CN112464422B - Greedy algorithm-based method for improving reliability of K-terminal network - Google Patents

Greedy algorithm-based method for improving reliability of K-terminal network Download PDF

Info

Publication number
CN112464422B
CN112464422B CN202011376971.8A CN202011376971A CN112464422B CN 112464422 B CN112464422 B CN 112464422B CN 202011376971 A CN202011376971 A CN 202011376971A CN 112464422 B CN112464422 B CN 112464422B
Authority
CN
China
Prior art keywords
network
edge
spectrum
edges
importance
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011376971.8A
Other languages
Chinese (zh)
Other versions
CN112464422A (en
Inventor
蔡志强
段锋
郭雅琪
司书宾
王宇航
张攀
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Northwestern Polytechnical University
Original Assignee
Northwestern Polytechnical University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Northwestern Polytechnical University filed Critical Northwestern Polytechnical University
Priority to CN202011376971.8A priority Critical patent/CN112464422B/en
Publication of CN112464422A publication Critical patent/CN112464422A/en
Application granted granted Critical
Publication of CN112464422B publication Critical patent/CN112464422B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
  • Complex Calculations (AREA)

Abstract

The invention belongs to the field of research on the reliability of a rule network system, and particularly relates to a greedy algorithm-based method for improving the reliability of a K-terminal network. The method adopts a greedy algorithm and a Monte Carlo algorithm, combines importance analysis, and provides powerful support for numerical analysis research of medium or large K-terminal network reliability prediction. The method adopts the importance analysis and the Monte Carlo algorithm to estimate and search the optimization scheme of the network edge, and the modeling process is simple and efficient. The invention divides the large-scale network to be optimized into a plurality of groups of network edges, takes the network edges as basic optimization objects, can accurately and quickly provide an optimization scheme, thereby realizing the reliability optimization of the large-scale network and ensuring that the reliability index of the large-scale network meets the requirement.

