CN101881628A - Detecting method of weak periodic signal based on chaotic system and wavelet threshold denoising - Google Patents

Abstract

The invention discloses a detecting method of a weak periodic signal based on a chaotic system and wavelet threshold denoising, which comprises the following steps of: firstly carrying out wavelet decomposition on collected information, and determining a decomposition scale according to an actual signal-to-noise condition; denoising a wavelet high-frequency coefficient after the wavelet decomposition, wherein in the process of wavelet threshold denoising, the selection of a threshold is an important problem and directly influences a denoising result, so that the invention firstly provides a method for determining the threshold according to the scale for carrying out coefficient threshold processing to improve the denoising effect; reconstructing a signal after denoising, merging the signal to be detected after wavelet denoising reconstruction as one part of the driving force of the chaotic system into a chaotic detecting system, further inhabiting noise interference by utilizing the characteristics of the chaotic system for strong noise immunity, periodic weak signal sensitivity and the like, and effectively extracting the weak signal. The invention improves the detection threshold and the signal-to-noise ratio purely based on the chaotic detecting system.

Description

Detection method based on the weak periodic signal of chaos system and wavelet threshold denoising

Technical field

The present invention relates to a kind of detection method of the weak periodic signal based on chaos system and wavelet threshold denoising.

Technical background

Along with science and technology development; the demand that feeble signal detects is urgent day by day; detect feeble signal and be the important means of exploring and find the new natural law under developing high-tech, the extreme condition, significant to the development that promotes association areas such as national economy, national defense construction and environmental protection problem.Say so in some sense a kind of technology of special and noise struggle of Detection of Weak Signals, promptly under very noisy to quick, accurate, highly sensitive collection of feeble signal and treatment technology, be a new branch of science of extraction useful signal from noise.

Feeble signal means that not only the amplitude of signal is very little, and mainly refer to the signal that is flooded by noise, faint is relative noise, in order to detect the feeble signal that is covered by noise, people have carried out long term research, analyze reason and rule that noise produces, the characteristics of research measured signal, the statistical property of correlativity and noise is to seek out the method that detects useful signal from noise.The top priority of Detection of Weak Signals technology is to improve signal to noise ratio (S/N ratio), this just needs to adopt electronics, information theory, computing machine and physical method, so that from very noisy, detect useful signal, thereby satisfy the needs of modern scientific research and technological development, the Detection of Weak Signals technology is different from general detection technique, what it was paid attention to is not physical model and sensing principle, corresponding signaling conversion circuit and the instrument implementation method of sensor, but how to suppress noise and improve signal to noise ratio (S/N ratio), therefore we can say that Detection of Weak Signals is a special technology that suppresses noise.Measurement for various feeble signals, the for example low light level, weak magnetic, weak sound, little displacement, little electric capacity, micrometeor, minute-pressure power, little vibration, tepor difference etc., generally all be to be converted into little electric current or low-voltage by corresponding sensor, amplify through amplifier, its amplitude is in the hope of indicating measured size again.But because measured signal is very faint, and the interference noise in the intrinsic noise of the background noise of sensor, amplifying circuit and surveying instrument and the external world is often much bigger than the amplitude of useful signal, amplify the process of measured signal and also amplified noise simultaneously, and must also can add some extra noises, the for example inside intrinsic noise of amplifier and the influence of various external disturbance, therefore only can not come out Detection of Weak Signals by amplification, only under the condition that effectively suppresses noise, increase the amplitude of feeble signal, just can extract useful signal.In order to reach such purpose, must study the theory and technology method of Detection of Weak Signals.

Summary of the invention

The object of the present invention is to provide a kind of detection method of the weak periodic signal based on chaos system and wavelet threshold denoising, be somebody's turn to do detection method based on the weak periodic signal of chaos system and wavelet threshold denoising, earlier the information via wavelet threshold denoising of gathering is handled, the filtering partial noise, again information is introduced chaos detection system, because chaos system has stronger immunologic function to noise, thereby can effectively collect the feeble signal that the cycle changes.

