frequency, and time–frequency domains. Feature selection is a process used to define a small and concise feature subset through the removal of redundant features from a feature set and it is introduced in Section 2.3.3.1(A.1). In addition, an Autoencoder (AEN) as a popular ANN‐based feature extraction method [11, 12] is introduced in Section 2.3.3.4.
2.3.3.1 Time Domain
SFs extracted from time‐domain signals are very intuitive to understand how the signals change in the past or at a specific time. Statistical SFs and correlation‐based SFs are two main methods used to describe these changes in practical manufacturing applications.
In signal processing, SFs of the statistical description can essentially identify changes from the shape of the waveform; while SFs of cross‐correlation and autocorrelation, based on the Pearson product‐moment correlation coefficient [13], investigate similarity relationship between time‐varying signals. The feature extraction methods of statistical SFs, cross‐correlation SFs, and autocorrelation SFs are presented as follows.
Statistical SFs
If the machining parameters (such as feed rate, spindle speed, depth of cut, etc.) are fixed and the precision after machining is within specifications, then the machining operations are a kind of a quasi‐static condition [8]. Under this condition, Yang et al. [8] summarized that the nine most common SFs for various types of sensor signals are derived from all the elements of
For the de‐noised time‐domain signals
Arithmetic mean or average (avg)
Standard derivation (std)
Maximal magnitude (max)
Minimal magnitude (min)
Peak‐to‐peak amplitude for presenting difference of peaks (ptp)
Kurtosis for measuring the peakedness of signals (kurt)
Skewness for measuring the asymmetry of signals (skew)
Root mean square value for indicating the weighting effect of variances (RMS)
Crest factor for representing how extreme the peaks are in a waveform (CF)
Table 2.3 Definition of time‐domain SFs.
| SF | Formula | Description |
|---|---|---|
| avg |
|
|
| std |
|
|
| max |
|
|
| min |
|
|
| ptp |
|
|
| kurt |
|
|
| skew |
|
|
| RMS |
|
|
| CF |
|
|
As such, these nine SFs can be used as a feature set based on expert knowledge. Suppose that one vibration sensor and three current sensors are installed as the sensor fusion example illustrated in Figure 2.13, then there are 36 SFs in total because each sensor has nine SFs.
These 36 SFs may be adopted as the input variables of any intelligent system. However, redundancy, irrelevancy, and/or dependency may exist among these 36 SFs, which may deteriorate the model accuracy; and the more SFs,
