32 features are derived from vibration data collected during the idling periods by using the five‐level WPT. Figure 2.27 compares the two trends from 32 WPT features extracted from Z‐axis idling vibration (original data) and AEN training results using the same 32 WPT features (decoder data), under four different spindle speeds (3,000, 3,500, 4,500, and 5,000 rpm), where the node number starts counting from 0. Note that, the high similarity of both trends indicates that AEN is reliable.
Figure 2.27 Comparison of the original and decoded features under four idling conditions of spindle speeds: (a) 3,000 rpm; (b) 3,500 rpm; (c) 4,500 rpm; and (d) 5,000 rpm.
The reason why Z‐axis vibration is chosen to be a learning criterion for training the AEN model is that the main drilling loading occurs in Z‐axis but not in X‐axis or Y‐axis. The AEN accuracies would be worse if X‐axis or Y‐axis vibration is adopted to train AEN since loading difference between the idling section and the real drilling section is not significant enough.
Thus, once AEN learns the feature patterns of idling sections, it is able to achieve the period detection of tool–workpiece contact by comparing the certain distance between the idling section and the real machining section. Figure 2.28 illustrates the automated segmentation results of AEN. Figure 2.28a compares the distances between modeling features (Z‐axis vibration during idling) of the AEN model and testing features of real machining (X‐axis vibration during drilling) every 0.2 s from the beginning to the end of the data acquisition.
Figure 2.28 Automated segmentation of machining signals using an AEN: (a) distance derived by AEN based on idling vibration features of Z‐axis; (b) collected X‐axis vibration signal; and (c) zoom in segmented X‐axis signal.
As depicted in Figure 2.28a, a stable maximum distance, which means a high dissimilarity between the modeling and testing features, can be used to recognize a real drilling section. A certain duration of X‐axis vibration data can be segmented into the real drilling section according to Z‐axis vibration, as highlighted within the two red dotted lines in Figure 2.28a. In this manner, seven real drilling sections of Z‐axis vibration as in the bottom of Figure 2.26 can also be automatically segmented using AEN. To sum up, raw data can be segmented using the vibration characteristics of various rotor components such as motors and spindles to automatically reduce time‐consuming manual segmentation.
2.4.3 Tool State Diagnosis
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
