CN101887405B - Binary masking signal technique-based empirical mode decomposition signal processing method - Google Patents

Abstract

The invention discloses a binary masking signal technique-based empirical mode decomposition signal processing method, particularly relates to an unstable signal processing method and belongs to the field of signal processing. In the method, an empirical mode decomposition (EMD) method in signal processing is improved by a binary masking signal technique, a signal to be tested is decomposed into a plurality of narrow-band sub-signals of a set of intrinsic mode function, and useful information can be further extracted from subband signals. The method can improve the resolution of EMD and helps to solve the mode mixing problem of the EMD. Compared with a masking signal-based EMD method, the method has simpler and easier operation and can be used in signal processing and detection in various fields such as mechanical vibration, radar, acoustics, earthquake and the like.

Description

A kind of based on two advance masking signal technology empirical modal decomposed signal disposal route

Technical field

The present invention relates to a kind of based on two advance masking signal technology empirical modal decomposed signal disposal route, relate to a kind of non-stationary signal disposal route particularly, belong to the signal Processing field.

Background technology

In the signal Processing of numerous field of engineering technology such as mechanical vibration, acoustics, biology, thalassography, earthquake, meteorology and radar, often need the non-stationary signal of a large amount of existence be analyzed, reach the extraction practical information and be convenient to application aims.Just depend on advanced signal processing method such as extracting failure symptom in the non-stationary signal of slave unit vibration.Traditional disposal route has: Fourier conversion in short-term, Wigner-Ville distribution, the distribution of Cohen class and wavelet transformation etc.; From broad sense; These methods all are that certain correction has been carried out in the Fourier conversion, and the Fourier conversion is suitable for handling stationary signal.(empirical mode decomposition EMD) designs for handling non-stationary signal, in the signal Processing of numerous field of engineering technology, is used on a large scale at present in the empirical modal decomposition.We have proposed the empirical mode decomposition method that advances masking signal technology based on two in the present technique scheme, and this method can be improved the resolution of the EMD method of prior art, and can improve the real-time of the EMD method of prior art.

For content of the present invention is described better, faces empirical mode decomposition method and masking signal technology down and briefly introduce.

Propose the EMD method in 1998 by people such as Norden E.Huang, can handle non-stationary signal adaptively, received extensive concern.

The purpose that EMD decomposes is multiple-frequency signal to be resolved into be referred to as eigenmode state function (intrinsic modefunction, some narrow band sub-signals IMF), and the time-varying characteristics that the instantaneous frequency of IMF more can the accurate description signal.IMF need satisfy two conditions: 1) in whole data field, Local Extremum (comprising local maximum and local minimum) must equate with the zero crossing number or differ one at the most; 2) in the arbitrfary point, the mean value of the lower envelope line that coenvelope line that is made up of local maximum and local minimum constitute is zero.IMF has reflected the inherent undulatory property of signal.

For given signal x (t); After discretize, obtain signal x (n); Make

i ← 1; J ← 1, wherein ← the expression assignment operation, EMD computation process comprises the steps:

A1. find out all Local Extremum of signal

;

A2. respectively local maximum value minimal value sequence is carried out the match of segmentation cubic spline interpolation, form coenvelope line e _u(n) and lower envelope line e _d(n);

A3. calculate the average of upper and lower envelope: m _{I, j}(n)=(e _u(n)+e _d(n))/2;

A4. from signal, deduct average:

A5. judge whether to satisfy given screening stopping criterion? If satisfy then can think h _{I, j}(n) be an IMF, order: c _i(n)=h _{I, j}(n); If do not satisfy, upgrade J ← j+1 repeats above A1 to the A4 step;

A6. calculate remainder: make i ← i+1; J ← 1; Repeat above A1 to the A5 step, obtain another IMF subband signal;

A7. repeat above A1 to the A6 step until satisfying termination condition (signal to be decomposed dull or can not decompose again).

Steps A 1 to A4 is called as once screening, and like this, through the decomposition of EMD, signal x (n) just is broken down into limited IMF component and a remainder.

EMD is based on the method for experience, and simulation analysis and experimental study are still the main method of research EMD.Can regard EMD as one two for white noise and Gaussian noise and advance bank of filters.But, by tending to exist some overlapping between the direct IMF subband signal frequency band that extracts of EMD.And also there are problems such as mode aliasing, real-time difference in EMD.

