CN108540331B - Network flow prediction method based on improved ESN - Google Patents

Network flow prediction method based on improved ESN Download PDF

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CN108540331B
CN108540331B CN201810383828.8A CN201810383828A CN108540331B CN 108540331 B CN108540331 B CN 108540331B CN 201810383828 A CN201810383828 A CN 201810383828A CN 108540331 B CN108540331 B CN 108540331B
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CN108540331A (en
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孙力娟
杨欣颜
周剑
王娟
韩崇
肖甫
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Nanjing University of Posts and Telecommunications
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention provides a network flow prediction method based on an improved ESN, which comprises the steps of continuously collecting network flow data, and then carrying out noise reduction processing on the original network flow data on the basis of the collected network flow data to obtain noise-reduced network flow data; meanwhile, a network flow prediction model based on the improved ESN is constructed, the network flow data after noise reduction and the original network flow data are combined to be used as input, and a double-ring reserve pool structure with a fixed structure is constructed to replace a random reserve pool structure of the original ESN; finally, the ESN is improved through training, and a network traffic prediction model based on the improved ESN and used for network traffic prediction is obtained. By the method, the accuracy of the network flow prediction result can be improved, and a better prediction effect can be obtained in the nonlinear time series prediction.

Description

Network flow prediction method based on improved ESN
Technical Field
The invention relates to a network flow prediction method based on an improved ESN, belonging to the technical field of computer application.
Background
The network plays an important role in social life, enterprise production and management. With the development of internet technology, the network scale is continuously enlarged, the complexity of the network is higher and higher, and the requirements of people on network management are higher and higher. The network flow is an important parameter for evaluating the network load and the operation state, and is an important means for mastering the network operation state and realizing effective management and control by continuously monitoring the network flow and realizing accurate prediction. Therefore, it is of great significance to study the prediction of network traffic.
The network flow has the characteristics of self-similarity, long correlation, periodicity, chaos and the like. In recent years, with the continuous expansion of network scale, traditional linear prediction methods such as AR, ARMA, poisson model and the like cannot accurately describe the complex nonlinear relation of network traffic. With the intensive research on network traffic by researchers, most network traffic prediction models based on the traditional neural network have relatively good prediction performance, are simple and convenient, but have unstable performance. Therefore, compared with the traditional neural Network, the Echo State Network (ESN) has strong nonlinear processing capability and faster training speed, and can obtain better prediction effect in nonlinear time series prediction.
Disclosure of Invention
The invention provides a network flow prediction method based on an improved ESN, which improves the accuracy of a network flow prediction result and can obtain a better prediction effect in nonlinear time series prediction.
The network flow prediction method based on the improved ESN is characterized by comprising the following steps:
step 1: collecting network flow data;
step 2: carrying out noise reduction processing on the network flow data;
and step 3: constructing an improved ESN network flow prediction model with a double-ring reserve pool structure;
and 4, step 4: training the network flow prediction model based on the improved ESN constructed in the step 3 by using the collected network flow data and the noise-reduced network flow data;
and 5, predicting the network traffic at the future moment by using the network traffic prediction model trained in the step 4 and based on the improved ESN.
Further, in the step 1, in the step of collecting the network traffic data, the total number of data packets per minute is counted in the specified sampling time, and finally a certain number of network traffic data sets are obtained
Figure 49572DEST_PATH_IMAGE001
，
Figure 553978DEST_PATH_IMAGE002
Wherein
Figure 736698DEST_PATH_IMAGE003
Is the network traffic data at time t.
Further, in step 2, performing noise reduction processing on the acquired network traffic data requires performing phase space reconstruction on the network traffic data, then performing noise reduction processing on the known network traffic data by using a local projection method, and finally obtaining a certain number of noise-reduced network traffic data sets
Figure 250856DEST_PATH_IMAGE004
，
Figure 177223DEST_PATH_IMAGE005
Wherein
Figure 788333DEST_PATH_IMAGE006
And reducing noise data for the network flow at the moment t.
