A method for assessing the survivability of heavy platforms based on the DA-PSR model and complex networks

Abstract

This invention proposes a method for assessing the resilience of heavy platforms based on the DA-PSR model and complex networks. Taking heavy platforms as the object, an objective resilience assessment system is constructed. An assessment index system with causal relationships is established, and a screening method for the assessment index system based on node betweenness values ​​in complex network theory and the k-means algorithm is proposed. This results in a simplified assessment index system where the remaining node betweenness values ​​account for 52.99% of the total betweenness values ​​and the remaining cluster center values ​​account for 90.55% of the total cluster center values. An index weighting method based on mutual information theory and an index calculation method based on extreme damage quantification are proposed. The PSR framework theory is improved through dimensional analysis, and a resilience DA-PSR assessment model is constructed. Considering the performance requirements driven by tasks, a criterion quantification and dynamic grading method based on task requirements is proposed. The assessment shows that a heavy platform with a resilience assessment value of 0.7373 exhibits different assessment levels of "excellent," "medium," and "poor" under different tasks.

Description

Technical Field

[0001] This invention belongs to the field of heavy platform technology, specifically relating to a method for assessing the survivability of heavy platforms based on the DA-PSR model and complex networks. Background Technology

[0002] Damage resistance is the sensitivity of a heavy platform system's structure and function to damage and destruction. It characterizes the ability of a heavy platform to resist damage and maintain system functionality.

[0003] Currently, most assessment index construction focuses on conceptual indicators representing the hierarchical classification of equipment systems, neglecting the construction of technical indicators representing the anti-destruction response mechanism of equipment. This results in an assessment index system that emphasizes statistical induction and lacks objective physical description. Regarding assessment models, the aforementioned studies primarily employ methods such as the Analytic Hierarchy Process (AHP), entropy weight method, grey relational analysis, TOPSIS, and ADC, along with their related improvements. The main focus is on overcoming the ambiguity and randomness issues faced by the assessment index system in quantitative description. While subjective weighting assessment methods like the AHP are computationally convenient, they suffer from strong human intervention and low reliability. Objective weighting assessment methods like the entropy weight method ensure objectivity as much as possible, but exhibit poor physical interpretability. In terms of assessment level criteria, the aforementioned studies primarily use experimental and scoring methods. Experimental methods offer high reliability but require numerous trials. Scoring methods, where experts set the level criteria boundaries, are simple and clear but highly subjective. Therefore, current assessment research in the equipment field suffers from significant problems, including strong subjectivity, an overemphasis on statistics, and a lack of physical interpretation.

[0004] The evaluation indicator system is the foundation of evaluation research and also the part most influenced by human subjectivity in existing evaluation studies. For example, Li constructed a resource and environment evaluation indicator system from three aspects: economic and social aspects, resource utilization efficiency, and environmental pollution level; Xiao Yong et al. constructed an urban power distribution network evaluation indicator system from four morphological attributes: material form, systemic characteristics, temporal structure, and spatial structure. These common indicator system construction methods are based on the classification of characteristic information of the evaluation object. Different evaluation perspectives will extract different characteristic information, making them the most subjective. Evaluation indicator system construction methods based on causal relationships have begun to emerge, establishing causal relationships and system dynamics flow diagrams from indicators such as economic, political, and public sentiment; Naderi used system dynamics methods to propose regional water supply demand impact indicators from the correlation of food, energy, and water. The indicator system construction method based on system dynamics includes the causal influence mechanism of the evaluation object, with lower subjectivity, but the model construction is complex and the indicator system is large.

[0005] Evaluation methods are the core of evaluation problem research and a current research hotspot. Existing evaluation methods mainly fall into three categories: 1) Mathematical statistical methods, represented by analytic hierarchy process (AHP) and entropy weighting, which are currently the primary evaluation methods in the equipment field; 2) Knowledge inference methods, represented by DS evidence theory and Markov chains, which introduce probability theory and fuzzy theory to handle the randomness of indicator quantification, requiring high levels of sample data and expert experience; and 3) Pattern recognition methods, represented by rough set theory and complex network analysis, which can objectively extract the feature information of the evaluation object, have low dependence on prior knowledge, but have relatively high model complexity.

[0006] Evaluation grading criteria are the standards for evaluating evaluation problems. Currently, the grading criteria for various evaluation problems are mainly established using experimental and scoring methods. Experimental methods provide higher reliability for establishing grading criteria, but they also have higher research costs. Furthermore, for some complex systems, experimental research is even difficult. Therefore, experimental methods are not common in evaluation grading criterion research, and scoring methods remain the dominant approach. How to guide scoring methods to more objectively define grading boundaries is the most direct problem facing the engineering application of evaluation research at this stage. Summary of the Invention

[0007] To address the issues of strong subjectivity and weak physical interpretation in current equipment evaluation system research, this invention proposes a method for assessing the survivability of heavy platforms based on the DA-PSR model and complex networks.

