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Neural network detection of grinding burn from acoustic emission
International Journal of Machine Tools & Manufacture 41 (2001) 283–309
Neural network detection of grinding burn from acoustic emission Zhen Wang a, Peter Willett
a,*
, Paulo R. DeAguiar b, John Webster
c
a
b
Information & Computing Systems Group, Electrical and Systems Engineering Department, U-157, University of Connecticut, Storrs, CT, 06268-2157, USA Universidade Estadual Paulista – Unesp, Departamento de Engenharia Eletrica, Av. Luiz Edmundo C. Coube, s/n, Vargem Limpa, Bauru, Sa˜o Paulo, Cep 17033-360, Brazil c Unicorn International, Grinding Technology Centre, Tuffley Crescent, Gloucester GL1 5NG, UK Received 7 March 2000; accepted 30 June 2000
Abstract An artificial neural network (ANN) approach is proposed for the detection of workpiece “burn”, the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Acoustic emission; Grinding; Burn detection; Neural network
1. Introduction Acoustic emission (AE) is generally understood as the release of a vibrational wave emitted by a material reacting to applied stress. The acoustic emission generated during grinding and machining processes has been proved to be related to the process state and to the surface condition of the tool and workpiece [11,16]. AE technology has progressed significantly and has been widely
* Corresponding author. Tel.: +1-860-486-2195; fax: +1-860-486-5585. E-mail address: [email protected] (P. Willett).
0890-6955/01/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 5 7 - 2
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investigated as a non-destructive testing method for monitoring grinding and machining processes, including wheel/work contact [16,9], surface integrity [26], metal cutting [10], tool wear [5], etc. Most formal research has relied on AE root-mean-square (RMS) power and statistics derived therefrom to determine the grinding condition and performance. Since the “averaging” nature of RMS makes it insensitive to short-duration events (such as cracks) which may be of interest, here we use instead the raw AE signals as collected by a high-frequency (2.56 MHz) analog-to-digital (A/D) converter. Of particular interest to us here is the detection of superficial workpiece burn during the grinding process. When the energy in the wheel/workpiece contact area generates a temperature increase, this can lead to an increased tendency for adhesion of metal particles to the abrasive grains, thereby accelerating the rise in temperature. This causes burning of the workpiece. This is sometimes observable visually by a bluish temper color, but more generally requires time-consuming chemical means for its after-the-fact determination. To increase the effectiveness of the grinding process and reduce the cost, reasonable in-process detection of burn is clearly of major interest in grinding operations. Prior successful application of AE in grinding, and the fact that the AE signals are generated directly in the deformation zone of the grinding process and are therefore presumably closely connected to the condition of the workpiece surface, make AE a promising means to detect burn. Previously [4,14] AE amplitude analysis was used, based on the observation that sudden changes in the AE RMS power can be indicative of burn. In many cases, burn does not have a large signature in the power level of the AE signal. Wheel-period correlation was introduced in [8], and could be used quite accurately to determine the rotational speed of the grinding wheel. The variation in wheel speed and the level of self-correlation of the AE signal between wheel rotations were used to indicate burn. It should be noted that these are methods relying on single statistics, and hence may be termed threshold methods. When AE is applied to burn detection in grinding, the noise resulting from the normal grinding process complicates burn detection. It is difficult to separate AE signals from normal grinding and from burn generation — especially as they can be emitted simultaneously from essentially the same physical location — with a threshold method. We have applied a number of (thresholdable) statistics in this paper. One of these is statistical analysis based on the distribution moments of the AE signal. A popular one of these is the kurtosis [2,12], defined as a ratio of the fourth central moment to the square of the second central moment. The kurtosis and skewness statistics have attracted considerable interest [18], since it is supposed that they are sensitive to a process change, such as metal fracture, the occurrence of tool failure or burn. The skewness (normalized central third moment) measures the symmetry of a probability distribution, while the kurtosis is a measure both of the sharpness of the distribution’s peak and the probability of outlying (unexpectedly large) samples. Both time- and frequency-domain kurtosis analyses have been explored using real data; it is apparent that some more sophisticated approach is necessary. Despite the name, a neural network (NN) is basically an adaptive non-linear functional approximator. The non-linear mapping implicit to the NN is determined by adjustable parameters, with these trained from a data set. There are two broad classes of NN. The most easily recognized is the multi-layer perceptron (MLP), whose feed-forward structure and sigmoidal “neurons” were originally supposed to mimic those of the brain. The other structure is that of the radial basis
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function (RBF) network, which can be thought of as a functional approximator using (usually) Gaussian-shaped kernels. For the present discussion, the important characteristics of both NNs are their ability to recognize and realize general functions as suggested by training data, and their correlative ability to explain their outputs by groups of input data, taken jointly. Thus it is natural to consider an NN when a threshold method does not work. In this paper, a neural network was trained and tested to identify burn during grinding. Our approach distinguishes itself by using the RBF architecture, and through the use of Wiener coefficients as input features. NNs based on AE have been successfully applied to a number of relevant problems [1,25], such as the identification of grinding vibration [20,7] and the detection of tool degradation [27]. Most NNs applied to AE have been of the MLP variety. There are two reasons for our selection of the RBF structure. First, while it is quite common to use an MLP for classification (that is, with a discrete and finite-valued output alphabet, such as normal or burn), the MLP’s smooth approximation makes this an uneasy marriage. By contrast, although an RBF network can have a smooth output, when configured as a mixture-density hypothesis test its application to classification is quite natural. Second, training of an RBF is relatively quick and predictable, while that of an MLP can be (and usually is) glacial; in the grinding application, this could imply many minutes of machine down-time awaiting a computed result. A positive aspect of the MLP architecture is that, to some extent at least, there is internal selforganization in that “weights” accorded to informative features are increased and those accorded to less relevant features reduced. Thus it is important, if an RBF is used, that the raw AE signals be preprocessed to a decent feature set prior to their NN use. In the literature, various features of the acoustic signature have been taken as the input of the NN, such as fast Fourier-transformed data [7], the peaks of RMS acoustic emission [27] and the overall shape of the frequency spectrum. In this research we have tested a variety of parameters, such as power spectrum frequency components and histograms of amplitude, for characterizing the AE signal from the grinding process, and used them as input to the NN. On the basis of our tests and analysis, Wiener filter coefficients have been most useful. Based on the real grinding experiments, it turns out that the trained NN can indicate burn successfully. The objective of this paper is to provide effective ways to identify the occurrence of burn during grinding, and especially to examine the potential of the NN approach. The paper first provides an introduction to the grinding experiment used here and gives some brief idea of the AE raw signal we will deal with later. A description of the statistics, especially the kurtosis, the constant false-alarm rate (CFAR) power law, the mean-value deviance (MVD) and the NN approach employed for burn detection, follows. Experimental results are presented and discussed. 2. Experiments The experiment was carried out on a Norton Grinder. Fig. 1 shows the instrument set-up. Specifically, data from eight different experiments, involving an easy-to-grind bearing steel (52100), were collected. The system consists of the sensor, a preamplifier, a post amplifier and a data-acquisition system. The AE signal was received by a commercially available AE sensor (PAC U80D-87, whose frequency characteristics are known) that was mounted directly on the workpiece via adhesive. The sensor’s AE signal was amplified by a preamplifier and a post ampli-
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Fig. 1. Set-up of the AE test.
fier. The overall amplification factor for the grinding test was 40 dB. The data-acquision system was a Hewlett-Packard E1430A running in continuous-sampling mode at 2.56 MHz sampling rate. The A/D accuracy was 16 bits per sample, and appropriate anti-aliasing filtering was performed internal to the HP system. Grinding parameters were as follows: 앫 앫 앫 앫 앫
wheel peripheral speed — 2000 rev/min; grind wheel type — aluminum oxide; wheel diameter — 9.6 in; workpiece feed rate — 103.7 in/min; coolant — Master Chemical VHP 200, with flow rate of 0.88 gal/min.