Masking signal (masking signals) technology is initial to be exactly that afterwards, it came to light again and can improve the resolution of EMD with the mode aliasing problem that solves EMD.To be referred to as EMD-MS based on the EMD of masking signal among the present invention.Masking signal is typically designed to:

s _m(t)＝A _mcos(2πf _mt)

A in the formula _mAnd f _mAmplitude and the frequency of representing masking signal respectively.

The common method of structure masking signal is based on quick Fourier transformation (FFT) technology, just earlier signal is carried out the FFT conversion, estimates the frequency and the ordering of signal, and then designs the frequency of masking signal through the estimated signals frequency.But because EMD and FFT are two distinct methods, construct masking signal through the FFT technology and seem not too harmonious with the mode aliasing problem that solves EMD, and too complicated based on the masking signal constructor of FFT, poor practicability.

Summary of the invention

The objective of the invention is in order to use EMD to have mode aliasing and real-time difference in the signal Processing that solves practical engineering application and, proposed a kind ofly to advance the technological empirical modal decomposed signal disposal route of masking signal based on two based on the masking signal constructor complicated problems of FFT.

The principle of this method is improved the EMD in the signal Processing for advancing masking signal (dyadic masking signals) technology with two, is referred to as the EMD that advances masking signal technology based on two among the present invention, is designated as EMD-DMS.This method can resolve into one group of IMF subband signal with measured signal, and then can from the IMF subband signal, extract useful information.

The concrete performing step of this method is following:

Step 1; Initialization; For given signal x (t); After discretize, obtain signal x (n), make

count parameter i ← 1.

Step 2 on the basis of step 1, is set the original frequency f of masking signal _{M, 1}

Frequency f _{M, i}(i=1,2 ...) span be f _{M, i}≤f _s/ 2, f wherein _sThe discrete sampling rate of expression original signal.

Frequency f _{M, 1}Be two to advance the key parameter of masking signal, be called original frequency.

Step 3, on the basis of step 2, structure two advances masking signal s _{M, i}(t), and with its discretize obtain masking signal s _{M, i}(n).

Described two to advance the building method of masking signal following:

Wherein,

The expression initial phase, Span be [0, π], two advance the amplitude A of masking signal _{M, i}Can confirm by following formula

$A_{m,i}=\frac{U_m}{L}\underset{l=1}{\overset{L}{\∑}}\left|y_D\left(l\right)\right|---\left(2\right)$

U wherein _mBe constant, be called amplitude factor, the number of L expression signal x (n) local maximum, y _D(l) the local maximum value sequence of expression signal x (n).Extreme value rate in order to obtain expecting needs U usually _mValue enough big, but too big U _mValue may be flooded original signal again, recommends U here _mValue between 5 and 20.

Step 4, obtain the masking signal of discretize in step 3 after, to

Carry out following steps, obtain the IMF subband signal z of a positive ₊(n)=h _{I, j}(n):

A1. make count parameter j ← 1, find out all Local Extremum of signal

;

A2. respectively local maximum value minimal value sequence is carried out the match of segmentation cubic spline interpolation, form coenvelope line e _u(n) and lower envelope line e _d(n);

A3. calculate the average of upper and lower envelope: m _{I, j}(n)=(e _u(n)+e _d(n))/2;

A4. from signal, deduct average:

A5. judge whether to satisfy given screening stopping criterion? If satisfy then can think h _{I, j}(n) be an IMF, order: z ₊(n)=h _{I, j}(n); If do not satisfy, upgrade

J ← j+1 repeats above A1 to the A4 step.

Similarly, to

Carry out following steps, obtain the IMF subband signal z of a negative _-(n)=h _{I, j}(n):

B1. make count parameter j ← 1, find out all Local Extremum of signal

;

B2. respectively local maximum value minimal value sequence is carried out the match of segmentation cubic spline interpolation, form coenvelope line e _u(n) and lower envelope line e _d(n);

B3. calculate the average of upper and lower envelope: m _{I, j}(n)=(e _u(n)+e _d(n))/2;

B4. from signal, deduct average:

B5. judge whether to satisfy given screening stopping criterion? If satisfy then can think h _{I, j}(n) be an IMF, order: z _-(n)=h _{I, j}(n); If do not satisfy, upgrade J ← j+1 repeats above B1 to the B4 step.