[0008] The technical solution to achieve the purpose of this invention is as follows:

[0009] A method for assessing the survivability of heavy platforms based on the DA-PSR model and complex networks, characterized by comprising:

[0010] Step 1: Construct a resilience assessment index system based on the PSR framework theory;

[0011] Step 2: Based on complex network theory, construct the topology network of heavy platform structural components and operational functions;

[0012] Step 3: Calculate the node betweenness values ​​of each node in the topology network to perform preliminary screening of the indicators in the damage assessment index system, then use the k-means algorithm to divide and cluster the node betweenness values, and use the cluster elimination screening method to perform secondary screening of the indicators.

[0013] Step 4: Based on the evaluation index system selected in Step 3, construct the heavy platform survivability DA-PSR evaluation model, use the index weighting model based on mutual information theory to assign weights to the platform survivability DA-PSR evaluation model, and then calculate the evaluation index based on the index calculation model of extreme damage quantification to obtain the evaluation calculation results.

[0014] Step 5: For different heavy missions, classify the assessment results of heavy platforms according to the survivability level criteria and determine their survivability.

[0015] Furthermore, the resilience assessment index system constructed in step 1 includes: resilience assessment stress index, resilience assessment status index, and resilience assessment response index;

[0016] The stress indicators for resilience assessment are used to measure the importance of heavy-duty platforms and include target value indicators;

[0017] The status indicators of survivability assessment are used to measure the functional failure tolerance of equipment, including the functional failure tolerance of the structural cylinder, the functional failure tolerance of the driver's cab, the functional failure tolerance of the equipment compartment, the functional failure tolerance of the tire system, and the functional failure tolerance of other components.

[0018] The response indicators for resilience assessment are used to measure the speed of failure response, including the failure response of the structural cylinder, the cab, the equipment compartment, the tire system, and other components.

[0019] Furthermore, the specific operational steps of step 3 include:

[0020] Step 31: The node betweenness value is used to represent the ratio of the number of shortest paths passing through a given node to the total number of shortest paths in the network. This is used to select nodes with significant influence as the primary indicator. The formula for calculating the node betweenness value is:

[0021]

[0022] In the formula, Let n be the number of edges in the shortest path between nodes j and k; jk Let i be the number of edges in the shortest path between nodes j and k that passes through node i.

[0023] Step 32: The k-means algorithm is used to divide and cluster the nodes of each component. This is used to select components corresponding to cluster levels with a high proportion of node betweenness cluster centroids and a small number of nodes. The Euclidean distance k-means algorithm criterion function S is:

[0024]

[0025] In the formula, α is the number of clusters, and c γ Let dist(c) be the center point of the γth cluster. γ (x) is c γ The distance to x;

[0026] Step 33: Calculate the proportion of the median value after removing the lowest class under different cluster numbers to the total median value, select the class with the highest proportion for deletion, thereby removing the failure tolerance of other components and the failure response degree of other components.

[0027] Step 34: Construct a resilience assessment index system with target value, structural tube functional failure tolerance, cab functional failure tolerance, equipment compartment functional failure tolerance, tire system functional failure tolerance, structural tube failure response degree, cab failure response degree, equipment compartment failure response degree, and tire system failure response degree as indicators.

[0028] Furthermore, the specific operational steps of step 4 include:

[0029] Step 41: Establish a survivability DA-PSR assessment model:

[0030]

[0031] In the formula, I represents the evaluation result, P represents the pressure index, S represents the state index, R represents the response index, and ω represents the ω value. i Let θ be the weight of the i-th indicator, θ be the number of indicators, and * be the standardization factor;

[0032] Step 42: Construct an indicator weighting model based on mutual information theory, and calculate the weight ω of the i-th indicator through the indicator weighting model. i ;

[0033] Step 43: Construct an index calculation model based on extreme damage quantification, and calculate the pressure index P, state index S, and response index R through the index calculation model;

[0034] Step 44: Obtain the final evaluation result of the heavy platform according to formula (5).

[0035] Furthermore, the specific operational steps of step 42 include:

[0036] Step 421: Define the mutual information M(i,j) between node i and node j as:

[0037]

[0038] Where, p i→j p represents the outgoing edge probability of node i; j←i Let be the probability of an incoming edge to node j;

[0039] The information content of node i is defined as the sum of mutual information from node i to all nodes pointing to node i minus the sum of mutual information from all nodes pointing to i to node i:

[0040]

[0041] In the formula, V out (i) is the set of nodes that a node points to, V in (i) is the set of nodes that point to nodes;

[0042] Step 422: Calculate the mutual information value of the key nodes using formulas (8)-(9), normalize the calculated mutual information value, and use the normalized mutual information value as the weight of the i-th indicator.