Description

Greedy algorithm-based method for improving reliability of K-terminal network
Technical Field
The invention belongs to the field of research on the reliability of a rule network system, and particularly relates to a greedy algorithm-based method for improving the reliability of a K-terminal network.
Background
Network systems are distributed in various fields in social life, network reliability is an important overall performance index of the network systems, the network reliability shows the capability of the network to maintain normal work, and the network with high reliability often has strong anti-interference capability. Because network systems are widely and critically important, the study on network reliability becomes particularly important. The Chinese patent with publication number CN107967545A discloses a method for calculating the importance of Birnbaum and structure importance of subsystem components in probability safety evaluation. Firstly, analyzing the importance of the component to the system through the Birnbaum importance and the structural importance of the system and the component. Then, an in-depth rule of the Birnbaum importance and the structure importance is disclosed, and the required Birnbaum importance and structure importance information is provided for the importance analysis of the safety evaluation. However, the traditional importance is mainly applied to the dual-end network system, and there is a fresh research in the field of K-terminal networks, and after the traditional importance is popularized to the K-terminal networks, the research on the calculation methods of each importance and the relationship between different network importance is very little and there is no theoretical guidance.
A network system usually consists of a plurality of nodes and a plurality of edges, and the influence of different network edges on the performance of the network system is different. Generally, due to practical cost limitation, a network system needs to be efficiently designed, performance enhanced and operated and maintained under limited resources, and at this time, resources need to be reasonably distributed according to the importance of the network side to the network system, and the limited resources are used on the most important small amount of network sides. The importance is a quantitative representation of importance, and particularly, the importance can quantify the degree of importance of a network edge to the entire network system. The network edges are sorted based on the importance, and when the network fails, the network edges which are maintained preferentially are determined according to the sorting result, so that the maintenance efficiency can be effectively improved.
Disclosure of Invention
In order to strengthen the weakest part causing the network system failure under the condition of limited optimization resources so as to improve the reliability of the network system, the invention provides a method for improving the reliability of a K-terminal network based on a greedy algorithm. The method adopts a greedy algorithm and a Monte Carlo algorithm, combines importance analysis, and provides powerful support for numerical analysis research of medium or large K-terminal network reliability prediction. The network edge importance degree predicted and obtained based on the method is sequenced, and the reliability of the K-terminal network can be effectively improved under the condition that the provided optimized resources are limited.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for improving reliability of a K-terminal network based on a greedy algorithm is characterized by comprising the following steps:
step 1, analyzing the structure of a K-terminal network;
this step analyzes a particular K-terminal network to obtain a set of nodes and network edges for the network, and a set of terminal nodes. The terminal node is a key node for determining whether the K-terminal network is connected or not.
Step 2, calculating the accumulated D-spectrum of the K-terminal network; the method specifically comprises the following substeps:
FIG. 1 is a flow chart of a greedy algorithm based Monte Carlo algorithm;
substep 1: the value of the net D-spectrum is estimated using a monte carlo algorithm based on a greedy algorithm. According to the definition of D-spectrum, a permutation combination pi (pi) of random simulation network edge 1 ,...,π r ,...,π n ) Then, simulating a continuous destruction process of the network edges, namely sequentially destroying the network edges from left to right according to the arrangement until the network fails, and recording the combination of the failed network edges; the process is repeated and simulated for M times, M>2；
Substep 2: let t be the current number of repeated operations, n be the number of network edges, a r Number of permutation combinations representing the failure of the first r edges to cause network failure, b ri Representing the number of permutations, c, that cause network failure when the first r edges fail and edge i also fails rij Representing the number of permutation and combination which cause network failure when the front r edges fail and the edges i and j also fail;
