CN107870005A - The normalization random resonant weak signal detection of empirical mode decomposition under over-sampling - Google Patents
The normalization random resonant weak signal detection of empirical mode decomposition under over-sampling Download PDFInfo
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Abstract
A kind of method of the normalization bistable bi-stable stochastic resonance theory detection small-signal side of empirical mode decomposition under over-sampling is claimed in the present invention, belongs to signal processing technology field.Empirical mode decomposition and normalization accidental resonance are bonded a new system by the present invention.Based on the method for the system to signals and associated noises carry out empirical mode decomposition it is basic on, superposed signal modal components, carry out parameter normalization, it is met accidental resonance small parameter requirement, be sent into stochastic resonance system, observation spectrogram sees whether there is obvious spike, calculate average signal-to-noise ratio gain, signal to noise ratio be increased after empirical mode decomposition, and signal to noise ratio is further added by after accidental resonance, be generally increased more preferable than accidental resonance is used alone.The normalization bi-stable stochastic resonance theory Detection of Weak Signals of empirical mode decomposition, is of universal significance in actual applications under over-sampling proposed by the present invention, reduces the complexity of parameter regulation and solves the problems, such as that big frequency is unsatisfactory for accidental resonance.
Description
Technical field
The invention belongs to signal processing technology field, the normalization accidental resonance of empirical mode decomposition specifically under over-sampling
Detection of Weak Signals.
Background technology
Small-signal, which refers to be present in various noises, to be difficult to be difficult to a kind of signal detected, such as the underwater sound is believed
Number, biomedicine signals, mechanical fault signals, seismic signal.Detection technique also from noise filtering excessively and utilizes noise these two aspects
To start with, traditional filtering detection method is all to eliminate noise, generally has an experience mode decomposition (EMD) using method, Wavelet Denoising Method,
Wave filter etc..Although these methods can eliminate noise, useful signal can be also weakened simultaneously so that detection is inaccurate.With
The accidental resonance occurred afterwards is that high-frequency energy is effectively converted into low frequency energy detection small-signal method by one kind, strengthens signal energy
Amount, noise energy is reduced, reaches testing goal, using nonlinear equation, numerical solution pair is carried out in input signal feeding system
Output signal is analyzed, and reaches the detection to echo signal.
Empirical mode decomposition (EMD) is a kind of novel process nonlinear and non local boundary value problem technology, for the purpose of weakening noise,
This method was proposed in 1999 by Huang.This method produces a series of basic friction angle composition IMF with different characteristic yardstick,
By carrying out Hilbert conversion to each component, Hilbert spectrums and its marginal spectrum are obtained, is used using empirical mode decomposition ratio
Wavelet transformation is simple many, and without finding mode function, adaptive is decomposited by signal according to different frequency, right
Produce different Intrinsic Mode components and carry out Hilbert transform, analyze its existing composition, can understand and draw signal frequency
Composition characteristic.
Stochastic Resonance Theory is that Benzi etc. proposes in the ancient meteorological glacier problem of research, in Stochastic Resonance Theory, is utilized
Signal, noise, system three reach enhancing signal effect when reaching cooperative effect.Big parameter be unsatisfactory for adiabatic approximation it is theoretical can
To realize frequency transformation by double sampling, realize that the high frequency of signal to the conversion of low frequency, reaches by introducing parameter using modulation
To the signal detection to arbitrarily large frequency, contradiction between sampled point and sample frequency is reduced by shift frequency frequency mutative scale.With
The research of machine resonance turns into the object that numerous scholars are favored, and many scholars also have been carried out the breakthrough of different levels, from
The small frequency most started to big frequency research, method have shift frequency, change of scale, double sampling, normalization, parameter compensation etc..
Stochastic resonance system domestic and foreign scholars are also steady from monostable, bistable to three, and analysis also moves to double potential wells from unipotential trap Brownian Particles
Brownian Particles move.It can only be vibrated accordingly, with respect to monostable stochastic resonance system in a potential well, bistable-state random resonance
System can make vibration particle that transition occur between potential well, and bi-stable stochastic resonance theory system is in noise utilization rate and accidental resonance effect side
Face is better than monostable stochastic resonance system.The basis based on more than, set forth herein the accidental resonance of empirical mode decomposition under over-sampling
Study, the component of None- identified carries out accidental resonance after empirical mode decomposition, finally reaches the purpose of detection echo signal.