Most parameters were kept constant among all tests, except that the depth of cut was varied. Generally, the more aggressive the cutting depth, the more likely burn was to occur. Details of the tests are shown in Table 1. To show “burn” and “non-burn” signatures in the same workpiece, in tests 4–8 the workpiece was ramped or tented as shown in the table. In these case, the depth of cut changed (piecewise) linearly. All workpieces were examined post-mortem to check the condition, and signs of burn were noted. The workpiece burn of steel 52100 is assayed visually and through laboratory testing. The visual burn location is indicated in Table 1. Both the surface hardness tests and the surface profile
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Table 1 The tests for the steel 52100 workpiece. All workpieces were 3.1 in long Test
Depth of cut (in)
Cut profile
Burn location (in)
Comments
1 2 3 4 5
0.001 0.0005 0.003 0.002 0.0015-0.004
flat flat flat flat
– – 0.06-3 0.2-2.9 1.0-3
no burn no burn almost all burn almost all burn a ramp cut
6
0.001-0.004
1.25-3
a ramp cut
7
0.0003-0.0048-0.0003
0.2-2.8
a tent cut
8
0.0005-0.0045-0.0005
0.4-2.5
a tent cut
measurements were taken to provide burn-recognition information. At 32 equally spaced points along each workpiece, a Leco M400-G2 Hardness Tester was used to record hardness values. The surface profile test was done by a computer-connected stylus surface measurement, and the surface roughness values obtained were used to quantify the workpiece surface characteristics. A typical AE trace observed and the corresponding power spectral density (PSD) are given in Fig. 2. It would be ideal to have data about the original AE; that is, the acoustic signature from the zone of the wheel/workpiece interface. However, since the signal is distorted by the sensor characteristic (it is in fact a strongly narrowband filter), and more particularly since the AE must pass through an unknown and changing medium involving the workpiece, coolant and apparatus on its way from the contact zone to the sensor, this is not reasonable.
3. Detection tools 3.1. What did not work A number of statistics were applied individually to the collected data for detection of burn. For the most part these statistics were normalized, or otherwise rendered independent of the local AE power: the AE RMS power can rise or fall for reasons having little to do with grinding condition, and in any case has been found to have limited predictive efficacy. 3.1.1. Zero-crossing rate (ZCR) “Count” technology is not new in AE applications [3]. As the name implies, this method counts the number of zero-crossing events during each block of observed data. For a monochromatic signal, twice the time between zero-crossings is the reciprocal of the frequency; for the complicated signals observed, the meaning is less clear. At any rate, little predictive capability was found in this statistic.
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Fig. 2. A typical “raw” AE trace (top) and the corresponding PSD spectrum (bottom) from the beginning of a grinding regime. Note that the spectrum is plotted logarithmically.
3.1.2. Ratio of power (ROP) It is natural to examine the behavior of the power spectrum of AE, with the idea that the frequency behavior of “good” and “bad” grinding may differ. Thus, for each block of data, the ROP was calculated from the normalized power spectrum as
冘 冘 n2
ROP⫽
N⫺1
兩Xk兩 / 2
k⫽n1
兩Xk兩2,
(1)
k⫽0
in which the denominator eliminates the effect of the local signal power. Here, N (N=1024) is the chosen length of fast Fourier transform (FFT), Xk is the kth DFT output, and the summation is over any range of frequency, represented as from discrete Fourier transform (DFT) “bins” n1 to n2. A significant effort went toward identification of promising frequency bands (and indeed sets of bands), with little success. Our conclusion is that either the effect is small, or it is irretrievably lost due to the sensor characteristic. 3.1.3. Amplitude histogram The amplitude histogram of each block data was obtained and analyzed. Effort was expended to find the difference between the distributions, but no promising relationship was noted.
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3.1.4. Wheel-period power correlation This statistic was introduced in [8], and is presented in more detail there. The basic idea is that the wheel profile (presumably the abrasive grains themselves) can be observed in the AE trace. Since the wheel’s profile is relatively constant from rotation to rotation (few grains dislodge or slip), there is a high degree of correlation between wheel-pass periods. This is manifested as an autocovariance “peak” whose lag is the wheel’s rotation period. As such, the wheel’s speed can be accurately measured from the time between peaks (a spindle-mounted speed sensor could do this too); but, more important, the amount of correlation was observed in [8] to be indicative of burn. Here, example results from test 3 are given in Fig. 3. The difference in the correlation values can be seen, but it is hard to set a reasonable threshold. The fact that this statistic worked elsewhere [8] and not here is attributed to the different apparatus: we hope that the wheel-period power correlation may prove useful in some applications, but apparently its utility is not universal. 3.1.5. Kurtosis It can be argued that the characteristics of the AE signal are related to those of the surface profile. The shape of the probability distribution of a surface profile can play a major role in revealing changes in the process producing the surface (e.g., tool wear) [19]. The kurtosis, the normalized fourth-order central moment, appears to be a useful measure. A high kurtosis value
Fig. 3. Wheel-period power correlation and wheel speed measured from AE for test 3.
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implies a sharp distribution peak and/or a high (relative to Gaussian) probability of observing an outlying sample. 3.1.5.1. Time-domain kurtosis (TDK) Let xi, i=1, …, n, represent the real discrete AE data, and let n be the number of data points of each block. The empirical kurtosis statistic [2] used in this paper has the form
冘 冋冘 册 n
Kt⫽
1 (x −x¯)4 ni⫽1 i n
1 (x −x¯)2 ni⫽1 i
,
2
(2)
where x¯ is the empirical sample mean:
冘 n
1 x. x¯⫽ ni⫽1 i
(3)
In our implementation we use n=76,800, meaning that each block lasts 30 ms or approximately one rotation of the wheel. Based on our experimental results it was found that TDK is related to burn as shown in the upper plot of Fig. 4, but large variation was observed. The variations make it difficult to set the reasonable threshold and certainly reduce the detection performance. TDK will be used later as the input to the NN.
Fig. 4.
TDK and FDK for test 6. Dashed vertical lines indicate the location of burn.
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3.1.5.2. Frequency-domain kurtosis (FDK) Particularly if the time-domain signal contains transient bursts of enhanced energy (e.g., from grain contact), higher-order moments of the complex frequency components may contain additional information that could be utilized in detecting signals. Thus we can compute the frequency-domain kurtosis (FDK) for the real or imaginary parts of the complex frequency components. The FDK [12,13] represents a measure for the probability distribution over a time interval consisting of N DFTs each of length M. The operation is described as
冘 冋冘 N
1 (X (q)−X¯k)4 Nq⫽1 k
Kf(k)⫽
N
1 (X (q)−X¯k)2 Nq⫽1 k
册
,
2
(4)
where X¯k is the empirical sample mean
冘 N
X¯k⫽
1 X (p) Nq⫽1 k
(5)
and Xk(q) is the real part of the kth DFT output of the segment q, k苸{1, M}. Only the real part will be discussed here, and of course a similar analysis can be used with the imaginary part. Our zero-mean raw AE signal was processed utilizing a 512-point FFT (M=512) and the FDK was obtained by appropriately dealing with the 150 consecutive FFT outputs (N=300), giving an overall time interval of 30 ms. The middle plot in Fig. 4, showing the FDK for k=60 (300 kHz), is typical: there is little predictive power. By contrast, the lowest plot in Fig. 4 shows the FDK for k=256 — it appears that this result is similar to that for the TDK. The results of FDK with k=256 for different tests are shown in Fig. 5, which can provide useful information to indicate burn. However, k=256 corresponds to 1280 kHz (half the sampling rate, otherwise known as the “folding frequency”) which is far out-of-band, Hence, while this is intriguing, it is mostly a curiosity. 3.2. What worked 3.2.1. CFAR power law As applied to the detection of transient events, a detector attracting much attention and interest is Nuttall’s power-law statistic [22]
冘
M⫺1
Tpl(X)⫽
Xnk ,
(6)
k⫽0
where the Xk is the kth magnitude-squared FFT bin, n is a changeable exponent and 2M is the total number of FFT bins (due to conjugate symmetry, only half of the magnitude-squared FFT bins need be interrogated). Respectively n=1 and n=⬁ correspond to the energy detector and max{Xk}; 2⬍n⬍3 provides good performance in a wide range. Although it is effective in some models and easy to implement, this statistic relies on pre-normalized data. Due to the fluctuation
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Fig. 5. FDK with k=256 for tests. Dashed vertical lines indicate the location of burn and dashed horizontal lines illustrate the possible threshold.