[0043] Furthermore, step 43 includes the following specific operational steps:

[0044] Step 431: Denote the actual state of a performance index of the heavy platform at a random moment as z. a In actual operation, the set of structural parameters corresponding to the performance index is denoted as Z. a Let the limiting state be denoted as z. l The set of structural parameters corresponding to the performance index at the limit state is denoted as Z. l ;

[0045] Step 432: Express the performance failure tolerance Δz as:

[0046] △z=z a -z l (10)

[0047] In the formula, z a For the actual state of performance indicators, z l This is the limiting state;

[0048] The formula for calculating the structural parameter failure tolerance ΔZ is as follows:

[0049] △Z=Z a -Z l (11);

[0050] Step 433: Establish the index calculation model for the quantification of ultimate damage according to equations (10)-(11), and calculate the pressure index P, state index S, and response index R through simulation tools.

[0051] Furthermore, the specific operational steps of step 5 include:

[0052] Step 51: Based on state node B that meets the task requirements and state node L that meets the basic operational requirements, divide the actual state A of the heavy platform into three stages:

[0053] 1) If A∈[C,B] and the generalized protection time I(A→L)≥I(B→L), then it is determined that this stage can meet the mission's anti-destruction requirements;

[0054] 2) If A ∈ [B, L], and the generalized protection time I(A → L) < I(B → L), and I(A → L) > 0, then it is determined that the requirements for the task's anti-destruction ability cannot be met in this stage, but the basic operation requirements can be met;

[0055] 3) If A ∈ [L, 0], and I(A → L) ≤ 0, then it is determined that the basic operation requirements cannot be met in this stage;

[0056] Step 52: If the heavy platform is in stage 1), its level is evaluated as excellent; if the heavy platform is in stage 2), its level is evaluated as medium; if the heavy platform is in stage 3), its level is evaluated as poor;

[0057] Step 53: For different heavy tasks, compare the evaluation calculation result when the heavy platform executes the task with the minimum performance index that meets the anti-destruction requirements when completing the task:

[0058] If it is greater, then the heavy platform is in stage 1) at this time, and the anti-destruction level of the heavy platform is "excellent";

[0059] If it is less, then compare the evaluation calculation result with the minimum performance index that meets the operation requirements:

[0060] i) If it is greater, then the heavy platform is in stage 2) at this time, and the anti-destruction level of the heavy platform is "medium";

[0061] ii) If it is less, then the heavy platform is in stage 3) at this time, and the anti-destruction level of the heavy platform is "poor".

[0062] Compared with the prior art, the method has the following beneficial effects:

[0063] This invention provides a systematic and objective quantitative assessment of the survivability of heavy platforms from three aspects: assessment index system, assessment method, and assessment level criteria. Compared with existing assessment technologies, it has the advantages of less subjectivity and stronger logical consistency. Regarding the assessment index system, a method for constructing a heavy platform survivability assessment index system based on the PSR framework theory is proposed. This system is built from three aspects: discriminant attack attributes, functional failure tolerance attributes, and failure response attributes. Furthermore, an initial index system screening method based on complex network theory and the k-means clustering grading algorithm is proposed, determining an assessment index system where the remaining node betweenness values ​​account for 52.99% of the total betweenness values ​​and the remaining cluster center values ​​account for 90.55% of the total cluster center values, thus constructing an assessment index system less affected by subjective factors. Regarding the assessment method, an index weighting method based on mutual information theory and an index calculation method based on extreme damage quantification are proposed. The PSR framework theory is improved through dimensional analysis, and a survivability DA-PSR assessment model is constructed. The normalized weights for the heavy platform survivability assessment indicators were calculated as follows: heavy-duty cylinder 0.42183, tire system 0.3678, cab 0.1555, and equipment compartment 0.0549. Based on this invention, the assessment method is less affected by subjective factors and has strong physical interpretability. Regarding the assessment level criteria, different tasks have different performance requirements, leading to different requirements for the heavy platform's survivability. A criterion quantification and dynamic grading method based on task requirements was proposed. The calculated survivability assessment value of 0.7373 for a heavy platform under different tasks showed assessment levels of "excellent," "medium," and "poor," indicating that the constructed assessment level criteria are less affected by subjective factors. Attached Figure Description

[0064] Figure 1 This is a flowchart of the evaluation method proposed in this invention;

[0065] Figure 2 A conceptual diagram of the PSR framework theory;

[0066] Figure 3 A schematic diagram illustrating the development process of heavy platform survivability;

[0067] Figure 4 For heavy-duty platform topology network models;

[0068] Figure 5 The intermediate value of each node in the heavy platform topology network model;

[0069] Figure 6 The results are from cluster analysis of the betweenness values ​​of nodes in the topological network model.

[0070] Figure 7 The comparison results of the middle value and mutual information value of key nodes in the topological network model;

[0071] Figure 8 A schematic diagram illustrating the process of equipment performance degradation.

[0072] Figure 9 The simulation results show the failure tolerance and rate of change of the damage assessment indicators of a certain type of heavy platform.

[0073] Figure 10 A diagram illustrating the process of equipment performance degradation during a mission.

