CN105488341B - A kind of denoising method based on mixing empirical mode decomposition - Google Patents
A kind of denoising method based on mixing empirical mode decomposition Download PDFInfo
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Abstract
The invention discloses one kind based on mixing empirical mode decomposition（Empirical Mode Decomposition, abbreviation EMD）Denoising method, belong to digital signal processing technique field.EEMD and MEMD algorithms are combined by the present invention, and carry out parameter optimization for the mask signal frequency used in MEMD algorithms, can more effectively eliminate modal overlap, denoising effect is more preferable；The present invention further in EEMD addition noise amplitude, the filtering threshold of noise correlation IMF, noise IMF filtering threshold targetedly optimized, so as to further improve global de-noising effect.Compared with prior art, the method for the present invention can more effectively eliminate modal overlap, and denoising effect is more preferable.
Description
Technical field
The present invention relates to a kind of denoising method more particularly to one kind based on mixing empirical mode decomposition (Empirical
Mode Decomposition, abbreviation EMD) denoising method, belong to digital signal processing technique field.
Background technology
(Ensemble Empirical Mode Decomposition gather empirical modal by EMD and the EEMD of derivation
Decompose) and masking signal EMD (mask signal method empirical mode decomposition, behind abbreviation MEMD in text) be in recent years
The signal processing method to grow up.It is decomposed based on signal time scale, is believed suitable for non-linear and unstable state
Number processing, due to not needing to determine the subjective experiences parameter setting such as basic function and Decomposition order, in some cases, compares wavelet transformation
With better discomposing effect.Nevertheless, EMD also has some problems and defect of oneself., mainly there is endpoint effect in the problem of EMD
It answers, modal overlap.For EEMD although EMD can be solved the problems, such as to a certain extent, it is uncertain to add in noise amplitude.EEMD
In practical applications, especially when signal-to-noise ratio is relatively low, modal overlap problem still remains, and the noise that EEMD is added at this time can be letter
Number noise decomposed as useful signal, so as to bring modal overlap and more falseness IMF (Spurious
modes).In addition, the amplitude selection of the ensemble noise of EEMD is related with the signal-to-noise ratio of signal, noise amplitude is accurately selected
There is certain difficulty, many experiments show when signal-to-noise ratio is low, and EMD decomposition will be advantageously.MEMD is determined by adding
High frequency mask signal solve the problems, such as extreme's distribution, therefore for modal overlap, MEMD has apparent advantage and meter
Calculate efficiency.Amplitude and the frequency parameter selection of the mask signal of MEMD are a committed steps, although giving reference value in text,
But in practical applications, reference frequency is often below the required requirements of masking signal, thus cannot reach elimination mould
The ideal effect of state aliasing, therefore, for different signals, the result of the parameter calculating of recommendation is simultaneously non-optimal.IMF filtering is main
There are wavelet filter, EMD directly to filter (EMD-DT) and EMD sections filtering (EMD-IT) and related derivative filtering method,
Middle small echo threshold coefficient error is larger, is not easy to find accurately in practice；EMD-DT cannot be guaranteed the continuity of signal, for more
The signal filtering signal of a amplitude range is bad；Although EMD-IT can guarantee the continuity of signal, but cannot guarantee that low order
The filtering performance of several value signals of IMF.To sum up, feature there are two EMD-IT filtering mainly, first, find relative
After (noise is related) IMF, " noise " IMF of low order is directly abandoned, does not account for the active ingredient wherein carried；Second, filter
Wave threshold value is not adaptive, and there are large errors for the filtering of several value signals for single threshold strategies.
Invention content
The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and to provide one kind based on mixing empirical modal
EEMD and MEMD algorithms are combined by the denoising method of decomposition, this method, and for the mask signal used in MEMD algorithms
Frequency carries out parameter optimization, can more effectively eliminate modal overlap, denoising effect is more preferable.
