CN108510076A - A kind of algorithm of metric sequence confusion degree - Google Patents
A kind of algorithm of metric sequence confusion degree Download PDFInfo
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Abstract
The present invention provides a kind of algorithms of metric sequence confusion degree, new EMD methods are organically combined with fuzzy entropy algorithm, i.e.,：EMD decomposition is carried out to original signal, true IMF components is filtered out with correlation coefficient process, finds out the percentage of energy of the true IMF components of every single order.The product for calculating the fuzzy entropy and percentage of energy per rank IMF, finally carries out summation operation, i.e., obtains final fuzzy entropy by weighted average.
Description
Technical field
The present invention relates to computer display field more particularly to a kind of anti-surfing style computer displays.
Background technology
Entropy can be to the confusion degree of measurement system earliest as the parameter for characterizing substance thermodynamic state. 1948
Year, entropy is introduced into information theory by information theory founder C.E.Shannon according to the concept of information content, it is proposed that comentropy, with
This by measure a time series complexity.Entropy is as a kind of nonlinear characteristic parameters for weighing sequence confusion degree, tool
There are the advantages such as high sensitivity, strong antijamming capability, has been widely used in fault diagnosis, error testing, image segmentation and quality
The different fields [1-6] such as assessment, and achieve good effect.
The type of entropy is various, and the ability of metric sequence confusion degree is also not quite similar, and how to judge that variety classes entropy describes
The size of chaos ability, and a kind of suitable means how to be selected to handle preferably to highlight the feature of entropy time series
Then become to have important practical significance.
Signal can obtain limited from high frequency to low frequency after EMD adaptive decompositions, and can be different-bandwidth, packet
Each order component of gained is called IMF points by the component for having contained signal actual physical information, capable of having reflected signal inside fluctuation
Amount.These IMF components meet：In a complete data segment, the number of extreme point and zero crossing must be identical or at most differs
One；Signal is about time axial symmetry, i.e., no matter which moment signal is in, the coenvelope be made of its local maximum and part
The average value for the lower envelope that minimum is constituted is zero.Empirical mode decomposition algorithm (EMD Empirical Mode
Decomposition) be Hilbert-Huang transformation core algorithm.EMD algorithms are defined by algorithmic procedure, and simultaneously
Non- to be defined by determining theoretical formula, so it is extremely difficult to carry out to it accurate theory analysis, we at present can only be by
A large amount of Digital Simulation experiment constantly carries out in-depth study to its performance.
Invention content
The main purpose of the present invention is to provide a kind of algorithms of metric sequence confusion degree, to solve above-mentioned skill
Art problem.
To achieve the above object, the technical solution that the present invention takes is：
A kind of algorithm of metric sequence confusion degree, which is characterized in that include the following steps：
S1, ambiguity in definition entropy, include the following steps：
S11：It is assumed that given time series x (t)=the pattern dimension of [x (1), x (2) ... x (N)] is m, then it can pass through
Original time series build m dimensional vectors：Xm(i)=[x (i), x (i+1) ... x (i+m-1)]-u (i), i=1 in formula, 2,
... N-m+1,
It enables,
S12：If vector Xm(i),XmThe distance between (j)Formula
Middle i, j=1,2 ... N-m+1；
S13：Introduce fuzzy membership function
In formula：R is similar tolerance, r=R*SD, (SD be former data standard poor),
Therefore two vector Xm(i)、Xm(j) similarity between is represented by:
S14：Defined function
It is available
S15：Step S11-S14 is repeated to m+1 dimensional pattern dimensions
S16：The fuzzy entropy for obtaining former time series is
FuzzyEn (m, r, N)=ln φm(r)-lnφm+1(r)。
S2：Selection emulates signal expression,
S3：Empirical mode decomposition is carried out to x (t)；
S4：The degree of correlation that each the rank IMF and original signal that are decomposed in step S3 are calculated using related coefficient, by setting
Threshold value is determined to reject false IMF components；
Shown in related coefficient is defined as follows：
C is the covariance matrix of matrix [x, IMF] in formula, and x (t) is that original signal obtains after false IMF component rejections
To the true ingredient for reflecting signal.
