CN103607292A - Fast distributed monitoring method for electric-power communication network services - Google Patents

Fast distributed monitoring method for electric-power communication network services Download PDF

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CN103607292A
CN103607292A CN201310517627.XA CN201310517627A CN103607292A CN 103607292 A CN103607292 A CN 103607292A CN 201310517627 A CN201310517627 A CN 201310517627A CN 103607292 A CN103607292 A CN 103607292A
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matrix
traffic
flow
stream
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CN103607292B (en
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夏菲
孟凡博
夏宗泽
于晓旭
黄笑伯
蒋定德
聂来森
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State Grid Corp of China SGCC
State Grid Liaoning Electric Power Co Ltd
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State Grid Liaoning Electric Power Co Ltd
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Abstract

The invention relates to a fast distributed monitoring method for electric-power communication network services. The method includes the following steps: generating a Bernoulli matrix and selecting OD streams which need to be measured directly through the matrix and constructing a traffic matrix; obtaining a measurement matrix; constructing an optimization greedy adaptive dictionary; and reconstructing the traffic matrix through compression sensing. In the fast distributed monitoring method for the electric-power communication-network services, part of OD streams, which need to be measured directly, are selected through a random matrix according power-law distribution of electric-power communication-network traffic and a traffic acquisition function is operated in part of routers as needed so as to obtain traffic information of the OD streams. An end-to-end network traffic reconstruction model is constructed through the traffic information and the model is solved through use of a compression-sensing reconstruction algorithm so as to obtain monitoring values of the traffic. The method is capable of obtaining the monitoring values of the traffic accurately in a real-time manner and at the same time reducing network traffic acquisition loss effectively.

Description

Fast distributed monitoring method towards power communication network service
Technical field
The present invention relates to the measurement of large scale network end-to-end flux and analysis field, particularly involvement aspect to the fast distributed monitoring method of power communication network service.
Background technology
Along with the fast development of powerline network, network supports for the production practices such as dispatching telephone, relaying protection, automation provide the basic communication technology.In order to realize the intellectuality of electrical network, access terminal and the bearer service of power telecom network becomes diversified.This has higher requirement to network traffic engineering management such as the network management of power telecom network, network monitoring, network design and the network plannings.Monitoring is important input parameter and the implementation basis of the operations such as network management, traffic engineering to end to end network flow (being source-object stream or OD stream), so end to end network flow monitoring has obtained paying close attention to widely.
Traditional network monitor technology can realize real-time reproduction and the prediction to large scale backbone network flow, and describes state of network traffic by traffic matrix.Network Traffic Monitoring technology can be divided into two large classes, is respectively direct measurement and flow and estimates.With respect to flow method of estimation, directly network traffics dynamic change situation can be more accurately described in measurement.Therefore network equipment supplier all provides network traffics acquisition function (for example, the NetFlow of cisco router) in the network equipment.As Fig. 1, traditional Network Traffic Monitoring method is collected flow status information by operating flux acquisition function on each router, and sends to Network Management Station by backbone network.This is the most direct method of obtaining flow status information.But operating flux acquisition function takies CPU and the memory source of router, therefore reduced the storage forwarding ability of router, the transmission of flow status information has additionally increased again the load of network in addition.In sum, the method has greatly increased via net loss, therefore applies in practice less.
By Network Management Station, control the flow collection function of router, build distributed flow monitoring system and collect part end to end network flow status information, and can obtain all end to end network flow monitoring values by flow reconstructing method, as shown in Figure 2.By reducing the number of the end to end network flow of direct measurement, reduce network operation energy consumption and offered load.How to confirm needs the part end to end network flow of directly measuring, and how all flow status information of reconstruct is the subject matter facing while building distributed network flow monitoring system in Network Management Station.Existing method is to optimize the distribution of operation acquisition function router mostly, and on minimum router, operating flux acquisition function is measured most end to end network flow information.Although this method can significantly reduce via net loss, the flow information of meeting lost part.Therefore studying distributed flow monitoring system obtains whole network traffic informations and has important Research Significance.
Summary of the invention
The shortcoming existing for prior art, solves end to end network flow Real-Time Monitoring problem, the invention provides the fast distributed monitoring method towards power communication network service.The method measures matrix according to Bernoulli Jacob and power-law distribution characteristic is selected the directly OD flow of measurement of part; According to these OD stream, set up linear inference problem, then, utilize and optimize greedy self-adapting dictionary (OGAD) learning algorithm, make linear inference problem observe compressed sensing specification requirement.Finally, use compressed sensing restructing algorithm to recover network traffics end to end.