Technical solution of the present invention is specific as follows：
A kind of denoising method based on mixing empirical mode decomposition, includes the following steps：
Step 1 decomposes original signal using gathering empirical mode decomposition EEMD methods, obtains a series of natural modes
State component IMF and discrepance, and noise IMF, noise correlation IMF, useful IMF are determined from all IMF；
Step 2, to noise IMF, IMF related to noise carries out threshold filter denoising, and using mask signal method to useful
The signal that IMF is formed carries out the elimination of modal overlap；Wherein, mask signal frequency used in mask signal method is according to following
Method determines：The signal formed first to useful IMF carries out first derivation, obtains first derivative signal；Then Xi Er is utilized
Bert transform method obtains the instantaneous frequency of the first derivative signal, then asks for the mean value of instantaneous frequency；Finally to described
The mean value of instantaneous frequency is multiplied by the weights that a value range is (1,2), and gained product is mask signal frequency；
Step 3, the noise IMF to after threshold filter denoising, noise correlation IMF eliminate the useful IMF institutes structure of modal overlap
Into signal and discrepance carry out signal reconstruction.
In order to improve the performance of EEMD, present invention further proposes following improvement project, to the addition noise in EEMD
Amplitude optimizes:
The amplitude of addition noise used in the EEMD methods predefines by the following method：First to original letter
It number is filtered, obtains filtered signal, and add the noise of different amplitudes respectively to original signal, obtain one group and add letter of making an uproar
Number；Then following handle is carried out respectively to each noisy signal：Empirical mode decomposition is carried out, and from experience to the noisy signal
Useful IMF is determined in the obtained IMF of mode decomposition；The related root mean square calculated between each useful IMF and filtered signal misses
The summation of related coefficient between the summation of difference and every two neighboring useful IMF；Finally made an uproar with minimum the adding of the sum of two summations
Amplitude of the amplitude of addition noise corresponding to signal as the addition noise used in EEMD methods.
In order to improve the threshold filter effect to noise correlation IMF, present invention further proposes following improvement projects：
Filtering threshold used in carrying out threshold filter denoising to noise correlation IMF determines in accordance with the following methods：First will
Each noise correlation IMF carries out decorrelative transformation with noise IMF respectively；According to amplitude is positive and negative will be after each decorrelative transformation
IMF points of noise correlation is two parts, obtains its amplitude mean value and energy filter threshold value respectively to each section, and the two is added
Power is summed to get the filtering threshold of the part.
In order to more effectively extract the useful information in noise IMF, present invention further propose that following improvement project：
Filtering threshold used in carrying out threshold filter denoising to noise IMF determines in accordance with the following methods：Calculate noise IMF
Amplitude mean value, and in noise IMF be more than amplitude mean value each amplitude carry out time-sequencing, obtain the time of the amplitude
Sequence；Periodic authentication is carried out respectively for the time series of obtained each amplitude, and therefrom selects periodically higher portion
Divide time series；Finally using the minimum value of amplitude corresponding to selected part-time sequence as the filtering threshold.
Compared with prior art, it the present invention and its is further improved technical solution and has the advantages that：
EEMD and MEMD algorithms of the present invention are combined, and are joined for the mask signal frequency used in MEMD algorithms
Number optimization, can more effectively eliminate modal overlap, denoising effect is more preferable；
The present invention is optimized further directed to the addition noise amplitude in EEMD, the Relative RMSE of useful IMF
The minimum selection criteria as EEMD addition noise amplitudes of the sum of value and related coefficient, so as to more effectively solve end effect
Caused problem；
The present invention is optimized further directed to the filtering threshold of noise correlation IMF, and plan is separated using positive and negative signal amplitude
Slightly, by decorrelation, take mean value and last filtering threshold determined according to the aspect of energy three, the filter to noise correlation IMF
Wave effect is more preferable；
The present invention further using the useful information in the method for periodic authentication extraction noise IMF, is avoided and is directly lost
The loss of useful information, further improves denoising effect caused by abandoning.
Description of the drawings
Fig. 1 is the flow diagram for determining EEMD addition noise amplitude methods；
Fig. 2 is the flow diagram of MEMD mask signal frequency determination methods；
The filtering threshold that Fig. 3 is noise correlation IMF determines method flow schematic diagram.
Specific embodiment
Technical scheme of the present invention is described in detail below in conjunction with the accompanying drawings：
The basic ideas of the present invention are to be combined EEMD and MEMD algorithms, and for the mask used in MEMD algorithms
Signal frequency carries out parameter optimization, can more effectively eliminate modal overlap, denoising effect is more preferable；The present invention is further in EEMD
Addition noise amplitude, the filtering threshold of noise correlation IMF, noise IMF filtering threshold targetedly optimized, thus into
One step improves global de-noising effect.
