CN102914325B - Dissipation synchronization-based detection method of small signal under chaos background - Google Patents

Abstract

The invention relates to a dissipation synchronization-based detection method of a weak signal under a chaos background. The dissipation synchronization-based detection method comprises the following steps of: 1, obtaining an embedded peacekeeping time delay of a chaos time sequence and reconstructing a chaos phase space; 2, fitting a chaos prediction model through a neutral network; 3, carrying out single-step prediction by using the chaos prediction model to obtain a predicated value, calculating an error between the predicted value and the practical value; and 4, analyzing an error value through methods of Fourier transform and the like and judging whether the weak signal exists in the error value, detecting the weak signal in the step 3, selecting a proper parameter for realizing dissipation synchronization of the time sequence and a chaos system, and determining a synchronization parameter K when the minimum mean square error of the error of the sum reaches the minimum value. The dissipation synchronization-based detection method has the advantages of weakening the characteristic that the chaos is extremely sensitive to the initial condition, considering the influence of factors such as the weak signal and noise on signal detection, and improving practical property.

Description

Method for detecting weak signals under a kind of Chaotic Background synchronous based on dissipation type

Technical field

The present invention relates to Technique of Weak Signal Detection, be specifically related to the method for detecting weak signals under a kind of Chaotic Background.

Background technology

Chaos non-linear knows system, has characteristics such as starting condition extreme sensitivity, short-term predictions, applied to the fields such as medical science, secret communication, the hydrology widely.Chaos is ubiquitous, and the Detection of Weak Signals under Chaotic Background, estimation are one of the focus and difficult point of the research of current signal transacting.At present, the Detection of Weak Signals Main Basis chaos phase space reconstruction under Chaotic Background and neural network.First, according to Takens embedding theorems, adopt pseudo-nearest neighbor method, C-C method, mutual information etc. to obtain the embedding dimension m and time delay τ of chaos time sequence, reconstruct chaos phase space; Then by neural network matching chaotic prediction model; Finally, utilize chaotic prediction model to carry out Single-step Prediction, obtain predicted value, and the error of computational prediction value and actual value, judge wherein whether there is feeble signal by methods analyst error amounts such as FFT.These class methods mainly discuss the situation that there is chaotic signal and feeble signal, usually only add suitable noise when discussing algorithm validity, but do not have concrete analysis to noise, only have a small amount of research analyzing noise.And in actual environment, noise is ubiquitous, the Practical Performance of this kind of algorithm also reduces greatly.Secondly, this kind of algorithm adopts chaos system to carry out Single-step Prediction, have ignored the impact of feeble signal, chaos system is very responsive to starting condition, the membership that adds of feeble signal produces impact to a certain degree to the motion state in later stage, and then affect chaotic time signal, particularly when periodic signal joins in chaos time sequence, this impact can be more obvious.AieeshP K etc. synchronously achieve the Weak Signal Processing under Chaotic Background by interpolation antithesis, first, adopt SVM to obtain drive system in conjunction with phase space reconstruction; Secondly, chaos coupled synchronization is adopted to obtain responding system; Finally, calculate the output error of two systems and FFT is carried out to it, if there is weak periodic signal, then in the frequency of correspondence, there is certain amplitude, and other frequency place, amplitude is then relatively little.The superiority of this method considers noise effect in analytic process, and the practicality of method improves greatly, and in article, the synchronous rear raising of algorithm in performance is introduced in detailed describing simultaneously.Chaotic Synchronous generally refers to that two chaos systems finally arrive synchronous process, and chaos is very responsive to starting condition, and two chaos systems seem and can not reach synchronous.But this method have employed two SVM systems, increases system complexity, concrete synchronous method is not also selected.

Summary of the invention

The object of the invention is on traditional basis based on chaotic prediction model, dissipation type coupled synchronization is joined in the method for detecting weak signals under Chaotic Background and weaken the characteristic of chaos system to starting condition sensitivity, Detection of Weak Signals under Chaotic Background is converted to the test problems of feeble signal under noise background, the Practical Performance of raising method, specifically has following technical scheme to realize:

Method for detecting weak signals under the described Chaotic Background synchronous based on dissipation type, comprises the steps:

1) the embedding dimension m and time delay τ of chaos time sequence is obtained, reconstruct chaos phase space;

2) by RBF neural matching chaotic prediction model;

3) utilize chaotic prediction model to carry out Single-step Prediction, obtain predicted value, and the error of computational prediction value and actual value;