Technical solution of the present invention is as follows:

A kind of detection method of the weak periodic signal based on chaos system and wavelet threshold denoising is characterized in that, may further comprise the steps:

Step 1: detected information is carried out wavelet transform filtering:

1) according to the mallat fast algorithm original signal of sampling is carried out J yardstick wavelet decomposition, obtain approaching approximate signal C _{J, k}With detail signal D _{I, k}, j=1 ... J, the J value is 3,4,5 or 6;

$\left\{\begin{array}{c}{C}_{j,k}=\underset{m}{\mathrm{\Σ}}{C}_{j-1,m}{h}_{m-2k}\\ D_{j,k}=\underset{m}{\mathrm{\Σ}}{D}_{j-1,m}{g}_{m-2k}\end{array}\right.k,m=\mathrm{0,1},...,N-1,$

Adopt sampled value f _kCoefficient of roughness initial value C as wavelet decomposition _{0, k}, C is promptly arranged _{0, k}=f _k, D _{0, k}=C _{0, k}, N is a sampling length;

h _M-2k, g _M-2kBe respectively low pass and Hi-pass filter, it is as follows to embody formula:

$\left\{\begin{array}{c}{h}_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&phi;}}_{j+1,m}>\\ g_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&psi;}}_{j+1,m}>\end{array}\right.,$ φ wherein _{J, k}(t) and ψ _{J, k}(t) be respectively scaling function and wavelet function in the mallat algorithm;

2) approach approximate signal C _JRemain unchanged, to the detail signal D on each different scale _{J, k}Carry out the hard-threshold denoising, the detail signal after obtaining handling

${\hat{D}}_{j,k}=\left\{\begin{array}{c}{D}_{j,k},\left|D_{j,k}\right|\&GreaterEqual;\mathrm{\&delta;}\\ 0,\left|D_{j,k}\right|<\mathrm{\&delta;}\end{array}\right.,$ Wherein δ is a threshold value,

For the D on the J yardstick _J, the δ value is δ _J:

${\mathrm{\&delta;}}_J={\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA0000022852860000016.png"\; state="\{\{state\}\}">J</figure-callout>}}\sqrt{2\log \left(N\right)}/\sqrt{J};$

σ _JBe the variance of signal on the J yardstick of gathering

To detail signal D _j, j=1,2...J-1, setting threshold is:

$\mathrm{\&delta;}=\widehat{\mathrm{\&sigma;}}\sqrt{2\log \left(N\right)}/\ln (e+j-1);$

3) reconstruction signal adopts the mallat fast algorithm that the small echo signal is rebuild, and corresponding wavelet reconstruction formula is

Obtain the signal after the reconstruct

The initial value of this formula is C _{J, m},

The highest scale coefficient after promptly handling;

By decomposition formula

The coefficient D that obtains after the decomposition _{0, k}, D _{1, k}, L D _{J, k}, C _{J, k}, and obtaining after high frequency coefficient (detail coefficients) the process threshold denoising processing wherein

Wherein

C _{J, m}It promptly is the highest scale coefficient after the described processing.

Step 2: detect weak periodic signal: the signal that obtains after measured signal denoising, the reconstruct by chaos system

Incorporate the duffing chaos system into, utilize the chaotic array method for scanning to realize detection, determine frequency, phase place and the amplitude of measured signal the cycle weak signal;

Step a: utilize layered transducer elements to measure the frequency of measured signal;

Use a limited array, the natural frequency of each oscillator is at 1～10rad/s in the array, and the natural frequency that makes each oscillator is that common ratio is the Geometric Sequence of a0;

Certainly the signal of frequency between 1～10 is imported in the array, carry out the threshold value correction according to the Melnikoff criterion, determine that system is changed into the threshold limit value f ' of cycle status by the chaos dress, make system be in the chaos critical conditions, so and stable intermittent chaos phenomenon only takes place on two adjacent oscillators, if be k and k+1 oscillator, other oscillators still are in chaos state

Then getting the measured signal frequency is

ω=[(ω _k+ Δ ω _k)+(ω _K+1-Δ ω _K+1)]/2, Δ ω wherein _k=2 π/T _k, Δ ω _K+1=2 π/T _K+1, T wherein _kAnd T _K+1Be respectively the cycle of k and k+1 oscillator;

Step b: the phase place of measured signal is measured in phase locking:

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, write down the amplitude in each cycle by computing machine, and compare, if amplitude increases with the last cycle, then expression is to existing together mutually, if no longer increase at t amplitude sometime, and begin to reduce, this moment t is exactly the measured signal moment identical with the system signal phase place so, the phase place of this moment is exactly the phase value of outer signals, and then the phase place of outer signals is

Δ ω wherein _kTmod (2 π) is Δ ω _kT is to (2 π) complementation, and the result equals (2 π) by Δ ω _kRemainder after t removes;

Step c: the amplitude of measured signal is measured in phase locking:

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, by phase-locked realization magnitude determination, the amplitude of this moment is f ', slowly reduce f ' after phase-locked to f ", make system come back to chaos state, then signal amplitude is

a＝f′-f″。

The a0 value is 1.03.

Beneficial effect:

The present invention at first carries out wavelet decomposition to the information of gathering, and determines decomposition scale according to actual noise situation; After the wavelet decomposition small echo high frequency coefficient is carried out denoising, in the wavelet threshold denoising process, the selection of threshold value is an important problem, directly influences denoising result, therefore the present invention's yardstick of at first giving chapter and verse is determined the method for threshold value, carries out the coefficient threshold process to improve denoising effect; After the denoising signal is reconstructed, again being incorporated in the chaos detection system as the hormetic part of chaos system through the measured signal after the small echo denoising, utilize chaos system to the strong immunity of noise with to features such as cycle weak signal susceptibility, further suppress noise, effectively extract feeble signal, the frequency adjustable of the chaos detection system that the present invention proposes can realize detecting the measured signal of different frequency.The present invention has overcome based on the defective that adopts methods such as filtering amplification, Fourier analysis: suppress not act on too significantly to having only millivolt level photoacoustic signal to be buried in easily to disturb in testing process very noisy under.The present invention has improved simple detection threshold and signal to noise ratio (S/N ratio) based on chaos detection system.Characteristics of the present invention comprise:

(1) decomposition scale to small echo is determined by ε and preset threshold, determines the wavelet decomposition yardstick according to concrete signal and noise situations self-adaptation.

(2) to different scale detail coefficients cD1, cD2 behind the wavelet transformation,, cD (J-1) carries out different threshold process, overcome the irrationality of broad sense threshold denoising.

(3) improve the duffing equation so that can detect the signal of different frequency, adopted the Melnikoff criterion simultaneously, strengthened accuracy and the applicability to signal amplitude detection based on the present invention of this equation.

(4) adopt layered transducer elements method and phaselock technique frequency and phase place to measured signal to measure, improved its accuracy of detection.

(5), reduced the thresholding and the signal to noise ratio (S/N ratio) of its input in conjunction with the feeble signal under wavelet threshold filtering and chaos detection system collection and the processing strong noise background.

The present invention handles the information via wavelet threshold denoising of gathering earlier, the filtering partial noise, incorporate information into chaos detection system again,, thereby can effectively collect the feeble signal that the cycle changes because chaos system has stronger immunologic function to noise and to the susceptibility of cycle feeble signal.Its advantage mainly contains following several respects: through after the small echo denoising, reduced the thresholding and the signal to noise ratio (S/N ratio) of input, the detection threshold and the signal to noise ratio (S/N ratio) of its amplitude reached respectively-100.0dB and-74.7dB under; Its small echo processing procedure has adopted adaptive wavelet to decompose the degree of depth and with the threshold process of dimensional variation, has made the denoising more convenient, more reasonable; According to improved duffing equation, adopted Melnikoff function chaos criterion, layered transducer elements method and phaselock technique, thereby improved practicality and accuracy greatly signal parameter detection, the detection error of frequency, phase place is about 0.04%.

Description of drawings

Fig. 1 emulation adds the preceding former figure that makes an uproar;

Fig. 2 is added with very noisy and disturbs back figure;

Fig. 3 chaos detection system chaos critical conditions phase path;

Fig. 4 large scale periodic motion phase path;

The intermittent chaotic motion time-domain diagram of Fig. 5;

The detected signal of Fig. 6 chaos system;

Fig. 7 is a process flow diagram of the present invention.

Embodiment

The present invention is further illustrated below in conjunction with instantiation and accompanying drawing.