substep 3: recording the minimum number of edges which cause network failure currently, namely the anchor r (pi) of the arrangement, and obtaining a by accumulating the count r And b ri (ii) a Then, using a r N! [ and ] M and b ri N! the/M estimation results in a network D-spectrum Z (k) and a D-spectrum Z (k, 0) of the network edge i i ) Then, according to the relation Z (k) Z (k, 1) between the D-spectrum and the D-spectrum of the network edge i i )+Z(k,0 i ) Obtaining Z (k, 1) i ) An estimated value of (d);
wherein, Z (k) represents that k network edges in the network fail, and the combined number of the network in the fault state when the (n-k) network edges run. Z (k, 1) i )(Z(k,0 i ) Represents the number of combinations that the network is in a failed state when there are k network edges failing and network edge i is running (failing). Called Z (k, 1) i )(Z(k,0 i ) D x-spectrum of network edge i).
Step 3, calculating a mixed D star-spectrum of the network edge i;
using c on the basis of the D-spectra obtained in step 2 rij N! the/M estimation yields a network edge mixture D-spectrum Z (k, 1) i ,1 j ). According to the relationship between the D-spectrum of the network edge i and the mixed D-spectrum of the network edge, Z (k, 1) i )＝Z(k,1 i ,0 j )+Z(k,1 i ,1 j )，Z(k,0 i )＝Z(k,0 i ,0 j )+Z(k,0 i ,1 j ) Further, a mixed D-spectrum Z (k, 1) of the network edge i and the network edge j is obtained i ,0 j )、Z(k,0 i ,1 j ) And Z (k, 0) i ,0 j ) An estimate of (d);
wherein, Z (k, 1) i ,0 j ) And the combination number indicates that when k network edges fail and the network edge i runs, the network edge j fails and the network is in a failure state. Scale Z (k, 1) i ,0 j ) Is the mixed D x-spectrum of network edge i.
Step 4, calculating the importance of the network edge based on the D star-spectrum;
and aiming at the Birnbaum importance, the Bayes importance and the replacement importance, respectively calculating the numerical values of the Birnbaum importance, the Bayes importance and the replacement importance under the K-terminal network by using the D-spectrum. The specific calculation processes are respectively as follows:
(1) the Birnbaum importance of the network edge i in the K-terminal network is as follows:
Figure BDA0002807391870000031
in the formula, q is the reliability of the network edge, p is the unreliability of the network edge, n is the total number of the network edges, k is the number of failed network edges, and i represents a specific network edge. According to the relation Z (k) Z (k, 1) of the D spectrum to the D spectrum of the network edge i i )+Z(k,0 i ) Thus, the above formula can also be expressed as:
Figure BDA0002807391870000032
(2) the Bayesian network importance of the network edge i in the K-terminal network is as follows:
Figure BDA0002807391870000033
(3) the replacement importance of the network edge i in the K-terminal network is as follows:
Figure BDA0002807391870000034
Figure BDA0002807391870000035
if G (0) i ,1 j ,p)≥G(1 i ,0 j P), then we say that the permutation importance of network edge i is higher than that of network edge j.
Step 5, analyzing the importance of the network edge to sort and group;
under the condition of a plurality of groups of different network edge reliability degrees p, the three importance degrees are measured, then each group of network edges is sequenced, and the network edges with similar importance degrees are divided into one group.
Step 6, carrying out reliability optimization on the K-terminal network;
and according to the arrangement result obtained in the step 5, taking the first K network edges, and replacing the original network edge with the network edge with higher reliability, so as to reduce the unreliability of the K-terminal network.
Has the beneficial effects that:
the method for improving the reliability of the K-terminal network based on the greedy algorithm adopts the importance analysis and the Monte Carlo algorithm to estimate and search the optimization scheme of the network edge, and the modeling process is simple and efficient. The invention divides the large-scale network to be optimized into a plurality of groups of network edges, and the network edges are taken as basic optimization objects, so that an optimization scheme can be accurately and quickly given, thereby realizing the reliability optimization of the large-scale network and enabling the reliability index to meet the requirement.
Drawings
The method for improving the reliability of the K-terminal network based on the greedy algorithm according to the present invention is further described in detail with reference to the accompanying drawings and the implementation manners.
FIG. 1 is a flowchart of the Monte Carlo algorithm based on the greedy algorithm in the embodiment.
Fig. 2 shows, in an embodiment, a three terminal network N3-terminal.
FIG. 3 is a Birnbaum importance value of network edge i in network N3-terminal under different p values in the embodiment.
FIG. 4 is a Bayesian importance value of the N3-terminal network edge i under different p-values in the embodiment.
FIG. 5 shows G (0) at different p-values in the examples 3 ,1 j P) and G (0) i ,1 3 P) value comparison graph.
FIG. 6 is a graph illustrating the network N3-terminal unreliability value obtained after optimizing different network edges i in the embodiment.
Detailed Description
The embodiment is a method for improving the reliability of a K-terminal network based on a greedy algorithm.
The present invention is further described in detail with reference to fig. 2-6 and the detailed description of the present invention with reference to the three-terminal network N3-terminal as an example, which specifically includes the following steps:
