## 3 Feature Extraction  
Datasets are built by running numerous model simulations and therefore collecting nominal and faulty signals, but classification algorithms only receive inputs in the form of a limited number of discrete parameters, which are extracted during the post-processing of data and serve to collect only the most important and characterizing information from any input. This feature extraction phase is the fundamental relationship between the information stored in a raw dataset and the learning abilities of classifiers. The decision on how to choose which parameters to extract is a main topic in the realm of fault diagnosis and signal processing: this research's contribution is to include parameters coming from different feature extraction philosophies. Table 1 defines the first batch of time-domain statistical features in the pool. Figure 6: Basic types of anomalous measurements. The signal taken as example is one-axis gyroscope data during a slew maneuver. In order: bias (**a**), drifting signal (**b**), erratic behavior (**c**), spikes (**d**), stuck signal (**e**), data loss (**f**). \[\text{AVG}=\mu_{x}=\frac{1}{N}\sum_{i=1}^{N}x_{i} \text{STD}=\sigma=\left(\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\mu_{x})^{ 2}\right)^{1/2}\] \[\text{MAX}=\text{max}(x) \text{MIN}=\text{min}(x)\] \[\text{RMS}=\left(\frac{1}{N}\sum_{i=1}^{N}x_{i}^{2}\right)^{1/2} \text{SRA}=\left(\frac{1}{N}\sum_{i=1}^{N}\sqrt{|x_{i}|}\right)^{2}\] \[\text{KV}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{x_{i}-\mu_{x}}{ \sigma}\right)^{4} \text{SV}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{x_{i}-\mu_{x}}{ \sigma}\right)^{3}\] \[\text{PPV}=\text{max}(x)-\text{min}(x) \text{CF}=\frac{\text{max}(|x|)}{\text{RMS}}\] \[\text{IF}=\frac{\text{max}(|x|)}{\frac{1}{N}\sum_{i=1}^{N}|x_{i}|} \text{MF}=\frac{\text{max}(|x|)}{\text{SRA}}\] \[\text{SF}=\frac{\text{RMS}}{\left(\frac{1}{N}\sum_{i=1}^{N}x_{i} ^{2}\right)^{1/2}} \text{KF}=\frac{\frac{1}{N}\sum_{i=1}^{N}\left(\frac{x_{i}-\mu_{x }}{\sigma}\right)^{4}}{\left(\frac{1}{N}\sum_{i=1}^{N}x_{i}^{2}\right)^{2}}\]  
The first four features include basic and standard statistical quantities, sufficient for what is called simple \"novelty detection\" on a signal: a change in these features is a very first and macroscopic indicator of a new behavior on the signal, not necessarily a fault [22]. These features are mean value (AVG), standard deviation (STD), maximum value (MAX), and minimum value (MIN), where standard deviation \(\sigma\) is simply the square root of the variance \(\sigma^{2}\), which was the main tracked feature for threshold-based detection. The other group of time-related statistical features in the table enhance the overall signal characterization: they are root mean square (RMS), square root of the amplitude (SRA), kurtosis value (KV), skewness value (SV), peak-to-peak value (PPV), crest factor (CF), impulse factor (IF), margin factor (MF), shape factor (SF), and kurtosis factor (KF). These features are well established for capturing behaviors and characterizing time-varying signals [6; 7], as they are particularly significant: kurtosis, for instance, helps define the amount of extreme values in a distribution, while skewness quantifies the asymmetry of said distribution. Peak-to-peak values, crest factor, impulse factor, and margin factor are signal-based statistical metrics that, especially for relatively regular or periodic signals, are potential markers for outliers. Finally, the shape factor of a signal relates to its shape, while being independent from its magnitude. Learning entities are provided with some more information concerning the frequency domain, through other typical signal processing features, added to the pool of this work as well [6].