Further, in the step 2, performing noise reduction processing on the network traffic data includes the following steps:
step 2-1: for collected traffic data sets
Figure 345217DEST_PATH_IMAGE001
The time delay required by phase space reconstruction is obtained by using an interactive information method
Figure 894141DEST_PATH_IMAGE007
；
Step 2-2: for collected traffic data sets
Figure 889779DEST_PATH_IMAGE001
Determining the embedding dimension for phase space reconstruction by using improved false nearest neighbor method
Figure 89816DEST_PATH_IMAGE008
；
Step 2-3: according to time delay
Figure 614338DEST_PATH_IMAGE007
And embedding dimension
Figure 103088DEST_PATH_IMAGE008
Performing phase space reconstruction on the known flow data, and storing the phase space reconstruction;
step 2-4: for each phase point in the phase space, selecting a corresponding local neighborhood, and performing noise reduction processing on the known network traffic data by adopting a local projection method to obtain a set of noise-reduced network traffic data
Figure 653149DEST_PATH_IMAGE004
。
Further, in step 3, weight needs to be set for constructing the dual-ring reserve pool structure
Figure 707693DEST_PATH_IMAGE009
Size of reserve pool
Figure 606379DEST_PATH_IMAGE010
Bicyclic neuronal septa
Figure 644742DEST_PATH_IMAGE011
And number of rings
Figure 716603DEST_PATH_IMAGE012
(ii) a Constructing a network traffic prediction model based on the improved ESN requires determining input and output vectors of the improved ESN; the input vector of the improved ESN is network flow historical data and the network flow historical data after noise reduction
Figure 828916DEST_PATH_IMAGE013
，
Figure 711552DEST_PATH_IMAGE014
Wherein
Figure 971632DEST_PATH_IMAGE015
Before time t
Figure 50447DEST_PATH_IMAGE016
A collection of historical data of individual network traffic,
Figure 79583DEST_PATH_IMAGE016
is the embedding dimension of the original network traffic sequence,
Figure 585650DEST_PATH_IMAGE017
wherein
Figure 333026DEST_PATH_IMAGE018
Before time t
Figure 949953DEST_PATH_IMAGE019
A set of denoised network traffic history data,
Figure 846977DEST_PATH_IMAGE019
for the embedding dimension of the noise-reduced sequence of network traffic,
Figure 523946DEST_PATH_IMAGE020
the total embedding dimension and the number of neurons in the input layer; output vector
Figure 961881DEST_PATH_IMAGE021
。
Further, in the step 3, constructing an improved ESN network traffic prediction model with a dual-ring reserve pool structure includes the following steps:
step 3-1: according to the size of the reserve tank
Figure 444814DEST_PATH_IMAGE022
And input layer neuron number
Figure 386226DEST_PATH_IMAGE023
Constructing the absolute value of the non-zero element as the weight
Figure 296413DEST_PATH_IMAGE024
A size of
Figure 956064DEST_PATH_IMAGE025
Input connection matrix of
Figure 977110DEST_PATH_IMAGE026
；
Step 3-2: according to bicyclic neuronal spacing
Figure 38607DEST_PATH_IMAGE027
And number of rings
Figure 604849DEST_PATH_IMAGE028
Constructing the absolute value of the non-zero element as the weight
Figure 17375DEST_PATH_IMAGE024
A size of
Figure 779795DEST_PATH_IMAGE029
Reserve pool connection matrix
Figure 758115DEST_PATH_IMAGE030
；
Step 3-3: for input vector
Figure 744526DEST_PATH_IMAGE031
Use of
Figure 378769DEST_PATH_IMAGE032
As a function of excitation inside the reserve tank
Figure 679301DEST_PATH_IMAGE033
The excitation state of the internal neurons in the improved ESN reserve pool is obtained by the following formula
Figure 777707DEST_PATH_IMAGE034
，
Figure 403860DEST_PATH_IMAGE035
；
Step 3-4: connecting matrices according to outputs
Figure 259821DEST_PATH_IMAGE036
Input vector
Figure 177092DEST_PATH_IMAGE031
And neuron excitation state inside the reserve pool
Figure 67688DEST_PATH_IMAGE034
Using an identity function as the output excitation function
Figure 864743DEST_PATH_IMAGE037
Obtaining an output vector by the following formula
Figure 270316DEST_PATH_IMAGE038
，
Figure 912650DEST_PATH_IMAGE039
。
Further, in the step 4, the specific steps of training the network traffic prediction model based on the improved ESN are as follows:
step 4-1: training sample pair for constructing input and output of improved ESN
Figure 720069DEST_PATH_IMAGE040
Wherein
Figure 688025DEST_PATH_IMAGE041
，
Figure 518578DEST_PATH_IMAGE042
；
Step 4-2: bringing the training sample pairs into the improved ESN, the collection time
Figure 26920DEST_PATH_IMAGE043
Arrival time
Figure 626528DEST_PATH_IMAGE044
Input vector of
