CN104281775A - Method for detecting weak signal on basis of parameter compensation multistable random resonance system - Google Patents

Abstract

The invention discloses a method for detecting a weak signal on the basis of a parameter compensation multistable random resonance system. The method comprises the following steps of (1) performing parameter compensation on a noise-containing weak signal, i.e. adding an amplifying link in a multistable Langevin equation, to offset the trend that an amplitude value is smaller after the signal passes through a multistable system, so that the method can be used for detecting a high-frequency weak signal; (2) inputting the compensated signal into the multistable system, wherein the multistable system is higher than a bistable system in detectability and can be used for detecting the weak signal with lower signal to noise ratio; (3) performing envelope demodulation analysis on the output signal of the multistable system, and analyzing an envelope diagram to extract the characteristics of the weak signal, so that detection on the weak signal is finished. By the method, the weak signal can be well extracted under the condition of extremely low signal to noise ratio, a low-frequency weak signal and a medium-high frequency weak signal can also be detected under the condition that the signal frequency is not known, and the signal processing ability is greatly improved.

Description

A kind of method for detecting weak signals based on the multistable stochastic resonance system of parametric compensation

Technical field

The invention belongs to signal processing technology field, particularly relate to the extracting method of low frequency and medium-high frequency feeble signal under a kind of low signal-to-noise ratio.

Background technology

Namely feeble signal is submerged in the low-yield signal under strong noise background, all need in a lot of field such as mechanical fault diagnosis, communication, seismic prospecting, oil prospect pit, biomedicine to extract useful signal by detecting feeble signal, therefore the detection of feeble signal is the focus that people study always.

Existing Technique of Weak Signal Detection obtains useful signal mainly through elimination, restraint speckle, while removal noise, also inevitably useful signal can be weakened, and the Detection of Weak Signals that signal to noise ratio (S/N ratio) is higher can only be used for, feeble signal is extracted under Arctic ice area, DeGrain, can not meet actual demand.

Research finds that application stochastic resonance method detects feeble signal and achieves good effect.Accidental resonance is that a kind of noise that utilizes is to strengthen the theory of feeble signal, when noise, nonlinear system, signal three reach optimum matching relation, noise energy can be transferred in signal energy, signal energy strengthens, make output signal-to-noise ratio be greater than input signal-to-noise ratio, the method makes signal obtain enhancing by utilizing noise instead of stress release treatment.But accidental resonance has certain limitation, namely stochastic resonance method strengthens DeGrain to large frequency feeble signal.Although can first utilize double sampling to be small frequency signal large frequency inverted, when not knowing feeble signal frequency, be difficult to determine scale factor.

In addition, parametric compensation principle is utilized can to improve the treatment effect of feeble signal.But when the feeble signal of actual treatment Arctic ice area, the effect of bi-stable stochastic resonance theory system does not often reach our re-set target, is easy to cause diagnostic result out of true, and even make a mistake diagnosis.

In sum, the parametric compensation bi-stable stochastic resonance theory system that the adopts method of extracting feeble signal cannot reach people's requirement present stage.

Summary of the invention

The object of the invention is the deficiency overcoming art methods, provide a kind of and improve the method for detecting weak signals based on the multistable stochastic resonance system of parametric compensation that Weak Signal Processing effect, transfer capability are strong, can detect more low signal-to-noise ratio feeble signal.

For achieving the above object, detection method of the present invention comprises the following steps:

(1) signals and associated noises is introduced a multistable stochastic resonance system; Described multistable stochastic resonance system is described by Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t);

In formula, U (x) is multistable stochastic resonance system potential-energy function, a, b, c are parameter, and parameter a, c and intrinsic parameter b have nothing to do; S (t) is feeble signal; η (t) is average is 0, variance is 1, intensity is the white noise of D;

(2) when intrinsic parameter b determines, then determine systematic parameter in multistable accidental resonance, guarantee that system is multistable stochastic resonance system; After b determines, when a and c gets different value, corresponding monostable stochastic resonance system, bi-stable stochastic resonance theory system, multistable stochastic resonance system respectively.By analysis after checking, represent that this system is multistable stochastic resonance system as a=20+5c (0<c<1) or as a=27.5-2.5c (1<c<3);

(3) in multistable stochastic resonance system, adopt parametric compensation method to improve the energy of feeble signal in signals and associated noises, namely in Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t), an amplifying element is added, after adding amplifying element, Langevin equation becomes

dx/dt＝K[-dU(x)/dx+s(t)+η(t)]