For the ease of public understanding, technical solution of the present invention is described in detail with a preferred embodiment below.
The present invention is based on the denoising methods of mixing empirical mode decomposition, specifically include following steps：
Step 1 decomposes original signal using gathering empirical mode decomposition EEMD methods, obtains a series of natural modes
State component IMF and discrepance, and noise IMF, noise correlation IMF, useful IMF are determined from all IMF.
Traditional EEMD methods can be used in this step to the decomposition of original signal or improve EEMD methods.EEMD is existing
Technology, detailed content can be found in document [Wu.Zhaohua, Huang N E, Ensemble empirical mode
decomposition:a noise assisted data analysis method,Adv.Adapt.DataAnal.1(1)
(2009)1–41.]。
As a kind of innovatory algorithm of EMD, EEMD although EMD can be solved the problems, such as to a certain extent, make an uproar by addition
Acoustic amplitude is uncertain.In practical applications, especially when signal-to-noise ratio is relatively low, modal overlap problem still remains EEMD, this
When the noises that add in of EEMD the noise of signal can be decomposed as useful signal, so as to bring modal overlap and more
False IMF (Spurious modes).In addition, the amplitude selection of the ensemble noise of EEMD and the signal-to-noise ratio of signal have
It closes, it is accurate that noise amplitude is selected to have certain difficulty.For this purpose, the present invention improves existing EEMD methods, make an uproar to addition
Acoustic amplitude optimizes, and the sum of the Relative RMSE values of useful IMF and related coefficient is minimum as EEMD addition noise width
The selection criteria of value, so as to more effectively solve the problems, such as caused by end effect.Specifically, as shown in Figure 1, the EEMD
The amplitude of addition noise used in method predefines by the following method：
Rough filtering (for the sake of simplicity, it is preferred to use median filter method) is carried out to original signal first, is filtered
Signal after wave, and add the noise of different amplitudes respectively to original signal, obtain one group of noisy signal；Preferably, it adds and makes an uproar
The amplitude section of sound is 0.001-0.4 times of original signal standard deviation；
Then following handle is carried out respectively to each noisy signal：EMD decomposition is carried out, and from EMD to the noisy signal
It decomposes and useful IMF is determined in obtained IMF；Calculate the related root-mean-square error between each useful IMF and filtered signal
The summation of related coefficient between the summation of Relative RMSE and every two neighboring useful IMF；Finally with two summations it
The amplitude of addition noise corresponding to the noisy signal of (representing the parameter by the use of Rel-Corr RMSE) minimum is as EEMD side
The amplitude of addition noise used in method.The mathematical expression of Rel-Corr RMSE is specific as follows：
Wherein,It is signal of the original signal after mean filter, ci,rel(k) it is i-th of useful IMF, corr ()
Expression seeks related coefficient to two signals in bracket.
After the amplitude for determining addition noise, you can original signal is decomposed using EEMD, and determines noise IMF, make an uproar
Acoustic correlation IMF and useful IMF.
Step 2, to noise IMF, IMF related to noise carries out threshold filter denoising, and using mask signal method to useful
The signal that IMF is formed carries out the elimination of modal overlap；Wherein, mask signal frequency used in mask signal method is according to following
Method determines：The signal formed first to useful IMF carries out first derivation, obtains first derivative signal；Then Xi Er is utilized
Bert transform method obtains the instantaneous frequency of the first derivative signal, then asks for the mean value of instantaneous frequency；Finally to described
The mean value of instantaneous frequency is multiplied by the weights that a value range is (1,2), and gained product is mask signal frequency.
The signal formed in the present embodiment using improved MEMD algorithms to useful IMF carries out the elimination of modal overlap,
And to noise IMF, IMF related to noise carries out threshold filter respectively using the filtering threshold optimized.It illustrates separately below.
(1) optimization of mask signal frequency
In practical applications, reference frequency is often below the required requirements of masking signal to existing MEMD algorithms, because
And the ideal effect for eliminating modal overlap cannot be reached, therefore, for different signals, the result that the parameter of recommendation calculates is not
It is optimal.For this purpose, the present invention improves existing MEMD algorithms, mixed by optimizing mask signal frequency to promote elimination mode
Folded effect.Specifically, as shown in Fig. 2, mask signal frequency determines in accordance with the following methods used in mask signal method：
The signal formed first to useful IMF carries out first derivation, obtains first derivative signal；Assuming that useful IMF institutes
The signal of composition is x1=x2+x3, x in ingredient2、x3Corresponding frequency is f1、f2, and assume f2>f1, then have：
x1'=x2′+x3′ (2)
First derivative is sought in apostrophe representative above.