In a wherein embodiment, empirical mode decomposition includes the following steps in the step S3：
S31：It determines all Local modulus maximas of original signal x (t), all local maximums is connected using cubic spline curve
It is worth point, forms coenvelope；
S32：It determines all local minizing points of signal x (t), all local minimums is connected using cubic spline curve
Point forms lower envelope；
S33：The mean value for calculating upper and lower envelope, is denoted as m1：
x(t)-m1=h1
If h1Meet two conditions of IMF, then h1It is just an IMF of x (t)；
S34：If h1It is not an IMF of x (t), then h1As original signal, repeats step S31-S32 and obtain
The new mean value m of lower envelope line11：
h1-m11=h11
Judge h11Whether meet IMF conditions, such as have not been met, then recirculate k times again, has：
h1k-1-m1k=h1k
Make h1kMeet IMF conditions, enables c1=h1k, c1As the first of signal x (t) IMF；
S35：The c that will be obtained1It separates, has from x (t)：
r1(t)=x (t)-c1(t)
R1(t) it is used as original signal, repeats second IMF that signal can be obtained in step S31-S34：c2, reciprocation cycle n
It is secondary, so that it may to obtain n IMF for belonging to x (t), simultaneously：
Work as rn(t) when becoming a monotonic function cannot decompose again, cycle terminates, and thus obtains：
In above formula, ci(t) i-th of the IMF, r for being x (t)n(t) residual components after being decomposed for x (t).
In a wherein embodiment, as pattern dimension m=1 or 2, similar tolerance r=(0.1-0.25) * SD.
Beneficial effects of the present invention：
The application is organically combined new EMD methods with fuzzy entropy algorithm, i.e.,：EMD decomposition is carried out to original signal,
True IMF components are filtered out with correlation coefficient process, find out the percentage of energy of the true IMF components of every single order.It calculates per rank IMF
Fuzzy entropy and percentage of energy product, finally carry out summation operation, i.e., final fuzzy entropy obtained by weighted average.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described.
Fig. 1 is present invention emulation signal x (t) oscillogram；
Fig. 2 is X (t) of the present invention through EMD treated results 1；
Fig. 3 is X (t) of the present invention through EMD treated results 2；
Fig. 4 is the Hilbert spectrums of true IMF synthesis of the invention；
Fig. 5 is the marginal spectrum of true IMF synthesis of the invention；
Fig. 6 is the flow chart schematic diagram of the present invention.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other without creative efforts
Embodiment shall fall within the protection scope of the present invention.
In order to be addressed further under the details and its advantage of technical solution of the present invention, said in conjunction with drawings and examples
It is bright.The false IMF components decomposed through EMD, the better bodies of true IMF for making decomposition obtain are rejected by related coefficient principle
The ingredient of existing signal, as Fig. 6 includes the following steps：
S1：Fuzzy entropy is defined as follows：
S11：It is assumed that given time series x (t)=the pattern dimension of [x (1), x (2) ... x (N)] is m, then it can pass through
Original time series build m dimensional vectors：Xm(i)=[x (i), x (i+1) ... x (i+m-1)]-u (i), i=1 in formula, 2,
...N-m+1。
It enables,
S12：If vector Xm(i),XmThe distance between (j)Formula
Middle i, j=1,2 ... N-m+1
S13：Introduce fuzzy membership function
In formula：R is similar tolerance, and r=R*SD, (SD is that former data standard is poor), R is scale factor, in practice it has proved that, work as r
When the * SD, i.e. R=0.1~0.25 of=(0.1~0.25), the classifying quality of fuzzy entropy is preferable.
Therefore two vector Xm(i)、Xm(j) similarity between is represented by
S14：Defined function
It is available
The value of fuzzy entropy is ln φm(r)-lnφm+1(r), φ is found outm(r) and φm+1(r).And φmIt (r) then can be by
The formula obtains.And then reverse recursion.
S15：Step S11-S14 is repeated to m+1 dimensional pattern dimensions
S16：The fuzzy entropy for obtaining former time series is
FuzzyEn (m, r, N)=ln φm(r)-lnφm+1(r)
As pattern dimension m=1 or 2, similar tolerance r=(0.1-0.25) * SD, the classifying quality of fuzzy entropy is preferable, tool
There is good statistics.