Wherein, K is enlargement factor, i.e. compensating factor; K=max{2 π f in theory _i, but in actual emulation is analyzed, the value of K is slightly larger than max{2 π f _i; f _ifor the frequency of input signal;

(4) the intrinsic parameter b=5 of the multistable stochastic resonance system of initialization and parametric compensation factor K=1, produce the frequency f of multistable stochastic resonance system _s;

(5) signals and associated noises being carried out parameter factors is K>=max{2 π f _iparametric compensation, obtain signal P (t)=K × [s (t)+η (t)];

(6) the intrinsic parameter a of multistable stochastic resonance system, b, c are carried out parametric compensation, become a ' respectively, b ', c '; Meet a '=a/K, $b^{\&prime;}=\frac{1+\mathrm{Kc}}{K+\mathrm{Kc}}b,$ c′＝K×c；

(7) signal P (t) solves langevin equation by fourth order Runge-Kutta numerical computation method, and the solution of trying to achieve is the output signal x (t) of multistable stochastic resonance system;

(8) will output signal x (t) and do envelope demodulation, and obtain Z (f), f is frequency values, and Z (f) is the envelope spectrum amplitude at frequency f place; Detected by Z (f) and isolate feeble signal.Concrete steps are:

First Hilbert conversion is done to signal x (t),

$H\left\{x\left(t\right)\right\}=\hat{x}\left(t\right)=x\left(t\right)*\frac{1}{\mathrm{\&pi;t}}=\frac{1}{\mathrm{\&pi;}}\&Integral;\frac{x\left(\mathrm{\&tau;}\right)}{t-\mathrm{\&tau;}}\mathrm{d\&tau;}$

The analytic signal of signal x (t) is,

$z\left(t\right)=x\left(t\right)+j\hat{x}\left(t\right)=A\left(t\right)e^{\mathrm{j\&phi;}\left(t\right)}$

Wherein amplitude A (t) is,

$A\left(t\right)=\sqrt{x^2\left(t\right)+{\hat{x}}^2\left(t\right)}$

A (t) is just the envelope of x (t), carries out FFT, obtain Z (f) to envelope signal.

Compared with prior art, tool of the present invention has the following advantages:

1, parametric compensation method is adopted effectively can to realize the detection of medium, high frequency feeble signal;

2, utilize multistable system to strengthen feeble signal, stronger than single, double steady system capacity transfer capability, the feeble signal of more low signal-to-noise ratio can be detected, enhance the spectrum of output frequency spectrum at frequency input signal place, finally detect feeble signal exactly;

3, detection method is applied widely, and can be used for, in the practical problemss such as the fault detect in mechanical engineering, Non-Destructive Testing, has good application prospect.

Accompanying drawing explanation

Fig. 1 is the structured flowchart of the inventive method.

Fig. 2 is the Detection of Weak Signals process flow diagram of the inventive method.

Fig. 3 is the time domain beamformer of simulate signal.

Fig. 4 is that simulate signal is by the time-frequency figure after preset parameter bistable SR system.

Fig. 5 is that simulate signal is by the time-frequency figure after the multistable SR system of preset parameter.

Fig. 6 is that simulate signal is by the time-frequency figure after parametric compensation bistable SR system.

Fig. 7 is that simulate signal is by the time-frequency figure after the multistable SR system of parametric compensation.

Fig. 8 is the time-frequency figure of embodiment 1 centre bearer fault-signal.

Fig. 9 is that embodiment 1 centre bearer fault-signal is by the time-frequency figure after parametric compensation bistable SR system.

Figure 10 is that embodiment 1 centre bearer fault-signal is by the time-frequency figure after the multistable SR system of parametric compensation.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described:

As illustrated in fig. 1 and 2, detection method of the present invention comprises the following steps:

(1) signals and associated noises is introduced a multistable stochastic resonance system; Described multistable stochastic resonance system is described by Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t);

In formula, U (x) is multistable stochastic resonance system potential-energy function, a, b, c are parameter, and parameter a, c and intrinsic parameter b have nothing to do; S (t) is feeble signal; η (t) is average is 0, variance is 1, intensity is the white noise of D;

(2) when intrinsic parameter b determines, then determine systematic parameter a and c in multistable accidental resonance, guarantee that system is multistable stochastic resonance system; After b determines, when a, c get different value, corresponding monostable stochastic resonance system, bi-stable stochastic resonance theory system, multistable stochastic resonance system respectively.By analysis after checking, represent that this system is multistable stochastic resonance system as a=20+5c (0<c<1) or as a=27.5-2.5c (1<c<3);

