CN106411591B - A kind of network security situation prediction method based on Hurst index - Google Patents

A kind of network security situation prediction method based on Hurst index Download PDF

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CN106411591B
CN106411591B CN201610871341.5A CN201610871341A CN106411591B CN 106411591 B CN106411591 B CN 106411591B CN 201610871341 A CN201610871341 A CN 201610871341A CN 106411591 B CN106411591 B CN 106411591B
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CN106411591A (en
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王继志
杨光
陈丽娟
杨英
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Shandong Computer Science Center
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Abstract

The invention discloses a kind of network security situation prediction methods based on Hurst index, criterion and optimization aim are predicted as network safety situation using the self-similarity index Hurst index of time series, it includes following three processes: (1) network safety situation time series predictability determines and length of time series determines, (2) in time series random component separation, the foundation of (3) prediction model and result output.The present invention, which is specified, calculates whether it has predictability according to actual network safety situation time series, and the optimal variable time sequence length for prediction is obtained by calculation, simultaneously by calculating irregular random component in removal time series, i.e. for predicting meaningless noise data, the influence of noise data is avoided on the basis of regularity in retention time sequence to the full extent；And prediction result and precision of prediction are calculated by prediction model.

Description

A kind of network security situation prediction method based on Hurst index
Technical field
The present invention relates to a kind of network security situation prediction methods based on Hurst index, belong to network information security skill Art field.
Background technique
With the application popularization of internet, network size is increasing, also becomes increasingly complex.Correspondingly, network attack Develop towards the direction of distribution, scale, complication.For network management personnel, there is an urgent need to can be to network security The safety product that whole situation is shown.
So-called network safety situation is to refer to expression attack and cyber-defence measure etc. by various factors institute The network safe state of composition, and shown in the form of numerical quantization.By the network safety situation value at each moment, with regard to structure The time series of network safe state, then the time series based on network safety situation are expressed at one, so that it may to future The network safety situation value at moment is predicted, to help the evolution trend of network management personnel's awareness network security postures, is adopted Take corresponding safety measure.
Currently, have it is some be related to the patent of network security situation prediction method, such as a kind of " network safety situation prediction side Method " (application number: 2011101052724), " a kind of network security situation prediction method and system " (application number: 2013105443158), " a kind of to report adaptive network security situation prediction method by mistake " (application number: 2014107050406) and A kind of " network security situation prediction method based on evidence theory " (application number: 2015101398133).These patents are based on not Same theory proposes the prediction technique of network safety situation from different angles.
However, the prediction technique of above-mentioned network safety situation all has ignored a precondition, i.e., and the not all time Sequence all can be used to prediction, and the time series being such as randomly generated, it is nonsensical that prediction is carried out to it.Therefore, it needs To determine whether the time series predicted for security postures has predictability first.On this basis, it also to solve to be used for The length of time series problem of prediction.Because the time series of network safety situation can increasingly be grown, very with the accumulation of time Long before network safety situation numerical value, intuitively for, may not influence to future time instance network safety situation value Prediction.Therefore, it is necessary to determine a suitable length of time series for prediction, however current method is all subjective choosing The length of the time series of a fixed length is selected, such as the network safety situation value in nearest one week is in predicting, being one month nearest Network safety situation value for predict etc..Simultaneously as attack has certain randomness, this causes network to be pacified Also contain randomness in the time series of full situation, that is to say, that network safety situation is simultaneously non-fully foreseeable, for it In random component can not be predicted.However existing method does not consider this problem, it is intended to containing random The network safety situation value of component is accurately predicted.Due to the prediction to random component be it is meaningless, more suitably do Method is to separate the random component in network safety situation time series, only to wherein regular, predictable component It is predicted, and determines precision of prediction.
Summary of the invention
In view of the above deficiencies, the present invention provides a kind of network security situation prediction method based on Hurst index, energy Enough network safety situation values predicted according to the historical data of network safety situation in following a period of time.
The present invention solves its technical problem and adopts the technical scheme that: a kind of network safety situation based on Hurst index Prediction technique, characterized in that sentenced using the self-similarity index Hurst index of time series as network safety situation prediction Calibration standard and optimization aim, it includes following three processes: (1) judgement of network safety situation time series predictability and time Sequence length determines that the separation of random component in (2) time series, the foundation of (3) prediction model and result export.
