CN106814396A - A kind of noise reduction filtering method of the mine microquake signal based on VMD - Google Patents

Abstract

The invention discloses a kind of noise reduction filtering method of the mine microquake signal based on VMD, belong to signal processing technology field, comprise the following steps：Read time series x (t) of noisy microseismic signals；Time series x (t) to microseismic signals carries out VMD decomposition；Calculate time series x (t) and each variation modal components u of microseismic signals_kCross-correlation coefficient；Variation modal components using centre frequency more than 200Hz and with the cross-correlation coefficient of time series x (t) of noisy microseismic signals less than 0.3 are reconstructed as noise filtering to remaining variation modal components, obtain the microseismic signals after noise reduction filtering.The present invention can be effectively prevented from modal overlap phenomenon, have the advantages that adaptivity and real-time, and can microseismic signals be carried out with effective noise reduction filtering treatment.

Description

A kind of noise reduction filtering method of the mine microquake signal based on VMD

Technical field

The invention belongs to signal processing technology field, and in particular to a kind of noise reduction filter of mine microquake signal based on VMD Wave method.

Background technology

Microseism is induced when rock ruptures, microseism data is formed, and underground coal mine noise pollution is serious, therefore microseism number A large amount of external noises are contained in, microseism useful signal need to be separated from noise.

The noise reduction filtering method of conventional rock rupture microseismic signals has experience mode decomposition (EMD), integrated experience at present Mode decomposition (EEMD), wavelet analysis etc., these method arithmetic speeds are slow, noiseproof feature is poor, False Rate is high, pickup precision is low, Algorithm real-time is not strong.As EMD can produce modal overlap phenomenon in decomposable process, that is, decompose one or more IMF for obtaining In comprising very different characteristic time scale, signal and noise are aliasing in one or more IMF, are extremely difficult to effectively drop Make an uproar filter effect.

The content of the invention

For above-mentioned technical problem present in prior art, the present invention proposes a kind of mine microquake letter based on VMD Number noise reduction filtering method, variation mode decomposition (VMD) is a kind of new signal decomposition method, compared to other mode decomposition skills Art, it efficiently solves modal overlap problem, with good noise robustness, overcomes the deficiencies in the prior art, has Good noise reduction.

To achieve these goals, the present invention is adopted the following technical scheme that：

A kind of noise reduction filtering method of the mine microquake signal based on VMD, comprises the following steps：

Step 1：Time series x (t) of noisy microseismic signals x is read, wherein, t=1,2 ..., N, N are microseismic signals Sampled point number；

Step 2：VMD decomposition is carried out to noisy microseismic signals x：

A series of variation modal components are decomposed into using VMD to noisy microseismic signals x, make each mode estimation bandwidth it And minimum, constraints is that each mode sum is equal to input signal x, and constraint variation model is described as formula (1) and formula (2)：

s.t.∑_ku_k=x (2)；

In formula (1), { u_k}:={ u₁,…,u_KIt is the variation modal components for decomposing the K finite bandwidth for obtaining, { ω_k}: ={ ω₁,…,ω_KBe each variation modal components center frequency, δ (t) is dirac (Dirac) function, and * represents convolution, j² =-1；In formula (2), x is noisy microseismic signals,It is that all of variation mode is sued for peace；

To solve the optimal solution of formula (1) and formula (2), constraint variation problem is changed into unconfinement by the Lagrange for introducing extension Variational problem, its expression formula is formula (3)：

Wherein, α is secondary penalty factor, and λ (t) is Lagrange multiplier operator；

Solve comprising the following steps that for the variational problem：

Step 2.1：Define the value of variation modal components number K values and penalty factor α；

Step 2.2：Initialization

Step 2.3：N=n+1 is made, whole circulation is performed；

Step 2.4：First circulation of internal layer is performed, u is updated according to formula (4)_k；

Wherein,It is the Fourier transform of signal x (t),

Step 2.5：K=k+1 is made, repeat step 2.4, until k=K, terminates first circulation of internal layer；

Step 2.6：Second circulation of internal layer is performed, ω is updated according to formula (5)_k；

Step 2.7：K=k+1 is made, repeat step 2.6, until k=K, terminates second circulation of internal layer；

Step 2.8：Outer loop is performed, λ is updated according to formula (6)；

Wherein, τ is the renewal step parameter of Lagrange multiplier operator λ (t)；

Step 2.9：Repeat step 2.3, until meeting shown in iteration stopping condition such as formula (7), terminates whole to step 2.8 Circulation, output result obtains K variation modal components；

Wherein, ε is solving precision；

Step 3：Original microseismic signals x (t) are calculated with each variation modal components u_kCross-correlation coefficient；

Applying equation (8) calculates time series x (t) and each variation modal components u of noisy microseismic signals x_kCross correlation Number；

Wherein, N is sampled point number, and

Step 4：Variation modal components by centre frequency more than 200Hz and with the cross-correlation coefficient of original signal x less than 0.3 As noise filtering, remaining variation modal components are reconstructed, obtain the microseismic signals after noise reduction filtering.

The principle of the invention is as follows：

To realize effective noise reduction filtering of microseismic signals, the present invention is directed to randomness, the non-stationary feature of microseismic signals, Read former noisy microseismic signals and carry out VMD decomposition, to obtaining each variation modal components u after decomposition_k, calculate original microseism letter Number x (t) and each variation modal components u_kCross-correlation coefficient, by centre frequency more than 200Hz and with original signal cross-correlation coefficient Variation modal components less than 0.3 are reconstructed as noise filtering to remaining variation modal components, after obtaining de-noising filtering Microseismic signals.

The Advantageous Effects that the present invention is brought：

The present invention is according to the good spectral decomposition features of VMD to low frequency variation modal components u_kIt is reconstructed, can be to actual letter Number carry out from decomposition is adapted to, it is right to the full extent on the basis of the feature of microseismic signals randomness and non-stationary is sufficiently reserved Microseismic signals are filtered, the algorithm have algorithm simple, adaptivity and it is real-time the characteristics of, mine microquake can be monitored The noisy microseismic signals of system pickup carry out effective noise reduction filtering, with good technological value and application prospect.

Brief description of the drawings

Fig. 1 is a kind of flow chart of the noise reduction filtering method of the mine microquake signal based on VMD of the present invention.

Fig. 2 is the schematic diagram of noisy microseismic signals time series x (t).

Fig. 3 is the 6 variation modal components schematic diagrames obtained after noisy microseismic signals x (t) are decomposed through VMD.

Fig. 4 is the corresponding spectrogram of 6 variation modal components.

Fig. 5 is the microseismic signals time series schematic diagram after noise reduction.

Fig. 6 is the comparison diagram of microseismic signals after noisy microseismic signals and noise reduction.

Specific embodiment

Below in conjunction with the accompanying drawings and specific embodiment is described in further detail to the present invention：

As shown in figure 1, a kind of noise reduction filtering method of the mine microquake signal based on VMD, specifically includes following steps：

Step 1：Time series x (t) of noisy micro seismic monitoring signal x is read, wherein, t=1,2 ..., N, N believe for microseism Number sampled point number；

Step 2：VMD decomposition is carried out to noisy microseismic signals x：

A series of variation modal components are decomposed into using VMD to noisy microseismic signals x, make each mode estimation bandwidth it And minimum, constraints is that each mode sum is equal to input signal x (t), and constraint variation model is described as formula (1) and formula (2)：

s.t.∑_ku_k=x (2)；

In formula (1), { u_k}:={ u₁,…,u_KIt is the variation modal components for decomposing the K finite bandwidth for obtaining, { ω_k}: ={ ω₁,…,ω_KBe each variation modal components center frequency, δ (t) is dirac (Dirac) function, and * represents convolution, j² =-1；In formula (2), x is former noisy microseismic signals,It is that all of variation mode is sued for peace.

To solve the optimal solution of formula (1) and formula (2), constraint variation problem is changed into unconfinement by the Lagrange for introducing extension Variational problem, its expression formula is formula (3)：

Wherein, α is secondary penalty factor, and λ (t) is Lagrange multiplier operator.

What is solved comprises the following steps that：

Step 2.1：Define the value of variation modal components number K values and penalty factor α；

Step 2.2：Initialization

Step 2.3：N=n+1 is made, whole circulation is performed；

Step 2.4：First circulation of internal layer is performed, u is updated according to formula (4)_k；

Wherein,It is the Fourier transform of signal x (t),

Step 2.5：K=k+1 is made, repeat step 2.4, until k=K, terminates first circulation of internal layer；

Step 2.6：Second circulation of internal layer is performed, ω is updated according to formula (5)_k；

Step 2.7：K=k+1 is made, repeat step 2.6, until k=K, terminates second circulation of internal layer；

Step 2.8：Outer loop is performed, λ is updated according to formula (6)；

Wherein, τ is the renewal step parameter of Lagrange multiplier operator λ (t)；

Step 2.9：Repeat step 2.3, until meeting shown in iteration stopping condition such as formula (7), terminates whole to step 2.8 Circulation, output result obtains K variation modal components；

Wherein, ε is solving precision；

Step 3：Original microseismic signals x (t) are calculated with each variation modal components u_kCross-correlation coefficient；

Applying equation (8) calculates original signal x (t) and each u_kCross-correlation coefficient between component：

Wherein, N is sampled point number, and

Step 4：Variation modal components by centre frequency more than 200Hz and with original signal x cross-correlation coefficients less than 0.3 are made It is noise filtering, remaining variation modal components is reconstructed, obtains the microseismic signals after noise reduction filtering.

As shown in Fig. 2 step 1 is obtained with the time (ms) as transverse axis, amplitude is the longitudinal axis, and microseismic signals time series is expressed as X (t), t=1,2 ..., 3000, microseismic signals sample point data is shown in Table 1.

The microseismic signals sample point data of table 1 (can be stored in Excel tables)

Sequence number	Moment (time/ms)	Amplitude
			1	1	‐1.83E‐05
2	2	‐0.12E‐05
			3	3	‐0.68E‐05
4	4	1.26E‐05
			5	5	0.34E‐05
…	…	…
			2999	2999	‐0.77E‐05
3000	3000	‐1.06E‐05

VMD algorithms according to step 2 carry out variation mode decomposition to microseismic signals time series x (t), take K=6, secondary Penalty factor α=5000,6 variation modal components u after decomposition_kAs shown in figure 3, the corresponding frequency spectrum of 6 variation modal components Figure is as shown in Figure 4.

According to the method for step 3, the cross-correlation of each variation modal components and former noisy microseismic signals x (t) in Fig. 3 is calculated Coefficient, as shown in table 2.

The original signal of table 2 and each u_kCross-correlation coefficient

						0.8396	0.4145	0.1832	0.1920	0.0735	0.0576

The center frequency value of each variation modal components in Fig. 3, as shown in table 3.

Each u of table 3_kCentre frequency

						25.5	83.6	169.4	238.4	335.4	418.6

According to the method for step 4, the variation by centre frequency more than 200Hz and with original signal cross-correlation coefficient less than 0.3 Modal components u₄、u₅、u₆As noise filtering, to remaining variation modal components u₁、u₂、u₃It is reconstructed, obtains de-noising filtering Microseismic signals afterwards, as shown in Figure 5.

Microseismic signals are the low frequency signals of randomness, non-stationary, and its frequency distribution more disperses, dominant frequency is distributed in 0~ 200Hz frequency bands, therefore can be by the u of HFS_kComponent is rejected, by remaining u_kComponent is reconstructed, you can realize noisy microseism The noise reduction filtering of signal.Advantages of the present invention：Being decomposed by VMD need not consider modal overlap, be sufficiently reserved microseismic signals On the basis of the non-stationary characteristic of itself, the noise mixed in signal is reduced and eliminated.

As shown in fig. 6, the microseismic signals contrast after by noisy microseismic signals and noise reduction filtering is as can be seen that application The noise reduction filtering that VMD carries out microseismic signals more fully remains the wave character of original signal, while also preferably remaining original The spike and Mutational part of signal, have obtained preferable noise reduction filtering effect.

Certainly, described above is not limitation of the present invention, and the present invention is also not limited to the example above, this technology neck Change, remodeling, addition or replacement that the technical staff in domain is made in essential scope of the invention, should also belong to of the invention Protection domain.

Claims (5)

1. a kind of noise reduction filtering method of the mine microquake signal based on VMD, it is characterised in that comprise the following steps：

Step 1：Time series x (t) of noisy microseismic signals x is read, wherein, t=1,2 ..., N, N are the sampling of microseismic signals Point number；

Step 2：VMD decomposition is carried out to noisy microseismic signals x, a series of variation modal components are obtained；

Step 3：Calculate time series x (t) and each variation modal components u of noisy microseismic signals x_kCross-correlation coefficient；

Step 4：Centre frequency is less than more than 200Hz and with the cross-correlation coefficient of time series x (t) of noisy microseismic signals x 0.3 variation modal components are reconstructed as noise filtering to remaining variation modal components, obtain micro- after noise reduction filtering Shake signal.

2. the noise reduction filtering method of the mine microquake signal based on VMD according to claim 1, it is characterised in that in step It is to make the estimation bandwidth sum of each modal components minimum to the constraints that noisy microseismic signals x carries out VMD decomposition in rapid 2, And each modal components sum is equal to noisy microseismic signals x, constraint variation model is formula (1) and formula (2)；

$\underset{\left\{u_k\right\}\left\{w_k\right\}}{min}\left\{{\Σ}_k\right||{\∂}_t\[\left(\mathrm{\δ}\right(t)+\frac{j}{\mathrm{\π}t})*u_k\left(t\right)\]e^{-{\mathrm{j\ω}}_{k}t}|{|}_2^2\}---\left(1\right);$

s.t.∑_ku_k=x (2)；

In formula (1), { u_k}:={ u₁,…,u_KIt is the variation modal components for decomposing the K finite bandwidth for obtaining, { ω_k}:= {ω₁,…,ω_KBe each variation modal components centre frequency, δ (t) is dirac (Dirac) function, and * represents convolution, j²=- 1；In formula (2), x is noisy microseismic signals,It is all variation modal components sums.

3. the noise reduction filtering method of the mine microquake signal based on VMD according to claim 2, it is characterised in that to ask Constraint variation problem is changed into unconfinement variational problem by the optimal solution of solution formula (1) and formula (2), the Lagrange for introducing extension, its Shown in expression formula such as formula (3)：

$\begin{array}{c}L\left(\right\{u_k\},\{w_k\},\mathrm{\&lambda;})=\mathrm{\&alpha;}{\&Sigma;}_k\left|\right|{\&part;}_t\&lsqb;\left(\mathrm{\&delta;}\right(t)+\frac{j}{\mathrm{\&pi;}t})*u_k\left(t\right)\&rsqb;e^{-{\mathrm{j\&omega;}}_{k}t}|{|}_2^2+||x\left(t\right)-{\&Sigma;}_k{u}_k\left(t\right)|{|}_2^2+\\ <\mathrm{\&lambda;}\left(t\right),x\left(t\right)-{\&Sigma;}_k{u}_k\left(t\right)>\end{array}---\left(3\right);$

Wherein, α is secondary penalty factor, and λ (t) is Lagrange multiplier operator.

4. the noise reduction filtering method of the mine microquake signal based on VMD according to claim 1, it is characterised in that in step In rapid 2, VMD decomposition is carried out to noisy microseismic signals x, specifically include following steps：

Step 2.1：Define the value of variation modal components number K values and penalty factor α；

Step 2.2：InitializationN=0；

Step 2.3：N=n+1 is made, whole circulation is performed；

Step 2.4：First circulation of internal layer is performed, u is updated according to formula (4)_k；

${\hat{u}}_k^{n+1}\left(\mathrm{\&omega;}\right)=\frac{\hat{x}\left(\mathrm{\&omega;}\right)-{\mathrm{\&Sigma;}}_{i\&NotEqual;k}{\hat{u}}_i\left(\mathrm{\&omega;}\right)+\frac{\widehat{\mathrm{\&lambda;}}\left(\mathrm{\&omega;}\right)}{2}}{1+2\mathrm{\&alpha;}{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_k)}^2}---\left(4\right);$

Wherein,It is the Fourier transform of time series x (t) of noisy microseismic signals x, j²=-1；

Step 2.5：K=k+1 is made, repeat step 2.4, until k=K, terminates first circulation of internal layer；

Step 2.6：Second circulation of internal layer is performed, ω is updated according to formula (5)_k；

${\mathrm{\&omega;}}_k^{n+1}=\frac{{\&Integral;}_0^{\mathrm{\&infin;}}\mathrm{\&omega;}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}{{\&Integral;}_0^{\mathrm{\&infin;}}{\left|{\hat{u}}_k\left(\mathrm{\&omega;}\right)\right|}^{2}d\mathrm{\&omega;}}---\left(5\right);$

Step 2.7：K=k+1 is made, repeat step 2.6, until k=K, terminates second circulation of internal layer；

Step 2.8：Outer loop is performed, λ is updated according to formula (6)；

${\widehat{\mathrm{\&lambda;}}}^{n+1}\left(\mathrm{\&omega;}\right)={\widehat{\mathrm{\&lambda;}}}^n\left(\mathrm{\&omega;}\right)+\mathrm{\&tau;}\left(\hat{x}\right(\mathrm{\&omega;})-{\&Sigma;}_k{\hat{u}}_k^{n+1}(\mathrm{\&omega;}\left)\right)---\left(6\right);$

Wherein, τ is the renewal step parameter of Lagrange multiplier operator λ (t)；

Step 2.9：To step 2.8, until meeting shown in iteration stopping condition such as formula (7), end is entirely followed repeat step 2.3 Ring, output result obtains K variation modal components；

${\mathrm{\&Sigma;}}_k\left(\frac{\left|\right|{\hat{u}}_k^{n+1}-{\hat{u}}_k^n|{|}_2^2}{\left|\right|{\hat{u}}_k^n|{|}_2^2}\right)<\mathrm{\&epsiv;}---\left(7\right);$

Wherein, ε is solving precision.

5. the noise reduction filtering method of the mine microquake signal based on VMD according to claim 1, it is characterised in that in step In rapid 3, time series x (t) and each variation modal components u of noisy microseismic signals x are calculated according to formula (8)_kCross-correlation coefficient；

$R(x,u_i)=\frac{{\mathrm{\&Sigma;}}_{i=0}^N\&lsqb;x\left(t\right)-\stackrel{\&OverBar;}{x}\&rsqb;\&lsqb;u_i\left(t\right)-\stackrel{\&OverBar;}{u_i}\&rsqb;}{{\left({\mathrm{\&Sigma;}}_{i=0}^N{(\&lsqb;x(t)-\stackrel{\&OverBar;}{x}\&rsqb;)}^2\right)}^{1/2}{\left({\mathrm{\&Sigma;}}_{i=0}^N{(\&lsqb;u_i(t)-\stackrel{\&OverBar;}{u_i}\&rsqb;)}^2\right)}^{1/2}}---\left(8\right);$

Wherein, N is sampled point number, and