A reliability modeling and prediction method for equipment system based on generalized effective OODA loop

Abstract

The present invention provides a reliability modeling and prediction method for equipment systems based on generalized effective OODA loops, providing theoretical and technical guidance for the definition, modeling, and prediction of equipment system reliability, thereby effectively improving the design capability and operational effectiveness of the equipment system. This method addresses the problems of high computational resource consumption, high cost, and low efficiency in the evaluation method based on real-time adversarial simulation, as well as the difficulty in meeting the real-time requirements of system reliability evaluation, in the research on equipment system reliability modeling and prediction methods. This method simulates the interference and reconstruction of the equipment system based on the topological structure and elements of the equipment system, considers internal and external interference strategies and dynamic reconstruction strategies, and innovatively establishes an equipment system reliability modeling and prediction method based on OODA loops by calculating the number of OODA loops in the equipment system. This method effectively improves the number of effective OODA loops and reliability of the equipment system under various failure modes, thereby improving the equipment system's adaptability and mission success rate in dynamic environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment systems, and in particular relates to a reliability modeling and prediction method for equipment systems based on a generalized effective OODA loop. Background Art

[0002] like Figure 3 As shown in the preceding text, a weapon system of systems (WSoS) refers to a new type of combat force formed by the coordinated and organic integration of multiple functionally interconnected and interactive equipment. For example, in a coordinated formation combat system, each platform can assume functions such as situational awareness, mission planning, command and decision-making, action control, and firepower strikes, playing a vital role in destroying vital points and disrupting systems in information warfare.

[0003] The equipment system uses logical space as its carrier, information space as its core, and data as its foundation, possessing the integrated characteristics of resource sharing and information fusion. The equipment system architecture requires a core focus on "principles," replacing the traditional "physics." This is reflected in the essential difference in reliability design between the two: Equipment system reliability design requires taking a system design perspective, fully considering all systems, networks, and elements within the equipment system, analyzing the failure mechanisms and modes of the equipment system, and formulating targeted reliability design criteria. This focuses on characterizing the equipment system's ability to cope with internal and external interference failures and continuously complete its mission. Equipment system reliability, on the other hand, is a characteristic that evaluates the equipment's susceptibility to failure, focusing on reducing or eliminating failures.

[0004] Weapon and equipment systems are characterized by vulnerable nodes, strong time constraints, highly dynamic tasks, and rapidly evolving topologies. Local anomalies (including internal disturbances such as node failures, functional degradation, and structural topology failures, as well as external disturbances such as mission changes, countermeasures, environmental impacts, and interception sabotage) can trigger global anomalies or failures, such as disconnection of the system's mission chain, collapse of the topology, interruption of information transmission, and paralysis of the kill network. These can increase the inherent risk of overall operation, degrade system performance, reduce mission execution efficiency, and even lead to top-level mission failure. To meet the demands of warfare, research on reliability modeling and prediction methods for equipment systems is being conducted to address issues such as the significant impact of strong countermeasures on system tasks and the difficulty in evaluating the dynamic impact of reliability. This is crucial for ensuring that equipment systems can safely and reliably complete various tasks under complex operational conditions such as cross-domain, agile, and highly interfering operations.

[0005] like Figure 1As shown in the figure, equipment systems are characterized by multi-system integration, large dimensions, numerous variable elements, and complex emergent and evolving characteristics. Therefore, current reliability engineering methods for complex systems are no longer effective in addressing and processing equipment system-related issues. System reliability is an important foundation for generating and maintaining system combat effectiveness. It not only directly affects the equipment's operational mode, operational scale, and sustained combat capability, as well as its effectiveness and improvement, and its lifecycle cost, but also directly reflects the system's combat readiness and the success rate of completing combat missions, significantly impacting the course of war. Therefore, to enhance the combat capability of equipment systems, research on equipment system reliability modeling and assessment methods is urgently needed to provide strong support for improving the combat effectiveness of equipment systems.

[0006] Currently, research on equipment system reliability in my country is still in its early stages, focusing primarily on concepts and frameworks. A comprehensive engineering methodology capable of addressing systemic issues has yet to be established. Existing complex network modeling methods only model and describe network topology characteristics and analyze platform complex network indicators. However, these indicators lack established evaluation and measurement standards, and they inadequately consider the heterogeneity of equipment system nodes and the directed nature of their edges.