Step 5 after step 4 obtains positive and negative IMF subband signal, calculates an IMF subband signal c _i(n)=[z ₊(n)+z _-(n)]/2.

Step 6 on the basis of step 5, is calculated remainder.

From original signal x (n), deduct the IMF sum that obtains, just obtain a remainder $r_i\left(n\right)=x\left(n\right)-\underset{i}{\∑}{c}_i\left(n\right).$

Step 7 judges whether to satisfy termination condition, and promptly the number of IMF satisfies actual needs or signal to be decomposed

Can not decompose again? If do not satisfy, then upgrade f _{M, i+1}← f _{M, i}/ 2 and i ← i+1. repeating step 3 to step 6, extract next IMF subband signal.If satisfy termination condition, then finish to decompose.

Signal has just obtained one group of IMF subband signal, and then can be easy to from these subband signals, extract Useful Information after the EMD-DMS of above step decomposes.

Beneficial effect

The present invention utilizes two to advance the masking signal technology and improve EMD, both can improve the resolution of EMD, helps to solve the mode aliasing problem of EMD again.Advance masking signal only disposable given original frequency of need and amplitude factor and construct two, therefore operand is compared with EMD-MS much smaller than the masking signal of structure based on the FFT technology, and EMD-DMS is more simple to operation.And the IMF subband signal that is extracted by EMD-DMS has more reasonably composes structure; Under the situation of same screening number of times, EMD-DMS has obtained the rational more IMF subband signal than EMD, thereby has improved the real-time of EMD.Method of the present invention can be widely applied in the signal Processing and detection of numerous areas such as mechanical vibration, radar, acoustics, earthquake.

Description of drawings

Fig. 1 is an EMD-DMS process flow diagram of the present invention;

Fig. 2 be in the embodiment EMD-DMS and EMD to the decomposition result contrast of white Gaussian noise;

Fig. 3 is embodiment air compressor actual signal and frequency spectrum thereof;

The IMF subband signal of Fig. 4 for adopting EMD-DMS from Fig. 3 signal, to extract in the embodiment;

The IMF subband signal of Fig. 5 for adopting EMD from Fig. 3 signal, to extract in the embodiment;

Fig. 6 is the frequency spectrum of each IMF subband signal among Fig. 4;

Fig. 7 is the frequency spectrum of each IMF subband signal among Fig. 5;

Fig. 8 is fan blower actual signal and a frequency spectrum thereof in the embodiment;

The IMF subband signal of Fig. 9 for adopting EMD-DMS from Fig. 8 signal, to extract in the embodiment;

The IMF subband signal of Figure 10 for adopting EMD from Fig. 8 signal, to extract in the embodiment;

Figure 11 is the frequency spectrum of each IMF subband signal among Fig. 9;

Figure 12 is the frequency spectrum of each IMF subband signal among Figure 10.

Embodiment

For objects and advantages of the present invention better are described, the present invention is done further detailed description below in conjunction with accompanying drawing and embodiment:

The process flow diagram of EMD-DMS of the present invention is as shown in Figure 1.

For the ease of in computing machine, handling, continuous signal at first needs discretize; Set the original frequency f of first masking signal then _{M, 1}, because f _{M, 1}Be two to advance the key parameter of masking signal technology, be recommended in here and get f in the practical application _{M, 1}=f _s/ 2, so just can construct masking signal, and then simplify structure, and guarantee that first IMF subband signal that is extracted does not receive the pollution of EMD noise that extraction process produces masking signal according to the discrete sampling rate of signal; Then, one two of structure advances masking signal; And then utilize EMD to extract a positive and an IMF subband signal negative; Obtain an IMF subband signal after it is averaged; Carry out the complementation item again; Next IMF subband signal is extracted in checking as do not satisfy termination condition and then change frequency structure next two and advance masking signal from remainder, so circulation obtains one group of IMF subband signal.

Be the validity of checking the method for the invention, this embodiment has provided three embodiment, and first embodiment is to simulate signal, and second and third embodiment is all to actual signal.

Embodiment 1:

Fig. 2 is for adopting EMD-DMS and the EMD emulation decomposition result contrast to a white Gaussian noise respectively in the present embodiment.The screening stopping criterion is each IMF subband signal screening 10 times.The top view of Fig. 2 is the frequency spectrum of original signal, and its left hurdle down is the frequency spectrum by 6 IMF subband signals of EMD-DMS extraction, and right hurdle is the frequency spectrum that adopts 6 IMF subband signals of EMD extraction under it.