Further, the process that the network safety situation time series predictability determines and length of time series determines The following steps are included:
Step 101: setting the time series of network safety situation as x1, x2..., xNIf the time series for prediction is long Degree indicates that wherein N and W is positive integer with W；
Step 102: if N > N0, then it is transferred to step 103；Otherwise indicate that the historical data of network safety situation is very few, no Meet to calculate and require, terminates and calculate；
Step 103: the initial value for taking W is P, that is, takes time series xN-P+1, xN-P+2..., xN-1, xN, total P numerical value, meter Calculate its Hurst index H1, wherein P < N0；
Step 104: enabling the value of W add 1, i.e. W=W+1, take time series xN-W+1, xN-W+2..., xN-1, xN, total W numerical value, Calculate its Hurst index H2；
Step 105: repeating step 104, until W=N, then obtain N-P+1 Hurst index: H altogether1, H2..., HN-P+1；
Step 106: enabling Hmax=max { H1, H2..., HN-P+1, that is, the maximum value in this N-P+1 Hurst index is taken, If Hmax≤ 0.5, then illustrate that the time series of the network safety situation is unpredictable, terminates and calculate；Otherwise, if obtaining maximum Value HmaxCorresponding length of time series be k, it is determined that W=k, that is, determine use time series xN-k-1, xN-k-2..., xN-1, xN, K number value is predicted altogether.
Further, in the time series random component separation process the following steps are included:
Step 201: by the above-mentioned sequence length of seclected time be k time series in order again marked as x1, x2..., xW, and by time series x1, x2..., xWBe converted to the matrix E of M × K:
Wherein, 1 < K < W, M=W-K；
Step 202: matrix E in formula (1) is subjected to singular value decomposition, the covariance matrix R=EE of order matrix ET, then have M A characteristic value and feature vector；Enable λ1,λ2,...,λMIt is the characteristic value of R, and λ1≥...≥λM；Enable U1,...,UMIt is corresponding Feature vector, then Vj=ETUj/λj 1/2, j=1 ..., M；So Ej=λj 1/2UjVj T, therefore, E=E1+E2+...+EM；
Step 203: the initial value for taking i is 1, enables E(1)=ΣiEi；E(2)=E-E(1), E(1)It represents predictable in time series Component, E(2)Represent uncertain random component in time series；
Step 204: pressing formula (2) and formula (3) for E(1), E(2)It is reconstructed into corresponding time series x1 (1), x2 (1)..., xW (1) And x1 (2), x2 (2)..., xW (2)；
X(t)(2)=X (t)-X (t)(1)(3)
In formula, K is enabled*=min (K, M), M*=max (K, M), eijIt is matrix E(1)Element, then as K < M, eij *=eij, Otherwise eij *=eji；
Step 205: calculating separately time series x1 (1), x2 (1)..., xW (1)Hurst index H(1)And x1 (2), x2 (2)..., xW (2)Hurst index H(2)；
Step 206: calculation optimization index ei=| (1-H(1))-(H(2)-0.5)|；
Step 207: enabling the value of i add 1, i.e. i=i+1, repeat step 203 to step 206；And compare eiAnd ei+1If ei<ei+1, then calculating is terminated, and take preceding i component as E(1), and corresponding time series x1 (1), x2 (1)..., xW (1)It carries out Otherwise network safety situation prediction continues to repeat step 3--6, until i=M.
Further, the foundation of the prediction model and result output process the following steps are included:
Step 301: selection parameter p and q, wherein 1≤p≤[W/4], 1≤q≤[W/4]；
Step 302: establish prediction model:
xt'=a1xt-1+a2xt-2+...+apxt-p-b1ut-1-...-bqut-q (4)
Wherein: ut=xt-xt',
By time series x1 (1), x2 (1)..., xW (1)Substitution formula (4), and parameter a is determined using least square method1..., apAnd b1..., bq；
Step 303: by xW (1), xW-1 (1)..., xW-p+1 (1)And uW, uw-1..., uw-qSubstitution formula (4), acquires prediction result xW+1。
Further, the process of the foundation of the prediction model and result output is further comprising the steps of:
Step 304: calculating precision of prediction θ, the calculation formula of precision of prediction θ are as follows:
In formula, θ is precision of prediction, xi (1)And xiFor time series.
Preferably, in the judgement of network safety situation time series predictability and length of time series determination process, 6≤ N0≤ 10,5≤P < N0, P and N0For positive integer.