[0007] In recent years, my country's research focus on equipment systems has shifted from random processes, complex networks and multi-agent systems to OODA loops and kill chain theories. However, research on equipment system reliability modeling and prediction methods is at an initial and primary stage, and most of them are static reliability models, which do not fully consider factors such as the various elements, levels, states, and structural and functional logical relationships in the dynamic changes of the equipment system. The evaluation method based on real-time confrontation simulation consumes a lot of computing resources, is high in cost, and has low efficiency. It is difficult to meet the real-time requirements of system reliability evaluation during combat missions. The degree of standardization of modeling is insufficient, which is not conducive to improving the credibility of the evaluation results. There is still a lack of theoretical, methodological and tool support for systematic reliability modeling and evaluation.

[0008] Therefore, the present invention proposes an equipment system reliability modeling and prediction method based on an effective OODA network by considering internal and external interference and dynamic reconstruction strategies to guide the design of equipment system architecture and ensure that the equipment system can be reliably executed in combat missions, thereby improving its combat effectiveness. Summary of the Invention

[0009] The purpose of the present invention is to solve the problems of large computational resource consumption, high cost and low efficiency of the evaluation method based on real-time confrontation simulation in the research of equipment system reliability modeling and prediction methods, and the difficulty in meeting the real-time requirements of system reliability evaluation during combat missions. To this end, an equipment system reliability modeling and prediction method based on an effective OODA network is provided.

[0010] To achieve the above objectives, the technical solutions provided by the present invention are:

[0011] A reliability modeling and prediction method for equipment systems based on a generalized effective OODA loop is characterized in that it includes the following steps:

[0012] Step 1: Initialize the heterogeneous directed network and construct an effective OODA network model;

[0013] Step 1.1: Initialize the heterogeneous directed network

[0014] Among them, V=(S,D,W) is the platform, S={s i |s1,s2,...,s I} is the detection node, D={d j |d1,d2,...,d J} is a decision node, W={w m |w1,w2,...,w M} is the attack node;

[0015] is a node type mapping function, where each node v∈V belongs to a specific node type;

[0016] For communication links, nodes are connected by edges Connect, connect Indicates from s i to d j information transmission;

[0017] ψ:E→ζ is an edge type mapping function, where each edge e∈E belongs to a specific relation;

[0018] Step 1.2: Construct an effective OODA network model:

[0019] eOODA_network = {A, V, E}

[0020] Among them, A=[A SD ,A DW ] is the transfer matrix, which represents the set of adjacency matrices connected between different nodes, A SD A represents the adjacency matrix of node S and node D; DW Represents the adjacency matrix of node D and node W;

[0021] Step 2: Simulate the disturbance and reconstruction of the equipment system and calculate the number of OODA loops of the equipment system;

[0022] Step 2.1: Simulate the interference to the equipment system and establish a node failure model;

[0023] Initialize the simulation data and set the simulation time t sim =0, the simulation time constraint is T sim , time step t = 1;

[0024] Step 2.2: Determine whether the simulation time has reached the end time:

[0025] If the end time is reached, the simulation ends and goes to step 2.3;

[0026] Otherwise, go to step 2.2.1;

[0027] Step 2.2.1: Initialize the iteration data and the list of failed nodes, and let the number of failures n sim =0, the failure count is constrained to N sim ;

[0028] Step 2.2.2: Determine the failure strategy, including random failure and intentional attack failure;

[0029] The random failure implementation process is as follows: randomly delete the failed nodes and their edges according to the sampling results, and add the failed nodes to the failed node list;

[0030] The intentional attack failure is the maximum degree failure, which is achieved by sorting the nodes in descending order according to their degrees, then selecting and removing a corresponding number of failed nodes and their edges, and adding the failed nodes to the failed node list;

[0031] set up Represents node s i ,d j ,w m degree;

[0032] Step 2.2.3: Traverse each failed node in the failed node list and select the corresponding dynamic reconstruction strategy:

[0033] Determine whether other similar nodes on the same platform can perform intra-cluster reconstruction:

[0034] If yes, go to step 2.2.4;

[0035] Otherwise, determine whether similar nodes in adjacent platforms of the platform where the node is located can perform inter-cluster reconstruction;

[0036] If yes, go to step 2.2.5;

[0037] Otherwise, go to step 2.2.6;

[0038] Step 2.2.4: Replace the same nodes between platforms and go to step 2.2.7;

[0039] Step 2.2.5: Select collaborative nodes on different platforms for functional replacement and proceed to step 2.2.7;

[0040] Step 2.2.6: Add new nodes or repair failed nodes using the Monte Carlo method to generate response nodes and edges, and then go to step 2.2.7;

[0041] Step 2.2.7: Calculate the existence probability of each node based on the attack pattern of the equipment system:

[0042] When the node is only subject to failure and generation constraints, the calculation formula is:

[0043]

[0044] in, and represents the cumulative distribution function of the time since each node was last repaired; and represents the complementary cumulative distribution function of the time since the failure of the failed node; and Indicates the time since each node was last repaired; and Indicates the time since the last failure of each node; and An indicator function indicating whether a node is removed under the maximum attack;

[0045] Step 2.2.8: Use matrix elements to represent the existence status of each node and edge;

[0046] Calculate the existence probability of each matrix element, the calculation formula is:

[0047]

[0048] Step 2.2.9: Calculate the connectivity probability of the communication link in the effective OODA loop of the equipment system. The calculation formula is:

[0049]

[0050] in, and is the reliability of the communication system, which is calculated by the distribution function of the communication system;

[0051] and is an indicator function, indicating whether the distance between nodes is within the effective communication range;

[0052] Step 2.2.10: Calculate the adjacency matrix elements to show whether the node exists at this time and whether the nodes are connected. The calculation formula is:

[0053]

[0054] Where α(·) represents the existence of each node and edge;

[0055] When node s i ,d j ,w m exists and the nodes are connected, the corresponding elements or

[0056] Otherwise, the element

[0057] Step 2.2.11: Calculate the number of valid OODA loops in this iteration using the formula:

[0058]

[0059] Step 2.2.12: Determine whether the number of failures has reached the termination number:

[0060] If it is reached, the iteration ends and goes to step 2.2;

[0061] Otherwise, go to step 2.2.1;

[0062] Step 2.3: Calculate the number of effective OODA loops and reliability observations of the equipment system at time t:

[0063] N eol (t) = sum(N eOODA (n sim )) / N sim

[0064] R sos (t) = N eol (t) / N OODA (0)

[0065] Among them, N eol (t) represents the average number of OODA loops in the simulation; n sim Indicates the number of nodes in a single iteration, N eOODA (n sim ) represents the number of effective OODA loops of the equipment system in this iteration; N sim Indicates the number of nodes in the equipment system; R sos (t) represents the reliability observation value at time t; N OODA (0) indicates the number of OODA in the equipment system.

[0066] Furthermore, when the failure or generation of nodes only obeys the exponential distribution, the step 2.2.7: calculating the existence probability of each node; the calculation formula is:

[0067]

[0068] Furthermore, when the failure and generation of nodes are only subject to the conditional constraint of the failure of the node due to the maximum attack, the step 2.2.7: calculating the existence probability of each node, the calculation formula is:

[0069]

[0070] in, and An indicator function indicating whether a node is removed under the maximum attack.

[0071] Furthermore, when the failure or generation of nodes obeys an exponential distribution and is subject to the constraint of maximum attack failure of nodes, the step 2.2.7: calculating the probability of existence of each node is calculated using the following formula:

[0072]

[0073] in, and An indicator function indicating whether a node is removed under the maximum attack.

[0074] Concept and principle of the present invention:

[0075] First, the node and link models of the heterogeneous directed network are initialized according to the topological structure and elements of the equipment system.

[0076] Subsequently, an effective OODA network model for equipment system was proposed using heterogeneous directed graph.

[0077] Then, the interference and reconstruction of the equipment system are simulated, internal and external interference strategies and dynamic reconstruction strategies are considered, and by calculating the number of OODA loops of the equipment system, an innovative equipment system reliability modeling and prediction method based on OODA loops is established.