The content of the invention
It is an object of the invention to for existing sample frequency it is larger in the case of, propose the empirical modal under a kind of over-sampling
Bi-stable stochastic resonance theory model is normalized after decomposition.
The technical solution adopted in the present invention is：Empirical mode decomposition is carried out under over-sampling, then is normalized random
Resonance.This method carries out over-sampling to signals and associated noises first, and general over-sampling frequency is more than 100 times of signal frequency, then observed
Level where echo signal, component superposition where extraction, stochastic resonance system is sent into superposition composition normalization, by decomposing again
The signal energy partial loss of synthesis, but frequency will not reduce, and also be now big frequency signal, and the present invention uses normalized,
And decomposed signal is sent into stochastic resonance system, target inband energy is improved, noise energy reduces.Accidental resonance
Principle is：The energy of output signal is concentrated mainly on low frequency region, and the energy transfer of high frequency region passes through accidental resonance to low frequency range
System, high frequency noise content weaken the energy enhancing of low frequency useful signal.Significance of the present invention experience under big sample frequency
Under mode decomposition, decompose None- identified signal when, then by normalize stochastic resonance system carry out accidental resonance be also can will
What target echo detection came out.
Brief description of the drawings
The block diagram of the normalization accidental resonance of empirical mode decomposition under Fig. 1 over-samplings of the present invention；
Empirical mode decomposition figure under the low sampling of Fig. 2 present invention；
Fig. 3 single-frequency empirical mode decomposition figures of the present invention；
Fig. 4 present invention normalization bi-stable stochastic resonance theory potential function figures；
Oscillogram before and after Fig. 5 single-frequency composite signal accidental resonances of the present invention；
Spectrogram before and after Fig. 6 single-frequency composite signal accidental resonances of the present invention；
Oscillogram before and after Fig. 7 multifrequency composite signal accidental resonances of the present invention；
Spectrogram before and after Fig. 8 multifrequency composite signal accidental resonances of the present invention；
Embodiment
Below in conjunction with accompanying drawing and instantiation, the implementation to the present invention is further described.Fig. 1 is experience under over-sampling
The accidental resonance FB(flow block) of mode decomposition, specific steps：The signal for being mixed with Gaussian noise is first passed through into EMD to decompose, then chosen
With echo signal decomposed component, converted using parameter normalization, big frequency signal is entered into line translation makes it meet adiabatic approximation
Theoretical small parameter signal, then small parameter signal is sent into stochastic resonance system, finally obtains stochastic resonance system output
Signal spectrum, spectral change figure before and after observation, and snr gain and rate of accuracy reached are to the purpose of detection signal.
Fig. 2 is empirical mode decomposition figure under low sampling, using multiple-frequency signal in the low exploded view adopted under frequency, A=
3000, f1=100Hz, f2=150Hz, f3=200Hz, white noise variance σ=7874, sample frequency are that 1000Hz is bright to signal
Aobvious to find out, when sample frequency is more than 100 times of signal frequencies, signal None- identified comes out, and Fig. 3 is that sample frequency is 10000Hz's
100Hz simple signals decompose, and decomposed signal can not accurately identify echo signal, so by empirical modal.The present invention uses
Be traditional empirical mode decomposition, decomposition is noisy single frequency sinusoidal signal, the algorithm of empirical mode decomposition include as
Lower step：
(1) signal local maximum minimum is calculated, envelope average value m up and down is fitted by 3 spline methods1
(t), and h is thought1(t)=x (t)-m1(t) it is residual components.
(2) ideally h1For first IMF component, h is judged1Whether it is to meet IMF components, is unsatisfactory for needing repeatedly
Screening, next by h1As new signal, repeat the above steps, after circulating k times, obtain IMF conditions h1k(t).Wherein screening time
Number constraint satisfaction Cauchy criterion：
T is signal time length in formula, and ε is that threshold value scope is (0.2-0.3)
(3) the first rank IMFc is obtained1(t) it is h1k(t), r1(t)=x (t)-c1(t), by c1(t) primary signal is regarded,
Both the above step is iteratively repeated, obtains c2(t)、c2(t)、c3, and residual components r (t)n(t) it is r, to decompose termination conditionn(t)
Dullness, it is possible thereby to be n empirical modal component by signal decomposition.