In order to realize object of the present invention, the technical solution used in the present invention is:
Fast distributed monitoring method towards power communication network service, comprises the steps:
Step 1: generate Bernoulli matrix, select to need the OD directly measuring to flow by this matrix, and build traffic matrix;
Step 2: obtain observing matrix;
The structure of observing matrix depends on traffic matrix X partin non-zero capable, the row of other neutral element represent that the unknown OD that needs reconstruct flows.Calculating observation matrix Y mmethod is as follows:
Y m=BX part(2) wherein, B is the Bernoulli matrix of M * N, X partit is the traffic matrix of N * T.By B, X partwith observing matrix Y mformed a linear system;
Step 3: build and optimize greedy self-adapting dictionary;
Step 4: by compressed sensing reconstruct traffic matrix.
Described step 1 specifically comprises the steps:
Step 1-1: generate Bernoulli matrix;
Generate the Bernoulli random matrix B of M * N (M < N), N is the number of OD stream in network, its equal network node quantity square.Bernoulli entry of a matrix element b (m, n) is independent identically distributed, and it is Pr that element equals 1 probability, and equaling 0 probability is 1-Pr.
Step 1-2: determine the number that needs the OD of measurement stream;
Each row of the Bernoulli matrix of M * N are carried out respectively to boolean's ' or ' computing,
Figure BDA0000403249650000021
make S=[S (1), S (2) ..., S (N)] tbe a column vector, needing the OD flow amount of measuring is L=||S|| 1, || || 1represent l 1norm.
Step 1-3: directly measure OD stream;
Calculate known historical traffic matrix X 0the average of every OD stream:
aver _ X ( n ) = &Sigma; t = 1 T 0 X 0 ( n , t ) n = 1,2 , . . . , N - - - ( 1 )
Wherein, T 0for the length of historical traffic matrix, N is OD flow amount.According to this average, Network Management Station is controlled the on off state of flow acquisition function on router, to reach, measures maximum L=||S|| 1the object of individual OD stream.By the L=||S|| having measured 1individual OD stream is designated as set { x mea(l) }, l=1,2 ..., L;
Step 1-4: according to known OD stream { x mea(l) }, l=1,2 ...., L builds traffic matrix;
Described step 1-4 specifically comprises the steps:
Step 1-4-1: generate Bernoulli random matrix B according to step 1-1, step 1-2, and its each row are carried out respectively to boolean's ' or ' computing;
Step 1-4-2: initialization traffic matrix is empty matrix,
Figure BDA0000403249650000031
make l=1, iterations j=1, maximum iteration time N;
Step 1-4-3: when S (j)=1, traffic matrix becomes
Figure BDA0000403249650000032
otherwise,
Step 1-4-4: iterations j adds 1, if j < is N, returns to step 1-4-3), until iteration N time.Obtain traffic matrix X part,
Step 1-4-5: traffic matrix builds and finishes.
Described step 3 specifically comprises the steps:
Step 3-1: initialization numeral dictionary D 0for sky, i.e. D 0=[];
Step 3-2: historical flow is carried out to singular value decomposition, and extract K principal component;
Step 3-3: redundancy is set
Figure BDA0000403249650000037
for K principal component of historical flow, and definite iterations iter=N, make j=1,
Step 3-4: calculate R jsparse index ξ a, and column index a corresponding to sparse index j;
a j = arg min a &NotElement; I j { &xi; a = | | R j ( a ) | | 1 / | | R j ( a ) | | 2 } - - - ( 5 )
R wherein j(a) be a row of the redundancy that obtains after the j time iteration, || || 2represent l 2norm;
Step 3-5: the row R that obtains having minimum sparse index according to step 3-4 j(a j), and will in redundancy, there is minimum sparse index ξ aa jthe positionization of itemizing, and it is made as to the j row of data dictionary, i.e. d j=R j(a j)/|| R j(a j) || 2;
Step 3-6: obtaining data dictionary according to step 3-5 is: D j=[D j-1| d j], I j=I j-1∪ { a j; Then to all row a;
Step 3-7: upgrade redundancy, each row: R j+1(a)=R j(a)-d j< d j, R j(a) >, wherein < > represents inner product;
Step 3-8: iterations j=j+1, if j < is N, returns to step 3-4, until carry out iteration N time.The greedy self-adapting dictionary D that is optimized, D=D j.
Step 3-9: optimize greedy self-adapting dictionary and built.
