## 2 PHM: Reference Methodologies, Frameworks, and Architectures
### Data Processing Function  
The DP function aims to process the raw data collected from machinery. This function is necessary for two reasons. First, raw signals are not able to directly reveal the health status of machinery. Rather, they present hidden patterns to discover. Second, raw signals are usually collected at very high frequencies to capture as much information as possible. However, the high number of observations and collected signals or the high number of features that result from signal processing strongly affect pattern recognition. Thus, the DP aim is to map the acquired data from a higher dimension to a lower dimension space, to provide a synthetic and meaningful representation of raw signals, preserving their structure and retaining as much information as possible [4]. For this aim, two main activities are usually carried out, namely, signal analysis, or feature extraction, and dimensionality reduction. When raw signals are collected at high frequencies, they are first divided into small segments of a certain length. Then, for each segment, synthetic parameters with a direct physical meaning, such as the mean, the energy, the maximum peak, and others, are computed. Signal analysis techniques are performed in the time domain, the frequency domain, and/or time-frequency domain [26]. Signal processing in the time domain is easy to implement and requires low computational complexity. However, many critical components show characteristic frequencies for some fault modes. When the fault is known, the frequency-domain analysis is preferred, as it easily allows us to identify and isolate frequency components of interest. For non-stationary signals, whose components contain rich fault-related information, the time-frequency-domain analysis is not only mandatory but also provides a more interpretable representation of the signal. In general, these techniques can be applied separately [25; 26; 27]. If raw signals are collected from many sensors, or a high number of features is extracted from signal processing, dimensionality reduction should be performed to reduce the number of variables of the dataset. Dimensionality reduction techniques are classified into feature selection methods and feature learning methods, depending on whether they change the original feature space [28]. Among feature selection methods, feature ranking methods, such as the Chisquare and ReliefF [29], and classifiers, such as the Decision Tree [30], are used for selecting the optimal features from a set of features extracted through signal analysis techniques. These methods are usually applied to critical components, for which labeled data under operating and more faulty conditions are available. Feature learning is projecting the original feature space into a new feature space with lower dimensionality. Among these methods, a distinction can be made between those that are applied to a set of features extracted during the signal processing phase, such as Principal Component Analysis (PCA) [31] and Locality Sensitive Discriminant Analysis (LSDA) [32], and those that are directly applied to the raw signal, such as methods based on sparse coding [33], dictionary learning [34], and Deep Learning [35]. Feature extraction and selection algorithms suffer from three mean issues [36]. First, they depend on prior knowledge about signal processing techniques and diagnostic expertise; second, they depend on the specific diagnostic task and may be unsuitable for other tasks; third, the extracted features may not carry the optimal information to classify the mechanical faults. Thus, the choice of one method over another depends on the component under analysis and requires deep knowledge of its behavior. Besides, signal analysis and feature selection techniques are used when it is possible to collect the data corresponding to a normal condition of the component and the data corresponding to one or more fault conditions under several operating conditions.