In this research, a chatter identification platform is developed to train models and evaluate their performance, using combinations of signal processing methods and classification algorithms and a dataset consisting of 143 cuts under various cutting condition. We compared several classification methods in terms of their performance on chatter identification after parameter optimization for each classifier. K-NN, Naïve Bayes, and SVM are the superior methods, with error rates from 5.21% to 5.647%. The effect on accuracy of feature selection is far more significant compared to classifier selection.
Efforts are put into parameter optimizations for each of these features. Using the optimal classifier, k-NN, and window size of 1.2 seconds and no overlap, the optimal error rate is achieved by using HHT and WPT together, at 4.856%. The rest are 𝐸𝑊𝑃𝑇, 𝐸1,𝐹𝐹𝑇, 𝐸2,𝐹𝐹𝑇, 𝐸3,𝐹𝐹𝑇, and autocorrelation coefficient, ordered by error rate, from low to high.
Autocorrelation coefficient proves to be the least effective, with an error rate of 16.42%.
Incidentally, using all three axes as feature is shown to be much better than using only 1 or 2 axes in some circumstances. Finally, the effect of window size on error rates and detection speeds is also investigated using the platform we developed. A window size around 0.3 to 0.5 seconds is optimal in terms of error rate, and the best error rate of 2.2%
was found using a window size of 0.37 seconds with HHT+WPT. However, HHT+WPT results in a marginally slower chatter detection compared to other features, and what comes as a surprise is that smaller window size does not lead to faster chatter detection.
There are some potential directions for future researches. Due to the large amount of possible variations in ANN architectures, it is not explored fully in this work and may be worth investigating. Another optimization opportunity is to use different window sizes for training and testing, and observe the trend of error rate and detection time.
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Appendix A. List of cutting conditions in the dataset
Note: The chip load is fixed at 0.1 mm/tooth.
Experimentally stable cutting conditions:
Spindle speed (rpm) Depth of cut (mm) Spindle speed (rpm) Depth of cut (mm)
4500 0.2 6100 0.5
Experimentally unstable cutting conditions:
Spindle speed (rpm) Depth of cut (mm) Spindle speed (rpm) Depth of cut (mm)
4500 0.32 5900 0.4
4500 0.4 5900 0.5
4600 0.3 6000 0.5
4700 0.2 6000 0.6
4700 0.3 6100 0.7
4800 0.2 6100 0.8
4800 0.3 6200 1.2
4900 0.4 6300 0.8
5000 1.1 6300 0.9
5100 0.7 6400 0.7
5200 0.5 6500 0.6
5200 0.6 6500 0.62
5300 0.3 6500 0.7
5300 0.4 6600 0.5
5400 0.3 6700 0.4
5500 0.3 6700 0.5
5600 0.3 6800 0.3
5700 0.2 6800 0.4
5700 0.3 6900 0.3
5800 0.3 7000 0.3
Appendix B. Model training and validation results
Note: The number in the parenthesis indicates the maximum error rate of the 3 validation datasets (in stratified k-fold validation with k=3). The other number is the average error rate of the three datasets.
Examples:
(a) Auto. Coeff., window=1.2, overlap=0.8, prominence=50%, a, xyz: The feature is autocorrelation
coefficient, window size 1.2 sec, overlap 0.8 sec, prominence 50%, using x-, y-, and z-axes acceleration as feature.
(b) kNN, k=auto[1-200], weight 1/r^3: The classification method is k-nearest neighbors, with k automatically selected between 1 to 200 for the lowest error rate, with weight 1/r^3.
(c) FFT, exp=2.75, n=5, d=100, bw=10: exponent 2.75, tooth pass filter bandwidth 10Hz, only 5 highest peaks are used, with the minimum distance between peaks being 100 Hz.
Feature Classification data
points FA (%) MA %) ER (%) Auto.
Coeff.
window=1.2, overlap=0.8,
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1216 6.961
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1736 7.258
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 2780 6.1
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 5895 6.493
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 456 6.895
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 608 6.806
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 972 6.361
prominence=50%, a, xyz kNN k=auto[1-200],
weight 1/r^3 2010 6.357
prominence=50%, a, xyz kNN k=auto[1-2000],
weight 1/r^3 6169 6.654
prominence=50%, a, xyz kNN k=auto[1-2000],
weight 1/r^3 12338 8.793
prominence=10%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1736 7.137
prominence=30%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1736 7.39
Auto.