step 1, analyzing the structure of a K-terminal network;
given a cuboid network N3-terminal, as shown in FIG. 2. The network N3-terminal consists of 8 nodes and 12 network edges. Wherein the set of nodes V ═ { V ═ V 1 ,v 2 ,v 3 ,v 4 ,v 5 ,v 6 ,v 7 ,v 8 A set of network edges E ═ 1,2,3,4,5,6,7,8,9,10,11,12}, a set of end nodes K ═ v } 1 ,v 3 ,v 8 }. The network N3-terminal is connected if and only if three end nodes are connected.
Step 2, calculating the accumulated D-spectrum of the K-terminal network;
a Monte Carlo algorithm based on greedy algorithm, using Matlab to pass through 10 6 Sub-loop estimation of D x spectrum Z (k, 0) of network edge i in network N3-terminal i )，Z(k,1 i ) And a D x-spectrum z (k) of network N3-terminal, wherein k is taken from 1 to 12; i is taken from 1 to 12. To watchThe grid is convenient to write, and Z (k, 0) in the table 1 is written i ) Abbreviated as Z k,i Let Z (k, 1) in Table 2 i ) Abbreviated as Z k,1.i 。
TABLE 1D-spectra Z (k, 0) of network edges at different k values in network N3-terminal i )
Figure BDA0002807391870000041
Figure BDA0002807391870000051
TABLE 2D-spectra Z (k, 1) of network edges at different k values in network N3-terminal i )
Figure BDA0002807391870000052
TABLE 3D spectrum Z (k) of network N3-terminal
Figure BDA0002807391870000053
Step 3, calculating a mixed D-spectrum of the network edge i;
a Monte Carlo algorithm based on a greedy algorithm, which is based on 10 by utilizing Matlab software 6 The repeated random permutations of times, the mixed D-spectrum for network edge i and network edge j in network N3-terminal was estimated. Since there are 12 net edges in net N3-terminal, the mixed D x-spectrum of any two net edges is very diverse. The magnitude of the mixed D x-spectrum of network edge 1, network edge 3, and network edge 8, respectively, and the remaining eleven network edges is calculated as follows.
Table 4 shows the mixed D x-spectrum Z (k, 0) of network edge 1 and network edge i 1 ,1 i ) Table 5 shows the mixed D x-spectrum Z (k, 0) of network edge 1 and network edge i i ,1 1 ) Wherein k is from 1 to 12; i is taken from 1 to 12. For convenience of writing the table, a mixed D x-spectrum Z (k, 0) of network edge 1 and network edge i in table 4 is used 1 ,1 i ) Is abbreviated as
Figure BDA0002807391870000061
The mixed D-spectrum Z (k, 0) of network edge 1 and network edge i in Table 5 i ,1 1 ) Is abbreviated as
Figure BDA0002807391870000062
Table 4 mixed D x-spectrum Z (k, 0) of network edge 1 and network edge i 1 ,1 i )
Figure BDA0002807391870000063
Table 5 mixed D x-spectrum Z (k, 0) of network edge 1 and network edge i i ,1 1 )
Figure BDA0002807391870000064
Figure BDA0002807391870000071
Table 6 shows the mixed D x-spectrum Z (k, 0) of network edge 3 and network edge i 3 ,1 i ) Table 7 shows the mixed D x-spectrum Z (k, 0) of network edge 3 and network edge i i ,1 3 )。
Table 6 mixed D x-spectrum Z (k, 0) of network edge 3 and network edge i 3 ,1 i )
Figure BDA0002807391870000072
Table 7 mixed D x-spectrum Z (k, 0) of network edge 3 and network edge i i ,1 3 )
Figure BDA0002807391870000073
Figure BDA0002807391870000081
Table 8 shows the mixed D x-spectrum Z (k, 0) of network edge 8 and network edge i 8 ,1 i ) Table 9 shows the mixed D x-spectrum Z (k, 0) of network edge 8 and network edge i i ,1 8 )。
Table 8 mixed D x-spectrum Z (k, 0) of network edge 8 and network edge i 8 ,1 i )
Figure BDA0002807391870000082
Table 9 mixed D x-spectrum Z (k, 0) of network edge 8 and network edge i i ,1 8 )
Figure BDA0002807391870000083
Figure BDA0002807391870000091
Step 4, calculating the importance of the network edge based on the D star-spectrum;
(1) brinbam importance
Birnbaum importance table 10 of net edge i in net N3-terminal is estimated by Monte Carlo algorithm based on greedy algorithm under different p-values (p is 0.2, 0.4, 0.6, 0.8 and 0.95 respectively). Moreover, according to the data in table 10, the Birnbaum importance (BIMi) values of network edge i in network N3-terminal are plotted by classifying with p values, and fig. 3 is a graph. Wherein i is 1,2,3,4,5,6,7,8,9,10,11, 12.
TABLE 10 Birnbaum Importance (BIM) of network edge i in network N3-terminal at different p-values i ) Numerical value
Figure BDA0002807391870000092
(2) Bayesian importance
The Bayesian importance values of network edge i in network N3-terminal were estimated using a greedy-based Monte Carlo algorithm for different values of p (p is 0.2, 0.4, 0.6, 0.8, and 0.95, respectively) (Table 11). Moreover, according to the data in table 11, the bayesian importance (Bayi) value of the network edge i in the network N3-terminal under different p values is plotted by classifying with p values, and fig. 4 is shown.
TABLE 11 network N at different p-values 3-terminal Bayesian importance of network edge i (Bay) i ) Numerical value
Figure BDA0002807391870000101
(3) Importance of permutation
The ranking results of the network edge replacement importance in the network N3-terminal are obtained by comparing the size of the mixed D-spectrum of the network edge 1, the network edge 3, and the network edge 8 with the remaining ten network edges, respectively. For network edge 1 and network edge i, the following relationship can be derived from 4 and table 5:
TABLE 12Z (k, 0) for network edge 1 and network edge i 1 ,1 i ) And Z (k, 0) i ,1 1 ) Size comparison and PeIM comparison
