1 the introduction
Acoustic emission (& emission, AE) technology is a new method of tool wear monitoring. The AE signal is transient and randomness, belong to non-stationary random signal. Fourier transform is a signal in the time domain statistical features of spectrum, it has no localization analysis of signal function [1], and as a method of signal processing, wavelet analysis with time domain and frequency domain at the same time the ability of denoting local signal characteristics, so for containing the transient analysis of AE signals are suitable for [2].
The wavelet analysis in the AE signal, the wavelet transform of wavelet base is not the only, so for the same signal after wavelet transformation to get different characteristics of signal is different. The selection of wavelet base is very important to accurately extract signal features, is the signal wavelet transform must be considered a key problem. At present, there are institutions at home and abroad, to some research was conducted on the method of choosing wavelet base, but the lack of the best wavelet base selection method system specification. Specific to the wavelet analysis, the AE signal on the AE signal wavelet base, there is no literature comprehensively and systematically reported [3]. Based on the properties of wavelet base and the characteristic of the cutting tool wear AE signal, the cutting tool wear AE signal wavelet analysis the selection of wavelet base question has carried on the theoretical analysis and the correctness of the theoretical analysis is verified by experiment.
2 cutting tool wear AE signal characteristics
Experimental study shows that in the process of metal cutting has a wealth of AE information. The so-called phenomenon of AE, is when the solid deformation or fracture emit elastic wave phenomenon, therefore, essentially the AE signal is a kind of mechanical wave, is the basic characteristic of the wave: the volatility and decay. In addition, the AE signal also has the characteristics of transient and diversity, belongs to the typical non-stationary signal. In the process of metal cutting tool knife surface friction and the chip after the impact, broken, shear zone and the plastic deformation, friction of rake face of the second area, etc. There will be [4] of AE signal.



3 wavelet definition and the energy of the wavelet packet decomposition
3. The definition of wavelet base
If the bits (x) is a real function and its spectrum meet conditions
Bits of C = ∫ up - up | bits (x) x < | | | x 2 d up (1)
The bits (x) is called a basic wavelet and wavelet. Also should satisfy
Bits (0) = 0] ∫ + up - up bits of d (x) = 0 x (2)
So, according to a basic wavelet bits (x), through the translation and scaling can generate a set of wavelet basis function {bits a, b (x)}, the bits of a, b (x) = 1 a bits (x - ba) (3)
Shall meet the conditions in the type a > 0 and a, b ∈ R. The variable a reflect the scale of a particular basis function, and b is pointed out the translation of it along the X axis. After determined the basis function, the original signal function f (x) in the wavelet bits (x) as the base of the continuous wavelet transform is the Wf (a, b) = ∫ + up - up f (x) bits a, b (x) d x (4)
3. 2 signal energy of wavelet packet decomposition
X (n) for signal after j scale of wavelet packet decomposition decomposable j = 2 j was the frequency range, that is each frequency component of energy:
EA0x (n) = Σ Nn - 1 (A0 (n)) x 2 (5) EDjx (n) = Σ n
N) (n - 1 (Djx) 2 (j = 1, 2,..., j - 1), (6)
Type EA0 x (n) signal in low frequency component of the energy on decomposition scale j, EDj x (n) signal in the high frequency on the decomposition scale j of energy.
The total energy of the signal is
The Ex (n) = EA0x (n) + EDjx (n) (7) 4 cutting tool wear AE signal selection of wavelet base
4. 1 theory analysis
According to the characteristics of the tool wear and the properties of wavelet base [5] can get the following conclusion:
(1) due to the tool wear is a gradual process, need a long time on the AE signal acquisition, thus makes the amount of data signal is relatively large. So from the consideration on the processing speed, should choose a small amount of calculation of wavelet base. Due to the discrete wavelet transform is smaller than the calculation capacity of the continuous wavelet transform, so the AE signal should be selected for the processing of discrete wavelet transform of wavelet base.
(2) in the process of machining, cutting tool will suddenly appear sometimes damage or collapse edge, and so on and so forth. In order to obtain the correct AE source information, must be able to pick up sudden AE signal accurately. The choice of the priority should be given in time domain is tight the wavelet base, at the same time in order to ensure that local analysis ability of wavelet base in the frequency domain, the requirements of wavelet base in frequency domain have rapid attenuation. 

