CN106197523A - Testing of Feeble Signals based on first-order linear system and recovery - Google Patents

Testing of Feeble Signals based on first-order linear system and recovery Download PDF

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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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signal
frequency
system
linear system
order linear
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CN201610511284.XA
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张刚
宋�莹
王俊霞
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重庆邮电大学
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D21/00Measuring or testing not otherwise provided for

Abstract

The present invention is claimed a kind of Testing of Feeble Signals based on first-order linear system and restored method, belongs to signal processing technology field.Utilize Fourth order Runge-Kutta, by with cross-correlation coefficient as index, probe into the broad sense Stochastic Resonance Phenomenon of first-order linear system structure parameter a, then proposed the low-and high-frequency weak signal restored method of linear system, finally realized the weak periodic signal of low-and high-frequency is restored.Research finds, the cross-correlation coefficient p of the biggest correspondence of D is the least and gradually tends towards stability, and p subtracts afterwards along with structural parameters a first increases, and when a increases to certain value, p does not continues to increase with a and changes, and keeps stable;In Inversion System, first-order linear system output signal is the biggest with the correlation coefficient of low frequency weak signal to be measured, and recovery effect is the best, and high and low frequency (multifrequency) weak signal recovery rule is the same.This method provides sound assurance for preferably research broad sense stochastic resonance system, to the detection of weak signal in engineer applied and restore significant.

Description

Testing of Feeble Signals based on first-order linear system and recovery

Technical field

The present invention relates to Detection of Weak Signals field, be specially with cross-correlation coefficient as index, study first-order linear system The Stochastic Resonance Phenomenon of system, and detect and restore the low-and high-frequency 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..Small-signal 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 small-signal, 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 non-monotonic 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 small-signal, for grinding that the amplitude of weak signal carries out detecting Study carefully less.In consideration of it, the present invention proposes first-order linear accidental resonance recovery system, first-order linear system model is simple, and structure is joined Number is single, it is possible to increase arithmetic accuracy.To a certain extent, first-order 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 first-order 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 Runge-Kutta, has probed into first-order linear The broad sense Stochastic Resonance Phenomenon of system structure parameter a, then proposes the low-and high-frequency weak signal restored method of linear system, finally Realize the weak periodic signal of low-and high-frequency is restored.

In dynamic system, first-order linear system model is as follows:

d x d t = - a x + A c o s ( 2 π f t ) + n ( t ) - - - ( 1 )

In formula (1), a is system structure parameter, and Acos (2 π ft) is small-signal to be measured, n (t) be average be 0, auto-correlation Function is the white Gaussian noise of<n (t) n (0)>=2D σ (t), and its noise intensity is D.

The Fourth order Runge-Kutta that the present invention carries out numerical simulation employing is as follows:

k1=h (-ax (n)+s (n))

k 2 = h ( - a ( x ( n ) + k 1 2 ) + s ( n ) )

k 3 = h ( - a ( x ( n ) + k 2 2 ) + s ( n + 1 ) )

k4=h (-a (x (n)+k3)+s(n+1))

x ( n + 1 ) = x ( n ) + 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) - - - ( 2 )

In above formula, x (n) and s (n) represents the n-th 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 signal-to-noise 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.

Cross-correlation function represents two stochastic signals x (t) and y (t) matching degree on different relative positions, such as formula (3):

Rxy(τ)=< x (t) y (t+ τ) > (3)

Cross-correlation coefficient is the normalized value of cross-correlation function, i.e.

&rho; x y ( &tau; ) = R x y ( &tau; ) &rho; x x ( 0 ) &rho; y y ( 0 ) - - - ( 4 )

Wherein, 0≤| ρxy(τ) |≤1, and | ρxy(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:

p = 1 n &Sigma; i = 1 n | &rho; x y ( &tau; ) | i - - - ( 5 )

If what i & lt experiment obtained is | ρxy(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 signal-to-noise ratio measured signal processes through first-order linear system self-adaption;

(2) the broad sense Stochastic Resonance Phenomenon of structural parameters a is discussed, and structural parameters a, noise intensity D is to cross-correlation coefficient p Action rule;

(3) for first-order linear SR system, signal restoring system is proposed;

(4) the low frequency small-signal to be measured of different signal to noise ratios is detected and restores, its rule is discussed;

(5) small-signal 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 self-adapting simulation result figure of Fig. 1 (a) to (d) first-order linear of the present invention system;

Fig. 2 cross-correlation coefficient of the present invention P is with the change curve of D;

Fig. 3 cross-correlation 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 signal-to-noise ratio of Fig. 5 (a) to (c), low frequency weak signal restores situation;

Under the different input signal-to-noise 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 signal-to-noise ratio measured signal processes through first-order linear system self-adaption;

The signals and associated noises choosing different signal to noise ratio drives first-order 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 fs=5Hz, takes points N=4000.Take D ∈ [0.1,4], and α ∈ (0,2], D is with 0.1 as initial value, and step-length is 0.1, and α is with 0.02 as initial value, and step-length is 0.02 to change simultaneously, calculates Corresponding p value, simulation result is as shown in Figure 1.Fig. 1 (a) be first-order 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 signal-to-noise ratio of signal is-16.4599dB, and this contains Shown in the input signal time-domain 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 first-order 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 signal-to-noise ratio between-25dB~0dB;D ∈ (0.6,1] time, p value is relatively low, now system Input signal-to-noise ratio is between-37dB~-25dB, and this shows that the input signal-to-noise 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 non-monotonic variation tendency that subtracts, i.e. first-order 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 first-order 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.