Figure 312856DEST_PATH_IMAGE045
And an internal state vector
Figure 896284DEST_PATH_IMAGE046
Form a state vector
Figure 145999DEST_PATH_IMAGE047
Obtained in a size of
Figure 662431DEST_PATH_IMAGE048
State matrix of
Figure 706611DEST_PATH_IMAGE049
(ii) a Collecting time
Figure 574073DEST_PATH_IMAGE043
Arrival time
Figure 627479DEST_PATH_IMAGE044
Desired output vector of
Figure 201680DEST_PATH_IMAGE050
To obtain a size of
Figure 479078DEST_PATH_IMAGE051
Desired output matrix of
Figure 37098DEST_PATH_IMAGE052
；
Figure 363037DEST_PATH_IMAGE043
Set to 100; the method is realized by the following formula:
Figure 601864DEST_PATH_IMAGE053
Figure 253425DEST_PATH_IMAGE054
Figure 829900DEST_PATH_IMAGE055
step 4-3: using pseudo-inverse metersComputing an output connection matrix
Figure 959530DEST_PATH_IMAGE056
(ii) a Computing network actual output
Figure 773902DEST_PATH_IMAGE057
And desired output
Figure 393103DEST_PATH_IMAGE050
Mean square error of
Figure 394557DEST_PATH_IMAGE058
So that the mean square error
Figure 593457DEST_PATH_IMAGE058
Minimum;
Figure 59073DEST_PATH_IMAGE059
is a state matrix
Figure 786858DEST_PATH_IMAGE049
The pseudo-inverse of (1); the method is realized by the following formula:
Figure 88657DEST_PATH_IMAGE060
Figure 825669DEST_PATH_IMAGE061
。
further, in the step 5, the total number of the packets per minute is counted to obtain a new network traffic data set
Figure 83475DEST_PATH_IMAGE062
And carrying out noise reduction treatment on the network flow data by using a local noise reduction projection method so as to obtain a noise-reduced network flow data set
Figure 310057DEST_PATH_IMAGE063
. Improved ESN-based mesh using training completionThe network flow prediction model predicts the future network flow data and outputs the network flow data at the next moment
Figure 286103DEST_PATH_IMAGE064
。
Advantageous effects
The invention is characterized in that the network flow data is continuously collected, and then the original network flow data is subjected to noise reduction treatment on the basis of the continuous collection of the network flow data to obtain the noise-reduced network flow data; meanwhile, a network flow prediction model based on the improved ESN is constructed as shown in FIG. 1, the network flow data after noise reduction and the original network flow data are combined to be used as input, and a double-ring reserve pool structure with a fixed structure is constructed to replace a random reserve pool structure of the original ESN; finally, the ESN is improved through training, and a network traffic prediction model based on the improved ESN and used for network traffic prediction is obtained. By the method, the accuracy of the network flow prediction result can be improved.
Drawings
Fig. 1 is a schematic diagram of a network traffic prediction model based on improved ESN.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
The invention provides a Network flow prediction method based on an improved Echo State Network (ESN), which comprises the following specific steps:
step 1: counting the total number of data packets per minute within a specified sampling time, and finally obtaining a certain number of network flow data sets
Figure 357965DEST_PATH_IMAGE065
，
Figure 735856DEST_PATH_IMAGE066
Wherein
Figure 71023DEST_PATH_IMAGE067
Is the network traffic data at time t.
Step 2: and carrying out noise reduction processing on the acquired network flow data. Firstly, reconstructing the phase space of network flow data, then using local projection method to make noise reduction treatment on the known network flow data, finally obtaining a certain quantity of noise-reduced network flow data set
Figure 596682DEST_PATH_IMAGE068
，
Figure 409917DEST_PATH_IMAGE069
Wherein
Figure 455365DEST_PATH_IMAGE070
And reducing noise data for the network flow at the moment t. The network flow data denoising steps are as follows:
step 2-1: for collected traffic data sets
Figure 961432DEST_PATH_IMAGE065
The time delay required by phase space reconstruction is obtained by using an interactive information method
Figure 912071DEST_PATH_IMAGE071
。
Step 2-2: for collected traffic data sets
Figure 591314DEST_PATH_IMAGE065
Determining the embedding dimension for phase space reconstruction by using improved false nearest neighbor method
Figure 678219DEST_PATH_IMAGE072
。
Step 2-3: according to time delay
Figure 417504DEST_PATH_IMAGE071
And embedding dimension
Figure 855439DEST_PATH_IMAGE072
And performing phase space reconstruction on the known flow data and storing the data.
