CN108319779A - Command and control cascade failure model method for building up based on m rank adjacency matrix - Google Patents
Command and control cascade failure model method for building up based on m rank adjacency matrix Download PDFInfo
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Abstract
The invention discloses a kind of command and control cascade failure model method for building up based on m rank adjacency matrix, is as follows：Step 1：Calculate each node angle value and node betweenness in network；Step 2：The initial load of calculate node；Step 3：Count operation link total number；Step 4：It calculates in sensing node to the shortest path between Strike node by the item number of specified node；Step 5：Calculate operation link betweenness；Step 6：Respectively initial load is calculated according to node degree and operation link betweenness；Step 7：Foundation degree index calculate node importance；Step 8：According to operation link betweenness calculate node importance；Step 9：Calculate the initial load of network；Step 10：Load capacity model is obtained according to initial load.The application establishes nonlinear load capacity model, effectively resists the cascading failure of command and control network, to improve the survivability of network according to the non-linear relation of load and capacity.
Description
Technical field
The invention belongs to military commanding and control field, specifically a kind of command and control based on m rank adjacency matrix
Cascade failure model method for building up.
Background technology
Command and control network under Information Condition assigns the hinge transmitted with information as command and control system order, with
The continuous improvement of battle field information degree, the command and control complicated network structure, information exchange are abnormally frequent, and network shows to save
The various heterogeneous, link of point it is multiple staggeredly the features such as.However, the cascading failure problem of research complex network interior nodes is still to establish
Load-capacity cascade failure model is main method.The model is when network node is under attack, and node can distribute load
To neighbor node, and then neighbor node load may be caused to cause whole network to be paralysed beyond load capacity.So how to accomplish
After node failure, load thereon is distributed to other nodes and node initial load how to determine it is big with node capacity
Small control is all problem needed to be considered.
Initial load model includes mainly：First, node definition initial load is based on, second is that defining initial load based on side.
The former is mainly that availability, node strength, neighbor node average degree, betweenness, random walk betweenness etc. are conventional and its improve index,
It is difficult to be suitable for large-scale charge network；The latter then defines initial network load according to the contribution margin on side, mainly from network
Performance Evaluation is carried out in terms of link structure robustness, it is difficult to accomplish to carry out comprehensive control to command and control network.Load capacity mould
In terms of type：Load capacity distribution, i.e. capacity and initial load proportional are carried out based on classical ML models, there is distribution
Non-uniform problem causes network performance poor.
Invention content
In view of the deficiencies of the prior art, the present invention accuses the topological structure and functional characteristic of network, root by in-depth analysis
According to Complex Networks Theory, the command and control cascade failure model based on m rank adjacency matrix is established, it is proposed that be based on m ranks
The initial load of adjacency matrix node contribution degree defines method, while considering pitch point importance and m ranks neighbor node to the section
Point percentage contribution establishes nonlinear load capacity model according to the non-linear relation of load and capacity, effectively resists commander's control
The cascading failure of network processed, to improve the survivability of network.
To realize above-mentioned purpose, the application the technical solution adopted is that, the command and control network based on m rank adjacency matrix
Cascading failure method for establishing model, is as follows：
Step 1：Calculate each node angle value and node betweenness in network；
Step 2：Initial load according to node angle value and node betweenness calculate node respectively；
Step 3：Count operation link total number：All sensing nodes are to the shortest path between all Strike nodes
Diameter total number；
Step 4：It calculates in sensing node to the shortest path between Strike node by the item number of specified node；
Step 5：Calculate operation link betweenness；
Step 6：Respectively initial load is calculated according to node degree and operation link betweenness；
Step 7：Foundation degree index calculate node importance；
Step 8：According to operation link betweenness calculate node importance；
Step 9：Calculate the initial load of network；
Step 10：Load capacity model is obtained according to initial load.
Further, the command and control network model is mainly by sensing node, command node, Strike node three
Class node forms.The sensing node refer to early warning, detection, scouting, surveillance coverage combat unit, as early warning radar,
Reconnaissance radar etc.；Command node refer to air situation fusion, commanding and decision-making, information synergism and distribution capability combat unit, such as refer to
Wave mechanism, information processing mechanism etc.；Strike node refers to the combat unit for having and the abilities such as intercepting, attack, injuring, such as all kinds of
Antiaircraft weapon etc..