Embodiment 1:

Below concrete enforcement of the present invention is elaborated, as Fig. 7.

1, detected information is carried out wavelet transform filtering:

Definition

Be the multiresolution analysis that generates by scaling function φ, W _jBe V _jAt V _J-1In the orthogonal complement space, W is promptly arranged _j=V _J-1-V _jIf φ _{J, k}Be metric space

One group of orthogonal basis, ψ _{J, k}Be little space { W _{J, k}One group of orthogonal basis.Other establishes f ∈ V _J-1, suppose from containing noise data f (t) release signal AS (t), f (t)=AS (t)+zs, AS (t) is a periodic signal; Zs is a noise signal.Then f can be projected to V _jAnd W _jThe space, promptly

Wherein

ψ _{J, k}Similar, promptly two of function advance translation and stretching; C _{J, k}And D _{J, k}Be respectively the coefficient of roughness and the wavelet coefficient of j metric space.

(1) wavelet decomposition of signal, select a wavelet basis that the signal of gathering is decomposed and definite wavelet decomposition number of plies J:

We select the Mallat fast algorithm to realize wavelet transformation in the practical application, if f _kBe the discrete sampling data of signal f (t), then f _k=C _{0, k}, i.e. C _{0, k}As the coefficient of roughness initial value of wavelet decomposition,

The orthogonal wavelet transformation decomposition formula of f (t) is

$\left\{\begin{array}{c}{C}_{j,k}=\underset{m}{\mathrm{\&Sigma;}}{C}_{j-1,m}{h}_{m-2k}\\ D_{j,k}=\underset{m}{\mathrm{\&Sigma;}}{C}_{j-1,m}{g}_{m-2k}\end{array}\right.,k=\mathrm{0,1},N-1.$

C like this _{J, k}, D _{J, k}Be respectively resolution 2 ^-jUnder the coefficient of roughness and detail coefficients, h _M-2k, g _M-2kBe respectively low pass and Hi-pass filter, by the scaling function φ of corresponding Mallat algorithm thought _{J, k}(t) and wavelet function ψ _{J, k}(t) decision, promptly

$\left\{\begin{array}{c}{h}_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&phi;}}_{j+1,m}>\\ g_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&psi;}}_{j+1,m}>\end{array}\right.$

The wavelet coefficient of noise on the higher decomposition layer of small echo is less, can ignore.And the wavelet coefficient of net signal in the higher decomposition layer of small echo is relatively large, and promptly the wavelet coefficient of signal in the higher decomposition layer of small echo with noise mainly is the wavelet coefficient of net signal.Adopt the wavelet decomposition number of plies of following method decision signals with noise according to this characteristic: be located in the wavelet decomposition j layer approach wavelet coefficient and the details wavelet coefficient is respectively C _{J, k}, D _{J, k}, D wherein _{J, k}Average be

${\stackrel{\&OverBar;}{D}}_{j,k}=\frac{1}{N_j}\underset{k=1}{\overset{N_j}{\mathrm{\&Sigma;}}}{D}_{j,k}$

Mean variance is

${\left|{\mathrm{ED}}_j\right|}^2=\frac{1}{N_j}\underset{k=1}{\overset{N_j}{\mathrm{\&Sigma;}}}{(D_{j,k}-{\stackrel{\&OverBar;}{D}}_{j,k})}^2$

N in the formula _jBe details wavelet coefficient D in the j layer _{J, k}Number.Then net signal details wavelet coefficient is in the j layer:

$D_{j,k}^{\%}=\left\{\begin{array}{c}0,|D_{j,k}-{\stackrel{\&OverBar;}{D}}_j|\&le;3\left|{\mathrm{ED}}_j\right|\\ D_{j,k},|D_{j,k}-{\stackrel{\&OverBar;}{D}}_j|>3\left|{\mathrm{ED}}_j\right|\end{array}\right.$

So the net signal wavelet coefficient is in the j layer:

$\left\{\begin{array}{c}{C}_j=C_{j,k}\\ D_j^{\%}=D_{j,k}^{\%}\end{array}\right.$

Order

$\mathrm{\&epsiv;}=\frac{{\left|\right|C_j\left|\right|}^2+{\left|\right|D_j^{\%}\left|\right|}^2}{{\left|\right|C_j\left|\right|}^2+{\left|\right|D_j\left|\right|}^2}$

Than the size of the ε decision wavelet decomposition number of plies, set a threshold value η (generally get 0.9196 more suitable) by the coefficient norm. as ε＜η, illustrate that the wavelet coefficient of noise in the j layer is bigger, need proceed wavelet decomposition.During ε＞η, illustrating that the wavelet coefficient of noise in the j layer is less, mainly is the wavelet coefficient of net signal, and decomposition ends, and obtains decomposing number of plies J value.