Figure BDA0002807391870000102
Figure BDA0002807391870000111
According to the definition of the importance of the replacement, the value of G (0) i ,1 j ,p)-G(0 j ,1 i When p) is greater than or equal to 0, there is PeIM i ≥PeIM j . To verify the above conclusions, the greedy algorithm-based monte carlo algorithm was used to estimate the reliability of the network edge at different p-values (p is 0.2, 0.4, 0.6, 0.8 and 0.95, respectively), G (0) for network edge 1 and network edge i 1 ,1 i P) (Table 13) and G (0) i ,1 1 P) (table 14).
TABLE 13G (0) for network edge 1 and network edge i for different values of p 1 ,1 i ,p)
Figure BDA0002807391870000112
TABLE 14G (0) for network edge 1 and network edge i for different values of p i ,1 1 ,p)
Figure BDA0002807391870000113
Figure BDA0002807391870000121
For a clearer observation of the obtained result, the combination of the network edge 1 and the other network edges is classified as an abscissa, and G (0) 1 ,1 i P) and G (0) 1 ，1 i P) is the ordinate, G (0) is plotted for different p values 1 ，1 i P) and G (0) 1 ，1 i P) where p is equal to 0.2, 0.4, 0.6, 0.8 and 0.95, respectively.
From tables 13, 14 and 5, G (0) of network edge 1 and network edge i is used based on the definition of the replacement importance 1 ,1 i P) and G (0) i ,1 1 P) are compared to the ranking of the replacement importance of network edge 1 and network edge i in the available network N3-terminal as follows.
TABLE 15G (0) for network edge 1 and network edge i 1 ,1 i P) and G (0) i ,1 1 P) size comparison and PeIM comparison
Figure BDA0002807391870000122
Similarly, for the network edge 3, the network edge 8 and the network edge i may obtain G of the network edge 3 and the network edge i through the same operation (G0 3 ,1 i P) and G (0) i ,1 3 P) value comparison (Table 16) and G (0) of network edge 8 to network edge i 8 ,1 i P) and G (0) i ,1 8 P) (Table 17).
TABLE 16G (0) of network edge 3 and network edge i 3 ,1 i P) and G (0) i ,1 3 P) size comparison and PeIM comparison
Figure BDA0002807391870000131
TABLE 17G (0) of network edge 8 and network edge i 8 ,1 i P) and G (0) i ,1 8 P) size comparison and PeIM comparison
Figure BDA0002807391870000132
Step 5, analyzing the importance of the network edge to carry out sequencing and grouping;
as can be seen from fig. 3, under different p values, the Birnbaum importance of the network edge is divided into 3 groups, and each group has almost the same value of the Birnbaum importance of the network edge. The first group is {1,2,5}, the second group is {3,4,6,7,9,10}, and the third group is {8,11,12 }.
From fig. 4, the bayesian importance of the network edges is sorted into 3 groups, each group having nearly the same value of the network edge D-spectrum. The first group is {1,2,5}, the second group is {3,4,6,7,9,10}, and the third group is {8,11,12 }.
From tables 15,16,17, the importance of finding network edges based on the importance of permutation can be divided into 3 groups, each group having nearly the same importance. The first group is {1,2,5}, the second group is {3,4,6,7,9,10}, and the third group is {8,11,12 }.
Step 6, carrying out reliability optimization on the K-terminal network;
assuming that the network nodes are absolutely reliable, the reliability of all network edges is independent of each other, and the reliability of each edge is 0.65, i.e., p is 0.65, the unreliability q of the network edge is 0.35. Using Matlab based onMonte Carlo algorithm of greedy algorithm, through 10 6 The sub-loop estimates that the unreliability of the network N3-terminal at this time is 2.333E-07.
If the optimized resources are limited, the reliability of 1 network edge in the network N3-terminal can be raised to v, and v is 0.85, that is, the unreliability of the optimized network edge is 0.15. For any 1 network edge i in the network N3-terminal, the unreliability of the optimized network is solved, and the unreliability of the network after the network edge i is optimized is obtained
Figure BDA0002807391870000141
Similarly, using Matlab, a greedy algorithm based Monte Carlo algorithm, through 10 6 Network N3-terminal unreliability Q obtained after sub-loop estimation to optimize different network edges i i Numerical values (Table 18).
Table 18 network N 3-terminal Degree of unreliability Q i Numerical value
Figure BDA0002807391870000142
The data in table 18 is shown in graphical form as shown in fig. 6. The abscissa in fig. 6 is the currently optimized network edge i; the ordinate is the network N3-terminal unreliability Q after the corresponding optimization network edge i i . On the basis, the network N3-terminal unreliability Q in the initial state before optimization is increased, and the abscissa is represented by a number '0'; the ordinate is the original network N3-terminal uncertainty Q.
From the results of table 18 and fig. 6, when optimizing only 1 network edge by fixing the optimized resources, the first group of network edges with relatively higher importance, i.e., network edge 1, network edge 2, and network edge 5, should be selected first. Therefore, in case of limited optimization resources, the reliability of the first set of network edges should be considered optimized first, second the second set of network edges, and finally the third set of network edges. Therefore, limited resources are utilized, the unreliability of the network is minimized, and the reliability of the network system is improved to the maximum extent.

