CN107870005A - Normalized stochastic resonance weak signal detection with empirical mode decomposition under oversampling - Google Patents

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

Normalized stochastic resonance weak signal detection with empirical mode decomposition under oversampling

technical field

The invention belongs to the technical field of signal processing, in particular to normalized stochastic resonance weak signal detection of empirical mode decomposition under oversampling.

Background technique

Weak signals refer to a type of signal that is difficult to identify and detect in various noises, such as underwater acoustic signals, biomedical signals, mechanical failure signals, and seismic signals. Detection technology also starts from the two aspects of filtering noise and using noise. The traditional filtering detection method is to eliminate noise. The commonly used methods include empirical mode decomposition (EMD), wavelet denoising, and filter. Although these methods can eliminate noise, at the same time the useful signal will be weakened, making the detection inaccurate. The subsequent stochastic resonance is an effective way to convert high-frequency energy into low-frequency energy to detect weak signals, enhance signal energy, reduce noise energy, and achieve the purpose of detection. Using nonlinear equations, the input signal is sent into the system for numerical solution to the output. The signal is analyzed to achieve the detection of the target signal.

Empirical Mode Decomposition (EMD) is a new technique for processing nonlinear and non-stationary signals, with the purpose of reducing noise. This method was proposed by Huang in 1999. This method produces a series of basic modal components IMF with different characteristic scales. By performing Hilbert transformation on each component, the Hilbert spectrum and its marginal spectrum are obtained. Using empirical mode decomposition is much simpler than using wavelet transform, and there is no need to find the modal function , adaptively decompose the signal according to different frequencies, perform Hilbert transform on the different intrinsic modal components, and analyze the existing components, so that the characteristics of the signal frequency components can be clearly obtained.

The stochastic resonance theory was proposed by Benzi et al. when they were studying paleoclimate glaciers. In the stochastic resonance theory, signal, noise, and system are used to achieve a synergistic effect to enhance the signal effect. If the large parameters do not satisfy the adiabatic approximation theory, the frequency conversion can be realized by resampling, and the high frequency to low frequency conversion of the signal can be realized by modulation. The signal detection of any large frequency can be achieved by introducing parameters, and the frequency can be reduced by shifting the frequency and changing the scale. There is a contradiction between the sampling point and the sampling frequency. The study of stochastic resonance has become the object favored by many scholars, and many scholars have achieved breakthroughs at different levels. From the initial small frequency to large frequency research, the methods include frequency shifting, scale transformation, subsampling, and normalization. , parameter compensation, etc. Scholars at home and abroad have also changed the stochastic resonance system from monostable, bistable to tristable, and analyzed from single potential well Brownian particle motion to double potential well Brownian particle motion. Therefore, compared with the monostable stochastic resonance system, which can only oscillate in one potential well, the bistable stochastic resonance system can make the oscillating particles transition between potential wells. Better than monostable stochastic resonance systems. Based on the above foundations, this paper proposes the stochastic resonance research of empirical mode decomposition under oversampling. After the empirical mode decomposition, the unidentifiable components are subjected to stochastic resonance, and finally the purpose of detecting the target signal is achieved.

Contents of the invention

The purpose of the present invention is to propose a normalized bistable stochastic resonance model after empirical mode decomposition under oversampling for the existing large sampling frequency.

The technical scheme adopted in the present invention is: performing empirical mode decomposition under oversampling, and then performing normalized stochastic resonance. In this method, the noise-containing signal is firstly oversampled. Generally, the oversampling frequency is 100 times greater than the signal frequency. Then, the level of the target signal is observed, the components are extracted and superimposed, and the superimposed components are normalized and sent to the stochastic resonance system. Part of the signal energy is lost, but the frequency will not decrease. At this time, it is still a high-frequency signal. The present invention adopts normalization processing, and sends the decomposed signal into the stochastic resonance system to increase the energy of the target signal and reduce the energy of noise. The principle of stochastic resonance is: the energy of the output signal is mainly concentrated in the low-frequency region, and the energy in the high-frequency region is transferred to the low-frequency region. Through the stochastic resonance system, the high-frequency noise components are weakened and the energy of the low-frequency useful signal is enhanced. The significance of the present invention is that under the empirical mode decomposition at a large sampling frequency, when the signal cannot be identified by decomposition, the target signal can also be detected by performing stochastic resonance through a normalized stochastic resonance system.