[0078] Finally, the effectiveness and feasibility of the reliability modeling and prediction method are verified by taking an equipment system containing multiple unmanned system nodes as an example.

[0079] The advantages of the present invention are:

[0080] 1. This invention provides theoretical and technical guidance for the definition, modeling and prediction of equipment system reliability, thereby effectively improving the equipment system design capability and combat effectiveness.

[0081] 2. In the present invention, the dynamic reconstruction strategy effectively improves the number and reliability of effective OODA loops of the equipment system under various failure modes, thereby improving the equipment system's adaptability and mission success rate in a dynamic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 : Schematic diagram of the hierarchical structure of physical resources in the equipment system;

[0083] Figure 2 : Schematic diagram of the weapon and equipment system structure based on the OODA loop;

[0084] Figure 3 :Effective OODA network model diagram of equipment system;

[0085] Figure 4 : Schematic diagram of equipment system reconstruction strategy based on rules;

[0086] Figure 5 : Schematic diagram of the impact of different attack strategies on the number of OODA loops;

[0087] Figure 6 : Schematic diagram of the impact of different attack strategies on the reliability of the equipment system;

[0088] Figure 7 : Analysis diagram of the effective OODA loop number of the equipment system considering random failure and dynamic reconstruction strategy;

[0089] Figure 8 : Equipment system reliability analysis diagram considering random failure and reconstruction strategy;

[0090] Figure 9 : Analysis diagram of the effective OODA loop number of the equipment system considering random failure, intentional attack failure and dynamic reconstruction strategy;

[0091] Figure 10 : Equipment system reliability analysis diagram considering random failure, intentional attack failure and reconstruction strategy;

[0092] Figure 11 :Flowchart of equipment system reliability modeling and prediction method based on generalized effective OODA loop. DETAILED DESCRIPTION

[0093] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments:

[0094] In order to verify the effectiveness of the evaluation algorithm proposed in this invention, this embodiment takes an unmanned equipment system composed of 100 multifunctional UAV nodes as the simulation object. This equipment system has various functions including reconnaissance, intelligence analysis, decision-making and firepower strike. Through efficient collaborative operations, it provides the unmanned equipment system with powerful intelligence acquisition and response capabilities, and analyzes its reliability in actual combat. A total of four analyses are proposed.

[0095] It contains 40 reconnaissance nodes, 20 decision nodes, and 40 fire nodes. Table 1 lists the other parameters required for simulation evaluation.

[0096] Table 1 Equipment system reliability evaluation algorithm parameters

[0097]

[0098]

[0099] like Figure 11 As shown, the process of the equipment system reliability modeling and prediction method based on the generalized effective OODA loop in this embodiment is as follows:

[0100] Step 1: Initialize the heterogeneous directed network and construct an effective OODA network model;

[0101] Step 1.1: Initialize the heterogeneous directed network

[0102] Among them, V=(S,D,W) is the platform, S={s i |s1,s2,...,s I} is the detection node, D={d j |d1,d2,...,d J} is a decision node, W={w m |w1,w2,...,w M} is the attack node;

[0103] is a node type mapping function, where each node v∈V belongs to a specific node type

[0104] For communication links, nodes are connected by edges Connect, connect Indicates from s i to d j information transmission;

[0105] Equipment system edges represent the communication and association relationships between nodes. The information carried by the edges facilitates data transmission, command, and task allocation between nodes within the system. The existence of edges indicates that there is a direct connection and interaction between the nodes it connects. It plays a vital role in achieving coordinated actions, collaboration, and information exchange between system nodes, ultimately improving the overall combat effectiveness of the equipment system. System nodes are connected through wired local area networks or wireless data links, and the communication between nodes is manifested as a directed relationship. Therefore, in this embodiment, the communication within and between clusters is defined as directed edges with different weights, and an equipment system edge model based on a weighted directed graph is given:

[0106]

[0107] Edge Transmitting reconnaissance mission information, taking into account the node s i and d j The communication distance and reliability between them.

[0108] The model is established as follows:

[0109]

[0110] in, and s respectively i and d j communication distance and reliability.