4) judge wherein whether there is feeble signal by methods analyst error amounts such as Fourier transforms,

In described step 3), comprise the steps:

A) the time series c that there is same chaos system is supposed _n, feeble signal s _n, white noise η _nthe mixed signal x formed _n, i.e. x _n=c _n+ s _n+ η _n, x _nas actual signal, from x _nin detect feeble signal s _n, suitable parameter K must be selected to realize time series x _nwith chaos system F (c _n) dissipation type synchronous, such as formula 1:

$c_{n+1}=F(c_n,x_n)=\left(\begin{array}{c}f\left(c_n\right)-K(x_n-c_n)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right)=\left(\begin{array}{c}f(c_n,c_{n-1,\·\·\·,}{c}_{n-(D-1)})-K(x_n-c_n)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right)\·---\left(1\right)$

Wherein, n=D ..., N, (x _n-c _n) be the margin of error, K is synchronization parameter, and the prediction of chaotic synchronizing system exports, such as formula 2;

${\hat{c}}_{n+1}=h\left(F(c_n,x_n)\right)\·\·\·\left(2\right)$

B) when can think chaos system and input signal Complete Synchronization, work as x _nwith the Minimum Mean Square Error of error reach minimum value, x _nwith synchronism best, Mse (K) is now exactly synchronization parameter K, such as formula 3.

$\mathrm{Mse}\left(K\right)=\underset{n=D+1}{\overset{N}{\mathrm{\Σ}}}{({\hat{c}}_n-x_n)}^2\·\·\·\left(3\right)$

The further design of described detection method is, defines pure chaos time sequence c in described step 1 according to Takens _ncarry out phase space reconfiguration, select normalized time delay τ=1, embed 2 times that dimension D is the embedding dimension m that pseudo-nearest neighbor method or Cao method are determined, i.e. D>=2m, obtains phase space c _n, such as formula 4.

c _n＝{c _n,c _n-1，...,c _n-(D-1)} ^T,n＝D,...，N-1················（4）

Wherein, T representing matrix transposition, z _n=c _n, n=D+1 ..., N, and composing training inputoutput pair { c _n, z _n+1, n=D ..., N-1.

The further design of described detection method is, in described step 2, the expression formula of RBF neural is such as formula (5):

$f\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_i\mathrm{\φ}\left(\right||x-x_i|\left|\right)\·\·\·\left(5\right)$

Wherein w _ibe weight, x is input, for Gaussian bases, w _iand x _ineed to carry out training to determine by known input and output.Adopt the training inputoutput pair { c in the 1st step _n, z _n+1, n=D ..., N-1, as training set, obtains chaotic prediction model its expression formula such as formula 6,

$c_{n+1}=F\left(c_n\right)=\left(\begin{array}{c}f\left(c_n\right)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right)\·\·\·\left(6\right)$

Wherein, n=D ..., N,

The output of chaotic prediction model is exactly in fact the one-component that Chaotic System Prediction exports

${\hat{c}}_{n+1}=f\left(c_n\right)=h\left(F\left(c_n\right)\right)\·\·\·\left(7\right)$

The further design of described detection method is, it is characterized in that, in described step 4, the error of predicted value and actual value is such as formula 8,

${\mathrm{err}}_n=x_n-{\hat{c}}_n=c_n+s_n+{\mathrm{\η}}_n-{\hat{c}}_n\≈s_n+{\mathrm{\η}}_n\·\·\·\left(8\right)$

Adopt Fast Fourier Transform (FFT) to carry out spectrum analysis to error, observe in spectrogram whether there is projection, if existed, illustrate in Chaotic Background that the weak periodic signal that there is this frequency spectrum or predominant frequency are the feeble signal of this frequency.

The present invention, in order to realize the Detection of Weak Signals under actual environment, proposes based on Detection of Weak Signals under the synchronous Chaotic Background of dissipation type.By the introducing that dissipation type is synchronous, weaken the characteristic that chaos is extremely responsive to starting condition, consider the impact of the factor such as feeble signal, noise on input simultaneously, improve the Practical Performance of detection method.

Accompanying drawing explanation

Fig. 1 is based on the minimal value determination synchronization parameter K of the Minimum Mean Square Error of input and output error.

The error of Fig. 2 drive singal and response signal and the energy frequency spectrum figure of error; (a) Error Graph; The energy frequency spectrum figure of (b) error.

