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, the more training samples are needed [4]. Conventional feature selection methods [6–8] can be applied to automatically search for key SFs to reduce the number of SFs during the model‐building and model‐refreshing processes so as to improve the model accuracy. However, due to the dynamic nature of these methods, the content of key SFs could vary after applying automatic search in each model refreshing, which might not be appropriate for implementation considerations.
For easy implementation, a fixed and concise set of SFs is required to represent the significance of the entire manufacturing process. Therefore, an expert‐knowledge‐based (EK‐based) selection procedure to find a fixed and concise set of SFs is illustrated below.
EK‐based Selection Procedure
In view of selecting the SFs of a vibration sensor (i.e. accelerometer), since the machining quality is affected directly by the tool states, SFs that can accurately monitor tool status should be selected. In high‐speed machining operations, a serious increase in cutting energy generated due to tool breakage or flank wear will amplify vibration magnitude that can be detected by the max, RMS, and avg of the vibration signal. These three SFs are crucial to the detection of vibration amplitude and energy variance between workpieces and tools.
A rolling bearing is one of the most important components widely embedded in machine tools. Therefore, abnormal statuses of rolling bearings may also cause breakdowns in rotating systems and result in serious machining failures. skew and kurt are two useful SFs to detect rolling bearing faults at an early stage. Besides, kurt, which works very well in the whole range from slow to very fast rolling speed, is sensitive enough to provide rich information of incipient faults for characterizing the impact existing in the rolling bearings. Further, std, a kind of precision‐related SF responsible for investigating any small changes during machining, can indicate good correlation with real precision values of workpieces.
Then, the essential and concise SFs of electric‐current signals are investigated. RMS of spindle current can correctly represent dynamic cutting‐force variation for monitoring tool fracture and precision prediction. When dealing with the alternating current (AC), CF is applied for detecting whether an electrical system has the ability to generate a particular current output. In addition, avg can also be used as an SF of tool flute breakage or tool‐wear estimations.
Finally, with the same reason as for vibration signals, max is used for detecting any abnormal current peaks