CN105930602A - Optimal weighted wavelet package entropy-based chattering detection method - Google Patents

Abstract

The invention discloses an optimal weighted wavelet package entropy-based chattering detection method. By modeling entropy values in chattering and stable states, an optimal weight interval can be obtained; a reasonable threshold is determined in combination with a visual algorithm by applying an extreme value statistics theory, so that the dependence on artificial experience is reduced; and finally, the chattering is detected in a non-occurrence stage, so that the damage of the chattering to workpieces and a machine tool is reduced.

Description

A kind of tremor detection method based on optimal weighting Wavelet Packet Entropy

Technical field

The present invention relates to turning flutter detection field, particularly relate to a kind of tremor based on optimal weighting Wavelet Packet Entropy detection Method.

Background technology

Cutting-vibration is a kind of wild effect, and it almost occurs, in all working angles, to show as cutter and workpiece Between high vibration.Especially in Thin-walled Workpiece turning, workpiece thinnest part only has 1 to 2 millimeters, workpiece Dynamic property is very poor, easily causes tremor.The generation of tremor can affect production efficiency and crudy, the most also may be used Causing excessive noise, tool damage etc., the harm to product quality, cutter and machine tool etc. need not be queried.Day Working (machining) efficiency, crudy, processing cost are had higher requirement by the manufacturing industry opened up increasingly, in order to a greater extent Reduce the adverse effect that causes of tremor, it is necessary to breed the stage in tremor and just tremor early detected, select subsequently Select stable cutting parameter, or take the control strategy of row, it is to avoid tremor is to workpiece and the infringement of machine tool component.

A lot of scholars did the research of tremor context of detection, had based on acceleration, cutting force and acoustical signal, mainly might be used Being divided into following three classes: the first kind is the analysis in signal frequency territory, such as wavelet transformation, S function converts, and Hilbert is yellow Conversion, adaptive-filtering and coherent function etc..According to Heisenberg-Gabor inequality, wavelet transformation can not be Time-frequency domain obtains high-resolution simultaneously.The amount of calculation of S function conversion and Hilbert-Huang transform is the biggest, it is impossible to be applied to Online tremor detection.Equations of The Second Kind is mode identification method, mainly has artificial neural network, support vector machine, case to push away Reason, fuzzy logic table etc., but need to do substantial amounts of experiment in early stage and carry out training pattern.3rd class is entropy method, As arranged entropy, coarseness entropy rate, approximate entropy, this kind of method detects tremor by extracting the random character of process, and It is widely used in milling, turning and boring.

Therefore, those skilled in the art is devoted to develop a kind of tremor detection method based on optimal weighting Wavelet Packet Entropy, Not only calculate speed fast, moreover it is possible to than existing turning flutter detection method earlier detect tremor, i.e. pregnant in tremor The stage of educating detects tremor.

Summary of the invention

Because the drawbacks described above of prior art, the technical problem to be solved is the most earlier to detect to quiver Shake, how to detect tremor in the stage of breeding of tremor.

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides one turning flutter detection method fast and effectively, The method is based on weighted wavelet bag entropy (Weighted Wavelet Packet Entropy, WWPE), energy Enough breed the stage in tremor and just tremor is detected.Whole tremor testing process see Fig. 1, the method be broadly divided into Under several steps:

(1) WAVELET PACKET DECOMPOSITION number of plies L is determined

If decomposition layer L is excessive, the frequency band that wavelet package transforms generates can be the narrowest, the finest frequency resolution.So And, if frequency band is the narrowest, the WWPE fluctuation that will amplify under steady statue.Source about this fluctuation is explained as follows: Due to complexity and the randomness of working angles, at steady state, the energy ratio of each frequency band can be 2^-LRipple Dynamic.Specifically, the measurement error that the fluctuation of Energy distribution is mostly derived from chip and forced vibration causes, and material, Time-varying dynamic characteristic caused by the discontinuity of temperature and cutting force.The wavelet packet coefficient definition of L layer jth frequency band For:

$\begin{array}{cc}{x}_L^j=\{c_{j,i},i=1,2,...,K\},& j=1,2,...,2^L\end{array}$

(2) weighting frequency band is determined

The determination of weighting frequency band, first passes through mode experiment and obtains process system natural frequency, belonging to natural frequency Frequency band is weighting frequency band.