of the AE signal during the grinding process, a constant false alarm-rate (CFAR) power-law [23] statistic is used
冘 冉冘 冊 M⫺1
Xnk
Tcpl(X)⫽
k⫽0
M⫺1
,
n
(7)
Xk
k⫽0
where Tcpl is clearly not affected by signal amplitude. With M=32, for each time interval of 1 ms, our {Xk} are taken as the PSD of the raw AE signal. The example results of power law and the CFAR power law are compared in Fig. 6. To see the results more clearly, the averaged statistic value in each wheel rotation (the length is 30 ms) was used instead. The CFAR power law appears
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Fig. 6. Results of power law and CFAR power law for test 8. Dashed vertical lines indicate the location of burn. From left to right, n is 0.5, 2.5 and ⬁, respectively.
to be an effective method to detect burn; the unnormalized power-law statistic may indeed be informative, but due to amplitude dependence its wide variation suggests that it is unsuitable. 3.2.2. MVD Processed in the frequency domain, the CFAR mean-value deviance (MVD) statistic [6] is defined as
冘
M⫺1
1 log[X¯/Xk], Tmvd(X)⫽ M k⫽0
(8)
where X¯ is the mean value of {Xk}; M and Xk have the same meanings as in the CFAR powerlaw statistics. The MVD statistic has been proved to be effective in the detection of transients in some applications. The MVD appears to be useful for burn detection. 3.2.3. Neural network detection scheme 3.2.3.1. Feature selection The NN-based detection scheme is shown in Figs. 7 and 8. The inputs in Fig. 7 are, in classification parlance, the features on which a decision is to be based. These must be chosen judiciously and succinctly, since the selection of a set of features too great for the number of training data usually results in “overtraining”; that is, of the adaptation of the classifier to spurious non-generalizable patterns [24]. Feature selection is at best an art, and is
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Fig. 7.
Detection scheme of burn recognition using feature set 2.
more usually a matter of trial and error. In this work the best results have been with two following feature vectors. 3.2.3.2. Feature vector 1: univariate statistics The frequency band power, the kurtosis and skew are informative features of the AE signals. Similar to the definition of kurtosis in Section 3.1.5, the empirical skew statistic has the form
冘 冋冘 册 n
Ts⫽
1 (x −x¯)3 ni⫽1 i n
1 (x −x¯)2 ni⫽1 i
1.5
,
(9)
where n=2560 in our implementation. The kurtosis is a measure of the sharpness of the peak while the skew measures the symmetry of the distribution about its mean. It has been observed that the 240–400 kHz band is informative, and hence we concentrate on that. The band power between 240 and 400 kHz, the kurtosis and the skew for test 5 are shown in the top part of Fig. 9. Large variations of these three features during grinding are observed, and affect the NN performance of detection. Consequently, for a stable NN input, we preprocess as
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Fig. 8. A generic radial basis network.
follows. For each specified block of AE signal, we calculate a feature series {T(i)}. For each feature series {T(i)} (this can refer to band power, kurtosis or skew), the mean and the standard deviation are calculated to form the new features:
冘 l
1 T(i) mT ⫽ l i⫽1
(10)
and sT⫽
冪
冘 l
1 (T(i)−mT)2, l−1i⫽1
(11)
where l is the window size. From the above process, the feature vector V1 corresponding to band power, kurtosis and skew is extracted V1⫽{mp, mk, ms, sp, sk, ss},
(12)
where mp, mk and ms are the mean values of the frequency band power, kurtosis and skew; and sp, sk and ss are the corresponding standard deviation values. The refined features of test 5 are plotted in the middle and bottom part of Fig. 7: it is clear that the values of the refined features fluctuate less. The window size l is experimentally based, and is set to 30 in our actual use; that is, each feature vector was extracted from a 30 ms block AE signal.
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Fig. 9. Features for test 5 using band power, kurtosis and skew. The top three plots show the statistics themselves as based on 1 ms block averages; the middle and lower plots are of means and standard deviations based on l=30 blocks. These latter six features form feature set 1.
3.2.3.3. Feature vector 2: Wiener coefficients In the linear prediction problem it is desired to estimate the nth element of a time series x(n) using {x(m)}n−1 m=n−M — the previous M time samples. That is, the vector h={h(1), h(2), …, h(M)} which minimizes
再冋 冘 M
T
2
E{[x(n)⫺h x(n)] }⫽E x(n)⫺
k⫽1
册冎 2
h(k)x(n⫺k)
(13)
is sought — this is a version of the Wiener filtering problem. It may appear strange to estimate x(n) based on the M prior samples when one could simply wait one sample and have it; but it is
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the form of the filter which matters. In fact, the vector h so derived coincides with that used for autoregressive (AR) and maximum entropy (ME) spectral modeling, in that the AR spectral estimate is fAR x (w)⫽
|冘
2
M
1−
k⫽1
h(k) e−jwk
|
(14)
in which is a proportionality constant. The Wiener/AR coefficients are also sometimes referred to as linear prediction coefficients (LPCs), and are used as signal descriptors both for speech coding/compression and speech recognition. At any rate, the point is that the Wiener coefficients summarize a considerable amount of spectral information in a relatively few numbers. In this work we regard each block with length 30 ms (76800 samples) — approximately one wheel period — as stationary, and compute the Wiener coefficients based on data from each block. Adaptive Wiener whitening [15] was performed on each individual raw AE signal segment 9 {x(n)}7679 n=0 . Let R denote the M×M correlation matrix of the tap inputs:
Fig. 10. The patterns of the w-coefficient feature vectors: (a) “burn” state; (b) “non-burn” state; (c) “no-grinding” state.
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冢
R⫽
r(0)
r(1)
… r(M−1)
r(1)
r(0)
… r(M−2)
⯗
⯗
哻 ⯗
r(M−1) r(M−2) … r(0)
冣
,
(15)
where M is the filter order, and the autocorrelation r(·) is estimated as
冘
N⫺k⫺1
r(k)⫽
(x(n)x(n⫹k)).
(16)
n⫽0
Correspondingly, let p denote the M×1 cross-correlation vector p⫽[r(1)r(2)…r(M)]T.
(17)
Thus, the M×1 coefficient vector of the Wiener filter is obtained by solving Rh⫽⫺p.
(18)
While either matrix inversion or Gaussian elimination [O(M3)] are sufficient to solve for the Wiener coefficients, a particularly efficient O(M2) algorithm due to Levinson and Durbin (again, see [15]) is also available. Fig. 10 shows a typical representation of the feature vectors reflecting the “burn”, “non-burn” and “no-grinding” states. The vectors themselves are shown in the upper plots, and the corresponding AR spectra in the lower. Note that the AR order M is determined experimentally. Various orders from M=5 to 50 were assayed; it was found that M=10 gave the best results.
Fig. 11. The detection results of the radial basis NN and feed-forward NN for test 2.
