CN102063894B - Rotor rubbing acoustic emission signal denoising method - Google Patents

Abstract

The invention discloses a rotor rubbing acoustic emission signal denoising method based on a conjugate gradient method and adaptive generalized morphological filtering. The invention puts forward a generalized morphological filter which utilizes the conjugate gradient method to realize the generalized morphological open and close of the filter and combines adaptive weighting on the basis of basic morphological transformation and a combining form of the mathematical morphology, and the generalized morphological filter is applied to the denoising of a rubbing acoustic emission signal. The adaptive generalized morphological filter based on the conjugate gradient method, which is put forward by the invention, can be used for obtaining a better denoising effect on the rubbing acoustic emission signal and a higher signal-to-noise ratio compared with a traditional morphological filter.

Description

Rotor rubbing acoustic emission signal noise-reduction method

Technical field

The present invention relates to a kind of acoustic emission signal noise-reduction method, particularly relate to a kind of rotor rubbing acoustic emission signal noise-reduction method based on method of conjugate gradient and self-adapting generalized shape filtering.

Background technology

Between rotating machinery sound part owing to uneven in the operational process, misalign, factor such as thermal flexure takes place bumps that to rub be more common typical fault.Acoustic emission (Acoustic Emission, AE) a kind of method of, characteristics become rotating machinery bump-scrape fault detect such as Hz-KHz wide highly sensitive with it.But in actual engineering survey; The acoustic emission signal of collection in worksite is often by various noise pollutions; Especially the relative bad working environment of rotating machinery and when operation the polyphyly very noisy that produces of equipment self, make bump-scrape acoustic emission signal can't reflect the actual state of rubbing that bumps of rotating machinery.From noise, extract with discerning useful acoustic emission signal is the research focus that acoustic emission is used always.

The basic thought of shape filtering is based on the geometry characteristic of signal, utilizes predefined structural element (being equivalent to spectral window) that signal is mated or local correction, to reach the extraction signal, suppresses the purpose of noise.Method of conjugate gradient is a kind of method of finding the solution unconstrained optimization problem.Utilize method of conjugate gradient to realize broad sense form open-close and close-optimal combination of Kai wave filter that the self-adapting generalized morphological filter that makes the combination back form can be rejected the noise in the rotor rubbing acoustic emission signal effectively.Therefore shape filtering and method of conjugate gradient are the theoretical foundations that we reject noise in the bump-scrape acoustic emission signal.

Summary of the invention

The technical matters that the present invention will solve is the defective to prior art, in conjunction with method of conjugate gradient, improves the algorithm of broad sense shape filtering, proposes a kind of noise-reduction method of rotor rubbing acoustic emission signal.

The present invention adopts following technical scheme:

The present invention is based on the rotor rubbing acoustic emission signal noise-reduction method of method of conjugate gradient and self-adapting generalized shape filtering, may further comprise the steps:

(1) obtains noisy bump-scrape acoustic emission signal;

(2) the noisy bump-scrape acoustic emission signal that step 1 obtained is carried out the broad sense open-close and closes-Kai filtering, obtain the broad sense open-close respectively and close-the output signal of Kai wave filter;

(3) set the broad sense open-close and close-the initial weight coefficient of Kai wave filter is 0.5, and the utilization method of conjugate gradient realizes the broad sense open-close and closes-and the weight coefficient adaptive transformation of Kai wave filter is to optimal value;

(4) with the resulting broad sense open-close of step 2 with close-the output signal of Kai wave filter set by step the weight coefficient optimal value ratio of 3 gained merge, can obtain the rotor rubbing acoustic emission signal behind the noise reduction.

Advantage of the present invention and effect are:

1. adopt method of conjugate gradient that weight coefficient is carried out iteration self-adapting and calculate to confirm the weight coefficient optimal value, the fixing weight coefficient than traditional broad sense shape filtering has improved noise reduction effectively.

2. whole noise reduction algorithm major part only relates to plus and minus calculation, and the multiplication and division computing is less, and noise reduction speed is very fast relatively.

Other advantages of the present invention and effect will continue to describe below.