(2) threshold value is selected a threshold value to the wavelet coefficient of wavelet decomposition, and detail coefficients is made threshold process, is about to the full zero setting of wavelet coefficient less than threshold value, only keeps the wavelet coefficient greater than threshold value; (nonlinear wavelet threshold method denoising improvement) hard-threshold method: as can be known by front first step analysis, if threshold value δ obtains too big, then the loss of signal is too many, if get too little, then remain with a lot of details, it is unclean to remove noise, influence filter effect, consider that the back also will import chaos system to signal, chaos system has very strong immunocompetence to noise, suitably the threshold value on the different decomposition layer is got forr a short time, can effectively keep faint useful signal like this.Know that by the noise wavelet conversion characteristics wavelet coefficient average of noise behind wavelet transformation is zero, variance is

White noise, it increases along with yardstick j, white noise wavelet coefficient amplitude will reduce.White Gaussian noise is lipschitz exponent (LipschitzExponent) α＜0 Distribute.Discrete white noise almost everywhere is unusual, and in multi-scale wavelet decomposed, along with the increase of yardstick, the wavelet coefficient of useful signal was more clearly, and the small echo of white noise fades away.Donoho and Johnstone proposed the broad sense threshold process:

$\mathrm{\&delta;}=\widehat{\mathrm{\&sigma;}}\sqrt{2\log \left(N\right)}$

The present invention revises it,

J=1,2...J-1, wherein,

{ N here, much less e should understand, the similar famous formula of N for noise variance

Be sampled data length, e is the power exponent truth of a matter } in actual applications, because noise variance

Generally be unknowable, can get during denoising

Promptly use intermediate value estimator estimation variance, can see that this is a monotonic decreasing function, along with the increase threshold value δ of j reduces gradually.This is just in time consistent with the amplitude minimizing that increases noise when yardstick, and as j=1 the time, just in time becomes the threshold value formula that Donoho and Johnstone propose.

(3) so when the present invention handled wavelet conversion coefficient, process was as follows:

1) according to previous step, signal is carried out J yardstick wavelet decomposition, obtain approaching approximate signal C _JWith detail signal D _j, j=1 ... J

2) approach approximate signal C _JRemain unchanged, the high-frequency signal on each different scale is carried out the hard-threshold denoising, at first: for the D on the J yardstick _J, its signal to noise ratio (S/N ratio) is than higher, and the energy of useful signal is bigger, occupies major part, so choosing of threshold value should be littler, in order to avoid remove too much useful signal, selected threshold is:

${\mathrm{\&sigma;}}_J={\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA0000022852860000016.png"\; state="\{\{state\}\}">J</figure-callout>}}\sqrt{2\log \left(N\right)}/\sqrt{J}$

σ _JBe the variance of signal on the J yardstick,

Once more: to detail signal D _j, j=1,2...J-1, signal to noise ratio (S/N ratio) is lower, and the energy of useful signal and the energy of noise are more approaching, and threshold value is should high point quite a lot of, and we are with improved threshold value formula

It is consistent with the propagation characteristic of wavelet transformation on yardstick of noise along with the variation of yardstick j.