Under the different state of signal-to-noise of Fig. 3, drive singal and response signal error mean square difference.

Detection of Weak Signals design sketch (a) SCR=-80db during Fig. 4 difference SCR; (b) SCR=-100db; (c) SCR=-120db.

Fig. 5 surveys the Detection of Weak Signals design sketch of chaos time sequence under different signal to noise ratio; (a) SCR=-25db; (b) SCR=-50db.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, the present invention is illustrated:

The present invention defines pure chaos time sequence c according to Takens _ncarry out phase space reconfiguration, select normalized time delay τ=1, embed 2 times that dimension D is the embedding dimension m that pseudo-nearest neighbor method or Cao method are determined, i.e. D>=2m, obtains phase space c _n={ c _n, c _n-1..., c _n-(D-1)} ^t, n=D ..., N-1, T representing matrix transposition, z _n=c _n, n=D+1 ..., N, and composing training inputoutput pair { c _n, z _n+1, n=D ..., N-1.Why embed dimension selects 2 times to be information in order to promote in chaos vector, so that better reduce chaos system.

Adopt RBF neural matching chaotic prediction model, RBF neural can realize the simulation of arbitrary function in theory, avoids local minimum problem, advantages of simple structure and simple.

The expression formula of RBF neural is as follows,

$f\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_i\mathrm{\φ}\left(\right||x-x_i|\left|\right)$

Wherein w _ibe weight, x is input, for Gaussian bases, w _iand x _ineed to carry out training to determine by known input and output.Adopt the training inputoutput pair { c in the 1st step _n, z _n+1, n=D ..., N-1, as training set, obtains chaotic prediction model

Adopt above-mentioned chaotic prediction Model Reconstruction chaos system, be shown below,

$c_{n+1}=F\left(c_n\right)=\left(\begin{array}{c}f\left(c_n\right)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right),n=D,...,N$

Shown in above formula, the output of chaotic prediction model is exactly in fact the one-component that Chaotic System Prediction exports from above formula, the later stage state of chaos system is subject to the impact of preneoplastic state.

Suppose the time series c that there is same chaos system _n, feeble signal s _n, white noise η _nthe mixed signal x formed _n, i.e. x _n=c _n+ s _n+ η _n.X _nas actual signal, feeble signal s to be detected from signal _n.Suitable coupling parameter K is selected to realize incorporation time sequence x _nwith chaos system F (c _n) dissipation type synchronous, shown in (4):

$c_{n+1}=F(c_n,x_n)=\left(\begin{array}{c}f\left(c_n\right)-K(x_n-c_n)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right)=\left(\begin{array}{c}f(c_n,c_{n-1,\·\·\·,}{c}_{n-(D-1)})-K(x_n-c_n)\\ c_n\\ \·\\ \·\\ \·\\ c_{n-(D-2)}\end{array}\right)$

Wherein, n=D ..., N, (x _n-c _n) be the margin of error, K is synchronization parameter.Simultaneously known, the prediction of chaotic synchronizing system exports and is shown below.

${\hat{c}}_{n+1}=h\left(F(c_n,x_n)\right)$

Dynamically determine coupling parameter K.Dissipation type Chaotic Synchronous essence makes input by regulable control parameter K and predicts that the difference between exporting reduces gradually, finally realizes Chaotic Synchronous, when can think and chaos system and input signal Complete Synchronization owing to there is noise and feeble signal in chaotic signal, can not Complete Synchronization be realized.Therefore coupling parameter K is by chaos time sequence x _nthe output of (drive singal) and responding system the Minimum Mean Square Error of (response signal) error is determined, is shown below, works as x _nwith the Minimum Mean Square Error of error reach minimum value, now x is described _nwith synchronism best, Mse(K now) be exactly synchronization parameter K.

$\mathrm{Mse}\left(K\right)=\underset{n=D+1}{\overset{N}{\mathrm{\Σ}}}{({\hat{c}}_n-x_n)}^2$

Thinking Mse(K in practice) K corresponding when local minimum be exactly coupling parameter K.Therefore the Minimum Mean Square Error Mse(K of the margin of error of input and output only need be determined to a series of K), the Mse(K corresponding when lowest mean square difference arrives local minimum) be exactly coupling parameter K.