(3) best initial weights is determined

The determination of best initial weights.Obtained by theory analysis and contrived experiment.Set up acceleration signal respectively at frequency domain Energy distribution model under steady statue and chatter state.At steady state, the ratio of gross energy shared by each frequency band It is worth identical:

E_L,j=2^-L, j=1,2 ..., 2^L

Assume that tremor basic frequency is positioned at pth frequency band, after being weighted by this frequency band, obtain the WWPE value under steady statue:

${\mathrm{\ρ}}_{steady}=-\frac{k}{2^L+k-1}ln\left(\frac{k}{2^L+k-1}\right)-\frac{2^L-1}{2^L+k-1}ln\left(\frac{1}{2^L+k-1}\right)$

When tremor occurs, the energy ratio of pth frequency band increases to:

E_L,p=2^-L+d,d>0

Wherein d is by the energy increments after gross energy normalization.In this, the WWPE under chatter state is:

$\begin{array}{c}{\mathrm{\ρ}}_{chatter}=-\frac{k(1+2^{L}d)}{k(1+2^{L}d)+2^L-1}\ln \left(\frac{k(1+2^{L}d)}{k(1+2^{L}d)+2^L-1}\right)\\ -\frac{2^L-1}{k(1+2^{L}d)+2^L-1}\ln \left(\frac{1}{k(1+2^{L}d)+2^L-1}\right)\end{array}$

So, the WWPE decrement that tremor causes is:

Δ ρ=ρ_steady-ρ_chatter

Δ ρ value is the biggest, and the difference of steady statue and chatter state is the biggest.Therefore, it is a kind of permissible for maximizing Δ ρ Directly promote the tremor detection performance of WWPE value.Δ ρ is the function of k, L, d, and wherein k, L, d are distributed representation Value, the wavelet decomposition number of plies, normalized energy increments.Figure it is seen that Δ ρ is first along with the increase of k And quickly increase, when k reaches extreme point, Δ ρ starts slowly to reduce along with the increase of k.According to theory analysis, To often organizing L and d, all there is best initial weights so that steady statue and tremor shape maximize.Based on this, design Experiment obtains best initial weights.

(4) WWPE is calculated

The energy of each frequency band of L layer is:

$E_{L,j}=\underset{i=1}{\overset{K}{\Σ}}{\left|c_{j,i}\right|}^2$

Wherein E_L,jRepresenting the energy of L layer jth frequency band, the gross energy of all frequency bands is

$E=\underset{j=1}{\overset{2^L}{\Σ}}{E}_{L,j}$

For simplicity, energy vectorsIt is normalized to

$\begin{array}{c}{V}^n=\left[\begin{array}{cccc}{E}_{L,1}^n& E_{L,2}^n& \mathrm{...}& E_{L,2^L}^n\end{array}\right]\\ =\frac{1}{E}\left[\begin{array}{cccc}{E}_{L,1}& E_{L,2}& \mathrm{...}& E_{L,2^L}\end{array}\right]\end{array}$

Wherein VⁿIt is normalized energy vector,It is E_L,jNormalized form.It not in general manner, make pth frequency band As being weighted frequency band:

$E_{L,p}^{nw}={\mathrm{kE}}_{L,p}^n$

Wherein k is weights, meets k ＞ 1.Weighted energy vector is now

$V^{nw}=\left[\begin{array}{ccccccc}{E}_{L,1}^n& \mathrm{...}& E_{L,p-1}^n& E_{L,p}^{nw}& E_{L,p+1}^n& \mathrm{...}& E_{L,2^L}^n\end{array}\right]$

Thus obtain WWPE

$\mathrm{\ρ}=-E_{L,p}^{nw}ln{E}_{L,p}^{nw}-\underset{j=1.j\≠p}{\overset{2^L}{\Σ}}{E}_{L,j}^{n}ln{E}_{L,j}^n$

(5) determine that tremor generation threshold value and tremor judge

Threshold is as follows:

A () selects suitable cutting parameter, carry out stable cutting.

B () calculates the WWPE of stable cutting

C () obtains sample { X₁,X₂,...,X_n, thus in sample, every 10 sample values take a maximum, constitute It is worth greatly subset

D () is by determining maximum distribution pattern depending on change algorithm

E (), by distribution pattern determined by maximum subset matching, determines threshold value finally according to level of confidence.

Finally, the threshold ratio that WWPE step 4 calculated and step 5 calculate relatively, when WWPE less than threshold value then It is judged to tremor, is otherwise stable.

Tremor detection method based on optimal weighting Wavelet Packet Entropy of the present invention, not only calculates speed fast, moreover it is possible to ratio Existing turning flutter detection method earlier detect tremor, i.e. detect tremor in the tremor stage of breeding.

Below with reference to accompanying drawing, the technique effect of design, concrete structure and the generation of the present invention is described further, with It is fully understood from the purpose of the present invention, feature and effect.

