any non-probabilistic functionally dependent component. Logical verification ensures that the two types of events do not overlap and cover all possible states. S33 When determining the statistical range of the probability of global propagation failure for non-probabilistic function-dependent components, the failure probability range for a single component in a single stage is set to 0.001 to 0.05 based on historical data, and failure data from approximately 500 to 1000 tasks are collected as a reference. S34 When integrating the probabilities of no global propagation failure for all non-probabilistic function-dependent components, a product operation is used to calculate the failure-free probability of each component sequentially, ultimately obtaining the joint probability of the event not occurring, with a range of 0.8 to 0.99. During the calculation process, it must be ensured that the probability parameters of each component accurately correspond to the operating conditions of its respective stage.

[0039] Preferred, such as Figure 4 As shown, S4 includes the following sub-steps: S41, analyze the occurrence pattern of local faults of the triggering component, and clarify the probability of local faults occurring in each stage and the persistence of the failure state; S42, define the sub-events in which the triggering component has no local faults throughout the entire process, and the sub-events in which a local fault occurs for the first time in each stage; S43, verify the mutual exclusivity and exhaustiveness of all sub-events, and construct a complete fault event space for the triggering component; S44, calculate the probability of each sub-event occurring based on the failure parameters of the triggering component and the stage duration.

[0040] Specifically, step S4 consists of four sub-steps that standardize the construction process and parameter settings for the trigger component failure event space. S41: When selecting trigger components, score them based on their core position in the functional dependency chain (out of 100). Components scoring 80 or higher are selected as trigger components, typically relay components or control components. Simultaneously, determine the degree of their failure impact; that is, the number of probabilistic functionally dependent components that a single trigger component failure may affect is between 2 and 8. Record the local failure occurrence time distribution type of the trigger component, such as exponential distribution or Weibull distribution. S42: When defining trigger component failure sub-events, construct H+1 mutually exclusive sub-events based on the total number of task stages H. Define the time boundary of each sub-event, with stage start and end times accurate to the second according to the task plan. The sub-event description must include key information such as the failure occurrence stage and the initial state, such as "No local failure occurred in the first 3 stages, but a local failure occurred in the 4th stage." When verifying the mutual exclusivity and exhaustiveness of sub-events in S43, a logical matrix verification method is used to ensure that the intersection of any two sub-events is an empty set, and the union of all sub-events represents all possible fault states of the triggering component. The number of verification samples is no less than 100 sets. In S44, when recording the local fault probability of the triggering component, the local fault probability range for a single stage is set to 0.01 to 0.1. The persistence of the state after a fault occurs is the entire remaining task duration. Simultaneously, the mean time between failures (MTBF) of the triggering component is recorded as ranging from 1000 hours to 10000 hours, providing basic parameters for subsequent probability calculations.

[0041] Preferred, such as Figure 5 As shown, S5 includes the following sub-steps: S51, for each triggering component failure sub-event, define all possible failure isolation events based on the isolation status of probabilistic functionally dependent components; S52, based on the failure occurrence sequence and topology reconstruction results, distinguish between the competing results dominated by failure propagation effect and failure isolation effect; S53, remove the probabilistic functionally dependent gates and triggering components from the dynamic fault tree model, and logically assign values ​​to the states of relevant components according to the isolation events to obtain a simplified fault tree model; S54, transform the simplified fault tree model into a multi-valued decision graph model, define node values ​​and edge probabilities, and construct a complete symbolic modeling structure.

[0042] Specifically, step S5 has four sub-steps, clarifying the specific implementation methods for handling competition failure behavior, model simplification, and multi-valued decision graph construction. S51 defines the set of fault isolation events, constructing 2^N isolation events based on the total number N of probabilistically functionally dependent components. Each isolation event corresponds to a specific component isolation combination. The success probability range for isolation of a single component is set to 0.1 to 0.9, and the occurrence probability range for a single fault isolation event is also set to 0.1 to 0.9. This probability is determined comprehensively based on factors such as the triggering component's isolation capability, current topology conditions, and communication mode. At least 50 sets of data are obtained through experimental testing for calibration. S52 distinguishes competition results, using the fault occurrence time difference (accurate to milliseconds), the success probability of topology reconstruction (range 0 to 1), and the feasibility of communication mode switching (0 indicates infeasibility, 1 indicates feasibility) as judgment parameters. When the propagation fault occurs more than 10 milliseconds earlier than the local fault, or the success probability of topology reconstruction is less than 0.3, the failure propagation effect is considered dominant. When the local fault occurs earlier and the success probability of topology reconstruction is greater than 0.3, the failure isolation effect is considered dominant. When simplifying the dynamic fault tree model in S53, probabilistic functional dependency gates and triggering components are removed, and the variables of the isolated components in the corresponding stages are assigned logical "1". The simplified model has 30% to 50% fewer nodes than the original model, ensuring a simple model structure while maintaining the core logic. In S54, when constructing the multi-valued decision graph model, component states, stage identifiers, and communication modes are treated as multi-valued variables. The number of node values ​​is set to 3 to 5, and the probability weights of edges are determined based on previously calculated event probabilities. The layer order of the decision graph strictly follows the task stage progress, ensuring the model can dynamically respond to stage switching and topology changes, supporting efficient subsequent probability calculations. Finally, the proposed modeling approach and analysis method are numerically verified using the Monte Carlo method. 5 A random simulation experiment was conducted, and the experimental results were compared and analyzed with the simulation results. The results showed that the two had a high degree of consistency, and the mean of their relative error was stably distributed in the range of 0.0001 to 0.001, thus verifying the effectiveness of the method in terms of accuracy and reliability.