Step 2-4:for each phase point in the phase space, selecting a corresponding local neighborhood, and performing noise reduction processing on the known network traffic data by adopting a local projection method to obtain a set of noise-reduced network traffic data
Figure 10477DEST_PATH_IMAGE068
。
And step 3: and constructing an improved ESN network flow prediction model with a double-ring reserve pool structure. Weight value required to be set for constructing double-ring storage pool structure
Figure 279784DEST_PATH_IMAGE073
Size of reserve pool
Figure 127654DEST_PATH_IMAGE074
Bicyclic neuronal septa
Figure 600355DEST_PATH_IMAGE075
And number of rings
Figure 559084DEST_PATH_IMAGE076
. Constructing a network traffic prediction model based on the improved ESN requires determining the input and output vectors of the improved ESN. The input vector of the improved ESN is network flow historical data and the network flow historical data after noise reduction
Figure 417319DEST_PATH_IMAGE077
，
Figure 436090DEST_PATH_IMAGE078
Wherein
Figure 848617DEST_PATH_IMAGE079
Before time t
Figure 673353DEST_PATH_IMAGE080
A collection of network traffic history data, wherein
Figure 589357DEST_PATH_IMAGE080
Is the embedding dimension of the original network traffic sequence,
Figure 575767DEST_PATH_IMAGE081
wherein
Figure 475590DEST_PATH_IMAGE082
Before time t
Figure 776122DEST_PATH_IMAGE083
A set of denoised network traffic history data,
Figure 622330DEST_PATH_IMAGE083
for the embedding dimension of the noise-reduced sequence of network traffic,
Figure 717325DEST_PATH_IMAGE084
the total embedding dimension, and the number of input layer neurons. Output vector
Figure 901182DEST_PATH_IMAGE085
. The specific steps of constructing an improved ESN network flow prediction model with a double-ring reserve pool structure are as follows:
step 3-1: according to the size of the reserve tank
Figure 270983DEST_PATH_IMAGE086
And input layer neuron number
Figure 896000DEST_PATH_IMAGE087
Constructing the absolute value of the non-zero element as the weight
Figure 489792DEST_PATH_IMAGE088
A size of
Figure 833049DEST_PATH_IMAGE089
Input connection matrix of
Figure 803279DEST_PATH_IMAGE090
。
Step 3-2: according to bicyclic neuronal spacing
Figure 813960DEST_PATH_IMAGE091
And number of rings
Figure 516337DEST_PATH_IMAGE092
Constructing the absolute value of the non-zero element as the weight
Figure 159939DEST_PATH_IMAGE088
A size of
Figure 605964DEST_PATH_IMAGE093
Reserve pool connection matrix
Figure 471152DEST_PATH_IMAGE094
。
Step 3-3: for input vector
Figure 406747DEST_PATH_IMAGE095
Use of
Figure 724596DEST_PATH_IMAGE096
As a function of excitation inside the reserve tank
Figure 771049DEST_PATH_IMAGE097
The excitation state of the internal neurons in the improved ESN reserve pool is obtained by the following formula
Figure 490743DEST_PATH_IMAGE046
，
Figure 800502DEST_PATH_IMAGE098
。
Step 3-4: connecting matrices according to outputs
Figure 667964DEST_PATH_IMAGE056
Input vector
Figure 455791DEST_PATH_IMAGE095
And neuron excitation state inside the reserve pool
Figure 843041DEST_PATH_IMAGE046
Using an identity function as the output excitation function
Figure 58122DEST_PATH_IMAGE099
Obtaining an output vector by the following formula
Figure 147301DEST_PATH_IMAGE100
，
Figure 4398DEST_PATH_IMAGE101
。
And 4, step 4: and (3) training the network traffic prediction model based on the improved ESN, which is constructed in the step (3), by using the network traffic data collected in the step (1) and the noise-reduced network traffic data in the step (2). The specific steps of training the network traffic prediction model based on the improved ESN are as follows:
step 4-1: training sample pair for constructing input and output of improved ESN
Figure 433106DEST_PATH_IMAGE102
，
Figure 881405DEST_PATH_IMAGE103
,
Figure 661142DEST_PATH_IMAGE104
。
Step 4-2: bringing the training sample pairs into the improved ESN, the collection time
Figure 853089DEST_PATH_IMAGE043
Arrival time
Figure 401882DEST_PATH_IMAGE044
Input vector of
Figure 224344DEST_PATH_IMAGE045