Described step 3-2 comprises the steps:
Step 3-2-1: obtain historical flow, historical flow is carried out to singular value decomposition;
The historical traffic matrix obtaining is designated as X 0his.To X 0hiscarry out singular value decomposition,
X 0 his = &Sigma; k = 1 N &sigma; k u k v k T - - - ( 3 )
σ wherein kfor singular value, u kbe called feature stream, v kbe called characteristic vector
Step 3-2-2: K large singular value before extracting, other little singular values are set to 0;
According to formula (3), have,
X 0 his pc = &Sigma; k = 1 K &sigma; k u k v k , K < N - - - ( 4 )
Figure BDA0000403249650000043
for having extracted the traffic matrix approximate matrix of K maximum singular value;
Described step 4 specifically comprises the steps:
Step 4-1: the dictionary D obtaining according to step 3, by following l 1the column vector of Norm minimum problem solving N * 1
Figure BDA0000403249650000044
&theta; ^ t arg min | | &theta; t | | 1 s . t . BD &theta; t = Y t - - - ( 6 )
Wherein, Y tthe t row of observing matrix Y;
Step 4-2: by T iteration, obtain N * T matrix
Figure BDA0000403249650000046
Step 4-3: calculated flow rate Matrix Estimation value
Figure BDA0000403249650000047
Advantage of the present invention:
The present invention is according to the power-law distribution of powerline network flow, the OD stream that utilizes random matrix selected part directly to measure, and according to demand in part router operating flux acquisition function obtain the OD stream flow information that part is directly measured.By the flow information measuring, build end to end network flow reconstruction model, utilized compressed sensing restructing algorithm to solve this model to obtain the monitor value of flow.Utilize the inventive method, can obtain accurately in real time flow monitoring value, can effectively reduce network traffics simultaneously and gather loss, be conducive to that network research person carries out network behavior analysis and network operator carries out the network traffic engineering management such as network management, network monitoring, network design and the network planning better.
Accompanying drawing explanation
Fig. 1 is typical power communication network service flow monitoring system block diagram in the present invention;
Fig. 2 is the distributed traffic monitoring system block diagram that the present invention proposes;
Fig. 3 is the new traffic matrix flow chart of the structure of the embodiment of the present invention;
Fig. 4 is the greedy self-adapting dictionary flow chart of the structure optimization of the embodiment of the present invention;
Fig. 5 is any OD stream CSOR method reconstruction value and the actual value schematic diagram of the embodiment of the present invention;
Fig. 6 is any OD stream SRSVD method reconstruction value and the actual value schematic diagram of the embodiment of the present invention;
Fig. 7 is embodiment of the present invention CSOR reconstructing method and the relative root-mean-square error schematic diagram of SRSVD method;
Fig. 8 is the estimated bias schematic diagram of embodiment of the present invention CSOR reconstructing method and SRSVD method;
Fig. 9 is the standard deviation schematic diagram of the estimated bias of embodiment of the present invention CSOR reconstructing method and SRSVD method;
Figure 10 is that embodiment of the present invention CSOR reconstructing method needs the directly cumulative distribution schematic diagram of the OD flow amount of measurement.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.
The emulation experiment that the inventive method is carried out, adopts U.S. Abilene backbone network data.Abilene backbone network is mainly used in education and scientific research, and it has 12 nodes, 30 inner link, and 24 peripheral links, totally 144 end-to-end fluxes, get M=54 in the embodiment of the present invention, N=144.Emulated data gathers by NetFlow, and the time interval is 5min, amounts to 2016 moment, and wherein the data on flows in front 500 moment, as the traffic matrix of measuring in advance, is got T=2016 in the embodiment of the present invention, T 0=500, to calculate the average of OD stream and set up the optimum reconstruction model (CSOR) based on compressed sensing, as shown in Figure 2.
The present invention is towards the fast distributed monitoring method of power communication network service, and step is as follows:
Step 1: generate Bernoulli matrix, select to need the OD directly measuring to flow by this matrix, and build traffic matrix;
Specifically comprise the steps:
Step 1-1: generate Bernoulli matrix;
Generate 54 * 144 Bernoulli random matrix B.Bernoulli entry of a matrix element b (m, n) is independent identically distributed, gets Pr=0.01 in the present embodiment, and to equal 1 probability be 0.01 to element, and equaling 0 probability is 0.99.
