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Generally speaking, tool wear is concomitant to vibration and it gradually increases due to long‐term usage. In this case, the vibration is acquired from the cutting tool used in the side milling at a sampling rate of 2,000 Hz and the data of the cutting tool records from new to worn status. The entire data set is available in [19] via IEEE DataPort.

Features are extracted from time‐domain signals into the number of 2⁴ WPT nodes based on the 4‐level WPT manner. Although differences in time‐domain signals between new and worn statuses are small as shown in the upper portion of Figure 2.29, the values of the 13, 14, and 15 WPTs of worn tool signals are clearly different from those of a new tool as portrayed in the middle portion of Figure 2.29. Here, the bandwidths of the 13, 14, and 15 WPTs are about 750–812.5, 812.5–875, and 875–937.5 Hz, respectively. The detailed amplitudes of each frequency band are illustrated in the lower portion of Figure 2.29.

Figure 2.29 Comparison of time‐domain signals (upper portion), WPT features (middle portion), and frequency‐domain spectrums (lower portion) between new and worn statuses.

Figure 2.30 illustrates four energy distributions of the 32 WPT features extracted from the X‐axis and Y‐axis vibrations under four cutting depths (from 4 to 7 mm). Note that, main differences of amplitudes exist among high‐frequency bands (especially from 13 to 15) between new and worn statuses. These features provide the AEN model with useful data source to extract information for the tool state diagnosis.

Figure 2.30 WPT distribution results for different cutting depths in the X and Y axis (node number counted from 0): (a) the new tool in X‐axis; (b) the worn tool in X‐axis; (c) the new tool in Y‐axis (d) the worn tool in Y‐axis.

Hence, 32 WPT‐based features of the X‐axis and Y‐axis serve as the inputs to the encoder in an AEN model. As shown in Figure 2.31, four SFs (fAE1, fAE2, fAE3, and fAE4) extracted from the fourth layer in encoder can be used as a compressed representation of the original feature set to reduce the number of feature dimensions; the left side (sample nos. 1–133) and right side (sample nos. 134–266) represent the new and worn cutting tools, respectively. Finally, the four SFs show their capability in classifying the new or the worn tool.

Figure 2.31 Comparison of four SFs extracted by using an AEN for samples of new and worn tools.

The accuracy of four feature sets are compared using a random forest (RF) model and evaluated in a cross‐validation scenario. As shown in Table 2.4, the average accuracies of tool state diagnosis when using 32 WPT‐based features and 4 fAE features are 89.5 and 69.1%, respectively. Furthermore, when the cutting depth is added as one of the inputs, the average accuracies are improved to 90.9 and 81.7%, respectively. This indicates that the accuracy by applying WPT‐based SFs is better than that by utilizing AE‐based SFs regardless of whether the cutting depth is added to the feature set or not.

Table 2.4 Tool diagnosis example: results of using an RF model.

Model inputs	Average (%)	Best (%)	Worst (%)
32 WPT SFs (X/Y axis with level = 4)	89.5	95.0	81.2
32 WPT SFs (X/Y axis with level = 4) + Cutting depth	90.9	96.2	85.0
fAE1~fAE4	69.1	77.5	60.0
fAE1~fAE4 + Cutting depth	81.7	90.0	76.2