3) reconstruction signal is rebuild the small echo signal according to the Mallat fast algorithm.Corresponding wavelet reconstruction algorithm is

${\hat{C}}_{j-1,k}=\underset{m}{\mathrm{\&Sigma;}}{\hat{C}}_{j,m}{h}_{k-2m}+\underset{m}{\mathrm{\&Sigma;}}{\hat{D}}_{j,m}{g}_{k-2m}$

2, chaos system detects information:

(1) ultimate principle of chaos detection:

Detect incorporating chaos detection system into as hormetic perturbation of cycle through the reconstruction signal after the small echo denoising, the ultimate principle of its detection signal is: the signal of gathering is incorporated into chaos detection system as hormetic perturbation of cycle, because chaos system has certain immunocompetence to noise, very responsive to the periodic signal that same frequency or frequency are more or less the same, if allow the motion of chaos system phase path be in chaos critical conditions (as Fig. 3) so regulate chaos system itself cycle driving force (f), in the time of the periodic signal that detects same frequency or be more or less the same, the phase path motion state can be converted to stable large scale periodic motion state (as Fig. 4) immediately, for the ease of detecting the signal of multiple frequency, the present invention is according to improved Duffing equation structure Duffing oscillator chaos detection system

Its improved Duffing equation is:

$\stackrel{\&CenterDot;}{X}=\mathrm{\&omega;y}$

$\stackrel{\&CenterDot;}{y}=\mathrm{\&omega;}(-\mathrm{ky}+X-X^3+f\cos \left(\mathrm{\&omega;t}\right))$

Fcos (ω t) is the cycle driving force ,+X-X ³Be non-linear restoring force, get damping ratio k=0.5,

(2) the chaos criterion of Duffing system:

For particular system Duffing equation, when satisfying certain relation between damping ratio, periodic signal amplitude to be measured and the forced frequency, chaos system will enter chaos state.Melnikoff (Melnikov) function of the homoclinic orbit equation of improved Duffing equation is

$M\left(t_0\right)={\&Integral;}_{-\&infin;}^{\&infin;}[-\mathrm{ky}\left(t\right)+f\cos \mathrm{\&omega;}\left({t+t}_0\right)]y\left(t\right)\mathrm{dt}$

$=-\frac{4}{3}k\&PlusMinus;\sqrt{2}\mathrm{\&pi;\&omega;}f\mathrm{sech}\left(\frac{\mathrm{\&pi;\&omega;}}{2}\right)\sin \mathrm{\&omega;}{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA0000022852860000011.png,HDA0000022852860000016.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

According to the Melnikoff criterion, the condition that chaotic motion under the Smale conversion meaning appears in system is that the Melnikoff function exists simple zero point, be that saddle point (0 is crossed by system, the stable invariant manifold of saddle point type fixed point 0) and unstable constant exile transverse intersection, transversal homoclinic point, ratio appear in system Minimum value be called the threshold value of chaos, promptly

$\min \left(\frac{f}{k}\right)=\frac{4\cosh \left(\frac{\mathrm{\&omega;\&pi;}}{2}\right)}{3\sqrt{2}\mathrm{\&pi;\&omega;}}\stackrel{\mathrm{def}}{=}{f}_{\mathrm{\&omega;}}$

Following formula shows, the threshold value of chaos is relevant with the cycle forced frequency, when cycle forced frequency ω is low, threshold value is lower, and change little, but along with the increase of ω, Chaotic Threshold increases, promptly under given damping ratio k, the perturbation of the low-frequency range that f is less will make system's generation chaos, and the perturbation of high band then needs bigger f.

(3) input:

After we determine good any frequency, allow chaos system be in the chaos critical conditions.To be ω=ω through frequency after the denoising ₀The periodic signal to be measured of+Δ ω

The forced frequency of adding system itself is ω=ω ₀The Duffing equation time.System's driving force becomes

At this moment duffing equation evolution is

$\stackrel{\&CenterDot;}{X}={\mathrm{\&omega;}}_{0}y$

Owing to added periodic signal, regulated ω ₀Value can make system undergo phase transition, and turns to periodic motion.Its time-domain diagram also can present intermittent chaos phenomenon, and experiment shows, when the difference on the frequency Δ ω of measured signal and hormetic frequency=0, system is in periodic motion state or intermittent chaotic motion all the time; When 0≤Δ ω≤0.03, promptly because Δ ω is very little, F (t) changes slower, is much more slowly than phase transition process, and system illustrates that to the hormetic gradual response that can be good at the oscillator phase transformation is very sensitive to small-signal.At this moment, cycle and chaotic motion are clearly demarcated appearance the in cycle, intermittent chaos phenomenon promptly occurs.Its cycle is easy to get

T＝2π/Δω

When Δ ω＞0.03, the excessive velocities of phase transformation, stable chaos or periodic motion state of long period be cannot say for sure to demonstrate,prove in system, promptly difficulty picks out intermittent chaos phenomenon clocklike, the phase transformation that the Duffing oscillator just has been described has strong immunity to the bigger periodic signal of frequency difference, and is promptly identical or differ less signal sensitivity to frequency.