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Fig. 12. The results of test 1, no burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “nonburn”, and ⫺1 “no-contact”. The dashed horizontal lines in the upper two plots denote the thresholds; values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
3.2.3.4. The radial basis NN approach The Matlab toolbox “NNET” was used in our NN implementation. The structure of the radial basis artificial neural network (ANN) using “NNET” is shown in Fig. 8. It includes an input layer, the radial basis function layer, and one linear layer output neuron. Each input vector is fully connected by a weight matrix to the radial basis layer, and these in turn are fully connected by another weight matrix to the linear output layer. To avoid “overcrowding”, a bias vector is used for each layer. There is only one output from the network, which shows whether grinding burn occurs or not. The RBF NNs, which have been widely advocated [21], are approximations of the form
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Fig. 13. The results of test 2, no burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “nonburn”, and ⫺1 “no-contact”. The dashed horizontal lines in the upper two plots denote the thresholds; values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
冘
bj G(储x⫺xj 储/sj )
y⫽a⫹
(19)
j
for centers xj, where G(r)=exp(⫺r2/2), s is a scale factor. Using RBFs as the basis functions, a network such as in Fig. 8 represents that the output is
冘 nj
y⫽b2⫹
j⫽1
冘 ni
2 1j
w2j exp[⫺b
i⫽1
(w1ji⫺xi)2],
(20)
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Fig. 14. The results of test 3, heavy burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
where x is the input vector with size ni×1, ni and nj are separately the numbers of neurons used in the input and “hidden” layers. The trainable parameters w1 and b1 are, respectively, an nj×ni weight matrix and the nj×1 bias vector for the hidden layer, and w2 and b2 are the corresponding 1×nj weight matrix and scalar bias for the linear (output) layer. The NN is established through the training phase. The number of neurons used in the radial basis layer, nj, was originally set as 1 and increased by one each time until performance was acceptable. The actual error is defined as the sum of the squared differences between the desired output and the actual output over a specified number of input vectors. During this development
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Fig. 15. The results of test 4, heavy burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
process, the network modifies the connections between individual processing neurons, represented by w1, w2, b1 and b2. Just as in any statistical analysis, an implied requirement for developing robust neural network models is that the training sets cover as many of the possible variations in the input and output vector as feasible. For practical considerations, a limited number of samples should be used. Thus care must be taken when choosing the training set to ensure that it be broad-based. There are three possible distinguished states during the grinding process: the no (workpiece/wheel) contact
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Fig. 16. The results of test 5, ramp cut with burn at end. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2 respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
stage; normal grinding; and burn. For our case, 10 “burn”, 10 “non-burn” and 10 “no-grinding” inputs were used to train the neural network. Where grinding burn was identified, the output of the NN was set to 1, 0 was set for the “non-burn” case and ⫺1 was chosen when the input featured “no-grinding”. The training allows the NN to provide detection results with reasonable confidence. Ultimately, the weight matrices and bias vectors were obtained, and served to decide the NN structure. Different kind of inputs result in different networks. The final NN structure has ni=6 and nj=5
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Fig. 17. The results of test 6, ramp cut with burn at end. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
when we used the feature vector V1 as inputs. Otherwise, if the inputs was taken as the feature vector V2 (the AR coefficients), the radial basis network utilized consists of ni=10 neurons in the input layer and nj=3 neurons in the radial basis layer. The two radial basis networks have been used successfully to detect grinding burn. If the value of the output was larger than 0.5, grinding burn was declared. The closer to 1 the output, the more confident the burn detection. The closer to 0 the output, the more it is possible to declare “non-burn”. Finally, a usually worthy competitor to the RBF NN is the perhaps more popular MLP feed-
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Fig. 18. The results of test 7, tent cut with burn in middle. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
forward network (multilayer perceptron) with a back-propagation training structure [24]. This also was also explored. In general, although performance is often reasonable, the feed-forward NN tends to give false alarms; an example output is offered in Fig. 11. Considering that RBF training is faster and usually more faithful than that for the MLP, we have opted for the RBF structure.
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Fig. 19. The results of test 8, tent cut with burn in middle. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”. In this test, the start and end parts of the workpiece were not ground.
4. Results The feature vectors 1 and 2 calculated from the raw AE signals of tests 1 to 8 were treated for the above NN implementations. The results of burn detection are shown in Figs. 12–19. Each block covers 30 ms of the grinding process, corresponding to the period of the wheel rotation. In each figure, the upper two plots are results of the CFAR power law and the MVD detectors used for reference and comparison; the middle two show the detection performance of the radial basis
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networks, where “NN output 1” indicates the output of the network using feature vector V1 as inputs and “NN output 2” is the output of the network using feature vector V2. The lowest plot in each shows the results from the post hardness and profile tests, which can identify cases of burn and non-burn. The hardness and the profile values are normalized by 1000 and 0.002, respectively. We can see that the CFAR power-law and the MVD methods provide useful information about burn. Based on our experiment, we set 5.15 as the threshold of the CFAR power law with n=0.5 and 0.05 as the threshold of the MVD detector. Burn is declared if the value of the CFAR powerlaw method is larger than 5.15 or the MVD value is less than 0.05. As with any threshold detectors, there is the disadvantage that the setting of the threshold is experience-based and may be situation-dependent. It was noted that the value difference between the “no-grinding” signal and the “burn” signal is quite small; in the NN approach, there is no such concern. It is easily noticed that the NN shows effective performance in all tests. It is clear from the post hardness and profile tests that the NN method indicates a “burn” signature before the occurrence of the true burn — a particularly useful characteristic. Note that despite the NN having been trained with but 30 samples (10 from each regime), the performance over the much larger test data set is remarkably stable: for feature sets 1 and 2, the plots show the NN outputs given at respectively 30 ms and 3 ms intervals!
Fig. 20.
A distorted AE signal due to preamplifier overload.
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5. Summary The goal has been to detect abnormal grinding conditions via appropriate digital signal processing of acoustic emission (AE) data, this information being sampled at a high (2.56 MHz) rate and used in its raw (i.e., not RMS) form. The data were collected from a sequence of tests on 52100 bearing steel and a variety of conditions; the workpieces were assayed post-mortem for their quality, so that this could be compared with the AE collected. For the most part, the “threshold”-oriented statistical tools — that is, those which digest the data to a single statistic to be compared with some preset value — were found to have limited ability in predicting grinding state. Exceptions to this include certain statistical tools recently finding application in the identification of transient events, particularly in sonar. The efficacy of these tools is intriguing, but for the most part they are eclipsed by a neural network approach based on the fast-training radial basis function (RBF) architecture. For these, despite training on a remarkably small set, identification of burn over a much larger test set is essentially perfect. Two families of “feature vectors” (inputs to the neural networks) are employed, one based on autoregressive parameters and the other on a vector of averaged statistical properties. In both cases the performance is good, and there does not seem to be a reason to prefer one over the other.
Acknowledgements This research was supported by the National Science Foundation under contract DMI-9634859.
Appendix A. Note about distortion There are some remarks about a somewhat obscure form of distortion in [17], and since this kind of distortion was indeed observed in the early phases of our work we would like to report on it here in the hope that other researchers may avoid the problem. The AE signals originating from the grinding zone were occasionally quite strong, and such high-amplitude signals could cause overload in the preamplifier and distortion of the signals, as shown in Fig. 20. One might expect an amplifier overload to be accompanied by a saturated or “clamped” output, and thus be easily discernible. But when the overload is of significant duration and there is a high-pass (or bandpass) filter between the overloaded amplifier and the point of observation, the effect is less clear. In fact, what is observed is an interval initially resembling the impulse response of the filter, and then with no signal at all. An example is shown in Fig. 20.