And an internal state vector
Figure 38848DEST_PATH_IMAGE046
Form a state vector
Figure 972168DEST_PATH_IMAGE047
Obtained in a size of
Figure 375468DEST_PATH_IMAGE048
State matrix of
Figure 431149DEST_PATH_IMAGE049
. Collecting time
Figure 919899DEST_PATH_IMAGE043
Arrival time
Figure 453648DEST_PATH_IMAGE044
Desired output vector of
Figure 977034DEST_PATH_IMAGE050
To obtain a size of
Figure 141299DEST_PATH_IMAGE051
Desired output matrix of
Figure 914083DEST_PATH_IMAGE052
. In the invention
Figure 189206DEST_PATH_IMAGE043
Set to 100. The method is realized by the following formula:
Figure 832677DEST_PATH_IMAGE053
Figure 470242DEST_PATH_IMAGE054
Figure 199164DEST_PATH_IMAGE055
step 4-3: obtaining an output connection matrix by using a pseudo-inverse method:
Figure 74716DEST_PATH_IMAGE056
. Computing network actual output
Figure 307114DEST_PATH_IMAGE057
And desired output
Figure 609919DEST_PATH_IMAGE050
Mean square error of
Figure 826137DEST_PATH_IMAGE058
So that the mean square error
Figure 443063DEST_PATH_IMAGE058
And minimum.
Figure 592285DEST_PATH_IMAGE059
Is a state matrix
Figure 269254DEST_PATH_IMAGE049
The pseudo-inverse of (1). The method is realized by the following formula:
Figure 707188DEST_PATH_IMAGE060
Figure 675276DEST_PATH_IMAGE061
and 5: and (4) predicting the network traffic at the future time by using the trained network traffic prediction model based on the improved ESN in the step 4. Counting the total number of data packets per minute to obtain a new network traffic data set
Figure 882266DEST_PATH_IMAGE062
And carrying out noise reduction treatment on the network flow data by using a local noise reduction projection method so as to obtain a noise-reduced network flow data set
Figure 526874DEST_PATH_IMAGE063
. Modification based on use of training completionThe network flow prediction model of the ESN predicts the future network flow data and outputs the network flow data at the next moment
Figure 452105DEST_PATH_IMAGE064
。
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (7)

1. The network flow prediction method based on the improved ESN is characterized by comprising the following steps:
step 1: collecting network flow data;
step 2: carrying out noise reduction processing on the network flow data;
and step 3: constructing an improved Echo State Network (ESN) network flow prediction model with a double-ring reserve pool structure, wherein the ESN network flow prediction model is based on a double-ring neuron interval dmaxAnd a ring number c, constructing a reserve pool connection matrix W with the absolute value of non-zero elements as a weight r and the size of NxN;
in the step 3, the steps of constructing the improved ESN network flow prediction model with the double-ring reserve pool structure are as follows:
step 3-1: constructing an input connection matrix W with the absolute value of non-zero elements as a weight r and the size of KxN according to the scale N of the reserve pool and the number K of neurons in an input layerin；
Step 3-2: according to the spacing d of bicyclic neuronsmaxAnd a ring number c, constructing a reserve pool connection matrix W with the absolute value of non-zero elements as a weight r and the size of NxN;
step 3-3: for the input vector u (t), tanh (-) is used as the incentive function f inside the poolinThe excitation state x (t), x (t) ═ f of the internal neurons in the improved ESN reservoir is obtained by the following formulain(Winu(t)+Wx(t-1))；
Step 3-4: according to the output connection matrix WoutInput ofVector u (t) and reservoir internal neuron excitation state x (t), using an identity function as output excitation function foutThe output vector y (t), y (t) f is obtained by the following formulaout(Wout(u(t)，x(t)))；
And 4, step 4: training the network flow prediction model based on the improved ESN constructed in the step 3 by using the collected network flow data and the noise-reduced network flow data;
and 5: and (4) predicting the network traffic at the future time by using the trained network traffic prediction model based on the improved ESN in the step 4.