Further, each node angle value, node angle value are expressed as the side being connected directly with the node in statistics network
The sum of number is formulated as：
Further, the calculation formula of node betweenness is expressed as：
In above formula, NjlIt indicates from node vjTo vlShortest path item number；Njl(i) it indicates from node vjTo vlShortest path
Diameter passes through node viItem number.
Further, calculate all sensing nodes to the shortest path total number between all Strike nodes formula
For：
Wherein, m (Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path item number, n be perception save
The number of point, N are the total number of operational node, and m is the number for accusing node.
Further, it calculates in sensing node to the shortest path between Strike node by the item number of specified node
Formula be：
Wherein mc(Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path in pass through node vcItem
Number, n are the number of sensing node, and N is the total number of operational node, and m is the number for accusing node.
Further, the operation link betweenness formula for calculating network node is：
In formula, i ≠ j ≠ c, i.e. sensing node, Strike node and the node v for passing through shortest pathcIt cannot be identical.
Further, the local message and consider according to node betweenness that the initial load Main Basiss node degree of node considers
Global information two from the aspect of.Initial load according to node degree is expressed as：
Wherein, kiIndicate that the degree of node, μ and α are adjustment parameter；Degree is bigger, and the side of connection is more, and the task of node is also
Heavier, corresponding initial load also increases；
Initial load according to node betweenness is expressed as：
Wherein, biIndicate that the betweenness of node, μ and α are adjustment parameter；The bigger explanation of betweenness passes through the information flow of the node more
More, the pivotal role of the node is stronger, and corresponding initial load is also relatively large.
Further, the intricate relationship of the hierarchical structure of command and control network makes single index be difficult to accurately measure section
The importance of point, and the importance of node is also influenced by the structure of network, also has prodigious correlation with neighbor node, layer
Level structure characteristic makes the operational commanding of high-level node be significantly lower than hierarchy node, the i.e. carrying of node with communication for coordination ability
Ability is related with level, and level is higher, and initial load is also bigger, therefore considers level.
Initial load based on degree is expressed as：
Initial load based on operation link betweenness is expressed as：
Wherein, diIndicate the layer where node；As number of plies diBigger, initial load is smaller.
Further, it is commented since command and control network cannot only rely on the single index such as node degree or operation link betweenness
Estimate node importance, need to consider network characteristic, while considering network multiple characteristic index, therefore with pitch point importance IiTable
Show：
Wherein, IiFor node viImportance, π(m)(i) it indicates and node viAll sets of node that connection distance is m, also referred to as
For node viM rank neighbor node set,To accuse node viM rank neighbor nodes be integrated into n-th of index about
To node v under beamiImportance contribution；ωiFor the weight proportion shared by different indexs, the sum of each index weights are 1, i.e.,Pass through flexible modulation coefficient ωiAnd then dynamically adjust the significance level of each index factor；μ and γ is adjustment parameter.
Further, degree index pitch point importance is expressed as：
The pitch point importance of operation link betweenness is expressed as：
Above-mentioned adjustment parameter meets as defined below：
u+γ+γ2+...+γm=1
μ is bigger, show node significance level more depend on itself importance, therefore, at the same consider local feature index and
The pitch point importance of global characteristics index operation link betweenness is expressed as：
Wherein, ω1And ω2The adjustment factor of degree of a representation and operation link betweenness respectively, and meet ω1+ω2=1, it is comprehensive
Upper described, node initial load is represented by：Li=Ii。
Further, nonlinear load capacity indicates that node is capable of the maximum capacity of carry load；Load capacity is got over
Greatly, construction cost is also higher, and excessive load capacity will also result in the wasting of resources, the level of command and control network structure
Property, it is non-linear also determine the non-linear of load capacity, therefore the non-linear table of command and control network load capacity is shown as：
Ci=Li+βLα i, i=1,2 ..., n
Wherein, LiFor node viInitial load, α, β be node load capacity customized parameter, α, β >=0, α, β are got over
Greatly, the extra duty that node can carry is more, and the capability to resist destruction of network is also stronger, but network cost can also increase, and need in net
Mutually weighed between network capability to resist destruction and cost.By adjusting the two parameters, load capacity and original negative can be analyzed
Which type of non-linear relation is presented between load, provides rational load capacity.
