CN102359815A - Wavelet fractal combination method for feature extraction of blasting vibration signal - Google Patents

Abstract

The invention discloses a wavelet fractal combination method for feature extraction of a blasting vibration signal. According to the method, on one hand, an optimal wavelet decomposition scale in wavelet threshold denoising processing is determined according to a change law of a fractal dimension on the condition of different decomposition scales; on the other hand, a fractal characteristic of a blasting vibration signal is scientifically verified according to similarity and self similarity of a wavelet component; and it is put forward that a fractal dimension of the blasting vibration signal is utilized as a new dimensionless parameter for characterizing blasting vibration according to a change law of a fractal dimension of the wavelet component of the blasting vibration signal with frequencies. According to the wavelet fractal combination method for feature extraction of a blasting vibration signal provided in the invention, the method has advantages of simple steps and strong operability; besides, a feature of a blasting vibration signal can be accurately obtained and a using demand of feature extraction during the blasting vibration signal analysis in engineering.

Description

A kind of blasting vibration signal characteristic extracting methods based on the small wave fractal combination

Technical field

The method for distilling of blasting vibration signal characteristic of the present invention is specifically related to a kind of blasting vibration signal characteristic extracting methods based on the small wave fractal combination.

Background technology

At present, the vibration effect of explosion that engineering explosion causes is one of most important in the public nuisance from blasting, and through the blasting vibration signal analysis, accurately extracting the blasting vibration characteristic is the basis of carrying out vibration effect of explosion analysis and blasting vibration harm control.

Because the blasting vibration signal belongs to typically nonstationary random process in short-term, be based upon methods such as Fourier conversion traditional on the stationary process and can't have reacted its essential characteristic, for the portrayal that can not become more meticulous of the time-frequency local characteristic of blasting vibration signal.

Summary of the invention

Goal of the invention: in order to overcome the deficiency that exists in the prior art, the present invention provides a kind of blasting vibration signal characteristic extracting methods based on the small wave fractal combination that can carry out the high precision portrayal to the blasting vibration signal characteristic.

Technical scheme: for realizing above-mentioned purpose; A kind of blasting vibration signal characteristic extracting methods of the present invention based on the small wave fractal combination; Be to extract the blasting vibration signal characteristic like this: at first, provide blasting vibration signal small wave fractal threshold denoising method, adopt the wavelet basis that is suitable for the blasting vibration signature analysis to carry out multiple dimensioned decomposition; High frequency coefficient is carried out the laggard line reconstruction of threshold value quantizing, obtain the denoising result under the different decomposition yardstick condition; Based on blasting vibration signal fractal box computation model; Confirm rectangular box size, k value; Calculate under the different decomposition yardstick condition FRACTAL DIMENSION numerical value of blasting vibration time-history curves after the denoising, according to box counting dimension a hour corresponding decomposition scale confirm as the wavelet threshold denoising that best wavelet decomposition yardstick carries out the blasting vibration signal; Then, through the similarity of blasting vibration signal wavelet coefficient and the fractal property of self-similarity checking blasting vibration signal; Through blasting vibration signal fractal dimension with the change of frequency rule, with the characteristic parameter of fractal dimension as the blasting vibration signal.

Specifically, a kind of blasting vibration signal characteristic extracting methods based on the small wave fractal combination of the present invention may further comprise the steps:

(a) set up the fractal dimension computation model, confirm blasting vibration signal fractal dimension

1. establish vibration time-history curves S ∈ R ², whole plane R * R that curve is covered is divided into as far as possible little grid (δ ₁* δ ₂), this grid is also referred to as rectangular box, and adopting basic step-length is k (δ ₁* δ ₂) rectangle cover signal to be analyzed, add up under the corresponding yardstick effective grid coverage and count N _{K δ}, establish the grid number that all and S intersect and do

Then vibrating the fractal dimension computing formula is:

$D_{{\mathrm{\δ}}_1\×{\mathrm{\δ}}_2}=\underset{{\mathrm{\δ}}_2\→0}{\underset{{\mathrm{\δ}}_1\→0}{\underset{\‾}{\mathrm{Lim}}}}\frac{\mathrm{Log}{N}_{k{\mathrm{\δ}}_i}}{-\mathrm{Log}{\mathrm{K\δ}}_i}$ (i=1 or 2) (1)

Wherein: k=1,2,3L representes the enlargement factor of grid,

$N_{k{\mathrm{\δ}}_i}=\left[(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right)/k{\mathrm{\δ}}_2\right]+\mathrm{\φ}\left(\mathrm{Rem}(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right),{\mathrm{K\δ}}_2)\right),$ (1, n), n is a sampling number to h ∈, rem (max (s (h))-min (s (h)), k δ ₂) expression (max (s (h))-min (s (h)) and k δ ₂Remainder when being divided by, $\mathrm{\φ}\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x=0\end{array}\right.;$

2. confirm enlargement factor k:1≤k≤[T/2 Δ t]+1 of grid, T is main shaking the cycle, and Δ t is a sampling time interval;

3. confirm size of mesh opening k (δ ₁* δ ₂): mesh width k δ ₁Maximum is no more than the width T/2 of vibration signal semiperiod, grid height k δ ₂Minimum value is not less than the minimum non-zero difference in magnitude Δ A between whole analytic signal consecutive number strong point _Min, while k δ ₂Be not more than the peak-peak A of signal _Max(actual definite δ ₂Sort among the Shi Caiyong Matlab (s) order is sorted to sampled data, thereby determines Δ A easily _Min);

4. according to vibration fractal dimension computing formula (1), in no scale district-logk δ _iWith

Satisfy equation of linear regression:

(i=1 or 2) is according to size of mesh opening and the enlargement factor confirmed, through doing The slope of (i=1 or 2) double-log matched curve is tried to achieve blasting vibration signal fractal dimension;

(b) the blasting vibration signal is carried out denoising

1. adopt wavelet transformation that signal is carried out multiple dimensioned decomposition;

2. carry out threshold process to decomposing gained high frequency details component by following formula:

$\hat{d}\left(k\right)=\mathrm{sgn}\left(d\left(k\right)\right)g\left(\right|d\left(k\right)|-T_j)=\left\{\begin{array}{c}0,\left|d\left(k\right)\right|\&le;T_j\\ d\left(k\right)-T_j,d\left(k\right)>T_j\\ d\left(k\right)+T_j,d\left(k\right)<-T_j\end{array}\right.---\left(2\right)$

Wherein the threshold value of each yardstick is pressed following formula and is confirmed:

T _jBe each decomposition scale corresponding threshold, j is a decomposition scale;

The noise variance σ of blasting vibration signal is unknown, is estimated by following formula: σ=median (| d _j(k) |)/0.6745, wherein, be median;

3. with approximation signal and the detail signal reconstruct after threshold process, obtain the blasting vibration signal after the denoising;

4. calculate under the different decomposition yardstick condition box counting dimension value of blasting vibration waveform after the denoising respectively, a fractal dimension hour corresponding decomposition scale is confirmed as best decomposition scale;

(c) confirm the fractal dimension characteristic of blasting vibration signal different frequency bands component of signal

1. actual measurement blasting vibration signal being carried out multi-scale wavelet decomposes;

2. the corresponding FRACTAL DIMENSION numerical value of the 1. middle gained Wavelet Component of calculation procedure is portrayed vibration time-history curves complexity;

3. the corresponding FRACTAL DIMENSION numerical value of Wavelet Component is with change of frequency, and frequency is high more, and fractal dimension is big more, and satisfy 1≤D in the engineering explosion vibration-testing signal≤2, D is a fractal box, with the new parameter of D value of fractal box as sign blasting vibration signal intermediate frequency rate composition.

Among the present invention, can be through blasting vibration signal fractal property being carried out wavelet analysis, checking blasting vibration signal fractal characteristic: 1. actual measurement blasting vibration signal is carried out the wavelet decomposition under the best decomposition layer said conditions; 2. blasting vibration signal and Wavelet Component are carried out continuous wavelet transform, draw the self similarity index map; 3. in the self similarity index map that after wavelet decomposition, shows, checking blasting vibration signal fractal characteristic.

Beneficial effect: a kind of blasting vibration signal characteristic extracting methods of the present invention based on the small wave fractal combination, confirm wavelet decomposition yardstick best in the wavelet threshold denoising through change of fractal dimension rule under the different decomposition yardstick condition on the one hand; Pass through the fractal property of the similar and self-similarity scientific validation blasting vibration signal of Wavelet Component on the other hand; Fractal dimension through blasting vibration signal Wavelet Component is with the change of frequency rule; Proposition is with the new dimensionless parameter of blasting vibration signal fractal dimension as the sign blasting vibration; This method step is simple, workable, can accurately obtain the characteristic of blasting vibration signal through this method, satisfies the user demand of feature extraction in the engineering borehole blasting analysis of vibration signal.

Description of drawings

Fig. 1 is typical blasting vibration measured signal figure;

Fig. 2 is rectangular box overlay model figure;

Fig. 3 is a different decomposition number of plies wavelet threshold denoising design sketch;

Fig. 4 is a box counting dimension value under the different decomposition number of plies condition;

Fig. 5 is a denoising design sketch under the best decomposition scale condition;

Fig. 6 is wavelet decomposition (j=3) figure;

Fig. 7 is time-yardstick-coefficient figure.

Embodiment

Below in conjunction with accompanying drawing the present invention is done explanation further.

In the present embodiment, at first obtain a typical blasting vibration measured signal s, as shown in Figure 1, wherein contain noise component; Fig. 2 is the two yardstick rectangular box overlay models of the blasting vibration of setting up in the present embodiment.A kind of blasting vibration signal characteristic extracting methods based on the small wave fractal combination of the present invention may further comprise the steps:

(a) set up the fractal dimension computation model, confirm blasting vibration signal fractal dimension

1. establish vibration time-history curves S ∈ R ², whole plane R * R that curve is covered is divided into as far as possible little grid (δ ₁* δ ₂), adopting basic step-length is k (δ ₁* δ ₂) rectangle cover signal to be analyzed, add up under the corresponding yardstick effective grid coverage and count N _{K δ}, establish the grid number that all and S intersect and do

Then vibrating the fractal dimension computing formula is:

$D_{{\mathrm{\&delta;}}_1\&times;{\mathrm{\&delta;}}_2}=\underset{{\mathrm{\&delta;}}_2\&RightArrow;0}{\underset{{\mathrm{\&delta;}}_1\&RightArrow;0}{\underset{\&OverBar;}{\mathrm{Lim}}}}\frac{\mathrm{Log}{N}_{k{\mathrm{\&delta;}}_i}}{-\mathrm{Log}{\mathrm{K\&delta;}}_i}$ (i=1 or 2) (1)

Wherein: k=1,2,3L representes the enlargement factor of grid,

$N_{k{\mathrm{\&delta;}}_i}=\left[(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right)/k{\mathrm{\&delta;}}_2\right]+\mathrm{\&phi;}\left(\mathrm{Rem}(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right),{\mathrm{K\&delta;}}_2)\right),$ (1, n), n is a sampling number to h ∈, rem (max (s (h))-min (s (h)), k δ ₂) expression (max (s (h))-min (s (h)) and k δ ₂Remainder when being divided by, $\mathrm{\&phi;}\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x=0\end{array}\right.;$

2. confirm enlargement factor k:1≤k≤[T/2/ Δ t]+1 of grid, T is main shaking the cycle, and Δ t is a sampling time interval;

3. confirm size of mesh opening k (δ ₁* δ ₂): mesh width k δ ₁Maximum is no more than the width T/2 of vibration signal semiperiod, grid height k δ ₂Minimum value is not less than the minimum non-zero difference in magnitude Δ A between whole analytic signal consecutive number strong point _Min, while k δ ₂Be not more than the peak-peak A of signal _Max

4. according to vibration fractal dimension computing formula (1), in no scale district-logk δ _iWith

Satisfy equation of linear regression:

(i=1 or 2) is according to size of mesh opening and the enlargement factor confirmed, through doing

The slope of (i=1 or 2) double-log matched curve is tried to achieve blasting vibration signal fractal dimension.

(b) the blasting vibration signal is carried out denoising

1. adopt " db7 " small echo to carry out multiple dimensioned decomposition to blasting vibration test signal shown in Figure 1,

2. carry out threshold process to decomposing gained high frequency details component by following formula:

$\hat{d}\left(k\right)=\mathrm{sgn}\left(d\left(k\right)\right)g\left(\right|d\left(k\right)|-T_j)=\left\{\begin{array}{c}0,\left|d\left(k\right)\right|\&le;T_j\\ d\left(k\right)-T_j,d\left(k\right)>T_j\\ d\left(k\right)+T_j,d\left(k\right)<-T_j\end{array}\right.---\left(2\right)$

Wherein the threshold value of each yardstick is pressed following formula and is confirmed: T _jBe each decomposition scale corresponding threshold, j is a decomposition scale;

The noise variance σ of blasting vibration signal is unknown, is estimated by following formula: σ=median (| d _j(k) |)/0.6745, wherein, be median;

3. with approximation signal and the detail signal reconstruct after threshold process, obtain the blasting vibration signal after the denoising, Fig. 3 is (j=1～5) wavelet threshold denoising design sketch under the different decomposition number of plies condition.

4. calculate under the different decomposition yardstick condition box counting dimension value of blasting vibration waveform after the denoising respectively; A fractal dimension hour corresponding decomposition scale is confirmed as best decomposition scale: according to the computing method of rectangular box overlay model shown in Figure 2 and formula (1); Calculate the fractal box value of passing through j=1～5 layer wavelet threshold denoising after vibration waveform respectively, as shown in Figure 4.When j=1～3; Along with the increase of decomposing the number of plies, FRACTAL DIMENSION numerical value D=1.2997～1.2915, FRACTAL DIMENSION numerical value increases along with decomposition scale and reduces; Along with the increase filtering of decomposition scale the more noise component, embodied actual blasting vibration rule more exactly; When j=3～5, fractal box value D=1.2915～1.2925, excessive decomposition makes the blasting vibration waveform distortion that is collected.Therefore, this moment, best decomposition scale was j=3.

At last, as shown in Figure 5 by the blasting vibration signal that j=3 carries out after the denoising, successfully remove the noise in the measured signal.

In the present embodiment, can verify blasting vibration signal fractal characteristic through blasting vibration signal fractal property is carried out wavelet analysis:

Actual measurement blasting vibration signal carries out the wavelet decomposition under the best decomposition layer said conditions: to blasting vibration test signal shown in Figure 1 based on the db7 small echo; Carry out the decomposition of j=3; And respectively low frequency, high fdrequency component are carried out reconstruct; Obtain the low frequency component A3 among Fig. 6, high fdrequency component D3, D2, D1 represent the oscillating component in the different frequency range among the original signal s respectively;

To blasting vibration signal s and Wavelet Component A3, D3, D2, D1 carry out continuous wavelet transform, draw the self similarity index map among Fig. 7;

In the self similarity index map that after wavelet decomposition, shows, checking blasting vibration signal fractal characteristic: each Wavelet Component A3, between D3, D2, the D1 and blasting vibration signal s and A3, the wavelet coefficient all similar between D3, D2, the D1.The lines that show on the vertical axis are because the self-similarity generation of signal.Wavelet coefficient is big more, and then the lines of performance are bright more among the figure.Result of study shows that the self-similarity of signal also is the fractal characteristic of signal, adopt scientific validation of the present invention the blasting vibration signal have fractal characteristic.

(c) confirm the fractal dimension characteristic of blasting vibration signal different frequency bands component of signal

According to the FRACTAL DIMENSION numerical value of the different frequency bands component of signal of wavelet decomposition gained in formula (1) the difference calculating chart 6, as shown in table 1:

The FRACTAL DIMENSION numerical value of table 1 different frequency bands component of signal

Analytical table 1 borehole blasting vibration different frequency bands component of signal fractal dimension value concerns with change of frequency: the box counting dimension of blasting vibration signal s is that the box counting dimension value scope of 1.3007, four Wavelet Component is 1.0470～1.5708.Therefore, along with the rising of A3, D3, D2, D1 corresponding frequency band frequency, its box counting dimension value also increases from low to high gradually.

It is thus clear that fractal box can reflect the complexity of oscillating curve.For the blasting vibration signal in the measurement signal in engineering; Its curve complexity can reflect according to its radio-frequency component; The high more respective signal of frequency changes fast more, and whole signal waveform is full of whole plane more, and box counting dimension value D levels off to the FRACTAL DIMENSION numerical value " 2 " of European how much midplanes more; Therefore box counting dimension value D can be used as the new parameter of reflection blasting vibration signal intermediate frequency rate composition, all plays an important role at aspects such as carrying out blasting vibration forecast, controlled blasting hazard of vibration effect.

The above only is a preferred implementation of the present invention; Be noted that for those skilled in the art; Under the prerequisite that does not break away from the principle of the invention, can also make some improvement and retouching, these improvement and retouching also should be regarded as protection scope of the present invention.

Claims (1)

1. blasting vibration signal characteristic extracting methods based on small wave fractal combination is characterized in that may further comprise the steps:

(a) set up the fractal dimension computation model, confirm blasting vibration signal fractal dimension

1. establish vibration time-history curves S ∈ R ², whole plane R * R that curve is covered is divided into as far as possible little grid (δ ₁* δ ₂), adopting basic step-length is k (δ ₁* δ ₂) rectangle cover signal to be analyzed, add up under the corresponding yardstick effective grid coverage and count N _{K δ}, establish the grid number that all and S intersect and do

Then vibrating the fractal dimension computing formula is:

$D_{{\mathrm{\&delta;}}_1\&times;{\mathrm{\&delta;}}_2}=\underset{{\mathrm{\&delta;}}_2\&RightArrow;0}{\underset{{\mathrm{\&delta;}}_1\&RightArrow;0}{\underset{\&OverBar;}{\mathrm{Lim}}}}\frac{\mathrm{Log}{N}_{k{\mathrm{\&delta;}}_i}}{-\mathrm{Log}{\mathrm{K\&delta;}}_i}$ (i=1 or 2) (1)

Wherein: k=1,2,3L representes the enlargement factor of grid,

$N_{k{\mathrm{\&delta;}}_i}=\left[(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right)/k{\mathrm{\&delta;}}_2\right]+\mathrm{\&phi;}\left(\mathrm{Rem}(\mathrm{Max}\left(s\left(h\right)\right)-\mathrm{Min}\left(s\left(h\right)\right),{\mathrm{K\&delta;}}_2)\right),$ (1, n), n is a sampling number to h ∈, rem (max (s (h))-min (s (h)), k δ ₂) expression (max (s (h))-min (s (h)) and k δ ₂Remainder when being divided by, $\mathrm{\&phi;}\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x=0\end{array}\right.;$

2. confirm enlargement factor k:1≤k≤[T/2 Δ t]+1 of grid, T is main shaking the cycle, and Δ t is a sampling time interval;

3. confirm size of mesh opening k (δ ₁* δ ₂): mesh width k δ ₁Maximum is no more than the width T/2 of vibration signal semiperiod, grid height k δ ₂Minimum value is not less than the minimum non-zero difference in magnitude Δ A between whole analytic signal consecutive number strong point _Min, while k δ ₂Be not more than the peak-peak A of signal _Max

4. according to vibration fractal dimension computing formula (1), in no scale district-logk δ _iWith

Satisfy equation of linear regression: (i=1 or 2) is according to size of mesh opening and the enlargement factor confirmed, through doing

The slope of (i=1 or 2) double-log matched curve is tried to achieve blasting vibration signal fractal dimension;

(b) the blasting vibration signal is carried out denoising

1. adopt wavelet transformation that signal is carried out multiple dimensioned decomposition;

2. carry out threshold process to decomposing gained high frequency details component by following formula:

$\hat{d}\left(k\right)=\mathrm{sgn}\left(d\left(k\right)\right)g\left(\right|d\left(k\right)|-T_j)=\left\{\begin{array}{c}0,\left|d\left(k\right)\right|\&le;T_j\\ d\left(k\right)-T_j,d\left(k\right)>T_j\\ d\left(k\right)+T_j,d\left(k\right)<-T_j\end{array}\right.---\left(2\right)$

Wherein the threshold value of each yardstick is pressed following formula and is confirmed:

T _jBe each decomposition scale corresponding threshold, j is a decomposition scale;

The noise variance σ of blasting vibration signal is unknown, is estimated by following formula: σ=median (| d _j(k) |)/0.6745, wherein, be median;

3. with approximation signal and the detail signal reconstruct after threshold process, obtain the blasting vibration signal after the denoising;

4. calculate under the different decomposition yardstick condition box counting dimension value of blasting vibration waveform after the denoising respectively, a fractal dimension hour corresponding decomposition scale is confirmed as best decomposition scale;

(c) confirm the fractal dimension characteristic of blasting vibration signal different frequency bands component of signal

1. actual measurement blasting vibration signal being carried out multi-scale wavelet decomposes;

2. the corresponding FRACTAL DIMENSION numerical value of the 1. middle gained Wavelet Component of calculation procedure is portrayed vibration time-history curves complexity;

3. the corresponding FRACTAL DIMENSION numerical value of Wavelet Component is with change of frequency, and frequency is high more, and fractal dimension is big more, and satisfy 1≤D in the engineering explosion vibration-testing signal≤2, D is a fractal box, with the new parameter of D value of fractal box as sign blasting vibration signal intermediate frequency rate composition.

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