S2：Selection emulates signal expression,
A represents value different between 0~1.The meaning of the formula is actually signalWith noise with difference
Ratio is mixed.
S3：New empirical mode decomposition.
S31：It determines all Local modulus maximas of original signal x (t), all local maximums is connected using cubic spline curve
It is worth point, forms coenvelope.
S32：It determines all local minizing points of signal x (t), all local minimums is connected using cubic spline curve
Point forms lower envelope.
S33：The mean value for calculating upper and lower envelope, is denoted as m1：
x(t)-m1=h1
Preferably, if h1Meet two conditions of IMF, then h1It is just an IMF of x (t).
S34：If h1It is not an IMF of x (t), then h1As original signal, repeats step S31-S32 and obtain
The new mean value m of lower envelope line11：
h1-m11=h11
Judge h11Whether meet IMF conditions, such as have not been met, then recirculate k times again, has：
h1k-1-m1k=h1k
Make h1kMeet IMF conditions, enables c1=h1k, c1As the first of signal x (t) IMF.
S35：The c that will be obtained1It separates, has from x (t)：
r1(t)=x (t)-c1(t)
R1(t) it is used as original signal, repeats second IMF that signal can be obtained in step S31-S34：c2.Reciprocation cycle n
It is secondary, so that it may to obtain n IMF for belonging to x (t), simultaneously：
Work as rn(t) when becoming a monotonic function cannot decompose again, cycle terminates, and thus obtains：
In formula (21), ci(t) i-th of the IMF, r for being x (t)n(t) residual components after being decomposed for x (t).
S4：The degree of correlation that can reflect each the rank IMF and original signal that decomposition obtains using related coefficient, by setting threshold
Value rejects false IMF components；
Shown in related coefficient is defined as follows：
C is the covariance matrix of matrix [x, IMF] in formula, and x (t) is original signal.After false IMF component rejections, from
It can clearly reflect the true ingredient of signal in spectrogram.
Embodiment one：
Illustrate by taking an emulation signal as an example below, emulation signal x (t) is：
X (t)=(1+0.8sin (2 π 6.5t)) cos (2 π 30t+0.6sin (2 π 10t))+sin (2 π
100t)
Sample frequency fs=1000Hz is set, and time t takes a little between [0,1] with 0.001 at equal intervals.
Signal x (t) waveform is emulated as shown in Fig. 1 emulation signal x (t) waveforms.The signal by a 100Hz sinusoidal signal
It is 30Hz with fundamental frequency, modulating frequency is that the amplitude-modulated signal of 10Hz is formed by stacking.The amplitude of its amplitude-modulated portions is：A (t)=1+
0.8sin(2π·6.5t)
So having：0.2≤a(t)≤1.8
Then to frequency modulation partial analysis, angular frequency is obtained to t derivations：
Frequency can be obtained by above formula：
The mobility scale of frequency is to known to：
24≤f≤36
EMD processing is carried out to x (t), 8 IMF components and 1 remainder can be obtained.As treated through EMD by Fig. 2,3X (t)
As a result shown in.IMF1 and IMF2 corresponds to the sine component and FM amplitude modulation ingredient of signal 100Hz respectively, corresponds to the solution of x (t)
Analysis formula can find that IMF3 to RES is unwanted component.This is because EMD is caused when decomposing using cubic spline difference approach
's.The related coefficient for seeking each rank IMF and original signal in addition to remainder, is shown in Table 1.
The related coefficient of table 1 each rank IMF and original signal
It can be found that IMF1 and IMF2 and the related coefficient of original signal are more significantly more than remaining IMF and original signal
Related coefficient.Herein, given threshold 0.2.I.e. when the related coefficient of IMF and original signal is more than 0.2, rank IMF is
True component, otherwise rank IMF is chaff component.To the more complicated emulation signal analysis shows original signal is passed through with it
The related coefficient of the IMF obtained after EMD processing can differentiate true IMF and falseness IMF to a certain extent.