[0074] Figure 11 This is the damage resistance assessment level for a certain type of heavy platform. Detailed Implementation

[0075] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0076] This invention proposes a method for assessing the survivability of heavy platforms based on the DA-PSR model and complex networks. The assessment process is as follows: Figure 1 As shown. To further objectively assess the survivability of heavy platforms, this invention studies the survivability assessment of heavy platforms from three aspects: assessment index system, assessment method, and assessment level criteria. By analyzing the structural layout and functional correlation of heavy platforms, as well as their damage response mechanism, a causal assessment index system is constructed based on the PSR framework theory; a highly interpretable objective weighting method is established based on the mutual information model of complex network theory; and a less subjective assessment level criterion is established by guiding the assessment results through task requirements. The assessment index system, assessment method, and assessment level criteria are described below.

[0077] 1. Damage resistance assessment index system

[0078] (1) PSR Framework Theory

[0079] The PSR (Pressure-State-Response Framework) theory is based on causal relationships. By analyzing the inherent causal connections within a system, it identifies the influencing factors. "Pressure (P)" represents the impact and incentives of human activities on the environment; "State (S)" represents the comprehensive reflection of the world's natural and social environment within a certain period; and "Response (R)" represents the policy measures taken by humans to promote sustainable environmental development. The PSR framework concept is as follows: Figure 2 As shown.

[0080] The evaluation index system based on the PSR framework theory conforms to the logical law of cause-effect-response. Starting from the incentive, it analyzes the change of state and the response of measures step by step. The indicators are interrelated and the whole system is complete. It is a relatively objective method for constructing evaluation index systems.

[0081] (2) Damage resistance assessment index system

[0082] Once the heavy platform is finalized and deployed, its mission value and structural functions are determined, making the process of maintaining its operational capabilities under battlefield threats essentially objective. To reasonably assess the survivability of heavy platforms, this objective process needs to be broken down. The following assumptions are made:

[0083] Assumption 1: No new ultra-high performance equipment will appear on either the offensive or defensive side of the battlefield, and the assessment environment will remain stable;

[0084] Assumption 2: The heavy-duty platform will not undergo any overall structural or functional modifications, and the evaluation object will remain stable;

[0085] Assumption 3: Ignore the impact of special damage conditions and maintain stability in the evaluation process.

[0086] The development process of heavy platforms to enhance their survivability under battlefield threats, such as... Figure 3 As shown. The scope of survivability assessment extends from when a heavy platform is detected by enemy reconnaissance until it is attacked, and includes determining the attack attributes, functional failure tolerance attributes, and failure response attributes.

[0087] ① Stress indicators in resilience assessment

[0088] After being detected by enemy reconnaissance, it is necessary to assess the military value of heavy platforms before connecting the source of damage to them. In other words, from the perspective of heavy platforms, their importance in the mission system and their cost-effectiveness in attack are the pressures on their resilience. The higher the importance of the heavy platform in the mission system and the greater its cost-effectiveness in attack, the easier it is to be attacked after being detected, and the greater the pressure on its resilience.

[0089] ② State indicators for damage resistance assessment

[0090] Due to the overall layout and functional interrelationships resulting from the design, each component of a heavy-duty platform has an inherent functional failure tolerance. Functional damage will only occur when the functional failure exceeds the tolerance value. Therefore, the functional failure tolerance of each component within a certain period is a comprehensive reflection of the heavy-duty platform's ability to maintain operational functionality and represents its resilience.

[0091] ③ Response indicators for resilience assessment

[0092] Due to the structural strength and functional transmission path designed for heavy platforms, resistance to structural and functional failures will occur during the impact and damage process of heavy platforms. This results in different degrees of variation in the functional failure process of heavy platforms, which is a response to catastrophic failure.

[0093] In summary, based on the PSR framework theory, a heavy platform survivability assessment index system is constructed from three aspects: stress, state, and response, divided into target layer, criterion layer, and indicator layer. The meaning of the assessment index and the effect of the assessment index are explained in Table 1.

[0094] Table 1. Heavy Platform Damage Assessment Index System

[0095]

[0096]

[0097] (3) Screening of damage resistance assessment index system

[0098] Heavy platform structures are complex and numerous, therefore the index system shown in Table 1 needs to be filtered to simplify the complexity of the evaluation model. Based on the overall layout and functional association paths of the heavy platform, and grounded in complex network theory, this invention treats components or highly integrated subsystems and functional modules as nodes in a complex network, and functional association paths and damage propagation paths as edges, establishing a topological network model of heavy platform structural components and operational functions, such as... Figure 4 As shown.

[0099] This topological network model has 37 nodes, 109 directed edges, a maximum node degree of 16, a minimum node degree of 3, a maximum in-degree of 15, and a maximum out-degree of 10.

[0100] Let the functional topology of the heavy platform structure be G=(V,E), where V={v1,v2,...,v...} n} represents the set of nodes in the topological network, E = {(v i ,v j )|v i ,v j Let A ∈ V} represent the set of edges in the topological network. n×n =(a ij ) n×n Let a be the corresponding adjacency matrix. ij =1, otherwise a ij =0.