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Neural network detection of grinding burn from acoustic emission Zhen Wang a, Peter Willett
a,*
, Paulo R. DeAguiar b, John Webster
c
a
b
Information & Computing Systems Group, Electrical and Systems Engineering Department, U-157, University of Connecticut, Storrs, CT, 06268-2157, USA Universidade Estadual Paulista – Unesp, Departamento de Engenharia Eletrica, Av. Luiz Edmundo C. Coube, s/n, Vargem Limpa, Bauru, Sa˜o Paulo, Cep 17033-360, Brazil c Unicorn International, Grinding Technology Centre, Tuffley Crescent, Gloucester GL1 5NG, UK Received 7 March 2000; accepted 30 June 2000
Abstract An artificial neural network (ANN) approach is proposed for the detection of workpiece “burn”, the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Acoustic emission; Grinding; Burn detection; Neural network
1. Introduction Acoustic emission (AE) is generally understood as the release of a vibrational wave emitted by a material reacting to applied stress. The acoustic emission generated during grinding and machining processes has been proved to be related to the process state and to the surface condition of the tool and workpiece [11,16]. AE technology has progressed significantly and has been widely
* Corresponding author. Tel.: +1-860-486-2195; fax: +1-860-486-5585. E-mail address: [email protected] (P. Willett).
0890-6955/01/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 5 7 - 2
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investigated as a non-destructive testing method for monitoring grinding and machining processes, including wheel/work contact [16,9], surface integrity [26], metal cutting [10], tool wear [5], etc. Most formal research has relied on AE root-mean-square (RMS) power and statistics derived therefrom to determine the grinding condition and performance. Since the “averaging” nature of RMS makes it insensitive to short-duration events (such as cracks) which may be of interest, here we use instead the raw AE signals as collected by a high-frequency (2.56 MHz) analog-to-digital (A/D) converter. Of particular interest to us here is the detection of superficial workpiece burn during the grinding process. When the energy in the wheel/workpiece contact area generates a temperature increase, this can lead to an increased tendency for adhesion of metal particles to the abrasive grains, thereby accelerating the rise in temperature. This causes burning of the workpiece. This is sometimes observable visually by a bluish temper color, but more generally requires time-consuming chemical means for its after-the-fact determination. To increase the effectiveness of the grinding process and reduce the cost, reasonable in-process detection of burn is clearly of major interest in grinding operations. Prior successful application of AE in grinding, and the fact that the AE signals are generated directly in the deformation zone of the grinding process and are therefore presumably closely connected to the condition of the workpiece surface, make AE a promising means to detect burn. Previously [4,14] AE amplitude analysis was used, based on the observation that sudden changes in the AE RMS power can be indicative of burn. In many cases, burn does not have a large signature in the power level of the AE signal. Wheel-period correlation was introduced in [8], and could be used quite accurately to determine the rotational speed of the grinding wheel. The variation in wheel speed and the level of self-correlation of the AE signal between wheel rotations were used to indicate burn. It should be noted that these are methods relying on single statistics, and hence may be termed threshold methods. When AE is applied to burn detection in grinding, the noise resulting from the normal grinding process complicates burn detection. It is difficult to separate AE signals from normal grinding and from burn generation — especially as they can be emitted simultaneously from essentially the same physical location — with a threshold method. We have applied a number of (thresholdable) statistics in this paper. One of these is statistical analysis based on the distribution moments of the AE signal. A popular one of these is the kurtosis [2,12], defined as a ratio of the fourth central moment to the square of the second central moment. The kurtosis and skewness statistics have attracted considerable interest [18], since it is supposed that they are sensitive to a process change, such as metal fracture, the occurrence of tool failure or burn. The skewness (normalized central third moment) measures the symmetry of a probability distribution, while the kurtosis is a measure both of the sharpness of the distribution’s peak and the probability of outlying (unexpectedly large) samples. Both time- and frequency-domain kurtosis analyses have been explored using real data; it is apparent that some more sophisticated approach is necessary. Despite the name, a neural network (NN) is basically an adaptive non-linear functional approximator. The non-linear mapping implicit to the NN is determined by adjustable parameters, with these trained from a data set. There are two broad classes of NN. The most easily recognized is the multi-layer perceptron (MLP), whose feed-forward structure and sigmoidal “neurons” were originally supposed to mimic those of the brain. The other structure is that of the radial basis
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function (RBF) network, which can be thought of as a functional approximator using (usually) Gaussian-shaped kernels. For the present discussion, the important characteristics of both NNs are their ability to recognize and realize general functions as suggested by training data, and their correlative ability to explain their outputs by groups of input data, taken jointly. Thus it is natural to consider an NN when a threshold method does not work. In this paper, a neural network was trained and tested to identify burn during grinding. Our approach distinguishes itself by using the RBF architecture, and through the use of Wiener coefficients as input features. NNs based on AE have been successfully applied to a number of relevant problems [1,25], such as the identification of grinding vibration [20,7] and the detection of tool degradation [27]. Most NNs applied to AE have been of the MLP variety. There are two reasons for our selection of the RBF structure. First, while it is quite common to use an MLP for classification (that is, with a discrete and finite-valued output alphabet, such as normal or burn), the MLP’s smooth approximation makes this an uneasy marriage. By contrast, although an RBF network can have a smooth output, when configured as a mixture-density hypothesis test its application to classification is quite natural. Second, training of an RBF is relatively quick and predictable, while that of an MLP can be (and usually is) glacial; in the grinding application, this could imply many minutes of machine down-time awaiting a computed result. A positive aspect of the MLP architecture is that, to some extent at least, there is internal selforganization in that “weights” accorded to informative features are increased and those accorded to less relevant features reduced. Thus it is important, if an RBF is used, that the raw AE signals be preprocessed to a decent feature set prior to their NN use. In the literature, various features of the acoustic signature have been taken as the input of the NN, such as fast Fourier-transformed data [7], the peaks of RMS acoustic emission [27] and the overall shape of the frequency spectrum. In this research we have tested a variety of parameters, such as power spectrum frequency components and histograms of amplitude, for characterizing the AE signal from the grinding process, and used them as input to the NN. On the basis of our tests and analysis, Wiener filter coefficients have been most useful. Based on the real grinding experiments, it turns out that the trained NN can indicate burn successfully. The objective of this paper is to provide effective ways to identify the occurrence of burn during grinding, and especially to examine the potential of the NN approach. The paper first provides an introduction to the grinding experiment used here and gives some brief idea of the AE raw signal we will deal with later. A description of the statistics, especially the kurtosis, the constant false-alarm rate (CFAR) power law, the mean-value deviance (MVD) and the NN approach employed for burn detection, follows. Experimental results are presented and discussed. 2. Experiments The experiment was carried out on a Norton Grinder. Fig. 1 shows the instrument set-up. Specifically, data from eight different experiments, involving an easy-to-grind bearing steel (52100), were collected. The system consists of the sensor, a preamplifier, a post amplifier and a data-acquisition system. The AE signal was received by a commercially available AE sensor (PAC U80D-87, whose frequency characteristics are known) that was mounted directly on the workpiece via adhesive. The sensor’s AE signal was amplified by a preamplifier and a post ampli-
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Fig. 1. Set-up of the AE test.
fier. The overall amplification factor for the grinding test was 40 dB. The data-acquision system was a Hewlett-Packard E1430A running in continuous-sampling mode at 2.56 MHz sampling rate. The A/D accuracy was 16 bits per sample, and appropriate anti-aliasing filtering was performed internal to the HP system. Grinding parameters were as follows: 앫 앫 앫 앫 앫
wheel peripheral speed — 2000 rev/min; grind wheel type — aluminum oxide; wheel diameter — 9.6 in; workpiece feed rate — 103.7 in/min; coolant — Master Chemical VHP 200, with flow rate of 0.88 gal/min.