Description of drawings

Fig. 1---based on the rotor rubbing acoustic emission signal noise-reduction method overview flow chart of method of conjugate gradient and self-adapting generalized shape filtering;

Fig. 2-1---bump the acoustic emission test unit that rubs; Fig. 2-2---bump the structural representation of the device that rubs;

The 1-motor; The 2-gearbox; The 3-shaft coupling; The 4-bearing; 5-clutch shaft bearing seat; 6-bumps the device that rubs; The 7-base; The 8-rotating disk; The 9-axle; 10-second bearing seat; The 21-stator; The 22-support; The 23-bolt.

Fig. 3---based on the self-adapting generalized shape filtering algorithm principle block diagram of method of conjugate gradient.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

Fig. 1 is based on the rotor rubbing acoustic emission signal noise-reduction method overview flow chart of method of conjugate gradient and self-adapting generalized shape filtering.The step of this method is following:

(1) employing is bumped the acoustic emission experiment device that rubs and is obtained noisy bump-scrape acoustic emission signal;

(2) the noisy bump-scrape acoustic emission signal that step 1 obtained is carried out the broad sense open-close and closes-Kai filtering, obtain the broad sense open-close respectively and close-the output signal of Kai wave filter;

(3) set the broad sense open-close and close-the initial weight coefficient of Kai wave filter is 0.5, and the utilization method of conjugate gradient realizes the broad sense open-close and closes-and the weight coefficient adaptive transformation of Kai wave filter is to optimal value;

(4) with the resulting broad sense open-close of step 2 with close-the output signal of Kai wave filter set by step the weight coefficient optimal value ratio of 3 gained merge, can obtain the rotor rubbing acoustic emission signal behind the noise reduction.

Below in conjunction with accompanying drawing and embodiment, technical scheme of the present invention is done further to set forth.

1, the rotor rubbing acoustic emission signal obtains

Bumping of this example rubs the acoustic emission experiment device shown in Fig. 2-1 and 2-2.Be installed in through one and movably bump the device 6 that rubs on the rotor platform base 7 and simulate to realize bumping between sound and rub.Motor 1 rotates through booster engine 2 and shaft coupling 3 driving shafts 9; 9 on axle bumps the device 6 that rubs and is installed between first and second bearing seats 5 and 10 on first and second bearing seats 5 and 10, and axle 9 is through and bumps device 6 stator center of rubbing.Bump several 4 telescopic bolts 23 are installed on the device 6 that rubs, bolt 23 radially faces toward axle 9 centers along rotating shaft, produces to bump through the position of regulating bolt 23 and then adjusting stator 21 disalignments and rubs.

This experimental provision is selected the UT-1000 sensor for use, frequency range 60～1000kHz; Pregain 40dB; The acoustic emission capture card is 18 A/D resolution.Sensor is installed on the clutch shaft bearing seat 5, and in rotating shaft, sampling rate is made as 1MHz to bump Mo Yuan (promptly bumping the device 6 that rubs), and the speed setting of this experimental provision rotor is at 1500r/min.After experimental simulation goes out the rotor rubbing acoustic emission signal, the signal to noise ratio (S/N ratio) that on acoustic emission signal, superposes (signal-to-noise ratio, SNR) for the random white noise of 0dB, 5dB, 10dB to simulate the bump-scrape acoustic emission signal of different pollution levels.

2, the broad sense open-close with close-Kai filtering

The thought of detection of being based on the mathematics shape filtering realizes.As the structural element of " probe ", can directly carry information (like form, size etc.), when probe constantly moves in signal, just can investigate the mutual relationship between the signal various piece, thus the architectural feature of research signal.Mathematical morphology has defined conversion basic in 2: expand and corrosion.If f (x) is a field of definition is 0,1 ..., the one dimension original signal of N}, g (x) be field of definition be 0,1 ..., the structural element of M}, M＜N, and define its initial point at the O place.The computing formula of expansion and erosion operation is respectively:

$(f\⊕g)\left(n\right)=\max \{f(n-m)+g\left(m\right)\}$ m＝0，1，...，M-1，n＝0，1，...，N+M-2(1)

(fΘg)(n)＝min{f(n+m)-g(m)} m＝0，1，...，M-1，n＝0，1，...，N-M(2)

Can obtain 2 very important morphological operator by the combination of expanding and corrode: the open and close computing, its computing formula is respectively:

$(f\·g)\left(x\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(x\right)---\left(4\right)$