[0111] Edge Transmitting combat mission information, taking into account node d j and w m The communication distance and reliability between them. The model is established as follows:

[0112]

[0113] in, and d j and w m communication distance and reliability.

[0114] ψ:E→ζ is an edge type mapping function, where each edge e∈E belongs to a specific relation ψ(e)∈ζ;

[0115] Step 1.2: If Figure 2 As shown, construct an effective OODA network model:

[0116] eOODA_network = {A, V, E}

[0117] Among them, A=[ASD ,A DW ] is the transfer matrix, which represents the set of adjacency matrices connected between different nodes, A SD Represents the adjacency matrix of node S and node D:

[0118]

[0119] in is the adjacency matrix A SD elements.

[0120] A DW Represents the adjacency matrix of node D and node W:

[0121]

[0122] Step 2: Simulate the disturbance and reconstruction of the equipment system and calculate the number of OODA loops of the equipment system;

[0123] Equipment will naturally degrade and fail randomly during missions. Furthermore, during combat missions, nodes or clusters are susceptible to various types of external shocks and interference, such as viruses, electromagnetic shocks, and fire strikes. Different types of shocks cause varying degrees of damage to different nodes, and can affect some or all nodes in the system simultaneously. Furthermore, nodes within the same platform or cluster are associated with each other, leading to common cause failures. Therefore, a node failure model is established that considers these failure modes.

[0124] Step 2.1: Simulate the interference to the equipment system and establish a node failure model;

[0125] Initialize the simulation data and set the simulation time t sim =0, the simulation time constraint is T sim , time step t = 1;

[0126] Step 2.2: Determine whether the simulation time has reached the end time:

[0127] If the end time is reached, the simulation ends and goes to step 2.3;

[0128] Otherwise, go to step 2.2.1;

[0129] Step 2.2.1: Initialize the iteration data and the list of failed nodes, and let the number of failures n sim =0, the failure count is constrained to N sim ;

[0130] Step 2.2.2: Determine the failure strategy;

[0131] This embodiment proposes two strategies: random failure and intentional attack failure; Represents node s i ,d j ,w m degree;

[0132] Analysis 1: Without considering the dynamic reconstruction strategy, we first analyze the effects of random failures and intentional attacks, and obtain the following results: Figure 5 and Figure 6 The number and reliability of effective OODA loops of the equipment system shown.

[0133] pass Figure 5 and Figure 6 By comparison, it can be concluded that under two different node failure modes, the number of effective OODA loops of the unmanned equipment system will decrease with the reduction of nodes, and the decline trend of both is faster in the early stage of simulation; in the later stage of simulation, the decline rate slows down.

[0134] Random failure is to randomly delete failed nodes and their edges according to the sampling results, and add the failed nodes to the failed node list. In this embodiment, the Monte Carlo simulation method is used to randomly delete failed nodes and their edges.

[0135] Intentional attack failure is maximum degree failure, that is, the nodes are sorted in descending order according to their degrees, and then a corresponding number of failed nodes and their edges are selected and removed, and the failed nodes are added to the failed node list;

[0136] Analysis 2: Comparing random failure and intentional attack strategies reveals that intentional attacks have a greater impact on the equipment system. This is because they selectively attack the nodes with the highest degree within the equipment system, causing more edges to disappear from the equipment system's combat network, accelerating the decline in the number of OODA loops and reliability. When both failure modes act together, the number of OODA loops and reliability in the equipment system's combat network decrease significantly initially, ultimately reaching zero at 45 seconds of simulation time. This significantly impacts the equipment system compared to the other two failure models, making it more susceptible to destruction and disintegration.

[0137] Step 2.2.3: Traverse each failed node in the failed node list, including the failed nodes that were not successfully repaired in the previous traversal, such as Figure 4 As shown, select the corresponding dynamic reconstruction strategy.

[0138] Due to the resource sharing and information fusion capabilities of the equipment system, internal and external disturbances of varying types and intensities can be suppressed through the topology regulation of the equipment system's coupled network. Dynamic reconfiguration strategies enable the equipment system to dynamically adjust its configuration and behavior based on changing mission requirements, resource availability, and environmental conditions.