The beneficial effects of the present invention are:
The predictability that the present invention is primarily based on Hurst exponent pair network safety situation time series determines, when Between sequence have predictability under the premise of obtain the length of time series for prediction, be then based on Hurst exponent separation and go out Wherein uncertain random component only retains predictable component, and final prediction result is finally provided according to prediction model And precision of prediction.
Compared with prior art, the present invention, which is specified, calculates whether it has according to actual network safety situation time series Have predictability, rather than assume its with predictability, and be obtained by calculation it is optimal for prediction variable time sequence Column length, rather than a regular time sequence length is selected with subjective experience；Simultaneously by calculating nothing in removal time series The random component of rule, i.e., it is regular in retention time sequence to the full extent for predicting meaningless noise data On the basis of, avoid the influence of noise data；And prediction result and precision of prediction are calculated by prediction model.
Detailed description of the invention
The present invention will be described with reference to the accompanying drawings of the specification.
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is network safety situation time series predictability of the present invention judgement and length of time series determination process Method flow diagram；
Fig. 3 is the method flow diagram of the separation process of random component in time series of the present invention；
Fig. 4 is the foundation of prediction model of the present invention and the method flow diagram of result output process.
Specific embodiment
In order to clarify the technical characteristics of the invention, below by specific embodiment, and its attached drawing is combined, to this hair It is bright to be described in detail.Following disclosure provides many different embodiments or example is used to realize different knots of the invention Structure.In order to simplify disclosure of the invention, hereinafter the component of specific examples and setting are described.In addition, the present invention can be with Repeat reference numerals and/or letter in different examples.This repetition is that for purposes of simplicity and clarity, itself is not indicated Relationship between various embodiments and/or setting is discussed.It should be noted that illustrated component is not necessarily to scale in the accompanying drawings It draws.Present invention omits the descriptions to known assemblies and treatment technology and process to avoid the present invention is unnecessarily limiting.
In order to overcome the shortcoming of current technology, the present invention provides a kind of new network security situation prediction method, The main thought of this method is using the self-similarity index Hurst index of time series come as criterion, if network is pacified The time series of full situation has self-similarity, then is foreseeable；Otherwise the time series is random, is unpredictable 's.Meanwhile using Hurst index as optimization aim, length, the time series of the time series for prediction are determined respectively The standard of middle separation random component, and the precision that estimation is finally predicted.
As shown in Figure 1, a kind of network security situation prediction method based on Hurst index of the invention, utilizes time sequence The self-similarity index Hurst index of column predicts criterion and optimization aim as network safety situation, it includes following Three processes: (1) network safety situation time series predictability determines and length of time series determines, in (2) time series The separation of random component, the foundation of (3) prediction model and result output.
As shown in Fig. 2, with N0Value is for 6, P value is 5, and network safety situation time series of the present invention can be pre- Survey the process that sex determination and length of time series determine the following steps are included:
Step 101: setting the time series of network safety situation as x1, x2..., xN, it is N number of altogether, prediction technique of the present invention Purpose is just to solve for the network safety situation value x at following next momentN+1；If the length of time series W table for prediction Show, wherein N and W is positive integer；
Step 102: if N > 6, is transferred to step 103；Otherwise indicate that the historical data of network safety situation is very few, no Meet to calculate and require, terminates and calculate；
Step 103: the initial value for taking W is 5, that is, takes time series xN-4, xN-3, xN-2, xN-1, xN, totally 5 numerical value, calculates Its Hurst index H1；
Step 104: enabling the value of W add 1, i.e. W=W+1, take time series xN-W+1, xN-W+2..., xN-1, xN, total W numerical value, Calculate its Hurst index H2；
Step 105: repeating step 104, until W=N, then obtain N-4 Hurst index: H altogether1, H2..., HN-4；
Step 106: enabling Hmax=max { H1, H2..., HN-P+1, that is, the maximum value in this N-P+1 Hurst index is taken, If Hmax≤ 0.5, then illustrate that the time series of the network safety situation is unpredictable, terminates and calculate；Otherwise, if obtaining maximum Value HmaxCorresponding length of time series be k, it is determined that W=k, that is, determine use time series xN-k-1, xN-k-2..., xN-1, xN, K number value is predicted altogether.