2. The improved ESN-based network traffic prediction method of claim 1, wherein: in the step 1, in the network traffic data, the total number of packets per minute is counted within a specified sampling time, and finally a certain number of network traffic data sets tr (t) are obtained, where tr (t) is the network traffic data at time t, { tr (1), tr (2),.., tr (t) }.
3. The improved ESN-based network traffic prediction method of claim 1, wherein: in the step 2, performing noise reduction processing on the acquired network traffic data requires performing phase space reconstruction on the network traffic data, then performing noise reduction processing on the known network traffic data by using a local projection method, and finally obtaining a certain number of noise-reduced network traffic data sets Trden(t)，Trden(t)＝{trden(1)，trden(2)，...，trden(t) }, in which trdenAnd (t) is network traffic noise reduction data at the time t.
4. The improved ESN-based network traffic prediction method of claim 1, wherein: in the step 2, the denoising processing of the network traffic data is divided into the following steps:
step 2-1: for the collected flow data set Tr (t), calculating the time delay tau required by phase space reconstruction by using an interactive information method;
step 2-2: for the collected flow data set Tr (t), solving an embedding dimension m required by phase space reconstruction by using an improved false nearest point method;
step 2-3: performing phase space reconstruction on the known flow data according to the time delay tau and the embedding dimension m, and storing the phase space reconstruction;
step 2-4: for each phase point in the phase space, selecting a corresponding local neighborhood, and performing noise reduction processing on the known network traffic data by adopting a local projection method to obtain a set Tr of the noise-reduced network traffic dataden(t)。
5. The improved ESN-based network traffic prediction method of claim 1, wherein: in step 3, a weight r needs to be set to 0.5, a pool scale N needs to be set to 80, and a bicyclic neuron interval d needs to be set for constructing a bicyclic pool structuremax8 and the number of rings c 2; constructing a network traffic prediction model based on the improved ESN requires determining input and output vectors of the improved ESN; the input vector of the improved ESN is network flow historical data and the network flow historical data after noise reduction
Figure FDA0003088197070000031
Figure FDA0003088197070000032
Wherein
Figure FDA0003088197070000033
K before time t1Set of individual network traffic history data, k1Is the embedding dimension of the original network traffic sequence,
Figure FDA0003088197070000034
Figure FDA0003088197070000035
wherein
Figure FDA0003088197070000036
K before time t2A set of noise-reduced network traffic history data, k2For embedding dimension of noise-reduced network traffic sequence, K ═ K1+k2The total embedding dimension and the number of neurons in the input layer; the output vector y (t) { tr (t) }.
6. The improved ESN-based network traffic prediction method of claim 1, wherein: in the step 4, the specific steps of training the network traffic prediction model based on the improved ESN are as follows:
step 4-1: training sample pair for constructing input and output of improved ESN (Enterprise service network) { U }train，Ytrain}t＝{{utrain(1)，ytrain(1)}，{utrain(2)，ytrain(2)}，...，{utrain(t)，ytrain(T) }, where T ═ 1, 2.., T }, T ═ 3000;
step 4-2: bringing the training sample pair into the improved ESN, collecting time t0Input vector u to time Ttrain(T) and an internal state vector x (T) constituting a state vector s (T) having a size of (K + N) x (T-T)0+1) state matrix S; collecting time t0Desired output vector y to time Ttrain(T) obtaining a size of Lx (T-T)0+1) desired output matrix Q; t is t0Set to 100; the method is realized by the following formula:
s(t)＝{utrain(t)；x(t)}
S＝{s(t0)，s(t0+1)，...，s(T)}
Q＝{ytrain(t0)，ytrain(t0+1)，...，ytrain(T)}
step 4-3: obtaining an output connection matrix W using a pseudo-inverse computationout(ii) a Computing network actual output
Figure FDA0003088197070000041
And the desired output ytrainMean square error of (t)
Figure FDA0003088197070000042
So that the mean square error
Figure FDA0003088197070000043
Minimum; s+Is the pseudo-inverse of the state matrix S; the method is realized by the following formula:
Figure FDA0003088197070000044
Wout＝Q·S+。
7. the improved ESN-based network traffic prediction method of claim 1, wherein: in the step 5, the total number of the data packets per minute is counted to obtain a new network traffic data set Tr '(t), and the noise reduction processing is performed on the network traffic data by using a local noise reduction projection method to obtain a noise-reduced network traffic data set Tr' (t)den′(t); predicting future network traffic data by using trained network traffic prediction model based on improved ESN, and outputting network traffic data tr at next momentpred(t+1)。
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