[0101] The node betweenness is used to characterize the ratio of the number of shortest paths passing through a given node to the total number of shortest paths in the network. This is used to study the influence of each node in the network topology, and then select nodes with significant influence as key performance indicators to construct an evaluation index system. That is, node betweenness B. i for:

[0102]

[0103] In the formula, Let n be the number of edges in the shortest path between nodes j and k; jk Let i be the number of edges in the shortest path between nodes j and k that passes through i.

[0104] Then, the k-means algorithm is used to divide and cluster the betweenness values ​​of the nodes of each component in the topological network G. The components corresponding to the clustering levels with a high proportion of cluster center values ​​of node betweenness values ​​and a small number of nodes are selected according to each clustering level.

[0105] The criterion function S of the Euclidean distance k-means algorithm is:

[0106]

[0107] In the formula, α is the number of clusters, and c γ Let dist(c) be the center point of the γth cluster. γ (x) is c γ The distance to x.

[0108] The intermediate values ​​of each node in the heavy platform topology network model are calculated as follows: Figure 5 As shown. By Figure 5 It can be seen that the larger the betweenness value, the greater the influence of the node on the topology network, and vice versa. Among them, there are 4 nodes with betweenness values ​​greater than 5, accounting for 12.50% of the total number of nodes. The maximum betweenness value of the node is 28.254, which is node 1 representing the heavy cylinder, indicating that the heavy cylinder has the greatest influence in the topology network. There are 19 nodes with betweenness values ​​greater than 1 but less than 5, accounting for 59.38% of the total number of nodes. The components and subsystems represented by these nodes are mainly concentrated in the outermost layer. The components represented by the nodes with betweenness values ​​less than 1 are mainly arranged in the inner layer, accounting for 28.12% of the total number of nodes.

[0109] The k-means algorithm is used to partition and cluster nodes based on their betweenness values. Figure 6 As shown. By Figure 6It can be seen that as the number of clusters increases, the number of nodes in the highest-order cluster remains unchanged, while the remaining nodes gradually divide into clusters, exhibiting a relatively obvious classification phenomenon. Furthermore, as the number of clusters increases, the cluster centers of the lowest and highest-order clusters tend to stabilize, at 0.7091 and 24.5495 respectively. This indicates that the media of each node in the heavy platform topology network model exhibits a certain regularity in clustering, and a cluster elimination screening method can be used to optimize the survivability assessment index system.

[0110] like Figure 6 As shown, the betweenness ratios after removing the lowest class were calculated for cluster numbers of 2, 3, 4, and 5. When the number of clusters was 4, after removing the 9 nodes of the lowest class, the betweenness values ​​of the remaining nodes accounted for 91.95% of the total betweenness values, and the remaining cluster center values ​​accounted for 98.03% of the total cluster center values. The remaining 23 nodes could relatively completely express the main information of the topology network. When removing the nodes of the lowest and second classes, the betweenness values ​​of the remaining nodes accounted for 52.99% of the total betweenness values, and the remaining cluster center values ​​accounted for 90.55% of the total cluster center values. Although the remaining 4 nodes showed a relatively lower completeness in expressing the topology network, the remaining clusters still retained more than 90% of the information of the total clusters. When removing the nodes of the lowest and second and third classes, the betweenness values ​​of the remaining nodes accounted for 36.97% of the total betweenness values, and the remaining cluster center values ​​accounted for 67.13% of the total cluster center values. The remaining 2 nodes could no longer relatively completely express the main information of the topology network. This shows that a cluster size of 4 is optimal. Therefore, a cluster size of 4 was chosen for class-based elimination, specifically eliminating nodes from the lowest and second classes when the cluster size is 4.

[0111] Therefore, the state and response layers in Table 1 were removed. Since these layers are related to the components of the heavy platform, and the number of components is too large, the computational complexity is high, so some need to be removed. Therefore, only the functional failure tolerance Si and failure response degree Ri of other components were removed. Finally, the functional failure tolerance and failure response attributes of the structural cylinder, driver's cab, equipment compartment, and tire system located on the outermost layer of the heavy platform (the layer of components exposed to the outside) were used as the evaluation index system.

[0112] 2. Evaluation Methods

[0113] (1) Construction of DA-PSR evaluation model based on dimensional analysis

[0114] Traditional PSR framework theories and their improved versions such as DPSR primarily address the construction of assessment index systems, lacking relevant mathematical calculation models. This invention, focusing on the management attributes among the pressure index P, response index R, and state index S, proposes a DA-PSR assessment model for heavy platform survivability based on dimensional analysis. The PSR framework theory involves three physical quantities: P, S, and R, and thus has the function:

[0115] f(P,S,R)=0 (3)

[0116] As shown in Table 1, the pressure index P is a dimensionless quantity, and the response indexes are correlated. Therefore:

[0117] I = P σ ·(SR -1 (4)

[0118] Where, σ represents the evaluation result, -1 represents the reciprocal of the target value coefficient of the heavy platform, and -1 represents the reciprocal of the target value coefficient.