Most parameters were kept constant among all tests, except that the depth of cut was varied. Generally, the more aggressive the cutting depth, the more likely burn was to occur. Details of the tests are shown in Table 1. To show “burn” and “non-burn” signatures in the same workpiece, in tests 4–8 the workpiece was ramped or tented as shown in the table. In these case, the depth of cut changed (piecewise) linearly. All workpieces were examined post-mortem to check the condition, and signs of burn were noted. The workpiece burn of steel 52100 is assayed visually and through laboratory testing. The visual burn location is indicated in Table 1. Both the surface hardness tests and the surface profile
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Table 1 The tests for the steel 52100 workpiece. All workpieces were 3.1 in long Test
Depth of cut (in)
Cut profile
Burn location (in)
Comments
1 2 3 4 5
0.001 0.0005 0.003 0.002 0.0015-0.004
flat flat flat flat
– – 0.06-3 0.2-2.9 1.0-3
no burn no burn almost all burn almost all burn a ramp cut
6
0.001-0.004
1.25-3
a ramp cut
7
0.0003-0.0048-0.0003
0.2-2.8
a tent cut
8
0.0005-0.0045-0.0005
0.4-2.5
a tent cut
measurements were taken to provide burn-recognition information. At 32 equally spaced points along each workpiece, a Leco M400-G2 Hardness Tester was used to record hardness values. The surface profile test was done by a computer-connected stylus surface measurement, and the surface roughness values obtained were used to quantify the workpiece surface characteristics. A typical AE trace observed and the corresponding power spectral density (PSD) are given in Fig. 2. It would be ideal to have data about the original AE; that is, the acoustic signature from the zone of the wheel/workpiece interface. However, since the signal is distorted by the sensor characteristic (it is in fact a strongly narrowband filter), and more particularly since the AE must pass through an unknown and changing medium involving the workpiece, coolant and apparatus on its way from the contact zone to the sensor, this is not reasonable.
3. Detection tools 3.1. What did not work A number of statistics were applied individually to the collected data for detection of burn. For the most part these statistics were normalized, or otherwise rendered independent of the local AE power: the AE RMS power can rise or fall for reasons having little to do with grinding condition, and in any case has been found to have limited predictive efficacy. 3.1.1. Zero-crossing rate (ZCR) “Count” technology is not new in AE applications [3]. As the name implies, this method counts the number of zero-crossing events during each block of observed data. For a monochromatic signal, twice the time between zero-crossings is the reciprocal of the frequency; for the complicated signals observed, the meaning is less clear. At any rate, little predictive capability was found in this statistic.
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Fig. 2. A typical “raw” AE trace (top) and the corresponding PSD spectrum (bottom) from the beginning of a grinding regime. Note that the spectrum is plotted logarithmically.
3.1.2. Ratio of power (ROP) It is natural to examine the behavior of the power spectrum of AE, with the idea that the frequency behavior of “good” and “bad” grinding may differ. Thus, for each block of data, the ROP was calculated from the normalized power spectrum as
冘 冘 n2
ROP⫽
N⫺1
兩Xk兩 / 2
k⫽n1
兩Xk兩2,
(1)
k⫽0
in which the denominator eliminates the effect of the local signal power. Here, N (N=1024) is the chosen length of fast Fourier transform (FFT), Xk is the kth DFT output, and the summation is over any range of frequency, represented as from discrete Fourier transform (DFT) “bins” n1 to n2. A significant effort went toward identification of promising frequency bands (and indeed sets of bands), with little success. Our conclusion is that either the effect is small, or it is irretrievably lost due to the sensor characteristic. 3.1.3. Amplitude histogram The amplitude histogram of each block data was obtained and analyzed. Effort was expended to find the difference between the distributions, but no promising relationship was noted.
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3.1.4. Wheel-period power correlation This statistic was introduced in [8], and is presented in more detail there. The basic idea is that the wheel profile (presumably the abrasive grains themselves) can be observed in the AE trace. Since the wheel’s profile is relatively constant from rotation to rotation (few grains dislodge or slip), there is a high degree of correlation between wheel-pass periods. This is manifested as an autocovariance “peak” whose lag is the wheel’s rotation period. As such, the wheel’s speed can be accurately measured from the time between peaks (a spindle-mounted speed sensor could do this too); but, more important, the amount of correlation was observed in [8] to be indicative of burn. Here, example results from test 3 are given in Fig. 3. The difference in the correlation values can be seen, but it is hard to set a reasonable threshold. The fact that this statistic worked elsewhere [8] and not here is attributed to the different apparatus: we hope that the wheel-period power correlation may prove useful in some applications, but apparently its utility is not universal. 3.1.5. Kurtosis It can be argued that the characteristics of the AE signal are related to those of the surface profile. The shape of the probability distribution of a surface profile can play a major role in revealing changes in the process producing the surface (e.g., tool wear) [19]. The kurtosis, the normalized fourth-order central moment, appears to be a useful measure. A high kurtosis value
Fig. 3. Wheel-period power correlation and wheel speed measured from AE for test 3.
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implies a sharp distribution peak and/or a high (relative to Gaussian) probability of observing an outlying sample. 3.1.5.1. Time-domain kurtosis (TDK) Let xi, i=1, …, n, represent the real discrete AE data, and let n be the number of data points of each block. The empirical kurtosis statistic [2] used in this paper has the form
冘 冋冘 册 n
Kt⫽
1 (x −x¯)4 ni⫽1 i n
1 (x −x¯)2 ni⫽1 i
,
2
(2)
where x¯ is the empirical sample mean:
冘 n
1 x. x¯⫽ ni⫽1 i
(3)
In our implementation we use n=76,800, meaning that each block lasts 30 ms or approximately one rotation of the wheel. Based on our experimental results it was found that TDK is related to burn as shown in the upper plot of Fig. 4, but large variation was observed. The variations make it difficult to set the reasonable threshold and certainly reduce the detection performance. TDK will be used later as the input to the NN.
Fig. 4.
TDK and FDK for test 6. Dashed vertical lines indicate the location of burn.
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3.1.5.2. Frequency-domain kurtosis (FDK) Particularly if the time-domain signal contains transient bursts of enhanced energy (e.g., from grain contact), higher-order moments of the complex frequency components may contain additional information that could be utilized in detecting signals. Thus we can compute the frequency-domain kurtosis (FDK) for the real or imaginary parts of the complex frequency components. The FDK [12,13] represents a measure for the probability distribution over a time interval consisting of N DFTs each of length M. The operation is described as
冘 冋冘 N
1 (X (q)−X¯k)4 Nq⫽1 k
Kf(k)⫽
N
1 (X (q)−X¯k)2 Nq⫽1 k
册
,
2
(4)
where X¯k is the empirical sample mean
冘 N
X¯k⫽
1 X (p) Nq⫽1 k
(5)
and Xk(q) is the real part of the kth DFT output of the segment q, k苸{1, M}. Only the real part will be discussed here, and of course a similar analysis can be used with the imaginary part. Our zero-mean raw AE signal was processed utilizing a 512-point FFT (M=512) and the FDK was obtained by appropriately dealing with the 150 consecutive FFT outputs (N=300), giving an overall time interval of 30 ms. The middle plot in Fig. 4, showing the FDK for k=60 (300 kHz), is typical: there is little predictive power. By contrast, the lowest plot in Fig. 4 shows the FDK for k=256 — it appears that this result is similar to that for the TDK. The results of FDK with k=256 for different tests are shown in Fig. 5, which can provide useful information to indicate burn. However, k=256 corresponds to 1280 kHz (half the sampling rate, otherwise known as the “folding frequency”) which is far out-of-band, Hence, while this is intriguing, it is mostly a curiosity. 3.2. What worked 3.2.1. CFAR power law As applied to the detection of transient events, a detector attracting much attention and interest is Nuttall’s power-law statistic [22]
冘
M⫺1
Tpl(X)⫽
Xnk ,
(6)
k⫽0
where the Xk is the kth magnitude-squared FFT bin, n is a changeable exponent and 2M is the total number of FFT bins (due to conjugate symmetry, only half of the magnitude-squared FFT bins need be interrogated). Respectively n=1 and n=⬁ correspond to the energy detector and max{Xk}; 2⬍n⬍3 provides good performance in a wide range. Although it is effective in some models and easy to implement, this statistic relies on pre-normalized data. Due to the fluctuation
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Fig. 5. FDK with k=256 for tests. Dashed vertical lines indicate the location of burn and dashed horizontal lines illustrate the possible threshold.