Then the instantaneous frequency of the first derivative signal is obtained using Hilbert transform methods, and asks for instantaneous frequency
Mean value；Its mathematical expression is as follows：
Wherein, H [(x1')] it is exactly to ask for Hilbert transformation,Represent the equal of the instantaneous frequency that Hilbert transformation acquires
Value, f1' (i) represents instantaneous frequency, f2Represent the frequency values of the highest ingredient of frequency in aliasing signal.
The weights that a value range is (1,2) are finally multiplied by the mean value f of instantaneous frequency, gained product is mask letter
Number frequency fmask, i.e.,：
(2) the filtering threshold optimization of noise correlation IMF
Problem is determined to the threshold value of noise correlation IMF, it is contemplated that asymmetry of the signal in noise IMF is needed to original
The positive and negative separate computations of signal framing value.First noise correlation IMF (IMFk) and noise IMF (IMF k=2,3...1) carry out
Decorrelation operates, removal partial noise interference, as shown in formula (6).Then the mean value of signal amplitude is asked for, such as formula (7) institute
Show, the comprehensive measurement as noise and useful signal；Further according to energy threshold formulaDetermine corresponding energy
Filtering threshold is measured, processing finally is weighted to the mean value of signal amplitude and energy filter threshold value, obtains final noise threshold,
Such as formula (7), (8).
Wherein, IMFKFor noise correlation IMF, IMF1For noise IMF, | ci| for the absolute value of IMF each point amplitudes, TmeanFor
The mean value of signal amplitude, N are signal number.For IMF1Energy square,For the energy estimators of k-th of IMF, β, ρ, C
It is constant, β=0.719, ρ=2.01, C ∈ [0.1,1.4], TuniFor the filtering threshold finally used.Two during weighted sum
A weights a1、a2Usually all it is 0.5.
(3) the filtering threshold optimization of noise IMF
The prior art is typically directly to abandon noise IMF, it is possible to lose useful information therein.The present embodiment thus
It is middle to determine filtering threshold using the method for periodic authentication, fully to extract the useful information in noise IMF.Specifically, to making an uproar
Filtering threshold used in sound IMF progress threshold filter denoisings determines in accordance with the following methods：The amplitude mean value of noise IMF is calculated,
And time-sequencing is carried out to each amplitude for being more than amplitude mean value in noise IMF, obtain the time series of the amplitude；For institute
The obtained time series of each amplitude carries out periodic authentication respectively, and therefrom selects periodically higher part-time sequence；
Finally using the minimum value of amplitude corresponding to selected part-time sequence as the filtering threshold.
Periodic authentication method in the present embodiment is specific as follows：To the time series of the amplitude, first adjacent amplitude
Time difference is in chronological sequence ranked sequentially, and obtains first time difference sequence, and calculates the mean value k of these time differences；Then to
Adjacent time difference makes the difference and is in chronological sequence ranked sequentially difference again in one time difference sequence, obtains the second time difference sequence；
To each data in the second time difference sequence, the quotient obtained by itself divided by mean value k and predetermined threshold value α are compared, less than α,
1 is assigned a value of, otherwise, is assigned a value of 0, so as to obtain a binary sequence；The Lempel-Ziv for calculating the binary sequence is complicated
Degree, complexity is lower, then the time series of the amplitude corresponding to the binary sequence is periodically higher.
Its algorithm is expressed as follows：Assuming that the time series of similar magnitude through making the difference obtained second time difference sequence twice
For { c (n1),c(n2),…,c(nm), binary conversion treatment is carried out to the second time difference sequence by following formula, obtains one new two
System sequence { Bc (n1),Bc(n2),…,Bc(nm)}：
Then binary sequence { Bc (n are calculated1),Bc(n2),…,Bc(nm) Lempel-Ziv complexities CLZN, and root
Whether the time series for judging the amplitude according to Lempel-Ziv complexities has periodically：
Wherein, c (ni) for i-th of element in the second time difference sequence；Bc(ni) for i-th yuan in binary sequence
Element；CLZNFor Lempel-Ziv complexities；β is the threshold value of Lempel-Ziv complexities, is to judge whether signal has periodically
Final step generally takes 0.5 the following value (the smaller the better).