Step 1-2: determine the number that needs the OD of measurement stream;
Each row of Bernoulli matrix to 54 * 144 carry out respectively boolean's ' or ' computing,
Figure BDA0000403249650000051
make S=[S (1), S (2) ..., S (144)] tbe a column vector, needing the OD flow amount of measuring is L=||S|| 1, || || 1represent l 1norm.
Step 1-3: directly measure OD stream;
Calculate known historical traffic matrix X 0the average of every OD stream:
aver _ X ( n ) = &Sigma; t = 1 T 0 X 0 ( n , t ) n = 1,2 , . . . , 144 - - - ( 1 )
Wherein, T 0for the length of historical traffic matrix, in embodiment, we intercept the historical flow in 500 moment, i.e. T 0=500.According to this average, Network Management Station is controlled the on off state of flow acquisition function on router, to reach, measures maximum L=||S|| 1the object of individual OD stream.By the L=||S|| having measured 1individual OD stream is designated as set { x mea(l) }, l=1,2 ..., L.
Step 1-4: according to known OD stream { x mea(l) }, l=1,2 ...., L builds traffic matrix, and as shown in Figure 3, concrete steps are as follows:
Step 1-4-1: generate Bernoulli random matrix B according to step 1-1, step 1-2, and its each row are carried out respectively to boolean's ' or ' computing;
Step 1-4-2: initialization traffic matrix is empty matrix, make l=1, iterations j=1, maximum iteration time 144;
Step 1-4-3: when S (j)=1, traffic matrix becomes l=l+1; Otherwise,
Figure BDA0000403249650000065
Step 1-4-4: iterations j adds 1, if j < 144 returns to step 1-4-3, until iteration 144 times.Obtain traffic matrix X part,
Figure BDA0000403249650000066
Step 1-4-5: traffic matrix builds and finishes.
Step 2: obtain observing matrix;
In the present invention, the structure of observing matrix only depends on traffic matrix X partin non-zero capable, the row of other neutral element represent that the unknown OD that needs reconstruct flows.Calculating observation matrix Y mmethod is as follows:
Y m=BX part(2) wherein, B and X partby step 1, obtain.By B, X partwith observing matrix Y mformed a linear system.
Step 3: build and optimize greedy self-adapting dictionary, as shown in Figure 4, concrete steps are as follows:
Step 3-1: initialization numeral dictionary D 0for sky, i.e. D 0=[];
Step 3-2: historical flow is carried out to singular value decomposition, and extract K principal component, get K=6 in embodiment, specifically comprise:
Step 3-2-1: obtain historical flow, historical flow is carried out to singular value decomposition;
The historical traffic matrix obtaining is designated as X 0his.To X 0hiscarry out singular value decomposition,
X 0 his = &Sigma; k = 1 144 &sigma; k u k v k T - - - ( 3 )
σ wherein kfor singular value, u kbe called feature stream, v kbe called characteristic vector
Step 3-2-2: extract front 6 large singular values, other little singular values are set to 0;
According to formula (3), have,
X 0 his pc = &Sigma; k = 1 6 &sigma; k u k v k , K < N - - - ( 4 )
Figure BDA0000403249650000073
for having extracted the traffic matrix approximate matrix of 6 maximum singular values;
Step 3-3: redundancy is set
Figure BDA0000403249650000077
for 6 principal components of historical flow, and definite iterations iter=144, make j=1,
Figure BDA0000403249650000074
Step 3-4: calculate R jsparse index ξ a, and column index a corresponding to sparse index j;
a j = arg min a &NotElement; I j { &xi; a = | | R j ( a ) | | 1 / | | R j ( a ) | | 2 } - - - ( 5 )
R wherein j(a) be a row of the redundancy that obtains after the j time iteration, || || 2represent l 2norm;
Step 3-5: the row R that obtains having minimum sparse index according to step 3-4 j(a j), and will in redundancy, there is minimum sparse index ξ aa jthe positionization of itemizing, and it is made as to the j row of data dictionary, i.e. d j=R j(a j)/|| R j(a j) || 2;
Step 3-6: obtaining data dictionary according to step 3-5 is: D j=[D j-1| d j], I j=I j-1∪ { a j; Then to all row a;
Step 3-7: upgrade redundancy, each row: R j+1(a)=R j(a)-d j< d j, R j(a) >, wherein < > represents inner product;
Step 3-8: iterations j=j+1, if j < 144 returns to step 3-4, until carry out iteration 144 times.The greedy self-adapting dictionary D that is optimized, D=D j.
Step 3-9: optimize greedy self-adapting dictionary and built.