Description of drawings

The block diagram of the normalized stochastic resonance of empirical mode decomposition under Fig. 1 oversampling of the present invention;

Fig. 2 empirical mode decomposition diagram under low sampling of the present invention;

Fig. 3 single-frequency empirical mode decomposition diagram of the present invention;

Fig. 4 normalized bistable stochastic resonance potential function figure of the present invention;

Fig. 5 waveform diagram before and after the stochastic resonance of the single-frequency synthetic signal of the present invention;

Fig. 6 is the spectrogram before and after the stochastic resonance of the single-frequency synthetic signal of the present invention;

Fig. 7 waveform diagram before and after stochastic resonance of the multi-frequency synthetic signal of the present invention;

Fig. 8 is the spectrogram before and after the stochastic resonance of the multi-frequency synthetic signal of the present invention;

Detailed ways

The implementation of the present invention will be further described below in conjunction with the accompanying drawings and specific examples. Figure 1 is a block diagram of the stochastic resonance process of empirical mode decomposition under oversampling. The specific steps are as follows: the signal mixed with Gaussian noise is decomposed by EMD first, and then the decomposition component with the target signal is selected, and the parameter normalization transformation is used to transform the large frequency signal Transform the small parameter signal to satisfy the adiabatic approximation theory, then send the small parameter signal into the stochastic resonance system, and finally get the signal spectrum output by the stochastic resonance system, the spectrum change diagram before and after observation, and the signal-to-noise ratio gain and accuracy rate reach The purpose of detecting signals.

Fig. 2 is the empirical mode decomposition diagram under low sampling frequency, using the decomposition diagram of multi-frequency signal at low sampling frequency, A=3000, f ₁ =100Hz, f ₂ =150Hz, f ₃ =200Hz, white noise variance σ =7874, the sampling frequency is 1000Hz. It is obvious to the signal that when the sampling frequency is greater than 100 times the signal frequency, the signal cannot be recognized. Figure 3 shows the decomposition of a 100Hz single-frequency signal with a sampling frequency of 10000Hz. The decomposed signal cannot accurately identify the target signal, so In the empirical mode. What the present invention adopts is traditional empirical mode decomposition, and what decompose is the single-frequency sinusoidal signal that contains noise, and the algorithm of empirical mode decomposition has included the following steps:

(1) Calculate the local maximum and minimum values of the signal, and fit the upper and lower envelope average values m ₁ (t) through the third-order spline interpolation method, and consider h ₁ (t)=x(t)-m ₁ (t) is the residual component.

(2) Ideally h ₁ is the first IMF component, judge whether h ₁ satisfies the IMF component, if not satisfied, it needs to be screened repeatedly, then use h ₁ as a new signal, repeat the above steps, and after k times of loops, get IMF condition h _1k (t). where the number of screening constraints satisfies the Cauchy criterion:

In the formula, T is the signal time length, ε is the threshold value range (0.2-0.3)

(3) Obtaining the first-order IMFc ₁ (t) is h _1k (t), r ₁ (t)=x(t)-c ₁ (t), taking c ₁ (t) as the original signal, and repeating the above Two steps, get c ₂ (t), c ₂ (t), c ₃ (t), and the residual component r _n (t), the decomposition end condition is r _n (t) monotone, thus the signal can be decomposed into n empirical modal components.