(3) b is the intrinsic parameter of multistable accidental resonance, is generally taken as b=5, and in order to detect high frequency weak signal, adopt compensating factor to be the parametric compensation of K, the value of K is described below:

If input signal is $s\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_i\sin \left(2\mathrm{\&pi;}{f}_{i}t\right),$ Then to formula

$\frac{\mathrm{dx}}{\mathrm{dt}}=-\frac{x^5}{a}+\frac{(1+c)x^3}{b}-\mathrm{cx}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_i\sin \left(2\mathrm{\&pi;}{f}_{i}t\right)+\mathrm{\&eta;}\left(t\right)$

The while of both sides, integration must output signal and be:

$\begin{array}{c}x\left(t\right)=\&Integral;[-\frac{x^5}{a}+\frac{(1+c)x^3}{b}-\mathrm{cx}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_i\sin \left(2\mathrm{\&pi;}{f}_{i}t\right)+\mathrm{\&eta;}\left(t\right)]\mathrm{dt}\\ =\&Integral;[-\frac{x^5}{a}+\frac{(1+c)x^3}{b}-\mathrm{cx}]\mathrm{dt}+\&Integral;\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_i\sin \left(2\mathrm{\&pi;}{f}_{i}t\right)\right]\mathrm{dt}+\&Integral;\left[\mathrm{\&eta;}\left(t\right)\right]\mathrm{dt}\\ =\&Integral;[-\frac{x^5}{a}+\frac{(1+c)x^3}{b}-\mathrm{cx}]\mathrm{dt}-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{A_i}{2\mathrm{\&pi;}{f}_i}\cos \left(2\mathrm{\&pi;}{f}_{i}t\right)+\&Integral;\left[\mathrm{\&eta;}\left(t\right)\right]\mathrm{dt}\end{array}$

Can be seen by Section 2 on the right of equation, input signal s (t) is after multistable accidental resonance, and its amplitude is reduced to 1/2 original π f _i, and along with the frequency f of input signal _iincrease, amplitude is less, even if high-frequency signal is by the process of multistable stochastic resonance system like this, also high-frequency signal cannot be detected in the output signal, and namely parametric compensation method adds an amplifying element in Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t), on the right of equation, be namely multiplied by a constant diminish trend to offset this amplitude.After adding amplifying element, Langevin equation becomes

dx/dt＝K[-dU(x)/dx+s(t)+η(t)]

Wherein K is enlargement factor, i.e. compensating factor, and K equals max{2 π f in theory _i, but in actual emulation is analyzed, in order to obtain obvious effect, the value of K is slightly larger than max{2 π f _i;

(4) the intrinsic parameter b=5 of the multistable stochastic resonance system of initialization and parametric compensation factor K=1, produce the frequency f of multistable stochastic resonance system _s;

(5) signals and associated noises being carried out parameter factors is K>=max{2 π f _iparametric compensation, obtain signal P (t)=K × [s (t)+η (t)];

(6) the intrinsic parameter a of multistable stochastic resonance system, b, c are carried out parametric compensation, become a ' respectively, b ', c '; Meet a '=a/K, $b^{\&prime;}=\frac{1+\mathrm{Kc}}{K+\mathrm{Kc}}b,$ c′＝K×c；

(7) signal P (t) solves langevin equation by fourth order Runge-Kutta numerical computation method, and the solution of trying to achieve is the output signal x (t) of multistable stochastic resonance system;

(8) x (t) will be outputed signal and do envelope demodulation, obtain Z (f); F is frequency values; Z (f) is the envelope spectrum amplitude at frequency f place; Detected by Z (f) and isolate feeble signal.Concrete steps are:

First Hilbert conversion is done to signal x (t),

$H\left\{x\left(t\right)\right\}=\hat{x}\left(t\right)=x\left(t\right)*\frac{1}{\mathrm{\&pi;t}}=\frac{1}{\mathrm{\&pi;}}\&Integral;\frac{x\left(\mathrm{\&tau;}\right)}{t-\mathrm{\&tau;}}\mathrm{d\&tau;}$

The analytic signal of signal x (t) is,

$z\left(t\right)=x\left(t\right)+j\hat{x}\left(t\right)=A\left(t\right)e^{\mathrm{j\&phi;}\left(t\right)}$

Wherein amplitude A (t) is,

$A\left(t\right)=\sqrt{x^2\left(t\right)+{\hat{x}}^2\left(t\right)}$

A (t) is just the envelope of x (t), carries out FFT, obtain Z (f) to envelope signal.