Can find out that by formula 3, formula 4 opening operation can be removed structures such as isolated point, burr and foot bridge, can suppress peak value (positive pulse) noise in the signal; Closed operation then can be filled and led up ditch, makes hole and gap up, can suppress low ebb (negative pulse) noise in the signal.In order to suppress the positive and negative impulsive noise in the signal simultaneously, adopt the structural element of different size, through the computing of cascade open and close, constructed the broad sense open-close and closed-the Kai wave filter.Set g ₁, g ₂Be structural element, and

Then the broad sense open-close with close-the Kai wave filter is defined as respectively:

GOC(f)＝(fοg ₁·g ₂)(x)(5)

GCO(f)＝(f·g ₁οg ₂)(x)(6)

But because broad sense shape filtering method is still by the open and close computing and forms, make it still have the statistical bias phenomenon, cause the output amplitude of open-close wave filter less than normal, and close-output amplitude of Kai wave filter is bigger than normal.Under many circumstances, use is difficult to obtain best filter effect separately.Considering that rotor rubbing AE signal amplitude changes in characteristics and the data of big rise and fall exists multiple noise component, can adopt the weighted array form of two kinds of wave filters, so that cancelling noise effectively.When weight coefficient was 0.5, the weighted array form of two kinds of wave filters was:

GMF(f)＝0.5×GOC(f)+0.5×GCO(f) (7)

Formula 7 definition be called the broad sense morphological filter.In the broad sense morphological filter, the broad sense open-close with close-weight coefficient of Kai wave filter is 0.5, weight coefficient remains unchanged in filtering.Fixing like this weight coefficient makes filtering output result can not reach best adaptively.In order to realize the optimization of filter effect, can revise weight coefficient, the combining adaptive method is utilized method of conjugate gradient, and iterative computation is to confirm best weight coefficient.With broad sense form open-close with close-the Kai wave filter carries out weighted array by the weight coefficient value of the best, can obtain the self-adapting generalized morphological filter based on method of conjugate gradient.

If noisy rotor rubbing acoustic emission signal x (n)=s (n)+u (n), n=1,2 ..., N, wherein x (n) is noisy bump-scrape acoustic emission signal, and s (n) is muting desirable bump-scrape acoustic emission signal, and u (n) is various noise.According to formula 5, formula 6, the broad sense open-close with close-the Kai wave filter is output as:

y ₁(n)＝GOC(x(n))＝(xοg ₁·g ₂)(n)(8)

y ₂(n)＝GCO(x(n))＝(x·g ₁οg ₂)(n)(9)

g ₁, g ₂Be structural element.Then during the k time iteration the broad sense open-close with close-weighted array of Kai wave filter is output as:

$y^k\left(n\right)=a_1^k\left(n\right)y_1\left(n\right)+a_2^k{y}_2\left(n\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{a}_i^k{y}_i\left(n\right)---\left(10\right)$

In the formula 10;

(i=1,2) weight coefficient sequence when being the k time iteration.

3, the weight coefficient adaptive iteration based on method of conjugate gradient calculates

The broad sense open-close with close-mean square deviation of the weighted array of Kai wave filter output signal is:

$E\left[e^2\left(n\right)\right]=E\left[{|s\left(n\right)-y\left(n\right)|}^2\right]=E\left[{|s\left(n\right)-\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{a}_i\left(n\right)y_i\left(n\right)|}^2\right]$

(11)

Adopt method of conjugate gradient, through modified weight coefficient sequence a progressively _i(i=1,2) make the output y (n) of wave filter under the mean square deviation meaning, approach ideal signal s (n) most.Calculate for simplifying, get square e of single error sample ²(n) replace E [e ²(n)].E then ²(n) to weight coefficient sequence a _iThe gradient of (i=1,2) is:

${\▿e}^2\left(n\right)={\left[\begin{array}{cc}\frac{\∂\left[e^2\left(n\right)\right]}{{\∂a}_1\left(n\right)}& \frac{\∂\left[e^2\left(n\right)\right]}{{\∂a}_2\left(n\right)}\end{array}\right]}^T={\left[\begin{array}{cc}{\mathrm{grad}}_1& {\mathrm{grad}}_2\end{array}\right]}^T$

(12)

Then single error sample is during the k time iteration:

[e(n)] ^k＝y ^k-1(n)-y ^k(n) (13)

Here use y ^K-1(n) replace s (n).Then gradient is:

${\left[{\▿e}^2\left(n\right)\right]}^k={\left[\begin{array}{cc}{\mathrm{grad}}_1^k& {\mathrm{grad}}_2^k\end{array}\right]}^T---\left(14\right)$

Determining factor

The calculation of means.The famous HS method that has Hestenes and Steifel to propose:

${\mathrm{\β}}_i^k=\frac{{\left({\mathrm{\Δ}\mathrm{grad}}_i^{k-1}\right)}^T{\mathrm{grad}}_i^k}{{\left({\mathrm{\Δ}\mathrm{grad}}_i^{k-1}\right)}^T{p}_i^k}---\left(15\right)$

The FR method that Fletcher and Reeves propose:

${\mathrm{\β}}_i^k=\frac{{\left({\mathrm{grad}}_i^k\right)}^T{\mathrm{grad}}_i^k}{{\left({\mathrm{grad}}_i^{k-1}\right)}^T{\mathrm{grad}}_i^{k-1}}---\left(16\right)$

The independent respectively PRP method that proposes of Polak, Ribiere and Polyak:

${\mathrm{\β}}_i^k=\frac{{\left({\mathrm{\Δ}\mathrm{grad}}_i^{k-1}\right)}^T{\mathrm{grad}}_i^k}{{\left({\mathrm{grad}}_i^{k-1}\right)}^T{\mathrm{grad}}_i^{k-1}}---\left(17\right)$

I the component of

direction vector when being k iteration in

formula 15 in formula 15, the formula 17; I=1,2.The present invention chooses FR method design factor

Each component of calculated direction vector

:

$p_i^k=-{\mathrm{grad}}_i^k+{\mathrm{\β}}_i^k{p}_i^{k-1}$ i＝1，2 (18)

Then the weight coefficient iterative formula is:

$a_i^{k+1}=a_i^k+{\mathrm{\μp}}_i^k---\left(19\right)$

In the formula 19, μ is a step parameter.Choosing of μ has very big influence to filter effect, the μ value conference cause convergence vibration, make filtering system unstable; Too small again can adjustment influence the wave filter speed of convergence because of weight coefficient can not get effectively.There is an optimal value in μ, and for the rotor rubbing acoustic emission signal that records among the present invention, the optimal value of μ is between 0.7～1.0.

In formula 10～formula 19, subscript k representes iterations, k=0, and 1,2 ....Initial weight coefficient

is got then

i=1 of coefficient

, 2.For the first time during iteration, get [e (n)] ⁰=x (n)-y ⁰(n).Utilize formula 11～formula 19 can realize the self-adaptation correction of weight coefficient sequence.

4, the result who merges in weight coefficient optimal value ratio

Mean square deviation E [e ²(n)] reach when preestablishing threshold value, iterative computation stops, and confirms weight coefficient sequence a _iThe optimal value of (i=1,2), then the output valve based on method of conjugate gradient and self-adapting generalized morphological filter is:

$y\left(n\right)=a_1\left(n\right)y_1\left(n\right)+a_2{y}_2\left(n\right)=\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{a}_i{y}_i\left(n\right)$ i＝1，2

(20)

Y in the formula 20 (n) is the rotor rubbing AE signal behind the noise reduction.Self-adapting generalized morphological filter algorithm principle block diagram based on method of conjugate gradient is seen shown in Figure 3.

5, experimental analysis

After experimental simulation goes out the rotor rubbing acoustic emission signal, the signal to noise ratio (S/N ratio) that on bump-scrape acoustic emission signal, superposes (signal-to-noise ratio, SNR) for the random white noise of 0dB, 5dB, 10dB to simulate the bump-scrape acoustic emission signal of different pollution levels.Adopt broad sense open-close wave filter (GOC), broad sense to close-Kai wave filter (GCO), broad sense morphological filter (GMF) and the rotor rubbing acoustic emission signal that adds after making an uproar is carried out noise reduction process based on the self-adapting generalized morphological filter (AGMF-G) of method of conjugate gradient respectively, the result is as shown in table 1.From table the noise reduction that draws of various noise reduction algorithms as a result signal to noise ratio (S/N ratio) can find out, obviously be better than other three kinds of noise reduction algorithms based on the noise reduction of the self-adapting generalized morphological filter of method of conjugate gradient.Show that the self-adapting generalized morphological filter based on method of conjugate gradient can reduce the noise contribution in the rotor rubbing AE signal effectively, reaches the purpose of noise reduction.

Table 1

Claims (2)

1. the rotor rubbing acoustic emission signal noise-reduction method based on method of conjugate gradient and self-adapting generalized shape filtering is characterized in that, may further comprise the steps:

Step 1: get noisy bump-scrape acoustic emission signal;

Step 2: the noisy bump-scrape acoustic emission signal that step 1 obtained is carried out the broad sense open-close respectively and closes-Kai filtering, obtain the broad sense open-close and close-the output signal of Kai wave filter;

Step 3: to set the broad sense open-close and close-the initial weight coefficient of Kai wave filter is 0.5, the utilization method of conjugate gradient realizes the broad sense open-close and closes-the weight coefficient adaptive transformation of Kai wave filter is to optimal value;

Step 4: with the resulting broad sense open-close of step 2 with close-the output signal of Kai wave filter set by step the weight coefficient optimal value ratio of 3 gained merge, obtain the rotor rubbing acoustic emission signal behind the noise reduction;

In the said step 2, the broad sense open-close with close-method of Kai filtering is

If f (x) is a field of definition is 0,1 ..., the one dimension original signal of N}, g (x) be field of definition be 0,1 ..., the structural element of M}, M＜N, and define its initial point at 0 place, expand and the computing formula of erosion operation is respectively:

m＝0，1，...，M-1，n＝0，1，...，N+M-2 (1)

(fΘg)(n)＝min{f(n+m)-g(m)} m＝0，1，...，M-1，n＝0，1，...，N-M (2)

The computing formula that obtains the open and close computing thus is:

Through the computing of cascade open and close, constructed the broad sense open-close and closed-the Kai wave filter, set g ₁, g ₂Be structural element, and Then the broad sense open-close with close-the Kai wave filter is defined as respectively:

GOC(f)＝(fοg ₁·g ₂)(x)(5)

GCO(f)＝(f·g ₁οg ₂)(x)(6)

Owing to have multiple noise component in the characteristics of rotor rubbing AE signal amplitude variation big rise and fall and the data; The weighted array form that can adopt two kinds of wave filters is so that cancelling noise effectively; When weight coefficient was 0.5, the weighted array form of two kinds of wave filters was:

GMF(f)＝0.5×GOC(f)+0.5×GCO(f) (7)

Formula 7 definition be called the broad sense morphological filter;

In the said step 3,

If noisy rotor rubbing acoustic emission signal x (n)=s (n)+u (n), n=1,2 ..., N, wherein x (n) is noisy bump-scrape acoustic emission signal, and s (n) is muting desirable bump-scrape acoustic emission signal, and u (n) is various noise;

According to formula 5, formula 6, the broad sense open-close with close-the Kai wave filter is output as:

y ₁(n)＝GOC(x(n))＝(xοg ₁·g ₂)(n)(8)

y ₂(n)＝GCO(x(n))＝(x·g ₁οg ₂)(n)(9)

Then during the k time iteration the broad sense open-close with close-weighted array of Kai wave filter is output as:

Wherein,

weight coefficient sequence when being the k time iteration;

The broad sense open-close with close-mean square deviation of the weighted array of Kai wave filter output signal is:

Calculate for simplifying, get square e of single error sample ²(n) replace E [e ²(n)], e then ²(n) to weight coefficient sequence a _iThe gradient of (i=1,2) is:

Single error sample is during the k time iteration:

[e(n)] ^k＝y ^k-1(n)-y ^k(n) (13)

Here use y ^K-1(n) replace s (n), then gradient is:

can get with FR method design factor:

Each component of calculated direction vector

:

i＝1，2 (18)

Then the weight coefficient iterative formula is:

In the formula, μ is a step parameter;

In formula 10～formula 19, subscript k representes iterations, k=0, and 1,2 ..., initial weight coefficient

Get coefficient

Then I=1,2, for the first time during iteration, get [e (n)] ⁰=x (n)-y ⁰(n).

2. the rotor rubbing acoustic emission signal noise-reduction method based on method of conjugate gradient and self-adapting generalized shape filtering according to claim 1 is characterized in that in the said step 3), the scope of μ is 0.7～1.0.

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