[0119] The pressure index P measures the likelihood of attacking a heavy platform once it is detected by the enemy. Since P ∈ [0,1], we can set σ = 1 to obtain the general expression for the DA-PSR evaluation model:

[0120]

[0121] In the formula, ω i Let θ be the weight of the i-th indicator, θ be the number of indicators, and * be the standardization factor.

[0122] (2) Construction of an index weighting model based on mutual information theory

[0123] While node betweenness can reflect the influence of each node on the topology to some extent, it fails to capture the directed propagation characteristics of damage within the topology. Therefore, this invention introduces mutual information theory from complex networks to objectively calculate the weights of key nodes in the topology.

[0124] For directed networks, nodes exhibit the dual characteristics of receiving and outputting information. In mutual information theory, the outgoing edge probability of node i is defined as:

[0125]

[0126] Define the probability of an incoming edge to node j as:

[0127]

[0128] In the formula, k in k out These are the in-degree and out-degree of the node, respectively;

[0129] The mutual information M(i,j) between node i and node j is:

[0130]

[0131] The information content of node i is defined as the sum of the mutual information from node i to all nodes pointing to node i minus the sum of the mutual information from all nodes pointing to i to node i, that is:

[0132]

[0133] In the formula, V out (i) is the set of nodes that a node points to, V in (i) is the set of nodes that point to a node.

[0134] Compare the betweenness values ​​and mutual information values ​​of critical nodes in a topological network. Figure 7 As shown in Table 2, the mutual information values ​​and normalized weight values ​​of the key nodes are as follows.

[0135] Table 2 Mutual information values ​​and normalized weight values ​​of key nodes

[0136]

[0137] Depend on Figure 7 As shown in Table 2, the largest mutual information value among the key nodes of the heavy platform is that of the heavy cylinder, with a mutual information value of 19.4423, followed by the tires, the cab, and the equipment compartment. The mutual information values ​​of the heavy cylinder and the tires are similar. The distribution of the mutual information values ​​is generally consistent with that of the node betweenness, but the order of the cab and the equipment compartment is reversed. This is because the equipment compartment of the heavy platform contains more components and subsystems, so its amplitude is larger in the betweenness calculation. Although the cab contains relatively fewer components and subsystems, its concentration is higher. It can be seen that the mutual information theory is more comprehensive in terms of the characteristics included in calculating the importance of nodes in the topological network. Therefore, this invention uses mutual information values ​​to construct an index weighting model. After normalizing the mutual information values ​​of the key nodes, they can be used as their respective weights for the weighting calculation of the heavy platform's survivability assessment, that is, to calculate the weight ω in equation (5). i .

[0138] (3) Construction of index calculation model based on extreme damage quantification

[0139] Performance indicators are quantitative descriptions of equipment's functional attributes, derived from its structural parameters and mapped through relevant physical mechanisms. Examples include measuring the mobility and ejection overload of heavy platforms. When equipment suffers damage, its structural parameters are compromised, and the performance indicators resulting from these parameters decrease until they can no longer meet mission performance requirements. The performance degradation process is as follows: Figure 8 As shown.

[0140] Let z be a certain performance index of a heavy platform, Z be the set of structural parameters corresponding to it, and g be the mapping relationship of the physical mechanism. Then there exists z = g(Z). Here, we define the state of the equipment at a random moment as the actual state, and denot the actual state of the performance index as z. a The set of structural parameters corresponding to the performance index in the actual state is denoted as Z. a Furthermore, we define a critical state where performance degrades beyond this critical state, no longer meeting task requirements. This critical state is called the limit state, denoted as z. l The set of structural parameters corresponding to the performance index under the limiting state is denoted as Z. l Then the performance failure tolerance Δz and the structural parameter failure tolerance ΔZ are:

[0141] △z=z a -z l (10)

[0142] △Z=Z a -Z l (11)

[0143] Obviously, the larger the failure tolerance, the stronger the resilience. However, the magnitude of the failure tolerance cannot fully explain the resilience. The rate of change of response within the failure tolerance range should also be considered, that is, the rate of change of performance indicators from the intact state to the limit state. When the failure tolerance is the same, the faster the rate of change of state, the weaker the resilience.

[0144] The degree of failure response is reflected in the changes of structural parameter Z, which is mainly related to structural mechanics and materials mechanics. However, the mathematical model is relatively complex and cumbersome. Therefore, the degree of failure response V can also be obtained by experimental or simulation methods. The data is then standardized using the arctangent function.

[0145] D * =arctanD*2 / π (12)

[0146] Where D represents the standardized values, namely Z and V;

[0147] This invention adopts Figure 9The relevant physics mechanism modeling and simulation methods shown above analyze and calculate the failure tolerance and change rate of the anti - damage evaluation index of a certain type of heavy - duty platform respectively. Through the index calculation models of limit damage quantification (10) - (11), the values of P, S, and R in the total evaluation model (5) can be calculated. The specific calculation results are shown in Table 3.