The big frequency signal accidental resonance of parameter normalization change process is in the non-linear of classical bi-stable stochastic resonance theory model
Langevin equations improve for what is above done, and Langevin equations are：
S (t)=Asin (2 π ft) in formula, E (n (t))=0, var (n (t))=σ2Gaussian noise, research find inputting
A=1, b=1, A=0.3, f=0.01 under signal, meet to produce when the sample frequency of adiabatic approximation theory σ=0.7874 is 5Hz
Accidental resonance.Potential function when a, b value are 1 isFig. 4 is potential function figure, for describing
Brownian Particles laws of motion, when being not reaching to accidental resonance, Brownian Particles are distributed in two potential wells, produce accidental resonance
When Particles Moving carried out between two potential wells, cross potential barrier, back and forth transition, carry out energy transfer, when a, b value is not 1, order
τ=at (4)
(3) (4) formula, which is substituted into (2), to be obtained
A times of compression has been carried out in equation (5) on noise signal frequency domain, and n (t) is white Gaussian noise, in frequency domain
It is inside a constant component, there is identical power, frequency domain draws high the power that compression does not change noise, therefore n (τ/a) is still
Average is that 0 variance is σ2White noise, equation (5) is deformed into：
It is 1 by normalized bistable system parameter, realizes normalization, frequency input signal is changed into original 1/a
Times, periodic signal and noise amplitude value are all scaled in proportion, and equation (6) and equation (2) they are of equal value.
A=1, b=1, A=0.3, f=0.01, σ=0.7874 are small parameter situation, and this group of small parameter may be considered
Result is obtained after the normalization of a certain big parameter, big parameter is obtained according to normalization principle inverse transformation, when f=100Hz can be anti-
Other specification value, a=10000, b=10000 are pushed away, A=3000 sample frequencys reach 50000Hz, and bistable system produces random
Resonance, determine that parameter b values are Arbitrary Digit, the amplitude of the big parameter of mixed signal according to a values under normalization principle f=100Hz
ReduceTimes.Fig. 5 is IMF4-IMF7 superposed signals, composite signal waveform portion distortion, the output wave after accidental resonance
Shape becomes regular waveform.Fig. 6 is power spectrum size before and after 100Hz, is increased from 239.1 to 1269 more than 5 times.A=10000, b=
10000, f1=100Hz, f2=150Hz, f2=200Hz A=3000 sample frequencys reach 50000Hz, and Fig. 7 is multifrequency Empirical Mode
Signal composite diagram after state is decomposed, Fig. 8 are spectrogram before and after multifrequency composite signal accidental resonance, and the frequency spectrum of each frequency is understood in figure
All increase.
The measurement index of accidental resonance is a lot, mainly there is mutual relation number, power spectrum, snr gain etc., wherein, signal to noise ratio
Gain more can intuitively react accidental resonance effect, in order that data are more convincing, herein using average signal-to-noise ratio gain
As measurement index, it is defined as follows：
Wherein, SNRoutIt is output signal-to-noise ratio, SNRinIt is input signal-to-noise ratio, SNRgainIt is snr gain.Multiple-frequency signal weighs
Figureofmerit is defined as averagely to make an uproar than gain：
Wherein, n represents simulation times, (SNRgain)iRepresent the snr gain of ith emulation.For accidental resonance system
System, under a specific input noise intensity, can make average signal-to-noise ratio gain reach peak value, therefore optimal noise can
Produce maximum average signal-to-noise ratio yield value.Single-frequency 100Hz primary signals average signal-to-noise ratio is -12.2062dB, and empirical modal divides
Average signal-to-noise ratio is -3.8931dB after solution, and accidental resonance average signal-to-noise ratio is -3.4272dB, and average signal-to-noise ratio gain is
8.7789dB, multifrequency primary signal average signal-to-noise ratio are -36.8595dB, after empirical mode decomposition average signal-to-noise ratio for -
18.0963dB, average signal-to-noise ratio is -15.972dB after accidental resonance, and overall gain average signal-to-noise ratio is 20.8875dB, noise
Growth than gain shows that under the accidental resonance after empirical mode decomposition noise is nearly eliminated, and signal energy also increases
, signal so can be also detected under over-sampling frequency.