of the AE signal during the grinding process, a constant false alarm-rate (CFAR) power-law [23] statistic is used
冘 冉冘 冊 M⫺1
Xnk
Tcpl(X)⫽
k⫽0
M⫺1
,
n
(7)
Xk
k⫽0
where Tcpl is clearly not affected by signal amplitude. With M=32, for each time interval of 1 ms, our {Xk} are taken as the PSD of the raw AE signal. The example results of power law and the CFAR power law are compared in Fig. 6. To see the results more clearly, the averaged statistic value in each wheel rotation (the length is 30 ms) was used instead. The CFAR power law appears
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Fig. 6. Results of power law and CFAR power law for test 8. Dashed vertical lines indicate the location of burn. From left to right, n is 0.5, 2.5 and ⬁, respectively.
to be an effective method to detect burn; the unnormalized power-law statistic may indeed be informative, but due to amplitude dependence its wide variation suggests that it is unsuitable. 3.2.2. MVD Processed in the frequency domain, the CFAR mean-value deviance (MVD) statistic [6] is defined as
冘
M⫺1
1 log[X¯/Xk], Tmvd(X)⫽ M k⫽0
(8)
where X¯ is the mean value of {Xk}; M and Xk have the same meanings as in the CFAR powerlaw statistics. The MVD statistic has been proved to be effective in the detection of transients in some applications. The MVD appears to be useful for burn detection. 3.2.3. Neural network detection scheme 3.2.3.1. Feature selection The NN-based detection scheme is shown in Figs. 7 and 8. The inputs in Fig. 7 are, in classification parlance, the features on which a decision is to be based. These must be chosen judiciously and succinctly, since the selection of a set of features too great for the number of training data usually results in “overtraining”; that is, of the adaptation of the classifier to spurious non-generalizable patterns [24]. Feature selection is at best an art, and is
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Fig. 7.
Detection scheme of burn recognition using feature set 2.
more usually a matter of trial and error. In this work the best results have been with two following feature vectors. 3.2.3.2. Feature vector 1: univariate statistics The frequency band power, the kurtosis and skew are informative features of the AE signals. Similar to the definition of kurtosis in Section 3.1.5, the empirical skew statistic has the form
冘 冋冘 册 n
Ts⫽
1 (x −x¯)3 ni⫽1 i n
1 (x −x¯)2 ni⫽1 i
1.5
,
(9)
where n=2560 in our implementation. The kurtosis is a measure of the sharpness of the peak while the skew measures the symmetry of the distribution about its mean. It has been observed that the 240–400 kHz band is informative, and hence we concentrate on that. The band power between 240 and 400 kHz, the kurtosis and the skew for test 5 are shown in the top part of Fig. 9. Large variations of these three features during grinding are observed, and affect the NN performance of detection. Consequently, for a stable NN input, we preprocess as
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Fig. 8. A generic radial basis network.
follows. For each specified block of AE signal, we calculate a feature series {T(i)}. For each feature series {T(i)} (this can refer to band power, kurtosis or skew), the mean and the standard deviation are calculated to form the new features:
冘 l
1 T(i) mT ⫽ l i⫽1
(10)
and sT⫽
冪
冘 l
1 (T(i)−mT)2, l−1i⫽1
(11)
where l is the window size. From the above process, the feature vector V1 corresponding to band power, kurtosis and skew is extracted V1⫽{mp, mk, ms, sp, sk, ss},
(12)
where mp, mk and ms are the mean values of the frequency band power, kurtosis and skew; and sp, sk and ss are the corresponding standard deviation values. The refined features of test 5 are plotted in the middle and bottom part of Fig. 7: it is clear that the values of the refined features fluctuate less. The window size l is experimentally based, and is set to 30 in our actual use; that is, each feature vector was extracted from a 30 ms block AE signal.
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Fig. 9. Features for test 5 using band power, kurtosis and skew. The top three plots show the statistics themselves as based on 1 ms block averages; the middle and lower plots are of means and standard deviations based on l=30 blocks. These latter six features form feature set 1.
3.2.3.3. Feature vector 2: Wiener coefficients In the linear prediction problem it is desired to estimate the nth element of a time series x(n) using {x(m)}n−1 m=n−M — the previous M time samples. That is, the vector h={h(1), h(2), …, h(M)} which minimizes
再冋 冘 M
T
2
E{[x(n)⫺h x(n)] }⫽E x(n)⫺
k⫽1
册冎 2
h(k)x(n⫺k)
(13)
is sought — this is a version of the Wiener filtering problem. It may appear strange to estimate x(n) based on the M prior samples when one could simply wait one sample and have it; but it is
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the form of the filter which matters. In fact, the vector h so derived coincides with that used for autoregressive (AR) and maximum entropy (ME) spectral modeling, in that the AR spectral estimate is fAR x (w)⫽
|冘
2
M
1−
k⫽1
h(k) e−jwk
|
(14)
in which is a proportionality constant. The Wiener/AR coefficients are also sometimes referred to as linear prediction coefficients (LPCs), and are used as signal descriptors both for speech coding/compression and speech recognition. At any rate, the point is that the Wiener coefficients summarize a considerable amount of spectral information in a relatively few numbers. In this work we regard each block with length 30 ms (76800 samples) — approximately one wheel period — as stationary, and compute the Wiener coefficients based on data from each block. Adaptive Wiener whitening [15] was performed on each individual raw AE signal segment 9 {x(n)}7679 n=0 . Let R denote the M×M correlation matrix of the tap inputs:
Fig. 10. The patterns of the w-coefficient feature vectors: (a) “burn” state; (b) “non-burn” state; (c) “no-grinding” state.
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冢
R⫽
r(0)
r(1)
… r(M−1)
r(1)
r(0)
… r(M−2)
⯗
⯗
哻 ⯗
r(M−1) r(M−2) … r(0)
冣
,
(15)
where M is the filter order, and the autocorrelation r(·) is estimated as
冘
N⫺k⫺1
r(k)⫽
(x(n)x(n⫹k)).
(16)
n⫽0
Correspondingly, let p denote the M×1 cross-correlation vector p⫽[r(1)r(2)…r(M)]T.
(17)
Thus, the M×1 coefficient vector of the Wiener filter is obtained by solving Rh⫽⫺p.
(18)
While either matrix inversion or Gaussian elimination [O(M3)] are sufficient to solve for the Wiener coefficients, a particularly efficient O(M2) algorithm due to Levinson and Durbin (again, see [15]) is also available. Fig. 10 shows a typical representation of the feature vectors reflecting the “burn”, “non-burn” and “no-grinding” states. The vectors themselves are shown in the upper plots, and the corresponding AR spectra in the lower. Note that the AR order M is determined experimentally. Various orders from M=5 to 50 were assayed; it was found that M=10 gave the best results.
Fig. 11. The detection results of the radial basis NN and feed-forward NN for test 2.