Parameter normalization changes to deal with large-frequency signal stochastic resonance is an improvement on the nonlinear Langevin equation of the classic bistable stochastic resonance model. The Langevin equation is:

In the formula, s(t)=Asin(2πft), E(n(t))=0, var(n(t))=σ ² Gaussian noise, it is found that under the input signal a=1, b=1, A = 0.3, f = 0.01, satisfying the adiabatic approximation theory σ = 0.7874 When the sampling frequency is 5Hz, random resonance can be produced. The potential function when the values of a and b are 1 is Figure 4 is a graph of the potential function, which is used to describe the law of Brownian particle motion. When random resonance is not reached, Brownian particles are distributed in two potential wells. Transition, energy transfer, when the values of a and b are not 1, let

τ=at (4)

Substitute (3) (4) into (2) to get

The noise signal in Equation (5) is compressed by a times in the frequency domain, and n(t) is Gaussian white noise, which is a constant component in the frequency domain and has the same power. Change the power of the noise, so n(τ/a) is still a white noise with a mean value of 0 and a variance of ^σ2 , and the equation (5) is transformed into:

After normalization processing, the parameters of the bistable system are all 1, to achieve normalization, the frequency of the input signal becomes 1/a times of the original, and the periodic signal and noise amplitude values are scaled in the same proportion. Equation (6) and equation ( 2) are equivalent.

a=1, b=1, A=0.3, f=0.01, σ=0.7874 are small parameters, this group of small parameters can be considered as the result obtained after normalization of a certain large parameter, according to the normalization principle Transform to obtain large parameters. When f=100Hz, the values of other parameters can be deduced, a=10000, b=10000, A=3000, the sampling frequency reaches 50000Hz, and the bistable system produces stochastic resonance. According to the normalization principle, f=100Hz under a The value is determined, the value of parameter b is any number, and the amplitude of the large parameter of the mixed signal is reduced times. Figure 5 is the IMF4-IMF7 superposition signal, the composite signal waveform is partially distorted, and the output waveform becomes a regular waveform after random resonance. Figure 6 shows the size of the power spectrum before and after 100Hz, which increases more than five times from 239.1 to 1269. a = 10000, b = 10000, f ₁ = 100Hz, f ₂ = 150Hz, f ₂ = 200Hz A = 3000 The sampling frequency reaches 50000Hz, Figure 7 is the signal synthesis diagram after multi-frequency empirical mode decomposition, and Figure 8 is the multi-frequency synthesis The spectrum diagram before and after the random resonance of the signal shows that the spectrum of each frequency increases.

There are many measures of stochastic resonance, mainly including correlation coefficient, power spectrum, signal-to-noise ratio gain, etc. Among them, the signal-to-noise ratio gain can more intuitively reflect the stochastic resonance effect. In order to make the data more convincing, this paper adopts the average signal-to-noise ratio Specific gain is used as a measure, and its definition is as follows:

Among them, SNR _out is the output signal-to-noise ratio, SNR _in is the input signal-to-noise ratio, and SNR _gain is the signal-to-noise ratio gain. The multi-frequency signal metric is the average noise ratio gain defined as:

Among them, n represents the number of simulations, and (SNR _gain ) _i represents the signal-to-noise ratio gain of the ith simulation. For a stochastic resonant system, the average SNR gain can be peaked at a certain input noise level, so the optimal noise yields the largest average SNR gain. The average signal-to-noise ratio of single-frequency 100Hz original signal is -12.2062dB, the average signal-to-noise ratio after empirical mode decomposition is -3.8931dB, the average signal-to-noise ratio of stochastic resonance is -3.4272dB, and the average signal-to-noise ratio gain is 8.7789dB. The average signal-to-noise ratio of the original signal is -36.8595dB, the average signal-to-noise ratio after empirical mode decomposition is -18.0963dB, the average signal-to-noise ratio after stochastic resonance is -15.972dB, the average signal-to-noise ratio of the overall gain is 20.8875dB, the signal-to-noise ratio The increase of the gain shows that under the stochastic resonance after empirical mode decomposition, the noise is almost eliminated, and the signal energy is also increased, so that the signal can also be detected at the oversampling 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.