Beneficial effects of the present invention are：The application establishes the command and control cascade failure model based on m rank matrixes,
It proposes the initial load based on m rank neighbor node contribution degrees and defines method and nonlinear load capacity model, improve commander
Control the validity and feasibility of cascade failure model.
Description of the drawings
The present invention shares 5 width of attached drawing：
Fig. 1 is load capacity and initial load relational graph；
Fig. 2 is change curve of the node importance with parameter μ；
Fig. 3 is influence diagram of the node initial load parameter μ to cascading failure survivability；
Fig. 4 is influence diagrams of the nonlinear parameter α to cascade survivability；
Fig. 5 is the cascading failure survivability comparison diagram under different α are limited.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention clearer, right in the following with reference to the drawings and specific embodiments
The present invention is described in detail.
Below to involved in the application to word be explained：
Define 1：Operation link betweenness, operation link betweenness indicate in the entire network operational information stream from sensing node to
In Strike node process, by sensing node OiTo strike node FjBetween most short operation chain travel permit number pass through some node
vcItem number with by sensing node OiTo strike node FjBetween most short operation chain travel permit number ratio be expressed as operation link Jie
Number.
Define 2：Pitch point importance, because cannot rely on node degree or operation link betweenness in practical command and control network
Etc. single index evaluation node importance, need to consider meshed network characteristic, while considering multiple characteristic index, moreover, node
Actual contribution should be related according to the level where its node in a network, thus definition node importance be from many aspects into
Row weighs the node existing importance in the entire network, and pitch point importance is defined as：
Wherein, IiFor node viImportance, π(m)(i) it indicates and node viAll sets of node that connection distance is m, also referred to as
For node viM rank neighbor node set,To accuse node viM rank neighbor nodes be integrated into n-th of Index Constraints
Under to node viImportance contribution.ωiFor the weight proportion shared by different indexs, the sum of each index weights are 1, i.e.,Pass through flexible modulation coefficient ωiThe significance level of each index factor can dynamically be adjusted.μ and γ is adjustment parameter.
Embodiment 1
The present embodiment is the cascading failure method for establishing model of the command and control network based on m rank adjacency matrix, specific to walk
It is rapid as follows：
Step 1：Each node angle value in network is calculated, calculation formula is
The value of the betweenness of each node in network is calculated, calculation formula is
Wherein, NjlIt indicates from node vjTo vlShortest path item number；Njl(i) it indicates from node vjTo vlShortest path
By node viItem number.
Step 2：Initial load according to node angle value and node betweenness calculate node respectively；
Initial load based on node degree is：
Initial load based on node betweenness is：
Step 3：Count operation link total number, calculate all sensing nodes between all Strike nodes most
The formula of short path total number is：
Wherein, m (Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path item number, n be perception save
The number of point, N are the total number of operational node, and m is the number for accusing node.
Step 4：Calculate the item number in sensing node to the shortest path between Strike node by specified node
Formula is：
Wherein mc(Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path in pass through node vcItem
Number, n are the number of sensing node, and N is the total number of operational node, and m is the number for accusing node.
Step 5：The operation link betweenness of network is calculated, calculation formula is：
In formula, i ≠ j ≠ c, i.e. sensing node, Strike node and the node v for passing through shortest pathcIt cannot be identical.
Step 6：The initial load of solution node degreeWith the initial load of operation link betweenness
Initial load based on degree can be expressed as：
Initial load based on operation link betweenness can be expressed as：
Step 7：The pitch point importance of solution degree indexDegree index pitch point importance can obtain：
Step 8：Solve the pitch point importance of operation link betweennessThe pitch point importance of operation link betweenness is：
Step 9：Calculate the initial load I of networki, initial load is expressed as：
Step 10：Calculate network load capacity Ci, network load capacity model is expressed as：
Ci=Li+βLα i, i=1,2 ..., n
Embodiment 2
The present embodiment is by a kind of cascading failure model of the command and control network based on m rank adjacency matrix proposed by the present invention
Method for building up analyzes and researches to node load and load capacity, the layer where different nodes in control network
Secondary structure simulates the load of different levels node, to obtain the relationship between node load and load capacity to net
The disturbance degree of the cascading failure of network.