[0148] Table 3 Calculation Results of Evaluation Indexes

[0149]

[0150] 3. Evaluation Grade Criteria

[0151] (1) Criterion Quantification Oriented to Requirements

[0152] The essence of equipment is to complete tasks. Equipment evaluation without considering tasks is incomplete. When equipment is performing tasks, it is mainly restricted by task objectives and environmental conditions. Among them, task objectives are quantitative constraints on equipment performance indicators. For example, "conducting mobile deployment of a specified distance within a specified time" is a quantification of the mobility performance of equipment, and "completing a specified projectile task within a specified time" is a quantification of the heavy - duty performance of equipment.

[0153] (2) Task - Driven Dynamic Grading of Evaluation

[0154] The performance damage process with task status added is as Figure 10 shown. As Figure 10 can be seen, starting from the complete state C after the equipment is put into service, there are two key nodes in the performance damage process: the state node B that meets the task requirements and the state node L that meets the basic operation requirements. These two nodes divide the position of the actual state A of the equipment into three stages.

[0155] 1) When A ∈ [C, B], I(A → L) ≥ I(B → L), and this stage can meet the requirements of task anti - damage.

[0156] 2) When A ∈ [B, L], I(A → L) < I(B → L), and I(A → L) > 0. This stage cannot meet the requirements of task anti - damage, but can meet the basic operation requirements.

[0157] 3) When A ∈ [L, 0], I(A → L) ≤ 0. This stage cannot meet the basic operation requirements.

[0158] For the above three stages, an anti - damage evaluation grade criterion as shown in Table 4 based on the generalized protection time and performance indicators can be established. According to Table 4, the evaluation index calculation results in Table 3 are graded.

[0159] Table 4 Anti - damage Grade Criterion Table

[0160]

[0161] Suppose there are three tasks:

[0162] a. Capture a heavy position 15 kilometers away within 20 minutes and complete the mission;

[0163] b. Move to a random location 15 kilometers away within 20 minutes and complete the mission;

[0164] c. The nearby heavy positions were destroyed. Within one hour, the team moved to seize a heavy position 65 kilometers away and completed the mission.

[0165] The heavy platform shown in Table 3 needs to meet different specified speed and launch pressure requirements under the three mission requirements mentioned above, which determines the survivability assessment level of this type of heavy platform. Figure 11 As shown.

[0166] Depend on Figure 11 It is known that the requirements for the survivability of heavy platforms vary depending on the performance requirements of different tasks, and therefore the evaluation levels differ. When this type of heavy platform performs mission a, the requirements for maneuver speed and ejection pressure are relatively low. The minimum performance index to meet the mission requirements is 0.6475. The evaluation result of this type of heavy platform, 0.7373, is greater than this value. Therefore, its survivability assessment level for mission a is "excellent". When this type of heavy platform performs mission b, compared with mission a, the requirements for maneuver speed are increased. The minimum performance index to meet the mission requirements is 0.8244. The evaluation result of this type of heavy platform, 0.7373, is less than this value, but greater than the minimum performance index for operational requirements of 0.6475. Therefore, its survivability assessment level for mission b is "medium". When this type of heavy platform performs mission c, compared with mission a, the requirements for ejection pressure are increased. The minimum performance index to meet the mission requirements is 0.8362. The evaluation result of this type of heavy platform, 0.7373, is less than this value, but greater than the minimum performance index for operational requirements of 0.6475. Therefore, its survivability assessment level for mission c is "medium".