Step 3, the noise IMF to after threshold filter denoising, noise correlation IMF eliminate the useful IMF institutes structure of modal overlap
Into signal and discrepance carry out signal reconstruction.
Claims (6)
1. a kind of denoising method based on mixing empirical mode decomposition, which is characterized in that include the following steps：
Step 1 decomposes original signal using gathering empirical mode decomposition EEMD methods, obtains a series of natural mode of vibration point
IMF and discrepance are measured, and noise IMF, noise correlation IMF, useful IMF are determined from all IMF；Made in the EEMD methods
The amplitude of addition noise predefines by the following method：Original signal is filtered first, obtains filtered signal,
And add the noise of different amplitudes respectively to original signal, obtain one group of noisy signal；Then each noisy signal is distinguished
Carry out following handle：Empirical mode decomposition is carried out, and determined from the obtained IMF of empirical mode decomposition to the noisy signal
Use IMF；Calculate the summation of the related root-mean-square error between each useful IMF and filtered signal and per two neighboring useful
The summation of related coefficient between IMF；Finally with the amplitude of the addition noise corresponding to the noisy signal of the sum of two summations minimum
Amplitude as the addition noise used in EEMD methods；
Step 2, to noise IMF, IMF related to noise carries out threshold filter denoising, and using mask signal method to useful IMF institutes
The signal of composition carries out the elimination of modal overlap；Wherein, mask signal frequency used in mask signal method is in accordance with the following methods
It determines：The signal formed first to useful IMF carries out first derivation, obtains first derivative signal；Then Hilbert is utilized
Transform method obtains the instantaneous frequency of the first derivative signal, then asks for the mean value of instantaneous frequency；Finally to described instantaneous
The mean value of frequency is multiplied by the weights that a value range is (1,2), and gained product is mask signal frequency；
Step 3, the noise IMF to after threshold filter denoising, noise correlation IMF eliminate what the useful IMF of modal overlap was formed
Signal and discrepance carry out signal reconstruction.
2. denoising method as described in claim 1, which is characterized in that the width of the noise of different amplitudes added to original signal
The original signal standard deviation of ranging from 0.001-0.4 times of value.
3. denoising method as described in claim 1, which is characterized in that threshold filter denoising is carried out to noise correlation IMF and is used
Filtering threshold determine in accordance with the following methods：Each noise correlation IMF is subjected to decorrelative transformation with noise IMF respectively first；Root
It is two parts according to positive and negative IMF points of the noise correlation by after each decorrelative transformation of amplitude, obtains its width respectively to each section
It is worth mean value and energy filter threshold value, and by the two weighted sum to get the filtering threshold of the noise correlation IMF after decorrelative transformation
Value.
4. denoising method as claimed in claim 3, which is characterized in that summation is weighted to amplitude mean value and energy filter threshold value
When, the weights of the two are 0.5.
5. denoising method as described in claim 1, which is characterized in that filter used in threshold filter denoising is carried out to noise IMF
Wave threshold value determines in accordance with the following methods：The amplitude mean value of noise IMF is calculated, and to being more than each of amplitude mean value in noise IMF
A amplitude carries out time-sequencing, obtains the time series of the amplitude；The time series of obtained each amplitude is carried out respectively
Periodic authentication, and therefrom select periodically higher part-time sequence；It is finally right with selected part-time sequence institute
The minimum value of amplitude is answered as the filtering threshold.
6. denoising method as claimed in claim 5, which is characterized in that for the time series of any one amplitude, the period
Property verification it is specific as follows：To the time series of the amplitude, first the time difference of adjacent amplitude is in chronological sequence ranked sequentially, is obtained
First time difference sequence, and calculate the mean value k of these time differences；Then adjacent time difference in first time difference sequence is made the difference again
And be in chronological sequence ranked sequentially difference, obtain the second time difference sequence；It, will to each data in the second time difference sequence
Quotient obtained by itself divided by mean value k is compared with predetermined threshold value α, less than α, is assigned a value of 1, otherwise, is assigned a value of 0, so as to obtain one
A binary sequence；The Lempel-Ziv complexities of the binary sequence are calculated, complexity is lower, then binary sequence institute is right
The periodicity of the time series for the amplitude answered is higher.
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