(3) (4) using wavelet transform formula 'x = x - b after mathematics replace wavelet transform formula can be written
Wf (a, b) = 1 | a | ∫ + up - up f (x + b) bits (xa) d x (8)
Will type (4) and wavelet basis function type (8), can be found under different scale wavelet transformation is, in fact, the correlation of wavelet basis function and signal. The correlation of wavelet and signal, the better, the feature extraction of wavelet transform to signal that is, the more with the characteristics of wavelet analysis the signal more accurately. And AE signal in time domain is usually characterized by a class with a certain impact properties and approximate exponential decay properties of waveform signals, and have ability to continue. So the choice of wavelet base should have similar properties to the AE signal feature of providing better analysis results.
(4) the AE signal wavelet transformation, in order to ensure the accuracy of the AE signal characteristics, should minimize the distortion of the signal. By signal analysis theory, the choice with linear phase wavelet base in signal decomposition and reconstruction can avoid or reduce the signal distortion, and symmetry or antisymmetry function with linear phase, so the AE signal should choose as far as possible with symmetry of wavelet base.
(5) cutting tool in machining, the AE signal produced by the inevitable to be mixed with noise interference. After the wavelet transform to how to extract the AE signal from noise interference is a key problem to solve. By the properties of wavelet base, has a certain order disappear moment of wavelet base can effectively highlight the various exotic features of signal, the higher disappear moment, frequency domain localization ability is stronger. So choose to have a certain order disappear moment of wavelet base, can highlight the characteristics of AE signals.
4. 2 of wavelet base selection on AE signal analysis
According to the above analysis, meet the discrete wavelet transform and the time domain with tight branch disappear, symmetry, and has certain torque requirements of the commonly used wavelet has four kinds: Haar wavelet, Daubechies wavelet and wavelet and Symlets Coiflets wavelet [6]. Four kinds of wavelet function and the spectrum diagram is shown in figure 1 as shown in figure 1 a ~ d, respectively. 

You can see from figure 1, Haar wavelet maximum local analysis of time domain, but it isn't fast attenuation spectrum, frequency domain local analysis ability is poor. From the time domain waveform, Haar wavelet do not have the properties of approximate exponential decay, so time domain analysis ability of the Haar wavelet is not suitable for analysis of approximate exponential decay characteristics of AE signals. The other three kinds of wavelet in time domain is tight. Their spectrum also has fast attenuation, examine their time domain waveform, have certain oscillation damping characteristics, and the loss of this three kinds of wavelet has a certain moment, compared to disappear moment of 1 Haar wavelet is more suitable for analysis of AE signals. Based on the above analysis, we can draw the conclusion: in several kinds of commonly used wavelet, wavelet and wavelet and Symlets Daubechie Coiflets wavelet is suitable for the analysis of the AE signal wavelet. 

5 test and result analysis
5. 1 test process
Test conducted on numerical control lathe, the workpiece material for GH648, cutting tool material for KC5010; Using Beijing PengXiang PXR30 AE sensors, set the sampling frequency of 2 MHZ, sampling points to 12000. Cutting tool wear AE signal and its spectrum is shown in figure 2.
5. 2 cutting tool wear AE signal frequency domain energy feature extraction
By type (7), the signal after wavelet packet transform the energy equivalence relation and the original signal energy exists. Therefore measured by wavelet energy distribution of the original signal energy is reliable. By the wavelet packet analysis theory, the wavelet packet to multi-layer decomposition of signal, signal decomposition can be on any fine frequency band, on the frequency band energy statistics, form the characteristic vector, more hasten is reasonable [7].
In this paper to extract the subband after wavelet packet decomposition energy as feature vectors, is used to verify the correctness of the wavelet base selection. Specific steps are as follows: 

(1) adopt the Haar wavelet, wavelet, Daubechies8 Sym2lets8 wavelet and Coiflets4 for wavelet, wavelet packet function structure, the AE signal three layer wavelet packet transform. The theory of wavelet analysis shows that after three layer wavelet packet decomposition, the frequencies of each frequency band of the signal range as shown in table 1. 

(2) from each subband of wavelet packet transform coefficients, in order to each subband energy as feature parameters and characteristic vector E, is E = [E3, 1 E3, 2 E3, 3 E3, 4 E3, 5 E3, 6 E3, E3, 7, 8]. Make a characteristic vector bar chart is shown in figure 3. 

5. 3 validation results
(1) the figure 3, 3 b, 3 c, 3 d energy distribution of the change is more obvious, but the energy distribution of a figure changes relatively flat, namely the energy distribution in wide frequency range. This is mainly because the Haar wavelet frequency domain is not fast attenuation in the frequency domain local analysis ability is poor; In addition, because the Haar wavelet is not has approximate exponential decay properties of AE signal, the AE signal feature analysis ability is bad. According to the comparison in figure 3, shall not apply to AE signals Haar wavelet analysis, wavelet and wavelet and Symlets and Daubechie Coiflets wavelet is suitable for AE signal analysis.
(2) can be seen from the figure 2 signal spectrum diagram: tool of AE signal amplitude before 200 KHZ, around 450 KHZ and 850 KHZ after three areas of amplitude is bigger, other areas significantly smaller amplitude. From table 1 shows the above several frequency range most of the 1, 2 in figure 3, 4, 8 in four bands. Figure 3 illustrates the 3 b, 3 c, 3 d can reflect the energy concentrated in 1, 2, 4 band, but not 3 c, 3 d figure reflects the energy concentrated in band 8, only 3 b figure fully reflect the energy in 1, 2, 4, 8 bands, namely 3 b figure of each frequency band energy distribution can be optimally reflects the change of signal spectrum. Therefore, this experiment select db8 wavelet.
6 conclusion
Cutting tool wear AE signal wavelet analysis, the author of this paper the selection of wavelet base problems in theoretical analysis and experimental results show that although the wavelet and wavelet, Symlets8 Daubechies8 Coiflets4 wavelet are suitable for the characteristics of the cutting tool wear AE signal analysis, concrete analysis should be done but for specific AE signal, to choose the optimum wavelet base.