Attached drawing 1 is load capacity and initial load relational graph, as adjustment parameter α=1, Ci=(1+ β) Li, at this time initially
In a linear relationship between load and load capacity, model degradation is the ML models of classics.Nonlinear load capacity is given in figure
The relationship of model and linear ML models load capacity and initial load under logarithmic coordinates system.The original negative of nonlinear load model
There is relatively large load capacity when carrying smaller, residual capacity is also relatively large, and when initial load is larger, load capacity is less than ML moulds
The load capacity of type, residual capacity can be smaller.
Attached drawing 2 is change curve of the node importance with parameter μ, the weight of node when taking different parameters by comparative analysis μ
The property wanted changes, it will be seen that as μ=1.0, the importance of node is only related to itself importance, i.e. the degree by node itself and operation
Link betweenness determines, does not account for influence of the neighbor node to the node.As 0.5 ＜ μ ＜ 1, node importance is by itself weight
It spends and neighbor node contribution degree codetermines, with the reduction of μ, increase effect of the m ranks neighbor node to this node, it can not only
The importance of enough accurately Evaluation Center nodes, also can obviously distinguish effect of the edge leaf node to this node.It is average to lose
Effect scale CF can analyze shadow of the cascading failure dynamic process to Survivabilities of Networks as the important indicator for weighing network performance
It rings.
Attached drawing 3 is influence of the node initial load parameter μ to cascade survivability, is the initial ginseng of further analysis to Fig. 2
When number μ goes how to be worth, command and control cascade survivability can be more preferable.Refer to using average failure scale CF as cascade survivability evaluation
Mark, when parameter alpha takes different value, Comprehensive Correlation cascading failure survivability is with the variation tendency for tolerating parameter beta.
Attached drawing 4 is influences of the nonlinear parameter α to cascade survivability, takes α ∈ { 0.6,0.1,1.0,1.2,1.4 },
When setup parameter μ=0.6, after Multi simulation running is averaged, the influence of Survivabilities of Networks parameter beta, it can be seen from the figure that, with
Parameter alpha and the increase of β, the scale CF that averagely fails declines rapidly, and the anti-cascading failure ability of command and control network also accordingly carries
Height, but after β is more than 0.2, variation tendency tends to straight line, is had little effect to the average failure scale of network.
Attached drawing 5 is the cascade survivability comparison diagram that different α first fix, and is by proposed in this paper based on m rank adjacency matrix
Cascading failure model is compared and analyzed with typical cascading failure model, the initial load selection degree of model and the definition of betweenness
Method.Different restriction parameter alpha comprehensive verification this paper models are taken, cascade survivability index CF is with the variation tendency for tolerating parameter beta.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Any one skilled in the art in the technical scope of present disclosure, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (10)
1. the command and control cascade failure model method for building up based on m rank adjacency matrix, which is characterized in that specific steps are such as
Under：
Step 1：Calculate each node angle value and node betweenness in network；
Step 2：Initial load according to node angle value and node betweenness calculate node respectively；
Step 3：Count operation link total number：All sensing nodes are total to the shortest path between all Strike nodes
Item number；
Step 4：It calculates in sensing node to the shortest path between Strike node by the item number of specified node；
Step 5：Calculate operation link betweenness；
Step 6：Respectively initial load is calculated according to node degree and operation link betweenness；
Step 7：Foundation degree index calculate node importance；
Step 8：According to operation link betweenness calculate node importance；
Step 9：Calculate the initial load of network；
Step 10：Load capacity model is obtained according to initial load.
2. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is that each node angle value in statistics network, node angle value is expressed as the sum of the number on side being connected directly with the node, uses
Formula is expressed as：
3. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is that the calculation formula of node betweenness is expressed as：
In above formula, NjlIt indicates from node vjTo vlShortest path item number；Njl(i) it indicates from node vjTo vlShortest path warp
Cross node viItem number.
4. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is that the formula for calculating all sensing nodes to the shortest path total number between all Strike nodes is：
Wherein, m (Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path item number, n be sensing node
Number, N are the total number of operational node, and m is the number for accusing node.
5. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is that the formula for calculating the item number in sensing node to the shortest path between Strike node by specified node is：
Wherein mc(Oi,Fj) it is sensing node OiTo Strike node FjBetween shortest path in pass through node vcItem number, n
For the number of sensing node, N is the total number of operational node, and m is the number for accusing node.
6. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 4 or 5,
It is characterized in that, the operation link betweenness formula for calculating network node is：
In formula, i ≠ j ≠ c, i.e. sensing node, Strike node and the node v for passing through shortest pathcIt cannot be identical.
7. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is that the initial load according to node degree is expressed as：
Wherein, kiIndicate that the degree of node, μ and α are adjustment parameter；Degree is bigger, and the side of connection is more, and the task of node is also more numerous
Weight, corresponding initial load also increase；
Initial load according to node betweenness is expressed as：
Wherein, biIndicate that the betweenness of node, μ and α are adjustment parameter；Betweenness is bigger, and explanation is more by the information flow of the node, should
The pivotal role of node is stronger, and corresponding initial load is also relatively large.
8. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 7, special
Sign is,
Initial load based on degree is expressed as：
Initial load based on operation link betweenness is expressed as：
Wherein, diIndicate the layer where node；As number of plies diBigger, initial load is smaller.
9. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 1, special
Sign is, pitch point importance IiIt indicates：
Wherein, IiFor node viImportance, π(m)(i) it indicates and node viAll sets of node that connection distance is m, are also referred to as saved
Point viM rank neighbor node set,To accuse node viM rank neighbor nodes be integrated into it is right under n-th of Index Constraints
Node viImportance contribution；ωiFor the weight proportion shared by different indexs, the sum of each index weights are 1, i.e.,
Pass through flexible modulation coefficient ωiAnd then dynamically adjust the significance level of each index factor；μ and γ is adjustment parameter；
Degree index pitch point importance is expressed as：
The pitch point importance of operation link betweenness is expressed as：
Above-mentioned adjustment parameter meets as defined below：
u+γ+γ2+...+γm=1
μ is bigger, shows that node significance level more depends on itself importance, therefore, while considering local feature index and the overall situation
The pitch point importance of characteristic index operation link betweenness is expressed as：
Wherein, ω1And ω2The adjustment factor of degree of a representation and operation link betweenness respectively, and meet ω1+ω2=1, to sum up institute
It states, node initial load is represented by：Li=Ii。
10. the command and control cascade failure model method for building up based on m rank adjacency matrix according to claim 9,
It is characterized in that, the non-linear table of command and control network load capacity is shown as：
Ci=Li+βLα i, i=1,2 ..., n
Wherein, LiFor node viInitial load, α, β be node load capacity customized parameter, α, β >=0, α, β are bigger, section
The extra duty that point can carry is more, and the capability to resist destruction of network is also stronger.
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| CN111784135A (en) * | 2020-06-22 | 2020-10-16 | 中国人民解放军军事科学院国防科技创新研究院 | System combat capability quantitative analysis method based on hyper-network and OODA (object oriented data acquisition) ring theory |
| CN111784135B (en) * | 2020-06-22 | 2021-06-11 | 中国人民解放军军事科学院国防科技创新研究院 | System combat capability quantitative analysis method based on hyper-network and OODA (object oriented data acquisition) ring theory |
| CN112291827A (en) * | 2020-10-29 | 2021-01-29 | 王程 | Social attribute driven delay tolerant network route improvement algorithm |
| CN113342523A (en) * | 2021-06-04 | 2021-09-03 | 中国人民解放军军事科学院评估论证研究中心 | Method, device, equipment and medium for analyzing equilibrium of combat system structure |
| CN113342523B (en) * | 2021-06-04 | 2023-10-03 | 中国人民解放军军事科学院评估论证研究中心 | Battle architecture balance analysis method, device, equipment and medium |
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