Emulation testing is carried out to the inventive method below.The parameter of emulation is:

1) bi-stable stochastic resonance theory system: intrinsic parameter a=1, b=1, sample frequency f _s=3000, input sinusoidal simulate signal, s (t)=0.1sin (2 π × 10 × t)+0.3sin (2 π × 80 × t)+0.2sin (2 π × 600 × t)+η (t);

2) multistable stochastic resonance system: intrinsic parameter a=22.5, b=5, c=2, sample frequency f _s=8000, input sinusoidal simulate signal, s (t)=0.1sin (2 π × 10 × t)+0.3sin (2 π × 80 × t)+0.2sin (2 π × 600 × t)+η (t).

Fig. 3 is the time domain beamformer of simulate signal s (t), now can not find out the cycle of signal from figure, can not extract the features such as the frequency of signal, phase place.

Fig. 4 is that simulate signal s (t) is by the time-frequency figure after preset parameter bistable SR system.Not there is Stochastic Resonance Phenomenon by bistable system in large frequency signal as we can see from the figure, and the frequecy characteristic of signal can not extract, and cannot detect feeble signal.

Fig. 5 is that simulate signal s (t) is by the time-frequency figure after the multistable SR system of preset parameter.From figure, can see that large frequency signal Stochastic Resonance Phenomenon does not occur by multistable system equally, this illustrates that stochastic resonance system can not be directly used in and detects high frequency weak signal.

Fig. 6 is that simulate signal s (t) is by the time-frequency figure after parametric compensation bistable SR system, compensating factor K=4000, feeble signal can be observed after bistable system, there occurs Stochastic Resonance Phenomenon, in figure, the general shape of signal can be differentiated, each frequency range there is the noise of can not ignore exist, substantially the frequency of signal can be found out, but frequency place amplitude is less, signal amplitude increases to some extent on the whole, this illustrates that feeble signal obtains certain noise energy, also illustrate that parametric compensation bi-stable stochastic resonance theory system has the function strengthening feeble signal.

Fig. 7 is that simulate signal s (t) is by the time-frequency figure after the multistable SR system of parametric compensation, first its signal amplitude is made to become 400,1200,800 respectively through parametric compensation, multistable system parameter becomes 0.005625,3.33375,8000 respectively, obtain signal P (t), then by outputing signal x (t) after multistable stochastic resonance system, x (t) being carried out Envelope Demodulation Analysis and obtains envelope spectrogram.There is obvious spike at feeble signal frequency place as can see from Figure 7, and spike place amplitude is greatly improved, except the spectrum amplitude at other frequency place at signal frequency place is very little, can ignore, this illustrates that noise obtains good suppression, and feeble signal obtains enough energy.

Can draw after Fig. 6 and Fig. 7 is compared, Amplitude Ration Fig. 6 frequency place of Fig. 7 medium frequency place amplitude is much bigger, and little than in Fig. 6 of other frequency place amplitudes, illustrate that multistable stochastic resonance system is stronger to the transfer capability of feeble signal energy than bi-stable stochastic resonance theory system noise energy, feeble signal can well be extracted in Arctic ice area situation, have better detectability.

Emulation experiment shows: by the multistable stochastic resonance method of parametric compensation, the frequecy characteristic of feeble signal can well be extracted, strengthen the energy of feeble signal, inhibit noise again simultaneously, compare bi-stable stochastic resonance theory, multistable accidental resonance has better Detection results when detecting feeble signal.

Embodiment 1:

In order to verify feasibility and the superiority of this inventive method further, a bearing fault signal data is adopted to analyze.

Described bearing size information is as shown in table 1.

Inner ring diameter/mm	Race diameter/mm	Pitch diameter/mm	Ball diameter/mm	Ball number	Contact angle/(°)
						25.001	51.999	39.040	7.940	10.000	0

Table 1

The fault characteristic frequency of each parts of described bearing is as shown in table 2, and sample frequency is 12K.

Bearing element	Inner ring	Outer ring	Retainer	Rolling body
					Failure-frequency/Hz	157.961	104.569	11.618	137.493

Table 2

For inner ring fault, obtaining inner ring fault by theory calculate is 157.961Hz.

Fig. 8 is the time-frequency figure of bearing fault signal.As can be seen from Figure 8, exist in time-domain diagram and periodically impact, obvious spike is not had in spectrogram, bearing fault characteristics frequency is submerged in noise, in spectrogram, energy distribution is uneven, and more greatly, low-frequency range energy is less for high band energy, and characteristic frequency is generally in low-frequency range, fault characteristic frequency is not easily detected.