[0139] Dynamic reconstruction strategies include:

[0140] Reconstruction strategy I: Intra-cluster reconstruction. When a node in a cluster fails, similar nodes in the same cluster (same platform) can be collaboratively reconstructed. This strategy allows the system to be downgraded and maintained above the task baseline.

[0141] Reconstruction strategy II: Inter-cluster reconstruction. When a node in cluster k fails, similar nodes in adjacent clusters (adjacent platforms) can collaborate through relay nodes. This strategy allows the system to be downgraded and remain above the task baseline.

[0142] Reconstruction Strategy III: When a node fails, the system can be restored to its original state by repairing or adding new nodes. However, this strategy requires additional resources and costs.

[0143] First, determine whether other similar nodes on the same platform can perform intra-cluster reconstruction:

[0144] If yes, go to step 2.2.4;

[0145] Otherwise, determine whether similar nodes on adjacent platforms of the node's platform can perform inter-cluster reconstruction:

[0146] If yes, go to step 2.2.5;

[0147] Otherwise, go to step 2.2.6;

[0148] Step 2.2.4: Replace the same nodes between platforms and go to step 2.2.7;

[0149] Step 2.2.5: Select collaborative nodes on different platforms for functional replacement and proceed to step 2.2.7;

[0150] Step 2.2.6: Add new nodes or repair failed nodes using the Monte Carlo method to generate response nodes and edges, and then go to step 2.2.7;

[0151] Analysis 3: Analyze and compare the number of OODA loops and reliability of the equipment system under the influence of dynamic reconstruction strategy, consider random failure and three dynamic reconstruction strategies, and conduct simulation analysis to obtain the following results: Figure 7 and Figure 8 The number of active OODA loops and equipment system reliability shown;

[0152] It can be concluded that, taking into account the allocation of combat entities and physical resource constraints, the number and reliability of OODA loops of the equipment system based on the dynamic reconstruction strategy have roughly the same trend over time in the actual combat process.

[0153] Step 2.2.7: Calculate the existence probability of each node based on the attack pattern of the equipment system:

[0154] Determine the existence of nodes based on characteristic functions and Monte Carlo methods, and determine the existence of edges based on characteristic functions and Monte Carlo methods:

[0155] This embodiment provides four modes:

[0156] The first is a common attack mode;

[0157] The second is a random failure mode;

[0158] The third is the deliberate attack mode;

[0159] The fourth is the combined effect of random failures and deliberate attacks;

[0160] When the node is only subject to failure and generation constraints, the calculation formula for the existence probability of each node is:

[0161]

[0162] When the failure or generation of nodes only obeys the exponential distribution, the calculation formula is:

[0163]

[0164] When the failure and generation of nodes are only subject to the condition constraint of the maximum attack failure of nodes, the calculation formula is:

[0165]

[0166] When the failure or generation of nodes obeys the exponential distribution and is subject to the constraint of maximum attack failure of nodes, the calculation formula is:

[0167]

[0168] in, and represents the cumulative distribution function of the time since each node was last repaired; and represents the complementary cumulative distribution function of the time since the failure of the failed node; and Indicates the time since each node was last repaired; and Indicates the time since the last failure of each node; and An indicator function indicating whether a node is removed under the maximum attack;

[0169] Step 2.2.8: Use matrix elements to represent the existence status of each node and edge;

[0170] Compute the existence probability of each matrix element:

[0171] The existence probability of each matrix element can be expressed as the product of the existence probabilities of two nodes and the existence probabilities of their edges. The calculation formula is:

[0172]

[0173] Step 2.2.9: Calculate the connectivity probability of the communication link in the effective OODA loop of the equipment system. The calculation formula is:

[0174]

[0175] in, and is the reliability of the communication system, which is calculated by the distribution function of the communication system;

[0176] and Indicates whether the distance between nodes is within the effective communication range, which is represented by the following indicator function:

[0177]

[0178]

[0179] Step 2.2.10: Calculate the adjacency matrix elements. The calculation formula is:

[0180]

[0181] Where α(·) represents the existence of each node and edge;

[0182] When node s i ,d j ,w m exists and the nodes are connected, the corresponding elements