According to the above-mentioned coupling parameter K determined, the error of predicted value and actual value is shown below:

${\mathrm{err}}_n=x_n-{\hat{c}}_n=c_n+s_n+{\mathrm{\η}}_n-{\hat{c}}_n\≈s_n+{\mathrm{\η}}_n$

From above formula, mainly feeble signal and noise contribution in this error signal.If there is weak periodic signal, fast Fourier (FFT) transfer pair error is then adopted to carry out spectrum analysis, observe in spectrogram and whether there is projection, if exist, illustrate in Chaotic Background that the weak periodic signal that there is this frequency spectrum or predominant frequency are the feeble signal of this frequency.If there is transient signal, then direct error to be judged to usually can there is projection at the regional area that there is feeble signal.

In order to the rationality of the method is described, classical Rossler chaos system (being shown below) is adopted to carry out simulating, verifying as experimental subjects.

$\frac{\mathrm{dx}}{\mathrm{dt}}=-y-z;$ $\frac{\mathrm{dy}}{\mathrm{dt}}=x+\mathrm{ay};$ $\frac{\mathrm{dz}}{\mathrm{dt}}=b+z(x-c)$

Wherein a=0.15, b=0.2, c=10, integration step is 0.05s, and selection mode x is as chaos time sequence, and integration step can be used as the sampling time interval in reality, gets 4000 chaos time sequences as Chaotic Background, is denoted as c _n, n=1 ..., 4000.In order to the versatility of illustration method, the MKS-CEC-III new chaotic Evolution Control experiment instrument of Nanjing permanent Rieter photoelectric instrument factory is relied on to test, this experiment instrument can produce Coullet chaos, and the state x gathering Coullet chaos carries out the analysis & verification of method as experimental data.

The feeble signal detected is periodic signal, adopts sinusoidal signal as detection target, is shown below:

$s_n=A*\sin \left(2\mathrm{\πn}\frac{f}{f_s}\right)=A*\sin \left(2\mathrm{\πnf}{T}_s\right)=A*\sin \left(2\mathrm{\πwn}\right)$

Wherein A is signal amplitude, f, f _sbe respectively signal frequency and sample frequency, T _sfor time sampling interval, integration step can be adopted to replace, w is numerical frequency.

In order to quantitative analysis noise, chaos clutter are on the impact of Detection of Weak Signals performance, avoid the impact of noise and chaos clutter to mix, introduce signal to noise ratio (snr) and signal to noise ratio (SCR) two definition.

$\mathrm{SNR}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{s}_i^2}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_i^2}$

$\mathrm{SCR}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{s}_i^2}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{c}_i^2}$

In analytic process, add suitable white noise composition, discuss along with SNR change, algorithm detects the performance change of feeble signal, and the impact of noise on input is described.

For simulation actual signal, at known chaotic signal c _nthe white noise of middle interpolation SCR=-25db, SNR=-5db and sinusoidal signal, wherein f=4Hz, f _s=20Hz (selection of signal frequency need meet nyquist sampling theorem), i.e. w=0.2rad, the relative chaotic signal of sinusoidal signal can be considered feeble signal.First determine coupling parameter, for a series of K, if the error of synchro system input and output exists minimum point, then the K that this minimum point is corresponding both can be used as synchronization parameter K.As shown in Figure 1, as K=0.61, in the mean square deviation figure of error amount, there is local minimum, therefore can think that the mixed signal of employing SCR=-25db, SNR=-5db drives the synchronization parameter K=0.61 of synchro system.

Whether the synchro system determining synchronization parameter exists feeble signal under can be used to analyze Chaotic Background, first the error inputting and export (response signal) with synchro system is calculated, then error is analyzed, the introducing of synchro system makes detection model be no longer simple single step chaotic prediction system, feeble signal, noise all can affect the later stage state of chaos system, there is the feature of feeble signal, noise in the error obtained by synchro system, therefore whether can there is feeble signal in analytical error determination signal.Fig. 2 (a) is the error of drive singal and response signal, and this error amount is similar to noise, does not have obvious cyclophysis, and this illustrates that Chaotic Synchronous inhibits chaotic signal preferably, to make in error mainly noise and feeble signal composition.Adopt FFT to carry out spectrum analysis to error, before spectrum analysis, suitable pre-service can be done, as removed direct current signal etc.The energy frequency spectrum figure of error is as shown in Fig. 5 (b), obvious projection is there is at w=0.2rad place, just be the frequency of added weak periodic signal, and the energy at other frequency places is far longer than at the energy at this frequency place, the capacity spectrum of other frequency place signals is very little, can intuitive judgment go out in signal to there is weak periodic signal.The introducing of Chaotic Synchronous considers the impact of noise, feeble signal, and the error amount that determined error ratio single step chaotic prediction model is determined is more abundant, and closing to reality situation more, can better solve test problems.

After synchronously processing, the error of constrained input is formed primarily of error and feeble signal, therefore must analyze the impact of noise on Detection of Weak Signals performance, c in Chaotic Background _nadd the Weak Sinusoidal Signal of SCR=-25db, but the signal to noise ratio snr adding noise is respectively-20db ,-15db ,-10db ,-5db, 0db, 5db, 10db, 15db, 100db as drive singal, wherein 100db is to simulate muting situation, drive synchro system respectively, SCR is constant, and SNR only affects noise contribution, can think that synchronization parameter K is approximate constant, calculated response signal and drive singal mean square of error difference, as shown in Figure 3.As seen from the figure, when noise contribution is more, mean square deviation is larger, illustrate that noise can cause the error randomness of drive singal and response signal stronger, it is more and more less that SNR increases explanation noise contribution, also can be more and more less from mean square deviation, and finally trend towards plateau, as SNR >=0db, mean square deviation is substantially identical, illustrate in the detectable situation of feeble signal, when signal to noise ratio (S/N ratio) is higher, the impact of noise on Detection of Weak Signals is little, but as SNR <-10db, mean square deviation change is violent, illustrates that now noise effect is obvious.

Along with SCR constantly reduces, under Chaotic Background, feeble signal and noise contribution reduce, and response signal and drive singal mean square of error difference can trend towards 0, finally by the existence of perception less than signal, and then the detection of feeble signal can not be realized, therefore the performance of algorithm can not be described with mean square deviation.Select SCR be-120db ,-100db ,-80db incorporation time sequence as research object, the change of SCR can cause noise and signal to there is larger change, different synchronization factor K need be selected to the drive singal of different SCR, then feeble signal is detected, Detection results as shown in Figure 4, wherein x-axis is numerical frequency, and y-axis is energy intensity.As seen from the figure, as SCR=-80db, there is spike at the frequency place added in spectrogram, and be far smaller than the peak value at this frequency place at the spike peak value at other frequency places, therefore can easily detect feeble signal.As SCR=-100db, occurred more spike in spectrogram, but this frequency place still exists spike, and the value at other frequency places of peakedness ratio is all large, therefore peak value still can be used as detection foundation, but may cause erroneous judgement.As SCR=-120db, there is not spike in this frequency place, also just can not realize the detection of signal.By experimental verification repeatedly, as SCR=-110db, the method still can realize the detection of weak periodic signal.In order to the versatility of illustration method, rely on the MKS-CEC-III new chaotic Evolution Control experiment instrument of Nanjing permanent Rieter photoelectric instrument factory to test, this experiment instrument can produce Coullet chaos.First Coullet phase space plot is debugged out in conjunction with analog oscilloscope ^[33], when after generation Coullet phase space plot, the x state gathering Coullet, as chaos time sequence, gathers the real data in a certain moment and adopts the method for running mean to obtain level and smooth sequence to data.Fetch data front 2000 as training data, rear 2000 as test data, SCR=-25db is added in test data, the sinusoidal signal of SNR=-5db w=0.1rad and noise are as test data A, add SCR=-50db, SNR=-5db, the sinusoidal signal of w=0.3rad and noise are as test data B, adopt the matching of RBF real-time performance Single-step Prediction model, training error is selected at about 1e-7, then to test data A, B determines synchronization parameter K respectively, as SCR=-25db, synchronization parameter K=0.09, and as SCR=-50db, K=0.19, illustrate that the synchronization parameter of system there are differences in different signal to noise ratio situation.Finally carry out the detection of feeble signal, the effect of two kinds of different signal to noise ratio Detection of Weak Signals as shown in Figure 5, as seen from the figure, in two kinds of different signal to noise ratio situations, all occurred obvious spike in figure, but there is difference in peak amplitude, describe the difference of feeble signal energy.There is good Detection results at two kinds of different frequency places, describe the method very little on the impact being subject to feeble signal frequency.Being applicable to different chaos system by analyzing known the method above, the detection of different frequency feeble signal can being realized, there is stronger versatility.

Claims (4)

1., based on a method for detecting weak signals under the synchronous Chaotic Background of dissipation type, comprise the steps:

1) the embedding dimension m and time delay τ of chaos time sequence is obtained, reconstruct chaos phase space;

2) by RBF neural matching chaotic prediction model;

3) utilize chaotic prediction model to carry out Single-step Prediction, obtain predicted value, and the error of computational prediction value and actual value;

4) judge wherein whether there is feeble signal by Fourier transform analytical error value,

It is characterized in that, described step 3) in, comprise the steps:

A) the time series c that there is same chaos system is supposed _n, feeble signal s _n, white noise η _nthe mixed signal x formed _n, i.e. x _n=c _n+ s _n+ η _n, x _nas actual signal, from x _nin detect feeble signal s _n, suitable parameter K must be selected to realize time series x _nwith chaos system F (c _n) dissipation type synchronous, such as formula 1:

$c_{n+1}=F(c_n,x_n)=\left(\begin{array}{c}f\left(c_n\right)-K(x_n-c_n)\\ c_n\\ .\\ .\\ .\\ c_{n-(D-2)}\end{array}\right)=\left(\begin{array}{c}f(c_n,c_{n-1},...,c_{n-(D-1)})-K(x_n-c_n)\\ c_n\\ .\\ .\\ .\\ c_{n-(D-2)}\end{array}\right)....\left(1\right)$

Wherein, n=D ..., N, (x _n-c _n) be the margin of error, K is synchronization parameter, and the prediction of chaotic synchronizing system exports, such as formula 2;

${\hat{c}}_{n+1}=h\left(F(c_n,x_n)\right)...\left(2\right)$

B) when can think chaos system and input signal Complete Synchronization, work as x _nwith the Minimum Mean Square Error of error reach minimum value, x _nwith synchronism best, Mse (K) is now exactly synchronization parameter K, such as formula 3;

$\mathrm{Mse}\left(k\right)=\underset{n=D+1}{\overset{N}{\mathrm{\&Sigma;}}}{({\hat{c}}_n-x_n)}^2...\left(3\right)$

2. detection method according to claim 1, is characterized in that, defines pure chaos time sequence c in described step 1 according to Takens _ncarry out phase space reconfiguration, select normalized time delay τ=1, embed 2 times that dimension D is the embedding dimension m that pseudo-nearest neighbor method is determined, i.e. D>=2m, obtains phase space c _n, such as formula 4;

c _n＝{c _n,c _n-1,...,c _n-(D-1)} ^T,n＝D,...,N-1················(4)

Wherein, T representing matrix transposition, z _n=c _n, n=D+1 ..., N, and composing training inputoutput pair { c _n, z _n+1, n=D ..., N-1.

3. detection method according to claim 1, is characterized in that, in described step 2, the expression formula of RBF neural is such as formula (5):

$f\left(x\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{w}_i\mathrm{\&phi;}\left(\right||x-x_i|\left|\right)...\left(5\right)$

Wherein w _ibe weight, x is input, $\mathrm{\&phi;}\left(\right||x-x_i|\left|\right)=\exp \left(\frac{-{\left|\right|x-x_i\left|\right|}^2}{{2\mathrm{\&delta;}}^2}\right)$ For Gaussian bases, w _iand x _ineed to carry out training to determine by known input and output.Adopt the training inputoutput pair { c in the 1st step _n, z _n+1, n=D ..., N-1, as training set, obtains chaotic prediction model its expression formula such as formula 6,

$c_{n+1}=F\left(c_n\right)=\left(\begin{array}{c}f\left(c_n\right)\\ c_n\\ .\\ .\\ .\\ c_{n-(D-2)}\end{array}\right)...\left(6\right)$

Wherein, n=D ..., N,

The output of chaotic prediction model is exactly in fact the one-component that Chaotic System Prediction exports

${\hat{c}}_{n+1}=f\left(c_n\right)=h\left(F\left(c_n\right)\right)...\left(7\right)$

4. detection method according to claim 1, is characterized in that, in described step 4, the error of predicted value and actual value is such as formula 8,

${\mathrm{err}}_n=x_n-{\hat{c}}_n=c_n+s_n+{\mathrm{\&eta;}}_n-{\hat{c}}_n\&ap;s_n+{\mathrm{\&eta;}}_n...\left(8\right)$

Adopt Fast Fourier Transform (FFT) to carry out spectrum analysis to error, observe in spectrogram whether there is projection, if existed, illustrate in Chaotic Background that the weak periodic signal that there is this frequency spectrum or predominant frequency are the feeble signal of this frequency.