[0167] Contents not described in detail in this specification are existing technologies known to those skilled in the art. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for invulnerability evaluation of heavy platform based on DA-PSR model and complex network, characterized in that, The application relates to a method for evaluating the invulnerability of a heavy platform, which comprises the following steps: step 1, constructing an invulnerability evaluation index system based on a PSR framework theory; step 2, constructing a topological network of heavy platform structure components and operation functions based on a complex network theory; step 3, calculating the node betweenness value of each node in the topological network, preliminarily screening the indexes in the invulnerability evaluation index system, and then adopting a k-mean algorithm to divide and cluster the node betweenness value, and adopting a screening method of class elimination to secondarily screen the indexes; step 4, constructing a heavy platform invulnerability DA-PSR evaluation model based on the evaluation index system screened in step 3, weighting the platform invulnerability DA-PSR evaluation model by using an index weighting model based on a mutual information theory, and then calculating the evaluation indexes by using an index calculation model based on a limit damage quantification, so as to obtain an evaluation calculation result; and step 5, dividing the evaluation calculation result of the heavy platform into different grades according to an invulnerability grade criterion, and judging the invulnerability of the heavy platform. The specific steps for constructing the heavy platform invulnerability DA-PSR evaluation model comprise the following steps: step 41, establishing the invulnerability DA-PSR evaluation model; step 42, constructing an index calculation model based on a limit damage quantification, and calculating the pressure index P, the state index S and the response index R by using the index calculation model; and step 44, obtaining the final evaluation result of the heavy platform according to formula (5). The invulnerability evaluation index system constructed in step 1 comprises the following indexes: an invulnerability evaluation pressure index, an invulnerability evaluation state index and an invulnerability evaluation response index. The invulnerability evaluation pressure index is used for measuring the importance of the heavy platform, and comprises a target value index. The invulnerability evaluation state index is used for measuring the function failure tolerance of the equipment, and comprises a structure cylinder function failure tolerance, a cab function failure tolerance, an equipment cabin function failure tolerance, a tire system function failure tolerance and other component function failure tolerances. The invulnerability evaluation response index is used for measuring the speed of the failure response, and comprises a structure cylinder failure response degree, a cab failure response degree, an equipment cabin failure response degree, a tire system failure response degree and other component failure response degrees. The specific operation steps of step 3 comprise the following steps: step 31, adopting a node betweenness to represent the ratio of the number of the shortest paths passing through a certain node to the number of the shortest paths in the network, and using the node betweenness value to screen out the nodes with greater influences as the main index components; the calculation formula of the node betweenness value is as follows: step 32, adopting a k-mean algorithm to divide and cluster the component node betweenness, and using the algorithm to screen the components corresponding to the clustering levels with high node betweenness cluster center value ratios and small node numbers; and a Euclidean distance k-mean algorithm criterion function S is as follows: step 33, calculating the betweenness value ratios of the betweenness values of the lowest classes after the class elimination under different cluster numbers, selecting the class with the highest betweenness value ratio for class elimination, and thus eliminating the other component function failure tolerances and the other component failure response degrees. ​ where I is the evaluation result, P is the pressure index, S is the state index, R is the response index, ω i is the weight of the i-th index, θ is the number of indices, and * is the standardization. Step 42: constructing an index weighting model based on mutual information theory, and calculating the weight ω of the i-th index through the index weighting model i ; ​ ​ 2. The method according to claim 1, wherein, ​ ​ ​ ​ 3. The method of claim 1, wherein the method is characterized by, ​ ​ wherein is the number of edges of the shortest path between nodes j and k; n jk is the number of edges of the shortest path between nodes j and k through i; ​ where a is the number of clusters, c γ is the center point of the yth cluster, dist(c γ , x) is the distance from c γ to x. ​ Step 34: constructing a survivability evaluation index system with target value, structural cylinder function failure tolerance, cab function failure tolerance, equipment cabin function failure tolerance, tire system function failure tolerance, structural cylinder failure response degree, cab failure response degree, equipment cabin failure response degree, and tire system failure response degree as indexes.

4. The method according to claim 3, wherein, The specific operation steps of step 42 include: Step 421: define the mutual information M(i,j) from node i to node j as: where p i→j is the out-edge probability of node i; p j←i is the in-edge probability of node j; The information amount of node i is defined as the sum of mutual information from all nodes pointing to node i to node i minus the sum of mutual information from all nodes pointing to i to node i: wherein V out (i) is a set of nodes pointed to by the node, V in (i) is a set of nodes pointed to by the node; Step 422: calculate the mutual information value of the key node using formulas (8)-(9), and normalize the calculated mutual information value as the weight of the i-th index.

5. The method according to claim 4, wherein, The specific operation steps of step 43 include: Step 431: record the actual state of a performance index of the heavy platform at a random time as z a , record the structure parameter set corresponding to the performance index at the actual state as Z a , record the limit state as z l , record the structure parameter set corresponding to the performance index at the limit state as Z l ; Step 432: express the performance failure tolerance Δz as: Δz = z a - z l (10) where z a is the performance index actual state, z l is the limit state; The structural parameter failure tolerance ΔZ calculation formula: ΔZ = Z a - Z l (11); Step 433: establish an index calculation model for limit damage quantification according to formulas (10)-(11), and calculate the pressure index P, the state index S, and the response index R through a simulation tool.

6. The method according to claim 5, wherein, The specific operation steps of step 5 include: Step 51: divide the position of the actual state A of the heavy platform into three stages according to the state node B meeting the task requirements and the state node L meeting the basic operation requirements: 1) If A∈[C,B] and the generalized protection time I(A→L)≥I(B→L), it is judged that this stage can meet the requirements of the task against damage; 2) If A∈[B,L] and the generalized protection time I(A→L)<I(B→L) and I(A→L)>0, it is judged that this stage cannot meet the requirements of the task against damage, but can meet the basic operation requirements; 3) If A∈[L,0] and I(A→L)≤0, it is judged that this stage cannot meet the basic operation requirements; Step 52: if the heavy platform is in stage 1), its level is evaluated as excellent, if the heavy platform is in stage 2), its level is evaluated as medium, and if the heavy platform is in stage 3), its level is evaluated as poor; Step 53: for different heavy tasks, compare the evaluation calculation result of the heavy platform when performing the task with the minimum performance index meeting the survivability requirements when completing the task: If greater, the heavy platform is in stage 1) at this time, and the survivability level of the heavy platform is "excellent"; If less, then compare the evaluation calculation result with the minimum performance index meeting the operation requirements: i) If greater, the heavy platform is in stage 2) at this time, and the survivability level of the heavy platform is "medium"; ii) If less, the heavy platform is in stage 3) at this time, and the survivability level of the heavy platform is "poor".

Images