Can find out from the simulation result contrast of Fig. 2 Zuo Xialan and the corresponding figure in hurdle, bottom right; The overlapping IMF that extracts with EMD that obviously will be less than between the IMF frequency band that employing EMD-DMS extracts; Especially only contain radio-frequency component in first IMF subband that EMD-DMS extracts, and contain a large amount of low-frequency components in first IMF subband by the EMD extraction.In addition, compare with EMD, the frequency spectrum of the IMF subband signal that is extracted by EMD-DMS has taken place to move to front end.Through knowing this, EMD-DMS has improved the decomposability of EMD conscientiously.

Embodiment 2:

Fig. 3 is the actual signal that picks up from an air compressor of domestic certain petro-chemical corporation.Wherein, last figure is the time domain waveform of signal, and figure below is the frequency spectrum of signal.By seeing on the original signal spectrum among Fig. 3, contain a large amount of high order harmonics compositions in the vibration signal of this compressor.

The decomposition contrast of 6 IMF subband signals that Fig. 4, Fig. 5 extract when adopting EMD-DMS and EMD to carry out signal Processing respectively for the actual signal to Fig. 3.The screening stopping criterion is each IMF subband signal screening 10 times.Fig. 6 is the frequency spectrum of each IMF subband signal among Fig. 4 of extracting of the employing EMD-DMS of present embodiment.Fig. 7 is the frequency spectrum of each IMF subband signal among Fig. 5 of extracting of the employing EMD of present embodiment.

Can find out through contrast; Except that with Fig. 2 has identical spectrum overlapping phenomenon; This example is also found out: EMD-DMS has decomposed the dominant frequency of this signal in the 5th the IMF subband (shown in the C5 of Fig. 4); EMD has then decomposed its dominant frequency in the 3rd the IMF subband (shown in the C3 of Fig. 5), we can say that therefore the IMF subband signal number that is extracted by EMD-DMS will be more than EMD.In addition, Fig. 5 shows in the decomposition result of EMD and has the mode aliasing, and do not have the mode aliasing among Fig. 4 in the decomposition result of EMD-DMS.

Embodiment 3:

Fig. 8 is the start-up course vibration signal that picks up from domestic certain fan blower of company, and wherein, last figure is the time domain waveform of signal, and figure below is the frequency spectrum of signal.

The decomposition contrast of 7 IMF subband signals that Fig. 9, Figure 10 extract when adopting EMD-DMS and EMD to carry out signal Processing respectively for the actual signal to Fig. 8.The screening stopping criterion is each IMF subband signal screening 10 times.Wherein, the R figure of Fig. 9 is a remainder, and each sub-graphs is the IMF subband signal that EMD-DMS extracts on it, and the R figure of Figure 10 is a remainder, and each sub-graphs is the IMF subband signal that EMD extracts on it.

Figure 11 is the frequency spectrum of each IMF subband signal among Fig. 9 of extracting of the employing EMD-DMS of present embodiment.Figure 12 is the frequency spectrum of each IMF subband signal among Figure 10 of extracting of the employing EMD of present embodiment.

Figure 10 shows in the decomposition result of EMD and has the mode aliasing, and on IMF subband spectrum shown in Figure 12, can see that EMD can't distinguish the low-and high-frequency composition effectively, from the IMF subband that EMD extracts, is difficult to obtain valuable information.And in contrast thereto; From Fig. 9 and combine IMF subband spectrum shown in Figure 11; Can see that EMD-DMS resolves into a plurality of subband signals with signal successively from the high frequency to the low frequency; Only exist a bit overlapping between these subband signals, these subband signals have been described the fluctuation information of different frequency composition from the time domain angle.

More than three embodiment can know the decomposition contrast of simulate signal and two actual signals with EMD through investigating EMD-DMS: the EMD-DMS of the present invention's proposition can obviously improve the performance of EMD; Prevent the generation of EMD mode aliasing, the IMF subband signal that is extracted by EMD-DMS has more reasonably composes structure; Under a small amount of screening round-robin situation, EMD-DMS just can obtain rational IMF subband signal, thereby has improved the real-time of EMD.