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Fig. 12. The results of test 1, no burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “nonburn”, and ⫺1 “no-contact”. The dashed horizontal lines in the upper two plots denote the thresholds; values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
3.2.3.4. The radial basis NN approach The Matlab toolbox “NNET” was used in our NN implementation. The structure of the radial basis artificial neural network (ANN) using “NNET” is shown in Fig. 8. It includes an input layer, the radial basis function layer, and one linear layer output neuron. Each input vector is fully connected by a weight matrix to the radial basis layer, and these in turn are fully connected by another weight matrix to the linear output layer. To avoid “overcrowding”, a bias vector is used for each layer. There is only one output from the network, which shows whether grinding burn occurs or not. The RBF NNs, which have been widely advocated [21], are approximations of the form
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Fig. 13. The results of test 2, no burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “nonburn”, and ⫺1 “no-contact”. The dashed horizontal lines in the upper two plots denote the thresholds; values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
冘
bj G(储x⫺xj 储/sj )
y⫽a⫹
(19)
j
for centers xj, where G(r)=exp(⫺r2/2), s is a scale factor. Using RBFs as the basis functions, a network such as in Fig. 8 represents that the output is
冘 nj
y⫽b2⫹
j⫽1
冘 ni
2 1j
w2j exp[⫺b
i⫽1
(w1ji⫺xi)2],
(20)
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Fig. 14. The results of test 3, heavy burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
where x is the input vector with size ni×1, ni and nj are separately the numbers of neurons used in the input and “hidden” layers. The trainable parameters w1 and b1 are, respectively, an nj×ni weight matrix and the nj×1 bias vector for the hidden layer, and w2 and b2 are the corresponding 1×nj weight matrix and scalar bias for the linear (output) layer. The NN is established through the training phase. The number of neurons used in the radial basis layer, nj, was originally set as 1 and increased by one each time until performance was acceptable. The actual error is defined as the sum of the squared differences between the desired output and the actual output over a specified number of input vectors. During this development
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Fig. 15. The results of test 4, heavy burn. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
process, the network modifies the connections between individual processing neurons, represented by w1, w2, b1 and b2. Just as in any statistical analysis, an implied requirement for developing robust neural network models is that the training sets cover as many of the possible variations in the input and output vector as feasible. For practical considerations, a limited number of samples should be used. Thus care must be taken when choosing the training set to ensure that it be broad-based. There are three possible distinguished states during the grinding process: the no (workpiece/wheel) contact
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Fig. 16. The results of test 5, ramp cut with burn at end. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2 respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
stage; normal grinding; and burn. For our case, 10 “burn”, 10 “non-burn” and 10 “no-grinding” inputs were used to train the neural network. Where grinding burn was identified, the output of the NN was set to 1, 0 was set for the “non-burn” case and ⫺1 was chosen when the input featured “no-grinding”. The training allows the NN to provide detection results with reasonable confidence. Ultimately, the weight matrices and bias vectors were obtained, and served to decide the NN structure. Different kind of inputs result in different networks. The final NN structure has ni=6 and nj=5
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Fig. 17. The results of test 6, ramp cut with burn at end. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
when we used the feature vector V1 as inputs. Otherwise, if the inputs was taken as the feature vector V2 (the AR coefficients), the radial basis network utilized consists of ni=10 neurons in the input layer and nj=3 neurons in the radial basis layer. The two radial basis networks have been used successfully to detect grinding burn. If the value of the output was larger than 0.5, grinding burn was declared. The closer to 1 the output, the more confident the burn detection. The closer to 0 the output, the more it is possible to declare “non-burn”. Finally, a usually worthy competitor to the RBF NN is the perhaps more popular MLP feed-
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Fig. 18. The results of test 7, tent cut with burn in middle. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”.
forward network (multilayer perceptron) with a back-propagation training structure [24]. This also was also explored. In general, although performance is often reasonable, the feed-forward NN tends to give false alarms; an example output is offered in Fig. 11. Considering that RBF training is faster and usually more faithful than that for the MLP, we have opted for the RBF structure.
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Fig. 19. The results of test 8, tent cut with burn in middle. CFAR pl, the CFAR power-law method; MVD, the MVD statistic; NN output 1 and 2, the NN result using feature set 1 and 2, respectively. 1 in the result represents “burn”, 0 represents “non-burn”, and ⫺1 “no-contact”. The dashed vertical lines indicate burn location observed visually; the dashed horizontal lines in the upper two plots denote the thresholds. Values larger than the threshold in the CFAR power law or less than the threshold in MVD indicate “burn”. In this test, the start and end parts of the workpiece were not ground.
4. Results The feature vectors 1 and 2 calculated from the raw AE signals of tests 1 to 8 were treated for the above NN implementations. The results of burn detection are shown in Figs. 12–19. Each block covers 30 ms of the grinding process, corresponding to the period of the wheel rotation. In each figure, the upper two plots are results of the CFAR power law and the MVD detectors used for reference and comparison; the middle two show the detection performance of the radial basis
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networks, where “NN output 1” indicates the output of the network using feature vector V1 as inputs and “NN output 2” is the output of the network using feature vector V2. The lowest plot in each shows the results from the post hardness and profile tests, which can identify cases of burn and non-burn. The hardness and the profile values are normalized by 1000 and 0.002, respectively. We can see that the CFAR power-law and the MVD methods provide useful information about burn. Based on our experiment, we set 5.15 as the threshold of the CFAR power law with n=0.5 and 0.05 as the threshold of the MVD detector. Burn is declared if the value of the CFAR powerlaw method is larger than 5.15 or the MVD value is less than 0.05. As with any threshold detectors, there is the disadvantage that the setting of the threshold is experience-based and may be situation-dependent. It was noted that the value difference between the “no-grinding” signal and the “burn” signal is quite small; in the NN approach, there is no such concern. It is easily noticed that the NN shows effective performance in all tests. It is clear from the post hardness and profile tests that the NN method indicates a “burn” signature before the occurrence of the true burn — a particularly useful characteristic. Note that despite the NN having been trained with but 30 samples (10 from each regime), the performance over the much larger test data set is remarkably stable: for feature sets 1 and 2, the plots show the NN outputs given at respectively 30 ms and 3 ms intervals!
Fig. 20.
A distorted AE signal due to preamplifier overload.
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5. Summary The goal has been to detect abnormal grinding conditions via appropriate digital signal processing of acoustic emission (AE) data, this information being sampled at a high (2.56 MHz) rate and used in its raw (i.e., not RMS) form. The data were collected from a sequence of tests on 52100 bearing steel and a variety of conditions; the workpieces were assayed post-mortem for their quality, so that this could be compared with the AE collected. For the most part, the “threshold”-oriented statistical tools — that is, those which digest the data to a single statistic to be compared with some preset value — were found to have limited ability in predicting grinding state. Exceptions to this include certain statistical tools recently finding application in the identification of transient events, particularly in sonar. The efficacy of these tools is intriguing, but for the most part they are eclipsed by a neural network approach based on the fast-training radial basis function (RBF) architecture. For these, despite training on a remarkably small set, identification of burn over a much larger test set is essentially perfect. Two families of “feature vectors” (inputs to the neural networks) are employed, one based on autoregressive parameters and the other on a vector of averaged statistical properties. In both cases the performance is good, and there does not seem to be a reason to prefer one over the other.
Acknowledgements This research was supported by the National Science Foundation under contract DMI-9634859.
Appendix A. Note about distortion There are some remarks about a somewhat obscure form of distortion in [17], and since this kind of distortion was indeed observed in the early phases of our work we would like to report on it here in the hope that other researchers may avoid the problem. The AE signals originating from the grinding zone were occasionally quite strong, and such high-amplitude signals could cause overload in the preamplifier and distortion of the signals, as shown in Fig. 20. One might expect an amplifier overload to be accompanied by a saturated or “clamped” output, and thus be easily discernible. But when the overload is of significant duration and there is a high-pass (or bandpass) filter between the overloaded amplifier and the point of observation, the effect is less clear. In fact, what is observed is an interval initially resembling the impulse response of the filter, and then with no signal at all. An example is shown in Fig. 20.
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