Coeff.
window=0.9, overlap=0.6,
prominence=70%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1736 6.805
prominence=90%, a, xyz kNN k=auto[1-200],
weight 1/r^3 1736 6.16
prominence=50%, v, xyz kNN k=auto[1-200],
weight 1/r^3 1736 7.548
prominence=50%, x, xyz kNN k=auto[1-200],
weight 1/r^3 1736 8.846
FFT window=1.2, overlap=0.8,
exp=0.5, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 8.539
FFT window=1.2, overlap=0.8,
exp=0.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 6.389
FFT window=1.2, overlap=0.8,
exp=1, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=1.25, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 3.228
FFT window=1.2, overlap=0.8,
exp=1.5, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.846
FFT window=1.2, overlap=0.8,
exp=1.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.601
FFT window=1.2, overlap=0.8,
exp=2, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=2.25, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 2.318
FFT window=1.2, overlap=0.8,
exp=2.5, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 2.332
FFT window=1.2, overlap=0.8,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.808
FFT window=1.2, overlap=0.8,
exp=3, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=3.5, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 2.643
FFT window=1.2, overlap=0.8,
exp=4, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=5, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=6, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=8, bw=10, xyz kNN k=auto[1-200],
FFT window=1.2, overlap=0.8,
exp=10, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 3.506
FFT window=1.2, overlap=0.8,
exp=2.75, bw=2.5, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.449
FFT window=1.2, overlap=0.8,
exp=2.75, bw=5, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.801
FFT window=1.2, overlap=0.8,
exp=2.75, bw=20, xyz kNN k=auto[1-200],
weight 1/r^3 1216 3.439
FFT window=1.2, overlap=0.8,
exp=2.75, bw=40, xyz kNN k=auto[1-200],
weight 1/r^3 1216 1.621
FFT window=0.9, overlap=0.6,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1736 1.721
FFT window=0.6, overlap=0.4,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 2780 2.455
FFT window=0.3, overlap=0.2,
exp=2.75, bw=10, xyz kNN k=auto[1-500],
weight 1/r^3 5895 3.582
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 456 1.705
FFT window=0.9, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 608 1.94
FFT window=0.6, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 972 2.679
FFT window=0.3, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 2010 2.917
FFT window=0.1, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-500],
weight 1/r^3 6169 3.803
FFT window=0.05, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-2000],
weight 1/r^3 12338 3.827
FFT
exp=2.75, coif8, bw=10, kNN k=auto[1-200],
1216 3.066 6.095 9.162
WPT
WPT
WPT window=1.2, overlap=0.8,
exp=2.75, db1, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 2.255
WPT window=1.2, overlap=0.8,
exp=2.75, db2, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 3.461
WPT window=1.2, overlap=0.8,
exp=2.75, db3, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 3.01
WPT window=1.2, overlap=0.8,
exp=2.75, db4, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 1216 2.477
WPT window=1.2, overlap=0.8,
exp=2.75, db20, bw=10, x kNN k=auto[1-200],
weight 1/r^3 1216 8.892
WPT window=1.2, overlap=0.8,
exp=2.75, db20, bw=10, y kNN k=auto[1-200],
weight 1/r^3 1216 9.433
WPT window=1.2, overlap=0.8,
exp=2.75, db20, bw=10, z kNN k=auto[1-200],
weight 1/r^3 1216 8.077
WPT window=1.2, overlap=0.8,
exp=2.75, db20, bw=10, xz kNN k=auto[1-200],
weight 1/r^3 1216 4.849
WPT window=1.2, overlap=0.8,
exp=2.75, db20, bw=10, yz kNN k=auto[1-200],
weight 1/r^3 1216 5.449
HHT window=1.2, overlap=0.8,
xyz kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, xyz kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, x kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, y kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, z kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, xy kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, xz kNN k=auto[1-200],
HHT window=1.2, overlap=0.8,
w/ WPT, yz kNN k=auto[1-200],
FFT window=1.2, overlap=0, exp=2.75, bw=10, xyz
Thres-hold 456 3.289 3.289 6.579
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz LOF n=auto[1-200],
10% unstable 456 10.4
(14.8)
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz LOF n=auto[1-200],
15% unstable 456 8.53
(14.4)
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz LOF n=auto[1-200],
20% unstable 456 9.01
(18.1)
FFT window=1.2, overlap=0, exp=2.75, bw=10, xyz
Naïve
Bayes Gaussian 456 2.193 3.07 5.263
FFT window=1.2, overlap=0, exp=2.75, bw=10, xyz
Naïve
Bayes Bernoulli 456 2.193 3.289 5.482
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight uniform 456 0.646
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r 456 1.065
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^2 456 1.275
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^3 456 1.485
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight 1/r^4 456 1.48
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight e^-r 456 0.646
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight e^-2r 456 0.646
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight e^-5r 456 0.646
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight e^-10r 456 0.8557
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz kNN k=auto[1-200],
weight e^-100r 456 2.096
FFT window=1.2, overlap=0,
exp=2.75, bw=10, xyz SVM