After false IMF component rejections, to preceding two ranks IMF synthesis Hilbert spectrums and marginal spectrum, such as Fig. 4,5 true IMF
Shown in the Hilbert spectrums and marginal spectrum of synthesis.It can clearly reflect the true ingredient of signal from spectrogram：Signal by
100Hz sinusoidal signals and FM amplitude modulation Signal averaging form, the amplitude fluctuations range of FM amplitude modulation part between 0.2-1.8,
Frequency range is between 24Hz-36Hz.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
With within principle, any modification, equivalent replacement, improvement and so on should all be included in the protection scope of the present invention god.
Claims (3)
1. a kind of algorithm of metric sequence confusion degree, which is characterized in that include the following steps：
S1, ambiguity in definition entropy,
S11：It is assumed that given time series x (t)=the pattern dimension of [x (1), x (2) ... x (N)] is m, then it can be by original
Time series builds m dimensional vectors：Xm(i)=[x (i), x (i+1) ... x (i+m-1)]-u (i), i=1 in formula, 2 ... N-m+
1,
It enables,
S12：If vector Xm(i),XmThe distance between (j)In formula
I, j=1,2 ... N-m+1；
S13：Introduce fuzzy membership function
In formula：R be similar tolerance, r=R*SD,
Therefore two vector Xm(i)、Xm(j) similarity between is represented by:
S14：Defined function
It is available
S15：Step S11-S14 is repeated to m+1 dimensional pattern dimensions
S16：The fuzzy entropy for obtaining former time series is
FuzzyEn (m, r, N)=ln φm(r)-lnφm+1(r)。
S2：Selection emulates signal expression,
S3：Empirical mode decomposition is carried out to x (t)；
S4：The degree of correlation that each the rank IMF and original signal that are decomposed in step S3 are calculated using related coefficient, by setting threshold
Value rejects false IMF components；
Shown in related coefficient is defined as follows：
C is the covariance matrix of matrix [x, IMF] in formula, and x (t) is original signal, after false IMF component rejections, is obtained anti-
Mirror the true ingredient of signal.
2. a kind of algorithm of metric sequence confusion degree as described in claim 1, it is characterised in that：Experience in the step S3
Mode decomposition includes the following steps：
S31：It determines all Local modulus maximas of original signal x (t), all local maximums is connected using cubic spline curve
Point forms coenvelope；
S32：It determines all local minizing points of signal x (t), all local minizing points, shape is connected using cubic spline curve
At lower envelope；
S33：The mean value for calculating upper and lower envelope, is denoted as m1：
x(t)-m1=h1
If h1Meet two conditions of IMF, then h1It is just an IMF of x (t)；
S34：If h1It is not an IMF of x (t), then h1As original signal, repeats step S31-S32 and obtain lower envelope
The new mean value m of line11：
h1-m11=h11
Judge h11Whether meet IMF conditions, such as have not been met, then recirculate k times again, has：
h1k-1-m1k=h1k
Make h1kMeet IMF conditions, enables c1=h1k, c1As the first of signal x (t) IMF；
S35：The c that will be obtained1It separates, has from x (t)：
r1(t)=x (t)-c1(t)
R1(t) it is used as original signal, repeats second IMF that signal can be obtained in step S31-S34：c2, reciprocation cycle n times, just
N IMF for belonging to x (t) can be obtained, simultaneously：
Work as rn(t) when becoming a monotonic function cannot decompose again, cycle terminates, and thus obtains：
In formula, ci(t) i-th of the IMF, r for being x (t)n(t) residual components after being decomposed for x (t).
3. a kind of algorithm of metric sequence confusion degree as described in claim 1, it is characterised in that：As pattern dimension m=1 or
2, similar tolerance r=(0.1-0.25) * SD.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110432891A (en) * | 2019-07-30 | 2019-11-12 | 天津工业大学 | The feature extraction and classification method of electrocardio beat are extracted in a kind of automation |
| CN110781781A (en) * | 2019-10-15 | 2020-02-11 | 山东师范大学 | Time series concept drift detection method, system, medium and equipment |
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2018
- 2018-03-07 CN CN201810183852.7A patent/CN108510076A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110432891A (en) * | 2019-07-30 | 2019-11-12 | 天津工业大学 | The feature extraction and classification method of electrocardio beat are extracted in a kind of automation |
| CN110781781A (en) * | 2019-10-15 | 2020-02-11 | 山东师范大学 | Time series concept drift detection method, system, medium and equipment |
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Application publication date: 20180907 |