Fig. 9 is that bearing fault signal is by the time-frequency figure after parametric compensation bistable SR system.As can be seen from Figure 9 some radio-frequency components are weakened, and useful signal is strengthened, in frequency domain figure, spike respective frequencies is 157.5Hz, substantially matches with theory calculate 157.961Hz, amplitude is herein increased to 1.586 by 0.04945, is greatly improved.

Figure 10 is that bearing fault signal is by the time-frequency figure after the multistable SR system of parametric compensation.Signal of rolling bearing fault characteristic frequency is carried out parametric compensation and through multistable stochastic resonance system, its output signal time-frequency figure as shown in Figure 10, in frequency domain figure, spike respective frequencies is 157.5Hz, and match with the 157.961Hz in theory calculate, amplitude is increased to 6.094 by 0.04945.

Draw after being contrasted by Fig. 9 and Figure 10, multistable accidental resonance and bi-stable stochastic resonance theory can detect feeble signal, but multistable stochastic resonance system is large failure-frequency place Amplitude Ration the latter, illustrates noise energy transfer ability stronger.

After above-mentioned bearing fault signal data is analyzed, demonstrate the feasibility of the inventive method further and detecting the superiority in feeble signal.

Above-described embodiment is only be described the preferred embodiment of the present invention; not scope of the present invention is limited; under not departing from the present invention and designing the prerequisite of spirit; the various distortion that those of ordinary skill in the art make technical scheme of the present invention and improvement, all should fall in protection domain that claims of the present invention determines.

Claims (4)

1. based on a method for detecting weak signals for the multistable stochastic resonance system of parametric compensation, it is characterized in that, described detection method comprises the following steps:

(1) signals and associated noises is introduced a multistable stochastic resonance system; Described multistable stochastic resonance system is described by Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t);

In formula, U (x) is multistable stochastic resonance system potential-energy function, a, b, c are parameter, and parameter a, c and intrinsic parameter b have nothing to do; S (t) is feeble signal; η (t) is average is 0, variance is 1, intensity is the white noise of D;

(2) when intrinsic parameter b determines, then determine systematic parameter a and c in multistable accidental resonance, guarantee that system is multistable stochastic resonance system;

(3) in multistable stochastic resonance system, adopt parametric compensation method to improve the energy of feeble signal in signals and associated noises, namely in Langevin equation dx/dt=-dU (x)/dx+s (t)+η (t), an amplifying element is added, after adding amplifying element, Langevin equation becomes

dx/dt＝K[-dU(x)/dx+s(t)+η(t)]

Wherein, K is enlargement factor, i.e. compensating factor; K=max{2 π f in theory _i, but in actual emulation is analyzed, the value of K is slightly larger than max{2 π f _i; f _ifor the frequency of input signal;

(4) the intrinsic parameter b=5 of the multistable stochastic resonance system of initialization and parametric compensation factor K=1, produce the frequency f of multistable stochastic resonance system _s;

(5) signals and associated noises being carried out parameter factors is K>=max{2 π f _iparametric compensation, obtain signal P (t)=K × [s (t)+η (t)];

(6) the intrinsic parameter a of multistable stochastic resonance system, b, c are carried out parametric compensation, become a ' respectively, b ', c ';

(7) signal P (t) solves langevin equation by fourth order Runge-Kutta numerical computation method, and the solution of trying to achieve is the output signal x (t) of multistable stochastic resonance system;

(8) x (t) will be outputed signal and do envelope demodulation, obtain Z (f); F is frequency values; Z (f) is the envelope spectrum amplitude at frequency f place; Detected by Z (f) and isolate feeble signal.

2. a kind of method for detecting weak signals based on the multistable stochastic resonance system of parametric compensation according to claim 1, it is characterized in that: in described step (2), after b determines, represent that this system is multistable stochastic resonance system as a=20+5c (0<c<1) or as a=27.5-2.5c (1<c<3).

3. a kind of method for detecting weak signals based on the multistable stochastic resonance system of parametric compensation according to claim 1, is characterized in that: in described step (6), after multistable stochastic resonance system parametric compensation, meets a '=a/K, c '=K × c.

4. a kind of method for detecting weak signals based on the multistable stochastic resonance system of parametric compensation according to claim 1, is characterized in that, described step (8) is specially:

First Hilbert conversion is done to signal x (t),

The analytic signal of signal x (t) is,

Wherein amplitude A (t) is,

A (t) is just the envelope of x (t), carries out FFT, obtain Z (f) to envelope signal.