Step 4: by compressed sensing reconstruct traffic matrix;
Concrete steps are as follows:
Step 4-1: the dictionary D obtaining according to step 3, by following l 1the column vector of Norm minimum problem solving NX1
Figure BDA0000403249650000076
&theta; ^ t arg min | | &theta; t | | 1 s . t . BD &theta; t = Y t - - - ( 6 )
Wherein, Y tthe t row of observing matrix Y.
Step 4-2: by T=2016 iteration, obtain 144 * 2016 matrixes
Figure BDA0000403249650000082
Step 4-3: calculated flow rate Matrix Estimation value
Figure BDA0000403249650000083
In order better to assess reconstruction property of the present invention, it is poor that we calculate relative root-mean-square error, reconstruct deviation and deviation standard.
RRMSE ( t ) = &Sigma; n = 1 N ( X ( n , t ) - X ^ ( n , t ) ) 2 &Sigma; n = 1 N X ( n , t ) 2 - - - ( 7 )
bias ( n ) = 1 T &Sigma; t = 1 T ( X ^ ( n , t ) - X ( n , t ) ) - - - ( 8 )
SD ( n ) = 1 T - 1 &Sigma; t = 1 T ( ( X ^ ( n , t ) - X ( n , t ) ) - bisa ( n ) ) 2 - - - ( 9 )
In emulation experiment, algorithm that the present invention carries (CSOR) and sparse canonical singular value decomposition (SRSVD) algorithm are contrasted, result shows that algorithm that the present invention carries can reconstruct end to end network flow very accurately.Fig. 5 is the reconstruction result of CSOR algorithm to the 20th OD stream, and Fig. 6 is the reconstruction result of SRSVD algorithm to the 20th OD stream.Wherein, solid line represents real flow, and dotted line represents its reconstruction value.As can be seen from the figure, although CSOR reconstructing method more or less exists, estimated and owed to estimate that phenomenon, CSOR can follow the tracks of the dynamic change trend of OD stream well, approaching very much the actual value of OD stream.Fig. 7 is CSOR root-mean-square error relative to SRSVD algorithm.Wherein solid line is CSOR algorithm, and dotted line is SRSVD algorithm.As can be seen from the figure, the relative root-mean-square error of the inventive method CSOR is less.For the method that further assessment the present invention proposes, we introduce reconstruct deviation and deviation standard poor.From Fig. 8 and Fig. 9, can find out, the reconstruct deviation of CSOR method is less, and standard deviation is also very little in addition, and this explanation institute of the present invention extracting method has stronger stability.Next assess the economic benefit of CSOR, Figure 10 has drawn us needs directly to measure the cumulative distribution function of OD flow amount, therefrom can find out that in about 96% situation, we only need to measure 70 OD streams, that is to say that we only need to measure 49% OD stream and just can obtain the monitoring result that all 144 OD flow.

Claims (6)

1. towards the fast distributed monitoring method of power communication network service, it is characterized in that comprising the steps:
Step 1: generate Bernoulli matrix, select to need the OD directly measuring to flow by this matrix, and build traffic matrix;
Step 2: obtain observing matrix;
The structure of observing matrix depends on traffic matrix X partin non-zero capable, the row of other neutral element represent that the unknown OD that needs reconstruct flows.Calculating observation matrix Y mmethod is as follows:
Y m=B·X part (2)
Wherein, B is the Bernoulli matrix of M * N, X partit is the traffic matrix of N * T.By B, X partwith observing matrix Y mformed a linear system;
Step 3: build and optimize greedy self-adapting dictionary;
Step 4: by compressed sensing reconstruct traffic matrix.
2. the fast distributed monitoring method towards power communication network service according to claim 1, is characterized in that described step 1 specifically comprises the steps:
Step 1-1: generate Bernoulli matrix;
Generate the Bernoulli random matrix B of M * N (M < N), N is the number of OD stream in network, its equal network node quantity square; Bernoulli entry of a matrix element b (m, n) is independent identically distributed, and it is Pr that element equals 1 probability, and equaling 0 probability is 1-Pr;
Step 1-2: determine the number that needs the OD of measurement stream;
Each row of the Bernoulli matrix of M * N are carried out respectively to boolean's ' or ' computing,
Figure FDA0000403249640000011
make S=[S (1), S (2) ..., S (N)] tbe a column vector, needing the OD flow amount of measuring is L=||S|| 1, || || 1represent l 1norm;
Step 1-3: directly measure OD stream;
Calculate known historical traffic matrix X 0the average of every OD stream:
aver _ X ( n ) = &Sigma; t = 1 T 0 X 0 ( n , t ) n = 1,2 , . . . , N - - - ( 1 )
Wherein, T 0for the length of historical traffic matrix, N is OD flow amount, and according to this average, Network Management Station is controlled the on off state of flow acquisition function on router, to reach, measures maximum L=||S|| 1the object of individual OD stream, by the L=||S|| having measured 1individual OD stream is designated as set { x mea(l) }, l=1,2 ..., L;
Step 1-4: according to known OD stream { x mea(l) }, l=1,2 ...., L builds traffic matrix.