Small-signal to be measured is after accidental resonance effect, and signal energy is strengthened, it is impossible to obtain measured signal amplitude. First-order 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 first-order linear system System carries out restoration disposal to system output signal.

If it is very big, in this up-to-date 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 considered-ax+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 first-order 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 first-order linear system is as follows:

S (t)=ax (t) (7)

Step 4: the low frequency small-signal 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 signal-to-noise ratio respectively, be now followed successively by-25.12dB ,- 18.13dB and-8.56dB, is input to first-order linear system by corresponding suspect signal, obtains output signal, calculates cross correlation Number p value, then output signal is sent into first-order linear Inversion System, obtaining release signal, emulation experiment design sketch is as shown in Figure 5.

As seen from the figure, first-order 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 small-signal 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 f1=100Hz, f2=200Hz, f3=300Hz, f4=400Hz and f5=500Hz, amplitude A1=A2=A3=A4=A5The random combine of=0.1V, is mixed into many high frequencies weak signal, sample frequency fs=50000Hz, takes two Secondary sample frequency fsr=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 high-frequency signals, (1) f3=300Hz single-frequency, SNRi=-21.25dB;(2)f2=200Hz and f4 =400Hz double frequency mixes, SNRi=-16.13dB;(3)f1=100Hz, f3=300Hz and f5=500Hz multifrequency mixes, SNRi =-8.56dB.It can be seen that first-order linear system still can produce Stochastic Resonance Phenomenon, and output signal to high-frequency 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 first-order 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 first-order 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 Cross-correlation coefficient p is the least and gradually tends towards stability;3) cross-correlation 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, first-order 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.

Claims (6)

1. Testing of Feeble Signals based on first-order linear system and a restored method, its step is, first with quadravalence dragon lattice Ku Tafa, with cross-correlation coefficient as index, has probed into the broad sense Stochastic Resonance Phenomenon of first-order linear system structure parameter a, then Propose the low-and high-frequency weak signal restored method of linear system, finally realize the weak periodic signal of low-and high-frequency is restored.
Method of estimation the most according to claim 1, it is characterised in that set up first-order linear system model Given system structure parameter a and noise intensity D, small-signal Acos to be measured (2 π ft) that by amplitude be A and frequency is f inputs one Rank linear system, utilizes fourth order Runge-Kutta algorithm to carry out numerical analysis.
Method of estimation the most according to claim 1, it is characterised in that the signals and associated noises choosing different signal to noise ratio drives single order Linear system, use fourth order Runge-Kutta algorithm, select average cross correlation coefficient p as system performance index, take D ∈ [0.1, 4], α ∈ (0,2], D is with 0.1 as initial value, and step-length is 0.1, and α is with 0.02 as initial value, and step-length is 0.02 to change simultaneously, study its from Adapt to Stochastic Resonance Phenomenon and the cross-correlation coefficient p rule with each Parameters variation.
Method of estimation the most according to claim 1, it is characterised in that if weak positive string signal to be measured meets small frequency (f < < 1) Condition, i.e. the cycle is very big, at this momentNegligible is 0, if weak sinusoidal signal frequency to be measured is very big, is unsatisfactory for adiabatic approximation fixed During reason, then use the methods such as traditional double sampling, change of scale or shift frequency to be translated into small frequency and process, so Formula (1) can be considered-ax+s (t)+D ξ (t)=0, i.e. s (t)=ax (t)-D ξ (t), and in formula, x (t) is first-order linear SR system Output signal.When noise intensity is sufficiently small, for restoring input signal s (t) to be measured, x (t) is carried out linear restoring, propose one Inversion System s (t) of rank linear system=ax (t).
Method of estimation the most according to claim 1, it is characterised in that take the low frequency (f=of different input signal-to-noise ratio respectively 0.01Hz) weak signal to be measured, is now followed successively by-25.12dB ,-18.13dB and-8.56dB, corresponding suspect signal is input to First-order linear system, obtains output signal, calculates cross-correlation coefficient p value, then output signal is sent into first-order linear Inversion System, Obtain release signal.
Method of estimation the most according to claim 1, it is characterised in that for big frequency signal, the present invention uses traditional Double sampling method is input to first-order linear system after being transferred into small frequency.Signal selecting frequency f1=100Hz, f2= 200Hz, f3=300Hz, f4=400Hz and f5=500Hz, amplitude A1=A2=A3=A4=A5The random combine of=0.8V, mixing Become many high frequencies weak signal, sample frequency fs=50000Hz, takes double sampling frequency fsr=5Hz carries out double sampling to signal, adopts Number of samples N=4000, inputs first-order linear system by the signal after double sampling and obtains output signal, calculate p value, then it is defeated Go out to send into Inversion System, obtain release signal.
CN201610511284.XA 2016-06-30 2016-06-30 Testing of Feeble Signals based on first-order linear system and recovery CN106197523A (en)

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Application publication date: 20161207