According to top analysis, the present invention utilizes the chaotic array method for scanning to realize detection to weak signal of following cycle of strong noise background, determines frequency, phase place and the amplitude of measured signal.

(1) utilize layered transducer elements to measure the frequency of measured signal

Imagination is used a limited array, and the natural frequency of each oscillator makes it to become a common ratio and be 1.03 Geometric Sequence at 1～10rad/s in the array.Then layered transducer elements is made up of 78 array elements, gets ω ₁=1, ω ₂=1.03, ω ₃=(1.03) ²...., ω ₇₈=(1.03) ⁷⁷=9.738.Here why selecting common ratio is 1.03, is to consider when measured signal and hormetic difference on the frequency Δ ω＞0.03, is difficult to observe intermittent chaos phenomenon, so adjacent two array element ω _k, ω _K+1The oscillator frequency differ can not be greater than 0.03 ω _k, i.e. ω _K+1-ω _k=0.03 ω _kSo, ω _K+1/ ω _k≤ 1.03, the natural frequency of its each oscillator is that common ratio is 1.03 Geometric Sequence.

If the signal of frequency between 1～10 is imported in the array, carry out the threshold value correction according to the Melnikoff criterion, determine that system is changed into the threshold limit value f ' of cycle status by the chaos dress, making system is the chaos critical conditions, so and stable intermittent chaos phenomenon only takes place on two adjacent oscillators, if be k and k+1 oscillator, other oscillators still are in chaos state, so the measured signal frequencies omega must satisfy:

ω _k≤ω≤ω _k+1

Just can accurately determine the frequency of signal, Δ ω by the cycle of measuring the intermittent chaos of two oscillators _k=2 π/T _k, Δ ω _K+1=2 π/T _K+1, wherein T can obtain by computer program, promptly by writing down the moment of two amplitude maximums in the adjacent constant time range of intermittent exercise It is long that its time difference is one-period Getting the measured signal frequency at last is

ω＝[(ω _k+Δω _k)+(ω _k+1-Δω _k+1)]/2

(2) phase place of measured signal is measured in phase locking

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, write down the amplitude in each cycle by computing machine, and compare, if amplitude increases with the last cycle, then expression is to existing together mutually, if no longer increase at amplitude sometime, and begin to reduce, this moment (t) is exactly the measured signal moment identical with the system signal phase place so, the phase place of this moment is exactly the phase value of outer signals, because intermittent chaos is with T _k=2 π/| ω-ω _k|=2 π/Δ ω _kFor the cycle, thereby the phase place that calculates measured signal is

(3) amplitude of measured signal is measured in phase locking

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, by phase-locked realization magnitude determination.Phase-locked back slowly is reduced to f to f from f ' ", make system come back to chaos state, at this time, the signal amplitude that records is exactly

a＝f′-f″。

Claims (2)

1. the detection method based on the weak periodic signal of chaos system and wavelet threshold denoising is characterized in that, may further comprise the steps:

Step 1: detected information is carried out wavelet transform filtering:

1) according to the mallat fast algorithm original signal of sampling is carried out J yardstick wavelet decomposition, obtain approaching approximate signal C _{J, k}With detail signal D _{J, k}, j=1 ... J, the J value is 3,4,5 or 6;

$\left\{\begin{array}{c}{C}_{j,k}=\underset{m}{\mathrm{\&Sigma;}}{C}_{j-1,m}{h}_{m-2k}\\ D_{j,k}=\underset{m}{\mathrm{\&Sigma;}}{D}_{j-1,m}{g}_{m-2k}\end{array}\right.k,m=\mathrm{0,1},...,N-1,$