3. the fast distributed monitoring method towards power communication network service according to claim 2, is characterized in that described step 1-4 specifically comprises the steps:
Step 1-4-1: generate Bernoulli random matrix B according to step 1-1, step 1-2, and its each row are carried out respectively to boolean's ' or ' computing;
Step 1-4-2: initialization traffic matrix is empty matrix,
Figure FDA0000403249640000021
make l=1, iterations j=1, maximum iteration time N;
Step 1-4-3: when S (j)=1, traffic matrix becomes
Figure FDA0000403249640000022
; Otherwise,
Step 1-4-4: iterations j adds 1, if j < is N, returns to step 1-4-3, until iteration N time obtains traffic matrix X part,
Figure FDA0000403249640000024
Step 1-4-5: traffic matrix builds and finishes.
4. the fast distributed monitoring method towards power communication network service according to claim 1, is characterized in that described step 3 specifically comprises the steps:
Step 3-1: initialization numeral dictionary D 0for sky, i.e. D 0=[];
Step 3-2: historical flow is carried out to singular value decomposition, and extract K principal component;
Step 3-3: redundancy is set
Figure FDA0000403249640000027
for K principal component of historical flow, and definite iterations iter=N, make j=1,
Figure FDA0000403249640000025
Step 3-4: calculate R jsparse index ξ a, and column index a corresponding to sparse index j;
a j = arg min a &NotElement; I j { &xi; a = | | R j ( a ) | | 1 / | | R j ( a ) | | 2 } - - - ( 5 ) R wherein j(a) be a row of the redundancy that obtains after the j time iteration, || || 2represent l 2norm;
Step 3-5: the row R that obtains having minimum sparse index according to step 3-4 j(a j), and will in redundancy, there is minimum sparse index ξ aa jthe positionization of itemizing, and it is made as to the j row of data dictionary, i.e. d j=R j(a j)/|| R j(a j) || 2;
Step 3-6: obtaining data dictionary according to step 3-5 is: D j=[D j-1| d j], I j=I j-1∪ { a j; Then to all row a;
Step 3-7: upgrade redundancy, each row: R j+1(a)=R j(a)-d j< d j, R j(a) >, wherein < > represents inner product;
Step 3-8: iterations j=j+1, if j < is N, returns to step 3-4, until carry out iteration N time, the greedy self-adapting dictionary D that is optimized, D=D j;
Step 3-9: optimize greedy self-adapting dictionary and built.
5. the fast distributed monitoring method towards power communication network service according to claim 4, is characterized in that described step 3-2 comprises the steps:
Step 3-2-1: obtain historical flow, historical flow is carried out to singular value decomposition;
The historical traffic matrix obtaining is designated as X 0his.To X 0hiscarry out singular value decomposition,
X 0 his = &Sigma; k = 1 N &sigma; k u k v k T - - - ( 3 )
σ wherein kfor singular value, u kbe called feature stream, v kbe called characteristic vector
Step 3-2-2: K large singular value before extracting, other little singular values are set to 0;
According to formula (3), have,
X 0 his pc = &Sigma; k = 1 K &sigma; k u k v k , K < N - - - ( 4 )
Figure FDA0000403249640000033
for having extracted the traffic matrix approximate matrix of K maximum singular value.
6. the fast distributed monitoring method towards power communication network service according to claim 1, is characterized in that described step 4 comprises the steps:
Step 4-1: the dictionary D obtaining according to step 3, by following l 1the column vector of Norm minimum problem solving N * 1
&theta; ^ t arg min | | &theta; t | | 1 s . t . BD &theta; t = Y t - - - ( 6 )
Wherein, Y tthe t row of observing matrix Y;
Step 4-2: by T iteration, obtain N * T matrix
Figure FDA0000403249640000036
Step 4-3: calculated flow rate Matrix Estimation value
Figure FDA0000403249640000037
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