Claims (3)
1. the Detection of Weak Signals of the normalization bi-stable stochastic resonance theory of empirical mode decomposition under a kind of over-sampling proposed by the present invention
Method, for the small-signal of strong noise background under effective detection over-sampling frequency, the present invention be a kind of empirical mode decomposition and
Normalize the system that bi-stable stochastic resonance theory system combines.Signals and associated noises are carried out with empirical mode decomposition, each layer of decomposition of observation
Frequency content burr is mostly for noise, judges which layer component signal substantially exists, except level will contain existing for denoising
Signal modal components are superimposed, and it is seldom to obtain ingredient noise, parameter normalization is then carried out, it is met accidental resonance small parameter
It is required that carrying out accidental resonance, observation spectrogram sees whether there is obvious spike, average signal-to-noise ratio gain is calculated, in empirical modal
Signal to noise ratio be increased after decomposition, and signal to noise ratio is further added by after accidental resonance, be generally increased more preferable than accidental resonance is used alone.
2. according to claim 1 under over-sampling empirical mode decomposition normalization bi-stable stochastic resonance theory Detection of Weak Signals
Method, it is characterised in that empirical mode decomposition is carried out to signals and associated noises, judges that signal is present in which layer, empirical mode decomposition
Principle be to come out the different signal decomposition of frequency, typically decompose from HFS to low frequency part, if existed in signal
Much noise, then first 3 layers are typically all noise contribution, and signal is present in one layer next or several layers of a, frequency into branch
The signal of rate is likely to be present in several layers of the insides, and important superposition is exactly the signal that most original is decomposed, and is to reduce in the present invention
The loss of signal, component existing for denoising will be removed and be superimposed, noise in signal is obtained and have been removed many.
3. the small-signal inspection of the normalization bi-stable stochastic resonance theory of empirical mode decomposition under over-sampling according to claim 1
Survey method, it is characterised in that the normalization of bistable system is just, relative to traditional Langevin equations：The a=1 of the parameter typically used in the case of small parameter, b=1 regulation noise variance σ=
0.7874, accidental resonance can also be produced using big frequency signal after normalization, normalize and do not adopted unlike double sampling
Sample frequency limit, it is that the amplitude of signal is compressed that big parameter signal will be appointed, which to be normalized into small parameter, and frequency is compressed.
Equation is changed into after normalization：
Normalized bi-stable stochastic resonance theory solves and uses quadravalence Long Gekuta algorithms (Runge-Kutta), and the big frequency after synthesis is believed
Number it is sent into normalized bistable system, the automatic boil down to of signal amplitudeFrequency is actual, which to be also compressed to original 1/a, expires
Sufficient small parameter condition, Stochastic Resonance Phenomenon is finally produced, realize detection echo signal purpose.
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| CN108444698A (en) * | 2018-06-15 | 2018-08-24 | 福州大学 | Epicyclic gearbox Incipient Fault Diagnosis method based on TEO demodulation accidental resonances |
| CN108663576A (en) * | 2018-05-08 | 2018-10-16 | 集美大学 | Weak electromagnetic red signal detection method under a kind of complex environment |
| CN110346143A (en) * | 2019-08-06 | 2019-10-18 | 江苏今创车辆有限公司 | Hyperfrequency noise assists empirical mode decomposition method |
| CN110705128A (en) * | 2019-10-25 | 2020-01-17 | 陕西师范大学 | Parameter-adjustable stochastic resonance simulation system |
| CN111914806A (en) * | 2020-08-18 | 2020-11-10 | 成都爱科特科技发展有限公司 | Ultrashort wave weak signal detection method and device in high-noise environment, terminal equipment and storage medium |
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| CN112087266A (en) * | 2020-08-21 | 2020-12-15 | 哈尔滨工程大学 | Time-varying broadband Doppler compensation method based on EMD-WFFT |
| CN116166931A (en) * | 2022-12-16 | 2023-05-26 | 北京科技大学 | Dangerous rock body first-order natural vibration frequency extraction method based on constant micro-motion |
| CN116166931B (en) * | 2022-12-16 | 2023-10-20 | 北京科技大学 | Dangerous rock body first-order natural vibration frequency extraction method based on constant micro-motion |
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Application publication date: 20180403 |