Adopt sampled value f _kCoefficient of roughness initial value C as wavelet decomposition _{0, k}, C is promptly arranged _{0, k}=f _k, D _{0, k}=C _{0, k}, N is a sampling length;

h _M-2k, g _M-2kBe respectively low pass and Hi-pass filter, it is as follows to embody formula:

$\left\{\begin{array}{c}{h}_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&phi;}}_{j+1,m}>\\ g_{k-2m}=<{\mathrm{\&phi;}}_{j,k},{\mathrm{\&psi;}}_{j+1,m}>\end{array}\right.,$ φ wherein _{J, k}(t) and ψ _{J, k}(t) be respectively scaling function and wavelet function in the mallat algorithm;

2) approach approximate signal C _JRemain unchanged, to the detail signal D on each different scale _{J, k}Carry out the hard-threshold denoising, the detail signal after obtaining handling

${\hat{D}}_{j,k}=\left\{\begin{array}{c}{D}_{j,k},\left|D_{j,k}\right|\&GreaterEqual;\mathrm{\&delta;}\\ 0,\left|D_{j,k}\right|<\mathrm{\&delta;}\end{array}\right.,$ Wherein δ is a threshold value,

For the D on the J yardstick _J, the δ value is δ _J:

${\mathrm{\&delta;}}_J={\mathrm{\&sigma;}}_J\sqrt{2\log \left(N\right)}/\sqrt{J};$

σ _JBe the variance of signal on the J yardstick of gathering

To detail signal D _j, j=1,2...J-1, setting threshold is:

$\mathrm{\&delta;}=\widehat{\mathrm{\&sigma;}}\sqrt{2\log \left(N\right)}/\ln (e+j-1);$

3) reconstruction signal adopts the mallat fast algorithm that the small echo signal is rebuild, and corresponding wavelet reconstruction formula is

Obtain the signal after the reconstruct

The initial value of this formula is C _{J, m},

The highest scale coefficient after promptly handling;

Step 2: detect weak periodic signal: the signal C that obtains after measured signal denoising, the reconstruct by chaos system _{0, k}Incorporate the duffing chaos system into, utilize the chaotic array method for scanning to realize detection, determine frequency, phase place and the amplitude of measured signal the cycle weak signal;

Step a: utilize layered transducer elements to measure the frequency of measured signal;

Use a limited array, the natural frequency of each oscillator is at 1～10rad/s in the array, and the natural frequency that makes each oscillator is that common ratio is the Geometric Sequence of a0;

Certainly the signal of frequency between 1～10 is imported in the array, carry out the threshold value correction according to the Melnikoff criterion, determine that system is changed into the threshold limit value f ' of cycle status by the chaos dress, make system be in the chaos critical conditions, so and stable intermittent chaos phenomenon only takes place on two adjacent oscillators, if be k and k+1 oscillator, other oscillators still are in chaos state

Then getting the measured signal frequency is

ω=[(ω _k+ Δ ω _k)+(ω _K+1-Δ ω _K+1)]/2, Δ ω wherein _k=2 π/T _k, Δ ω _K+1=2 π/T _K+1, T wherein _kAnd T _K+1Be respectively the cycle of k and k+1 oscillator;

Step b: the phase place of measured signal is measured in phase locking:

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, write down the amplitude in each cycle by computing machine, and compare, if amplitude increases with the last cycle, then expression is to existing together mutually, if no longer increase at t amplitude sometime, and begin to reduce, this moment t is exactly the measured signal moment identical with the system signal phase place so, the phase place of this moment is exactly the phase value of outer signals, and then the phase place of outer signals is

Δ ω wherein _kTmod (2 π) is Δ ω _kT is to (2 π) complementation, and the result equals (2 π) by Δ ω _kRemainder after t removes;

Step c: the amplitude of measured signal is measured in phase locking:

When frequency measurement, the moment of amplitude maximum is the system phase moment identical with the measured signal phase place in the intermittent periods it section, by phase-locked realization magnitude determination, the amplitude of this moment is f ', slowly reduce f ' after phase-locked to f ", make system come back to chaos state, then signal amplitude is

a＝f′-f″。

2. the detection method of the weak periodic signal based on chaos system and wavelet threshold denoising according to claim 1 is characterized in that the a0 value is 1.03.

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