Accompanying drawing explanation

Fig. 1 is the tremor overhaul flow chart of a preferred embodiment of the present invention；

Fig. 2 is Δ ρ and number of plies L, weights k, the graph of a relation of weighting frequency band energy change d；

Fig. 3 is moment tremor being detected and the weights k graph of a relation of a preferred embodiment of the present invention；

Fig. 4 is that the WWPE of a preferred embodiment of the present invention changes over graph of a relation.

Detailed description of the invention

Of the present invention tremor of based on optimal weighting Wavelet Packet Entropy is expanded on further below according to a preferred embodiment Detection method, comprises the steps:

(1) WAVELET PACKET DECOMPOSITION layer is determined

In the enforcement of wavelet package transforms, use eight rank Daubechies small echos, acceleration signal is decomposed the 4th Layer.The wavelet package transforms coefficient of the 4th layer is

${\left(\begin{array}{cccc}{x}_4^1& x_4^2& \mathrm{...}& x_4^{16}\end{array}\right)}^T,$

WhereinIt it is the wavelet packet coefficient of the 4th layer of jth frequency band.Structure energy vectors V=[E_4,1 E_4,2 … E_4,16], after normalization:

$V^n=\left[\begin{array}{cccc}{E}_{4,1}^n& E_{4,2}^n& \mathrm{...}& E_{4,16}^n\end{array}\right].$

(2) wavelet band that weight is selected.

And calculate WWPE.Lathe can be passed through for a given Machinetool workpiece system, flutter frequency or vibration frequency band The frequency response function experiment of workpiece system is predicted.Flutter frequency is generally than knife rest (or workpiece) minimum natural frequency Slightly larger 0-15%.The natural frequency of knife rest (or workpiece) can be obtained by mode experiment.In instances, according to mould The frequency response function that state experiment obtains, main flutter frequency is positioned at the 4th layer of the first frequency band.In order to improve WWPE for quivering The sensitivity shaken, the energy of the first frequency band than after weighting is:

$E_{4,1}^{nw}={\mathrm{kE}}_{4,1}^n$

Wherein k represents weights, and finally calculates WWPE.Fig. 1 gives the whole flow process of put forward tremor detection method.

(3) threshold value determines

Once, calculate WWPE, by remaining threshold ratio relatively, if entropy is less than threshold value, represent that tremor occurs.It is worth It is noted that threshold value is to obtain according to the WWPE under steady statue, and the threshold value under different weights is also different 's.Below by an experimental example, preferably annotate Threshold:

A () selects suitable cutting parameter, carry out stable cutting, gathers acceleration signal, is calculated 500 WWPE Value.

B () extracts a maximum from every 10 WWPE, therefore obtain maximum that 50 maximums are constituted Collection Ω.

C () utilizes and determines, depending on change algorithm, the distribution that maximum subset is obeyed,

(4) best initial weights is determined.

In order to study the k impact for WWPE, We conducted battery of tests, k from 1,2,3 to 50.Notice, Work as k=1, WWPE and deteriorate to WPE.For each k value, calculate WWPE and threshold value.Fig. 3 gives and detects The moment (detection moment) of tremor and the relation of k, best initial weights is taken as k ∈ [7,16], uses best initial weights interval During weights, WWPE can earlier detect tremor than using other weights.

(5) tremor detection is carried out with best initial weights

According to the experiment in step (4), it is thus achieved that the optimum interval of k is k ∈ [7,16], thus obtain optimum WWPE. In order to verify the effectiveness of optimum WWPE, Fig. 4 compares k=1 under three kinds of weights, the tremor detection of 8,30, WWPE Performance.It can be seen that use the weights being positioned at optimum interval, earlier to detect than the weights in non-optimal interval and quiver Shake.In detail, weights are that the WWPE of 8 detects tremor when the t=6.78 second, and the WWPE that weights are 1 and 30 Tremor is detected respectively in t=7.77 second and t=7.04 second.In other words, weights be the WWPE of 8 be 1 than weights Within 0.99 second and 0.26 second, detecting tremor in advance respectively with 30 two kinds of situations, this demonstrates the optimum power obtained in experiment Value interval.

The preferred embodiment of the present invention described in detail above.Should be appreciated that the ordinary skill of this area is without wound The property made work just can make many modifications and variations according to the design of the present invention.Therefore, all technology in the art Personnel can be obtained by logical analysis, reasoning, or a limited experiment the most on the basis of existing technology The technical scheme arrived, all should be in the protection domain being defined in the patent claims.