As shown in figure 3, in time series of the present invention random component separation process the following steps are included:
Step 201: for convenience of description, the time series that the above-mentioned sequence length of seclected time is k being marked again in order Number be x1, x2..., xW, and by time series x1, x2..., xWBe converted to the matrix E of M × K:
Wherein, 1 < K < W, M=W-K；
Step 202: matrix E in formula (1) is subjected to singular value decomposition, the covariance matrix R=EE of order matrix ET, then have M A characteristic value and feature vector；Enable λ1,λ2,...,λMIt is the characteristic value of R, and λ1≥...≥λM；Enable U1,...,UMIt is corresponding Feature vector, then Vj=ETUj/λj 1/2, j=1 ..., M；So Ej=λj 1/2UjVj T, therefore, E=E1+E2+...+EM；
Step 203: the initial value for taking i is 1, enables E(1)=ΣiEi；E(2)=E-E(1), E(1)It represents predictable in time series Component, E(2)Represent uncertain random component in time series；
Step 204: according to formula (2) and formula (3) by E(1), E(2)It is reconstructed into corresponding time series x1 (1), x2 (1)..., xW (1)And x1 (2), x2 (2)..., xW (2)；
X(t)(2)=X (t)-X (t)(1) (3)
In formula, K is enabled*=min (K, M), M*=max (K, M), eijIt is matrix E(1)Element, then as K < M, eij *=eij, Otherwise eij *=eji；
Step 205: calculating separately time series x1 (1), x2 (1)..., xW (1)Hurst index H(1)And x1 (2), x2 (2)..., xW (2)Hurst index H(2)；
Step 206: calculation optimization index ei=| (1-H(1))-(H(2)-0.5)|；
Step 207: enabling the value of i add 1, i.e. i=i+1, repeat step 203 to step 206；And compare eiAnd ei+1If ei<ei+1, then calculating is terminated, and take preceding i component as E(1), and corresponding time series x1 (1), x2 (1)..., xW (1)It carries out Otherwise network safety situation prediction continues to repeat step 3--6, until i=M.
As shown in figure 4, the foundation of prediction model of the present invention and result output process the following steps are included:
Step 301: selection parameter p and q, wherein 1≤p≤[W/4], 1≤q≤[W/4]；
Step 302: establish prediction model:
xt'=a1xt-1+a2xt-2+...+apxt-p-b1ut-1-...-bqut-q (4)
Wherein: ut=xt-xt', t is positive integer；
By time series x1 (1), x2 (1)..., xW (1)Substitution formula (4), and parameter a is determined using least square method1..., apAnd b1..., bq；
Step 303: by xW (1), xW-1 (1)..., xW-p+1 (1)And uW, uw-1..., uw-qSubstitution formula (4), acquires prediction result xW+1；
Step 304: calculating precision of prediction θ, the calculation formula of precision of prediction θ are as follows:
In formula, θ is precision of prediction, xi (1)And xiFor time series.
In above-described embodiment, in the judgement of network safety situation time series predictability and length of time series determination process In, with N0Value is for 6, P value is 5.Accurate quick, the N in order to calculate0Value range be preferably [6,10], the value of P Range preferably from [6, N0], but its protection scope is not unduly limited to this by the application, to N0It is suitably adjusted with the value of P The whole prediction for realizing network safety situation, equally also should be regarded as the protection scope of the application.
The present invention first determines the predictability of network safety situation time series, wherein can not be then demultiplex out The random component of prediction finally provides final prediction result, it is specified according to actual network safety situation time series Calculate whether it has predictability, rather than assume its with predictability, and be obtained by calculation it is optimal for prediction Variable time sequence length, rather than a regular time sequence length is selected with subjective experience；Simultaneously by calculating removal Irregular random component in time series, i.e., for predicting meaningless noise data, retention time sequence to the full extent In column on the basis of regularity, the influence of noise data is avoided；And prediction result and prediction are calculated by prediction model Precision.
The above is the preferred embodiment of the present invention, for those skilled in the art, Without departing from the principles of the invention, several improvements and modifications can also be made, these improvements and modifications are also regarded as this hair Bright protection scope.