Above-described specific descriptions; Purpose, technical scheme and beneficial effect to invention have carried out further explain, and institute it should be understood that the above is merely specific embodiment of the present invention; And be not used in qualification protection scope of the present invention; All within spirit of the present invention and principle, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. One kind based on two advance masking signal technology empirical modal decomposed signal disposal route, it is characterized in that comprising the steps:

   Step 1; Initialization; For given signal x (t); After discretize, obtain signal x (n), make variable

   

   make count parameter i=1;

   Step 2 on the basis of step 1, is set the original frequency f of masking signal _{M, 1}

   Frequency f _{M, i}Span be f _{M, i}≤f _s/ 2, i=1 wherein, 2 ..., f _sThe discrete sampling rate of expression original signal;

   Frequency f _{M, 1}Be two to advance the key parameter of masking signal, be called original frequency;

   Step 3, on the basis of step 2, structure two advances masking signal s _{M, i}(t), and with its discretize obtain masking signal s _{M, i}(n);

   The concrete building method of masking signal is following:

   

   Wherein,

   

   The expression initial phase,

   

   Span be [0, π], two advance the amplitude A of masking signal _{M, i}Can confirm by following formula

   $A_{m,i}=\frac{U_m}{L}\underset{l=1}{\overset{L}{\mathrm{\Σ}}}\left|y_D\left(l\right)\right|$

   U wherein _mBe constant, be called amplitude factor, the number of L expression signal x (n) local maximum, y _D(l) the local maximum value sequence of expression signal x (n); U _mValue between 5 and 20;

   Step 4, obtain the masking signal of discretize in step 3 after, to

   

   Carry out following A1 to A5 step, obtain IMF subband signal z+ (the n)=h of a positive _{I, j}(n):

   A1. make count parameter j=1, find out all Local Extremum of signal

   

   ;

   A2. respectively local maximum value minimal value sequence is carried out the match of segmentation cubic spline interpolation, form coenvelope line e _u(n) and lower envelope line e _d(n);

   A3. calculate the average of upper and lower envelope: m _{I, j}(n)=(e _u(n)+e _d(n))/2;

   A4. from signal, deduct average: $h_{i,j}\left(n\right)={\hat{x}}_{+}\left(n\right)-m_{i,j}\left(n\right);$

   A5. judge whether to satisfy given screening stopping criterion, if satisfy then can think h _{I, j}(n) be an IMF, order: z ₊(n)=h _{I, j}(n); If do not satisfy, upgrade

   

   J=j+1 repeats above A1 to the A4 step;

   Similarly, to Carry out following B1 to B5 step, obtain the IMF subband signal z of a negative _-(n)=h _{I, j}(n):

   B1. make count parameter j=1, find out all Local Extremum of signal ;

   B2. respectively local maximum value minimal value sequence is carried out the match of segmentation cubic spline interpolation, form coenvelope line e _u(n) and lower envelope line e _d(n);

   B3. calculate the average of upper and lower envelope: m _{I, j}(n)=(e _u(n)+e _d(n))/2;

   B4. from signal, deduct average: $h_{i,j}\left(n\right)={\hat{x}}_{-}\left(n\right)-m_{i,j}\left(n\right);$

   B5. judge whether to satisfy given screening stopping criterion, if satisfy then can think h _{I, j}(n) be an IMF, order: z _-(n)=h _{I, j}(n); If do not satisfy, upgrade

   

   J=j+1 repeats above B1 to the B4 step;

   Step 5 after step 4 obtains positive and negative IMF subband signal, calculates an IMF subband signal c _i(n)=[z ₊(n)+z _-(n)]/2;

   Step 6 on the basis of step 5, is calculated remainder;

   From original signal x (n), deduct the IMF sum that obtains, just obtain a remainder $r_i\left(n\right)=x\left(n\right)-\underset{i}{\mathrm{\Σ}}{c}_i\left(n\right);$

   Step 7 judges whether to satisfy termination condition, and promptly the number of IMF satisfies actual needs or signal to be decomposed

   

   Can not decompose again,, then upgrade if do not satisfy

   

   f _{M, i+1}=f _{M, i}/ 2 and i=i+1; Repeating step 3 extracts next IMF subband signal to step 6; If satisfy termination condition, then finish to decompose.

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