[0043] An adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD addresses the problem that static topology assumptions cannot characterize adaptive communication mode switching. It constructs a dynamic modeling mechanism based on the real-time topology relationship between task stages and components. By associating key operational variables with topology parameters, it achieves automated selection between direct and relay modes, realistically reflecting the dynamic reconfiguration of communication links as the task progresses, thus solving the reliability coupling problem between stage migration and topology switching. To address the distortion in probabilistic competitive failure modeling under dynamic topology, it incorporates communication mode switching probabilities and reconfiguration conditions into a temporal reasoning framework, accurately characterizing the dynamic competitive relationship between local faults in relay components and global propagation faults in dependent components. This makes failure isolation and propagation effects probabilistic events driven by real-time topology evolution, avoiding deterministic misjudgments. Addressing the bottleneck of low computational efficiency in traditional methods, it adopts a multi-valued decision graph as a unified modeling structure, directly embedding multi-state variables without binarization decomposition, effectively controlling model size expansion. Simultaneously, by simplifying the fault tree and reusing isomorphic subgraphs, it significantly reduces computational redundancy and substantially improves the efficiency of reliability analysis for complex systems.

[0044] The advantages of this method are reflected in a comprehensive improvement in modeling accuracy, adaptability, and engineering practicality. Its dynamic topology modeling mechanism breaks the limitations of traditional static dependency assumptions, enabling the system's operating mode to automatically adjust with stage evolution, making reliability assessment closer to real-world mission scenarios. The probabilistic competition failure model achieves precise quantification of complex fault propagation mechanisms, providing a reliable basis for system redundancy design and communication structure optimization. The integrated application of multi-valued decision graphs ensures model expressiveness while solving the computational complexity problem of multi-stage, multi-component systems, balancing analytical accuracy and timeliness. Through the synergy of multiple technological innovations, this method successfully achieves efficient and accurate modeling and analysis of the reliability of multi-stage mission systems under dynamic mission profiles, providing strong support for reliability design in various scenarios such as UAV swarms and satellite networks.

[0045] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0046] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An adaptive competitive failure modeling and analysis method for multi-stage task systems based on MDD, characterized in that, Includes the following steps: S1. Divide the system components into a set of probabilistic functionally dependent components and a set of non-probabilistic functionally dependent components, clarifying the occurrence characteristics of local faults and global propagation faults of each component, as well as the task stage division; S2. Construct a dynamic fault tree model for the multi-stage task system, embedding adaptive switching logic for communication modes, and determining the switching rules between direct connection mode and relay mode based on the real-time topology relationship between components and task stage parameters; S3. Separate global propagation fault events of non-probabilistic functionally dependent components, defining the mutually exclusive event boundaries between normal system operation and global collapse; S4. Construct a fault event space for triggering components, including all mutually exclusive sub-events of triggering components experiencing local faults at each stage and those without local faults throughout the entire process; S5. Define a fault isolation event set for different triggering component fault events, distinguishing between the competing results dominated by failure propagation effects and failure isolation effects, simplifying the dynamic fault tree model, and establishing a corresponding multi-valued decision graph model; S6. Calculate the occurrence probability and conditional failure probability of each event through the multi-valued decision graph model, and integrate them to obtain the overall failure probability of the multi-stage task system.

2. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, The probability that a globally propagated fault in a non-probabilistic function-dependent component has not occurred is calculated using the following formula: ,in, This represents a set of non-probabilistic, function-dependent components. Indicates components No global propagation failures occurred at any stage of the entire mission. Indicates the probability of an event occurring; component in the first... The probability of a local failure or a globally propagated failure occurring in a phase satisfies: ,in, Indicates components In the The probability of a local or global propagation failure occurring during a phase. Indicates the first The duration of the phase Indicates components The failure time probability density function for local faults or globally propagated faults. Indicates the first Phase system operational load intensity, Indicates the first Scale of the execution environment for the phased tasks This represents the functional relationship between the duration of a phase and the load intensity and environmental scale.

3. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, The overall failure probability of a multi-stage task system is calculated using the following formula: PMS failure PMS failure PMS failure , Where Pr(PMSfailure) represents the overall system failure probability. failure This represents the conditional probability of system failure when there is no globally propagated fault in a non-probabilistic function-dependent component. failure This represents the conditional probability of system failure when a globally propagated fault occurs in a non-probabilistic, function-dependent component. This indicates that no globally propagated failure has occurred in any of the non-probabilistic, function-dependent components. This indicates an event in which a globally propagated failure occurs in any non-probabilistic, function-dependent component.

4. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, The probability of condition failure is calculated using the following formula: ,in, This represents the probability of system conditional failure when there is no globally propagated fault in a non-probabilistic function-dependent component. This indicates the total number of task phases. Indicates the triggering component in the first Sub-events in a phase where a partial fault occurs or where there is no partial fault throughout the entire process. Indicates an event The probability of occurrence Indicates an event The conditional probability of system failure when it occurs.

5. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, When the triggering component has no partial fault, the relevant probabilities satisfy: ,in, This indicates an event that triggers a component without any localized faults throughout its entire lifecycle. This indicates an event where the triggering component has no local faults and none of the probabilistically dependent components have globally propagated faults. This indicates an event in which the triggering component has no local faults and at least one probabilistic functionally dependent component experiences a globally propagated fault. This represents a set of probabilistically functionally dependent components.

6. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, Triggering component in the When a local fault occurs during a phase, the probability of the fault isolation event and related calculations satisfy: ； ； in, Indicates the first The first stage when a component's partial failure is triggered A fault isolation event, This represents the set of probabilistically functionally dependent components that have been successfully isolated. Indicates triggering component isolation component The probability, This indicates the total number of probabilistically functionally dependent components. This indicates an event where the failure isolation effect is dominant. This indicates an event where the failure propagation effect is dominant. Indicates an event The conditional probability of system failure when it occurs.

7. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, S2 includes the following sub-steps: S21, sorting out the component configuration, operating environment and failure mechanism of each stage of the multi-stage task system, and clarifying the functional logic and reliability requirements of each stage; S22, analyzing the relative position change law of probabilistic functionally dependent components and convergence nodes, and determining the threshold conditions and triggering criteria for communication mode switching; S23, integrating adaptive switching logic into the dynamic fault tree model, and associating component failure paths under different communication modes through logic gates; S24, defining the variable value rules of the multi-value decision graph, and incorporating component status, communication mode, and stage identifier as multi-value variables into the modeling framework.

8. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, S3 includes the following sub-steps: S31, identifying the global propagation fault characteristics of non-probabilistic functionally dependent components and clarifying the impact path of their failure on the overall system; S32, defining the event boundary between the occurrence and non-occurrence of global propagation faults in non-probabilistic functionally dependent components, ensuring that the two types of events are mutually exclusive and exhaust all possibilities; S33, determining the probability that each non-probabilistic functionally dependent component has no global propagation fault at each stage based on the component failure time distribution and stage parameters; S34, integrating the probabilities of all non-probabilistic functionally dependent components having no global propagation faults through product operations to obtain the joint probability that the event did not occur.

9. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, S4 includes the following sub-steps: S41, analyze the occurrence pattern of local faults of the triggering component, and clarify the possibility of local faults occurring in each stage and the persistence of the failure state; S42, define the sub-events in which the triggering component has no local faults throughout the process, and the sub-events in which a local fault occurs for the first time in each stage. S43, verify the mutual exclusion and exhaustiveness of all sub-events, and construct the complete fault event space of the triggering component; S44, calculate the probability of each sub-event occurring based on the failure parameters of the triggering component and the stage duration.

10. The adaptive competition failure modeling and analysis method for multi-stage task systems based on MDD according to claim 1, characterized in that, S5 includes the following sub-steps: S51, for each triggering component fault sub-event, in combination with the isolation status of probabilistic functionally dependent components, define all possible fault isolation events; S52, Based on the fault occurrence sequence and topology reconstruction results, distinguish between the competing results dominated by the failure propagation effect and the failure isolation effect; S53, Remove the probabilistic functional dependency gates and triggering components in the dynamic fault tree model, and logically assign values ​​to the states of relevant components according to the isolation events to obtain a simplified fault tree model; S54, Transform the simplified fault tree model into a multi-valued decision graph model, define the node values ​​and edge probabilities, and construct a complete symbolic modeling structure.

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