Claims (2)

1. a kind of network security situation prediction method based on Hurst index, characterized in that utilize the self-similarity of time series Index Hurst index predicts criterion and optimization aim as network safety situation, it includes following three processes: (1) Network safety situation time series predictability determines and length of time series determines, point of random component in (2) time series From the foundation of (3) prediction model and result output；
The network safety situation time series predictability determines and length of time series determines process the following steps are included:
Step 101: setting the time series of network safety situation as x1, x2..., xNIf the length of time series W for prediction It indicates, wherein N and W is positive integer, N0For the preset value of time series number；
Step 102: if N > N0, then it is transferred to step 103；Otherwise it terminates and calculates；
Step 103: the initial value for taking W is P, that is, takes time series xN-P+1, xN-P+2..., xN-1, xN, total P numerical value calculates it Hurst index H1, wherein P < N0；
Step 104: enabling the value of W add 1, i.e. W=W+1, take time series xN-W+1, xN-W+2..., xN-1, xN, total W numerical value, calculating Its Hurst index H2；
Step 105: repeating step 104, until W=N, then obtain N-P+1 Hurst index: H altogether1, H2..., HN-P+1；
Step 106: enabling Hmax=max { H1, H2..., HN-P+1, if Hmax≤ 0.5, then illustrate the time of the network safety situation Sequence is unpredictable, terminates and calculates；Otherwise, if obtaining maximum value HmaxCorresponding length of time series be k, it is determined that W=k, It determines and uses time series xN-k-1, xN-k-2..., xN-1, xN, k number value is predicted altogether；
In the time series random component separation process the following steps are included:
Step 201: by the above-mentioned sequence length of seclected time be k time series in order again marked as x1, x2..., xW, And by time series x1, x2..., xWBe converted to the matrix E of M × K:
Wherein, 1 < K < W, M=W-K；
Step 202: matrix E in formula (1) is subjected to singular value decomposition, the covariance matrix R=EE of order matrix ET, then have M feature Value and feature vector；Enable λ1,λ2,...,λMIt is the characteristic value of R, and λ1≥...≥λM；Enable U1,...,UMCorresponding feature to It measures, then Vj=ETUj/λj 1/2, j=1 ..., M；So Ej=λj 1/2UjVj T, therefore, E=E1+E2+...+EM；
Step 203: the initial value for taking i is 1, enables E(1)=ΣiEi；E(2)=E-E(1), E(1)Predictable point is represented in time series Amount, E(2)Represent uncertain random component in time series；
Step 204: pressing formula (2) and formula (3) for E(1), E(2)It is reconstructed into corresponding time series x1 (1), x2 (1)..., xW (1)And x1 (2), x2 (2)..., xW (2)；
X(t)(2)=X (t)-X (t)(1) (3)
In formula, K is enabled*=min (K, M), M*=max (K, M), eijIt is matrix E(1)Element, then as K < M, eij *=eij, otherwise eij *=eji；
Step 205: calculating separately time series x1 (1), x2 (1)..., xW (1)Hurst index H(1)And x1 (2), x2 (2)..., xW (2)Hurst index H(2)；
Step 206: calculation optimization index ei=| (1-H(1))-(H(2)-0.5)|；
Step 207: enabling the value of i add 1, i.e. i=i+1, repeat step 203 to step 206；And compare eiAnd ei+1If ei< ei+1, then calculating is terminated, and take preceding i component as E(1), and corresponding time series x1 (1), x2 (1)..., xW (1)Carry out network Otherwise security postures prediction continues to repeat step 3--6, until i=M；
The foundation of the prediction model and result output process the following steps are included:
Step 301: selection parameter p and q, wherein 1≤p≤[W/4], 1≤q≤[W/4]；
Step 302: establish prediction model:
xt'=a1xt-1+a2xt-2+...+apxt-p-b1ut-1-...-bqut-q (4)
Wherein: ut=xt-xt',
By time series x1 (1), x2 (1)..., xW (1)Substitution formula (4), and parameter a is determined using least square method1..., apWith b1..., bq；
Step 303: by xW (1), xW-1 (1)..., xW-p+1 (1)And uW, uw-1..., uw-qSubstitution formula (4), acquires prediction result xW+1；
Step 304: calculating precision of prediction θ, the calculation formula of precision of prediction θ are as follows:
In formula, θ is precision of prediction, xi (1)And xiFor time series.
2. a kind of network security situation prediction method based on Hurst index according to claim 1, characterized in that In the judgement of network safety situation time series predictability and length of time series determination process, 6≤N0≤ 10,5≤P < N0, P and N0For positive integer.
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