Claims (1)

1. A method for improving reliability of a K-terminal network based on a greedy algorithm is characterized by comprising the following steps:
step 1, analyzing the structure of a K-terminal network;
this step analyzes a particular K-terminal network to obtain a set of nodes and network edges for the network, and a set of terminal nodes. The terminal node is a key node for determining whether the K-terminal network is connected or not.
Step 2, calculating the accumulated D-spectrum of the K-terminal network; the method specifically comprises the following substeps:
FIG. 1 is a flowchart of a greedy algorithm based Monte Carlo algorithm;
substep 1: the value of the net D-spectrum is estimated using a monte carlo algorithm based on a greedy algorithm. According to the definition of D-spectrum, a permutation combination pi ═ of random simulation network edge 1 ,...,π r ,...,π n ) Then, simulating a continuous destruction process of the network edges, namely sequentially destroying the network edges from left to right according to the arrangement until the network fails, and recording the combination of the failed network edges; the process is repeated and simulated for M times, M>2；
Substep 2: let t be the current number of repeated operations, n be the number of network edges, a r Number of permutation combinations representing the failure of the first r edges to cause network failure, b ri Representing the number of permutations that cause network failure when the first r edges fail and edge i also fails, c rij Representing the number of permutation and combination which cause network failure when the front r edges fail and the edges i and j also fail;
substep 3: recording the minimum number of edges which cause network failure currently, namely the anchor r (pi) of the arrangement, and obtaining a by accumulating the count r And b ri (ii) a Then, using a r N! [ and ] M and b ri N! the/M estimation results in a network D-spectrum Z (k) and a D-spectrum Z (k, 0) of the network edge i i ) Then, according to the relation between the D-spectrum and the D-spectrum of the network edge i, Z (k) ═ Z (k, 1) i )+Z(k,0 i ) Obtaining Z (k, 1) i ) An estimated value of (d);
wherein, Z (k) represents that k network edges in the network fail, and the combined number of the network in the fault state when the (n-k) network edges run. Z (k, 1) i )(Z(k,0 i ) Represents the number of combinations that the network is in a failed state when there are k network edges failing and network edge i is running (failing). Called Z (k, 1) i )(Z(k,0 i ) D x-spectrum of network edge i).
Step 3, calculating a mixed D-spectrum of the network edge i;
using c on the basis of the D-spectra obtained in step 2 rij N! the/M estimation obtains a network edge mixed D-spectrum Z (k, 1) i ,1 j ). According to the relationship between the D-spectrum of the network edge i and the mixed D-spectrum of the network edge, Z (k, 1) i )＝Z(k,1 i ,0 j )+Z(k,1 i ,1 j )，Z(k,0 i )＝Z(k,0 i ,0 j )+Z(k,0 i ,1 j ) Further, a mixed D-spectrum Z (k, 1) of the network edge i and the network edge j is obtained i ,0 j )、Z(k,0 i ,1 j ) And Z (k, 0) i ,0 j ) An estimated value of (a);
wherein, Z (k, 1) i ,0 j ) And the combination number indicates that when k network edges fail and the network edge i runs, the network edge j fails and the network is in a failure state. Called Z (k, 1) i ,0 j ) Is a mixed D-spectrum of network edge i.
Step 4, calculating the importance of the network edge based on the D star-spectrum;
and aiming at the Birnbaum importance, the Bayes importance and the replacement importance, respectively calculating the numerical values of the Birnbaum importance, the Bayes importance and the replacement importance under the K-terminal network by using the D-spectrum. The specific calculation processes are respectively as follows:
(1) the Birnbaum importance of the network edge i in the K-terminal network is as follows:
Figure FDA0002807391860000021
wherein q is the reliability of the network edge, p is the unreliability of the network edge, n is the total number of the network edges, and k is the failureI denotes a particular network edge. According to the relation between the D spectrum and the D spectrum of the network edge i, Z (k) Z (k, 1) i )+Z(k,0 i ) Thus, the above formula can also be expressed as:
Figure FDA0002807391860000022
(2) the Bayesian network importance of the network edge i in the K-terminal network is as follows:
Figure FDA0002807391860000023
(3) the replacement importance of the network edge i in the K-terminal network is as follows:
Figure FDA0002807391860000024
Figure FDA0002807391860000025
if G (0) i ,1 j ,p)≥G(1 i ,0 j P), then we say that the permutation importance of network edge i is higher than that of network edge j.
Step 5, analyzing the importance of the network edge to sort and group;
under the condition of a plurality of groups of different network edge reliability degrees p, the three importance degrees are measured, then each group of network edges is sequenced, and the network edges with similar importance degrees are divided into one group.
Step 6, carrying out reliability optimization on the K-terminal network;
and according to the arrangement result obtained in the step 5, taking the first K network edges, and replacing the original network edge with the network edge with higher reliability, so as to reduce the unreliability of the K-terminal network.
CN202011376971.8A 2020-11-30 2020-11-30 Greedy algorithm-based method for improving reliability of K-terminal network Active CN112464422B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011376971.8A CN112464422B (en) 2020-11-30 2020-11-30 Greedy algorithm-based method for improving reliability of K-terminal network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011376971.8A CN112464422B (en) 2020-11-30 2020-11-30 Greedy algorithm-based method for improving reliability of K-terminal network