Claims (7)

1. a tremor detection method based on optimal weighting Wavelet Packet Entropy, it is characterised in that comprise the following steps:

Step 1, determining WAVELET PACKET DECOMPOSITION number of plies L, wherein the wavelet packet coefficient of L layer jth frequency band is defined as:

$x_L^j=\{c_{j,i},i=1,2,...,K\},j=1,2,...,2^L$

Step 2, determine weighting frequency band；

Step 3, determine best initial weights；

Step 4, calculating weighted wavelet bag entropy；

Step 5, determine that tremor generation threshold value and tremor judge.

2. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 1, it is characterised in that In step 2, the determination method of described weighting frequency band is:

Step 21, by mode experiment obtain process system natural frequency；

Step 22, determine weighting frequency band according to frequency band belonging to natural frequency.

3. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 1, it is characterised in that In step 3, the determination method of described best initial weights is:

Step 31, set up the processing signal Energy distribution at frequency domain mould under steady statue and chatter state respectively Type；At steady state, the ratio of gross energy shared by each frequency band is identical:

E_L,j=2^-L, j=1,2 ..., 2^L

Step 32, assume that tremor basic frequency is positioned at pth frequency band, after being weighted by this frequency band, obtain steady statue Under weighted wavelet bag entropy value:

${\mathrm{\ρ}}_{steady}=-\frac{k}{2^L+k-1}ln\left(\frac{k}{2^L+k-1}\right)-\frac{2^L-1}{2^L+k-1}ln\left(\frac{1}{2^L+k-1}\right)$

Step 33, when tremor occurs, the energy ratio of pth frequency band increases to:

E_L,p=2^-L+d,d>0

Wherein d is by the energy increments after gross energy normalization；

Weighted wavelet bag entropy under step 34, chatter state is:

$\begin{array}{c}{\mathrm{\ρ}}_{chatter}=-\frac{k(1+2^{L}d)}{k(1+2^{L}d)+2^L-1}\ln \left(\frac{k(1+2^{L}d)}{k(1+2^{L}d)+2^L-1}\right)\\ -\frac{2^L-1}{k(1+2^{L}d)+2^L-1}\ln \left(\frac{1}{k(1+2^{L}d)+2^L-1}\right)\end{array}$

The weighted wavelet bag entropy decrement that step 35, tremor cause is Δ ρ, and described Δ ρ is the letter of k, L, d Number, wherein k, L, d represent weights, the wavelet decomposition number of plies, normalized energy increments respectively；To often organizing L With there is best initial weights in d, Δ ρ so that steady statue and tremor shape maximize.

4. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 3, it is characterised in that institute Stating processing signal is acceleration signal.

5. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 1, it is characterised in that In step 4, the computational methods of described weighted wavelet bag entropy are:

Step 41, the energy of each frequency band of L layer be:

$E_{L,j}=\underset{i=1}{\overset{K}{\Σ}}{\left|c_{j,i}\right|}^2$

Wherein E_L,jRepresenting the energy of L layer jth frequency band, the gross energy of all frequency bands is

$E=\underset{j=1}{\overset{2^L}{\Σ}}{E}_{L,j}$

Wherein VⁿIt is normalized energy vector,It is E_L,jNormalized form；

Step 43, make pth frequency band as being weighted frequency band:

$E_{L,p}^{nw}={\mathrm{kE}}_{L,p}^n$

Wherein k is weights, meets k ＞ 1；

Step 44, weighted energy vector are

$V^{nw}=\[E_{L,1}^n...E_{L,p-1}^n{E}_{L,p}^{nw}{E}_{L,p+1}^n...E_{L,2^L}^n\]$

Then weighted wavelet bag entropy is

$\mathrm{\ρ}=-E_{L,p}^{nw}\ln E_{L,p}^{nw}-\underset{j=1.j\≠p}{\overset{2^L}{\Σ}}{E}_{L,j}^n\ln E_{L,j}^n.$

6. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 1, it is characterised in that In step 5, described threshold value determination method comprises the steps:

Step 51, select suitable cutting parameter, carry out stable cutting；

Step 52, the weighted wavelet bag entropy of the stable cutting of calculating；

Step 53, acquisition sample { X₁,X₂,...,X_n, thus in sample, every 10 sample values take a maximum, Constitute maximum subset；

Step 54, determined maximum distribution pattern by visualized algorithm；

Distribution pattern determined by step 55, use maximum subset matching, determines threshold value according to level of confidence.

7. tremor detection method based on optimal weighting Wavelet Packet Entropy as claimed in claim 1, it is characterised in that In step 5, the decision method of described tremor is that weighted wavelet bag entropy step 4 calculated calculates with step 5 The threshold ratio gone out relatively, when weighted wavelet bag entropy is then judged to tremor less than threshold value, is otherwise stable.