[0183] Otherwise, the element

[0184] Step 2.2.11: Calculate the number of valid OODA loops in this iteration using the formula:

[0185]

[0186] Step 2.2.12: Determine whether the number of failures has reached the termination number:

[0187] If it is reached, the iteration ends and goes to step 2.3;

[0188] Otherwise, go to step 2.2.1;

[0189] Step 2.3: Calculate the number of effective OODA loops and reliability observations of the equipment system at time t. The calculation formula is:

[0190] N eol (t) = sum(N eOODA (n sim )) / N sim

[0191] R sos (t) = N eol (t) / N OODA (0)

[0192] Among them, N eol (t) represents the average number of OODA loops in the simulation; n sim Indicates the number of nodes in a single iteration, N eOODA (n sim ) represents the number of effective OODA loops of the equipment system in this iteration; N sim Indicates the number of nodes in the equipment system; R sos (t) represents the reliability observation value at time t; N OODA (0) indicates the number of OODA in the equipment system.

[0193] Analysis 4: With the addition of reconfiguration strategies I, II, and III, both changes remained relatively stable, showing a slowly decreasing trend. Across 1000 simulations, at t = 100, the average number of valid OODA loops was 156, and the equipment system reliability was 0.357. This compares to an average of 36 OODA loops and an equipment system reliability of 0.073 when the dynamic reconfiguration strategy was not implemented. This indicates that the implementation of the dynamic reconfiguration strategy significantly improves the number of valid OODA loops and reliability of the unmanned equipment system, enhancing its survivability and combat effectiveness.

[0194] pass Figure 5 、 Figure 6 It can be seen that when the two types of failure modes act together, the number of effective OODA loops and reliability of the equipment system are most affected, and the number of effective OODA loops and reliability of the equipment system tend to 0 more quickly. Here, the dynamic reconstruction strategy is added to compare the impact on the number of effective OODA loops and reliability of the equipment system. Figure 9 and Figure 10 shown.

[0195] Considering both random failure and deliberate attack modes, the number of effective OODA loops and reliability of the equipment system with a dynamic reconfiguration strategy exhibited roughly the same temporal trends during actual combat. With the addition of reconfiguration strategies I, II, and III, both trends remained relatively stable, exhibiting a slowly decreasing trend. Across 1000 simulations, at time t = 100, the average number of effective OODA loops was 82, and the equipment system reliability was 0.197. When the dynamic reconfiguration strategy was not used, both the number of effective OODA loops and the reliability of the equipment system dropped to zero at simulation time t. This indicates that the addition of a dynamic reconfiguration strategy significantly improves the number of effective OODA loops and reliability of the equipment system, effectively enhancing its survivability and combat effectiveness.

[0196] The analysis results show that with the passage of time, the effective OODA loop number and reliability of the equipment system gradually decrease, and the decline is faster in the initial stage and then gradually slows down; secondly, the impact of internal and external interference failures on the effective OODA loop number and reliability of the equipment system is greater than intentional attack failures and random failures.