Publications (2)

Publication Number Publication Date
CN112464422A CN112464422A (en) 2021-03-09
CN112464422B true CN112464422B (en) 2022-09-13

Family

ID=74806666

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011376971.8A Active CN112464422B (en) 2020-11-30 2020-11-30 Greedy algorithm-based method for improving reliability of K-terminal network

Country Status (1)

Country Link
CN (1) CN112464422B (en)

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102694395B (en) * 2012-05-29 2014-08-27 河南理工大学 Method for evaluating reliability of two terminals of power transmission network
CN105490836B (en) * 2015-11-19 2019-04-19 湘南学院 A kind of Monte Carlo appraisal procedure of complex network reliability

Also Published As

Publication number Publication date
CN112464422A (en) 2021-03-09

Similar Documents

Publication Publication Date Title
Ren et al. On querying historical evolving graph sequences
Candelieri et al. A graph based analysis of leak localization in urban water networks
CN104361169B (en) A kind of monitoring reliability method based on decomposition method modeling
CN112422571A (en) Method for carrying out exception alignment across multiple attribute networks
Yeh A sequential decomposition method for estimating flow in a multi-commodity, multistate network
CN105024645A (en) Matrix evolution-based photovoltaic array fault location method
CN105117430A (en) Repetitive task process discovery method based on equivalence class
CN104317794A (en) Chinese feature word association pattern mining method based on dynamic project weight and system thereof
Yun et al. An efficient approach for mining weighted approximate closed frequent patterns considering noise constraints
CN111414744A (en) Operation and maintenance alarm scene generation method based on community detection
CN111782532A (en) Software fault positioning method and system based on network abnormal node analysis
CN112464422B (en) Greedy algorithm-based method for improving reliability of K-terminal network
CN112966368B (en) Reliability evaluation method considering common cause failure PMS
Cai et al. Modelcoder: A fault model based automatic root cause localization framework for microservice systems
CN116662412A (en) Data mining method for big data of power grid distribution and utilization
Zhang et al. Software architecture modeling and reliability evaluation based on petri net
CN104360936B (en) Barrier operation property analysis method based on triggering operation
CN116225752A (en) Fault root cause analysis method and system for micro-service system based on fault mode library
CN113761460A (en) Ductile power distribution network load outage loss risk assessment method and system
CN114462093A (en) Space-time generalized trajectory data publishing method based on differential privacy
Naksinehaboon et al. High performance computing systems with various checkpointing schemes
CN108564135A (en) Structure skeleton program and the method for realizing the prediction of high-performance calculation program runtime
Bo et al. Detecting dense subgraphs in complex networks based on edge density coefficient
Bian et al. Research on a privacy preserving clustering method for social network
Rubino et al. Markovian models for dependability analysis

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant