CN106197523A  Testing of Feeble Signals based on firstorder linear system and recovery  Google Patents
Testing of Feeble Signals based on firstorder linear system and recovery Download PDFInfo
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 CN106197523A CN106197523A CN201610511284.XA CN201610511284A CN106197523A CN 106197523 A CN106197523 A CN 106197523A CN 201610511284 A CN201610511284 A CN 201610511284A CN 106197523 A CN106197523 A CN 106197523A
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Abstract
Description
Technical field
The present invention relates to Detection of Weak Signals field, be specially with crosscorrelation coefficient as index, study firstorder linear system The Stochastic Resonance Phenomenon of system, and detect and restore the lowand highfrequency weak periodic signal under different signal to noise ratio.
Background technology
Signal detection is a kind of method that can directly obtain bulk information, suffers from quite varied in a lot of scientific domains Application, such as Ship Axle Frequency Electric Field signal detection, the bearing fault detection of early stage, seismic prospecting, seabed natural electric field are measured, radar Receiver, metal detector etc..Smallsignal is not only signal amplitude and the least signal of each parameter, is primarily referred to as The signal flooded by noise." faint ", for noise, noise is ubiquitous, all of engineering actual should During with, signal and noise all coexist, and want to extract smallsignal, topmost task from strong noise background It it is the signal to noise ratio improving detecting system output signal.
1981, Benzi et al. was found that random being total in glacial epoch and the warm cycle of the research earth when being alternately present problem Shake.Accidental resonance refers to system, signal and noise three and reaches a cooperative effect, the energy of a part of low frequency in noise Being converted into signal energy makes signal energy be greatly improved, and optimizes a kind of means of snr gain with this.We can also manage Solve as, detecting weak signal when, adding suitable noise in nonlinear system, will be enhanced with the signal energy of frequency, Noise energy weakens simultaneously.Therefore, Stochastic Resonance Theory is that Chinese scholars provides new thinking in Testing of Feeble Signals field And method, many classical stochastic resonance system models are in succession suggested, and are used widely.Document “Gitterman.Classical harmonic oscillator with multiplicative noise.Physica A Statistical Mechanics&Its Applications, 2005 " have studied harmonic potential trap system, its potential function isThe output response of discovery system presents the phenomenon of nonmonotonic change with some characteristic parameter of noise；Document " Ji Yuandong, the broad sense accidental resonance of power function type unipotential trap Random Vibration System. Acta Physica Sinica, 2014 " simple harmonic quantity potential well is promoted Obtain the more monostable system of general power function type, and its Stochastic Resonance Phenomenon has been carried out the most deep analysis；
Most of stochastic resonance system are all the frequencies of detection smallsignal, for grinding that the amplitude of weak signal carries out detecting Study carefully less.In consideration of it, the present invention proposes firstorder linear accidental resonance recovery system, firstorder linear system model is simple, and structure is joined Number is single, it is possible to increase arithmetic accuracy.To a certain extent, firstorder linear system is better than bistable system in terms of weak signal recovery System.The present invention have studied its Stochastic Resonance Phenomenon, and the weak signal restored method for firstorder linear SR model, to different noises The weak signal to be measured of ratio is restored.
Summary of the invention
The problems referred to above existed for prior art, propose a kind of to detect the recovery side of weak periodic signal under noise background Method, the technical problem to be solved is: on existing accidental resonance Research foundation, explores a kind of more simple and efficient System model so that it can not only realize Detection of Weak Signals, also can obtain the amplitude of weak measured signal simultaneously, reaches to obtain The purpose of signal integrity information.
The present invention solves the technical scheme of the problems referred to above, first with Fourth order RungeKutta, has probed into firstorder linear The broad sense Stochastic Resonance Phenomenon of system structure parameter a, then proposes the lowand highfrequency weak signal restored method of linear system, finally Realize the weak periodic signal of lowand highfrequency is restored.
In dynamic system, firstorder linear system model is as follows:
In formula (1), a is system structure parameter, and Acos (2 π ft) is smallsignal to be measured, n (t) be average be 0, autocorrelation Function is the white Gaussian noise of<n (t) n (0)>=2D σ (t), and its noise intensity is D.
The Fourth order RungeKutta that the present invention carries out numerical simulation employing is as follows:
k_{1}=h (ax (n)+s (n))
k_{4}=h (a (x (n)+k_{3})+s(n+1))
In above formula, x (n) and s (n) represents the nth sampled value of output signal and input signal respectively, and h is material calculation. The index being used for weighing stochastic resonance system performance has a variety of, and that commonly used in recent years has snr gain, output signaltonoise ratio, this Two indices is commonly used to weigh the input weak signal degree that signal energy strengthens after stochastic resonance system, but can not represent Measured signal and the degree of correlation of signal output waveform, so the present invention selects the cross correlation of weak signal to be measured and output signal Number, as performance indications, has important references to be worth for recovering measured signal.
Crosscorrelation function represents two stochastic signals x (t) and y (t) matching degree on different relative positions, such as formula (3):
R_{xy}(τ)=＜ x (t) y (t+ τ) ＞ (3)
Crosscorrelation coefficient is the normalized value of crosscorrelation function, i.e.
Wherein, 0≤ ρ_{xy}(τ) ≤1, and  ρ_{xy}(τ)  the biggest expression degree of correlation is the best.For ensure experimental result can By property, the present invention take 50 times experiment assembly average p as final measurement index, as shown in (5) formula:
If what i & lt experiment obtained is  ρ_{xy}(τ)_{i}, wherein n is experiment number.
The present invention realizes mainly comprising the following steps of Detection of Weak Signals to be measured and recovery:
(1) mixed noisy low signaltonoise ratio measured signal processes through firstorder linear system selfadaption；
(2) the broad sense Stochastic Resonance Phenomenon of structural parameters a is discussed, and structural parameters a, noise intensity D is to crosscorrelation coefficient p Action rule；
(3) for firstorder linear SR system, signal restoring system is proposed；
(4) the low frequency smallsignal to be measured of different signal to noise ratios is detected and restores, its rule is discussed；
(5) smallsignal to be measured of the high multifrequency of different signal to noise ratios is carried out double sampling process, then with going back original system It is restored.
Accompanying drawing explanation
The selfadapting simulation result figure of Fig. 1 (a) to (d) firstorder linear of the present invention system；
Fig. 2 crosscorrelation coefficient of the present invention P is with the change curve of D；
Fig. 3 crosscorrelation coefficient of the present invention P is with the change curve of a；
Under Fig. 4 (a), (b) difference D of the present invention value, P is with the change curve of a and curve magnification figure thereof；
Under the different input signaltonoise ratio of Fig. 5 (a) to (c), low frequency weak signal restores situation；
Under the different input signaltonoise ratio of Fig. 6 (a) to (c), many high frequencies weak signal restores situation；
Detailed description of the invention
Below in conjunction with accompanying drawing and instantiation, the enforcement to the present invention is further described.
Step one: mixed noisy low signaltonoise ratio measured signal processes through firstorder linear system selfadaption；
The signals and associated noises choosing different signal to noise ratio drives firstorder linear system, uses algorithm above, selects the most mutually Pass coefficient p, as system performance index, studies its Stochastic Resonance Phenomenon and the Changing Pattern with each parameter thereof.Experiment keeps treat Survey amplitude A=0.1v of weak positive string signal, frequency f=0.01Hz, sample frequency f_{s}=5Hz, takes points N=4000.Take D ∈ [0.1,4], and α ∈ (0,2], D is with 0.1 as initial value, and steplength is 0.1, and α is with 0.02 as initial value, and steplength is 0.02 to change simultaneously, calculates Corresponding p value, simulation result is as shown in Figure 1.Fig. 1 (a) be firstorder linear system under white noise environment, its Stochastic Resonance Phenomenon The diagram of block that output performance index p changes with a and D.What in figure, p value was maximum is a bit (0.1,13.6) place, i.e. D= At 0.1 and a=13.6, average cross correlation coefficient p=0.9015, now the input signaltonoise ratio of signal is16.4599dB, and this contains Shown in the input signal timedomain diagram such as Fig. 1 (b) made an uproar, it is seen that waveform is disorderly and unsystematic, and useful information is all covered.Fig. 1 (c) is The power spectrum of this signal, now the frequency of signal can not be identified equally；Fig. 1 (d) is that this noisy weak positive string signal is inputted one Output spectrum after the linear system of rank, has an obvious spike, it was demonstrated that now input as we can see from the figure at f=0.01Hz The frequency of weak signal is acquired, creates Stochastic Resonance Phenomenon.
Step 2: the broad sense Stochastic Resonance Phenomenon of structural parameters a is discussed, and structural parameters a, noise intensity D is to cross correlation The action rule of number p；
Structural parameters a=0.2 is constant, average cross correlation coefficient p with noise intensity coefficient D change curve as shown in Figure 2； Fixing strength factor D=0.1, obtain average cross correlation coefficient p with structural parameters a change curve as shown in Figure 3.
Average cross correlation coefficient p is with noise intensity coefficient D monotone decreasing as can be seen from Figure 2, it is known that firstorder linear system Traditional Stochastic Resonance Phenomenon can not be produced.D ∈ (0,0.6] time, p value is maintained at a relatively high scope, this Time system measured signal input signaltonoise ratio between25dB～0dB；D ∈ (0.6,1] time, p value is relatively low, now system Input signaltonoise ratio is between37dB～25dB, and this shows that the input signaltonoise ratio of measured signal is the lowest, and output signal is to input letter Number waveform departure degree is the most remote, is more difficult to recover.
As seen from Figure 3 system structure parameter a ∈ (0,6] time, along with the increase of a, average cross correlation coefficient p presents and first increases After the nonmonotonic variation tendency that subtracts, i.e. firstorder linear system creates broad sense Stochastic Resonance Phenomenon, and has maximum at a=0.11 Value.A ∈ (6,10] time, curve p held stationary state.
Step 3: propose signal restoring system for firstorder linear SR system；
Taking noise intensity coefficient D=0.1, D=0.3, D=0.6 respectively, in experiment, weak signal parameter keeps constant, different Under noise intensity coefficient D, average cross correlation coefficient p is shown with change curve such as Fig. 4 (a) of structural parameters a, its partial enlarged drawing As shown in Fig. 4 (b).By this two width figure understand when D is definite value, p first increases along with a and subtracts afterwards, when a increases to certain value, p not with A continues to increase and change, and keeps stable.D is the biggest, and corresponding maximum p value is the least, and curve maximum presents and moves to left from top to bottom Trend, along with the increase of D, system produces the interval of accidental resonance and occurs the most early.
Smallsignal to be measured is after accidental resonance effect, and signal energy is strengthened, it is impossible to obtain measured signal amplitude. Firstorder linear system also improves arithmetic accuracy producing while broad sense Stochastic Resonance Phenomenon, this just the present invention study single order Linear system Stochastic Resonance Phenomenon and the reason restoring weak signal, the present invention proposes the inverting of a kind of firstorder linear system System carries out restoration disposal to system output signal.
If it is very big, in this uptodate style (1) that weak positive string signal to be measured meets the condition of small frequency (f < < 1), i.e. cycleCan Ignoring is 0, if weak sinusoidal signal frequency to be measured is very big, when being unsatisfactory for adiabatic approximation theorem, then uses traditional double sampling, chi Degree conversion or the method such as shift frequency are translated into small frequency and process, thus formula (1) can be consideredax+s (t)+D ξ (t)= 0, i.e.
S (t)=ax (t)D ξ (t) (6)
In formula (6), x (t) is the output signal of firstorder linear SR system.When noise intensity is sufficiently small, to be measured for restoring Input signal s (t), carries out linear restoring to x (t), and the Inversion System proposing firstorder linear system is as follows:
S (t)=ax (t) (7)
Step 4: the low frequency smallsignal to be measured of different signal to noise ratios is detected and restores, its rule is discussed；
Take low frequency (f=0.01Hz) weak signal to be measured of different input signaltonoise ratio respectively, be now followed successively by25.12dB , 18.13dB and8.56dB, is input to firstorder linear system by corresponding suspect signal, obtains output signal, calculates cross correlation Number p value, then output signal is sent into firstorder linear Inversion System, obtaining release signal, emulation experiment design sketch is as shown in Figure 5.
As seen from the figure, firstorder linear system output signal is the biggest with the correlation coefficient of low frequency weak signal to be measured, recovery effect The best, owing to the part energy that Stochastic Resonance Phenomenon is noise is transferred to weak signal, so the output signal width of accidental resonance Value can increase, and from figure, weak signal to be measured (dotted line) understands with the contrast of release signal (solid line) oscillogram, and output signal is through anti The amplitude of the release signal obtained after drilling system is almost equal, there is little burr pulse, and weak signal to be measured is restored, for Its engineer applied provides solid foundation.
Step 5: the smallsignal to be measured of the high multifrequency of different signal to noise ratios is carried out double sampling process, then with reduction It is restored by system.
For big frequency signal, the present invention uses traditional double sampling method to be input to one after being transferred into small frequency Rank linear system.Signal selecting frequency f_{1}=100Hz, f_{2}=200Hz, f_{3}=300Hz, f_{4}=400Hz and f_{5}=500Hz, amplitude A_{1}=A_{2}=A_{3}=A_{4}=A_{5}The random combine of=0.1V, is mixed into many high frequencies weak signal, sample frequency f_{s}=50000Hz, takes two Secondary sample frequency f_{sr}=5Hz carries out double sampling, sampling number N=4000 to signal, and the signal after double sampling is inputted one Rank linear system obtains output signal, calculates p value, then outputs it feeding Inversion System, obtains release signal, and emulation experiment is imitated Fruit figure is as shown in Figure 6.
Fig. 6 gives three groups of highfrequency signals, (1) f_{3}=300Hz singlefrequency, SNRi=21.25dB；(2)f_{2}=200Hz and f_{4} =400Hz double frequency mixes, SNRi=16.13dB；(3)f_{1}=100Hz, f_{3}=300Hz and f_{5}=500Hz multifrequency mixes, SNRi =8.56dB.It can be seen that firstorder linear system still can produce Stochastic Resonance Phenomenon, and output signal to highfrequency signal The biggest with the correlation coefficient of high frequency to be measured or many high frequencies weak signal, recovery effect is the best, and output signal is after Inversion System The amplitude of the release signal obtained is almost equal, restores as the conclusion that emulation obtains with low frequency weak signal.
The present invention have studied Stochastic Resonance Phenomenon and the Inversion System thereof of firstorder linear system, uses sinusoidal weak signal mould Type, by the broad sense Stochastic Resonance Phenomenon of simulation analysis structural parameters a, invents the inversion method for firstorder linear system, To draw a conclusion: 1) broad sense accidental resonance can be realized by regulation system structure parameter a；2) noise intensity D the biggest correspondence Crosscorrelation coefficient p is the least and gradually tends towards stability；3) crosscorrelation coefficient p subtracts afterwards along with structural parameters a first increases, and increases to one at a During definite value, p does not continues to increase with a and changes, and keeps stable；4), in Inversion System, firstorder linear system output signal is with to be measured The correlation coefficient of low frequency weak signal is the biggest, and recovery effect is the best, and high and low frequency (multifrequency) weak signal recovery rule is the same.Above Conclusion provides sound assurance for preferably research broad sense stochastic resonance system, for the detection of weak signal in engineer applied and multiple Former provide new method.
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CN101532920A (en) *  20090422  20090916  北京工业大学  Chaosbased method for detecting weak signals of low speed and heavyduty device 
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Application publication date: 20161207 