[0197] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A reliability modeling and prediction method for equipment systems based on a generalized effective OODA loop, characterized by: The following steps are involved: Step 1: Initialize the heterogeneous directed network and construct an effective OODA network model; Step 1.1: Initialize the heterogeneous directed network ; in, For the platform, To detect nodes, is the decision node, To strike nodes; is a node type mapping function, where each node All belong to a specific node type; For communication links, nodes are connected by edges 、 Connect, connect Indicates from arrive information transmission; is the edge type mapping function, where each edge All belong to a specific relationship; Step 1.2: Construct an effective OODA network model: in, is the transfer matrix, which represents the set of adjacency matrices connecting different nodes. Represents the adjacency matrix of node S and node D; Represents the adjacency matrix of node D and node W; Step 2: Simulate the disturbance and reconstruction of the equipment system and calculate the number of OODA loops of the equipment system; Step 2.1: Simulate the interference to the equipment system and establish a node failure model; Initialize simulation data and set simulation time , the simulation time constraint is , time step t=1; Step 2.2: Determine whether the simulation time has reached the end time: If the end time is reached, the simulation ends and goes to step 2.3; Otherwise, go to step 2.2.1; Step 2.2.1: Initialize the iteration data and the list of failed nodes, and set the number of failures , the failure number constraint is ; Step 2.2.2: Determine the failure strategy, including random failure and intentional attack failure; The random failure implementation process is as follows: randomly delete the failed nodes and their edges according to the sampling results, and add the failed nodes to the failed node list; The intentional attack failure is the maximum degree failure, which is achieved by sorting the nodes in descending order according to their degrees, then selecting and removing a corresponding number of failed nodes and their edges, and adding the failed nodes to the failed node list; set up Representation node degree; Step 2.2.3: Traverse each failed node in the failed node list and select the corresponding dynamic reconstruction strategy: Determine whether other similar nodes on the same platform can perform intra-cluster reconstruction: If yes, go to step 2.2.4; Otherwise, determine whether similar nodes in adjacent platforms of the platform where the node is located can perform inter-cluster reconstruction; If yes, go to step 2.2.5; Otherwise, go to step 2.2.6; Step 2.2.4: Replace the same nodes between platforms and go to step 2.2.7; Step 2.2.5: Select collaborative nodes on different platforms for functional replacement and proceed to step 2.2.7; Step 2.2.6: Add new nodes or repair failed nodes using the Monte Carlo method to generate response nodes and edges, and then go to step 2.2.7; Step 2.2.7: Calculate the existence probability of each node based on the attack pattern of the equipment system: When the node is only subject to failure and generation constraints, the calculation formula is: in, , and represents the cumulative distribution function of the time since each node was last repaired; , and represents the complementary cumulative distribution function of the time since the failure of the failed node; , and Indicates the time since each node was last repaired; , and Indicates the time since the last failure of each node; , and An indicator function indicating whether a node is removed under the maximum attack; Step 2.2.8: Use matrix elements to represent the existence status of each node and edge; Calculate the existence probability of each matrix element, the calculation formula is: is the adjacency matrix of node S and node D The elements in is the adjacency matrix of node D and node W Elements in Step 2.2.9: Calculate the connectivity probability of the communication link in the effective OODA loop of the equipment system. The calculation formula is: in, and is the reliability of the communication system, which is calculated by the distribution function of the communication system; and is an indicator function, indicating whether the distance between nodes is within the effective communication range; Step 2.2.10: Calculate the adjacency matrix elements to show whether the node exists at this time and whether the nodes are connected. The calculation formula is: in Indicates the existence of each node and edge; When the node exists and the nodes are connected, the corresponding elements or ; Otherwise, the element ; Step 2.2.11: Calculate the number of valid OODA loops in this iteration using the formula: Step 2.2.12: Determine whether the number of failures has reached the termination number: If it is reached, the iteration ends and goes to step 2.2; Otherwise, go to step 2.2.1; Step 2.3: Calculate the number of effective OODA loops and reliability observations of the equipment system at time t: in, represents the average number of OODA loops in the simulation; Indicates the number of nodes in a single iteration, Indicates the number of valid OODA loops of the equipment system in this iteration; Indicates the number of nodes in the equipment system; represents the reliability observation value at time t; Indicates the number of OODAs in the equipment system.

2. The equipment system reliability modeling and prediction method based on a generalized effective OODA loop according to claim 1 is characterized by: When the failure or generation of nodes only obeys the exponential distribution, the step 2.2.7: calculates the existence probability of each node; the calculation formula is: 。 3. The equipment system reliability modeling and prediction method based on a generalized effective OODA loop according to claim 1 is characterized by: When the failure and generation of nodes are only subject to the condition constraint of the maximum attack failure of the node, the step 2.2.7: calculating the existence probability of each node, the calculation formula is: in, , and An indicator function indicating whether a node is removed under the maximum attack.

4. The equipment system reliability modeling and prediction method based on a generalized effective OODA loop according to claim 1 is characterized by: When the failure or generation of nodes obeys an exponential distribution and is subject to the constraint of maximum attack failure of nodes, the step 2.2.7: calculating the probability of existence of each node is calculated using the following formula: in, , and An indicator function indicating whether a node is removed under the maximum attack.

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