## 2 PHM: Reference Methodologies, Frameworks, and Architectures
### Fault Diagnosis Assessment Function  
Diagnosis deals with the detection, isolation, and identification of a fault; in other words, it aims to detect the occurrence of a failure, to find its component and position, and to determine its pattern and severity. In a PHM system, these goals can be achieved by identifying the relationship between the information obtained in the measurement and/or features space and the machine fault pattern in the fault space [5]. As a pattern recognition problem, diagnostics can be faced by resorting to several Machine Learning algorithms [45]. A broad distinction can be made between supervised methods and unsupervised methods depending on whether the value (label or class) to predict is considered at the prediction time. In the context of PHM, the class corresponds to the health condition of the component. Supervised methods require signals, or features, to be associated with a known health condition to learn the relationships that best describe observations belonging to the same class and to classify future unknown observations. Instead, unsupervised methods can distinguish observations in the data set with no prior knowledge about their belonging classes, but only based on the structure of the data itself. In the context of PHM, ML algorithms can perform two main tasks: classification, for which supervised learning is adopted, and clustering, which is based on unsupervised learning. Classification models learn the relationships between the extracted features and the health status of the component. They provide a model that predicts the component health status when the health condition is unknown. The development of a classification model is performed in two steps [46]. In the first step, named training, a considerable amount of random samples is extracted from the original dataset to build the training set, which is used for deriving classification rules that match the target class to each observation included in this set. In the second step, named testing, the remaining instances, which constitute the testing set, are classified through classification rules generated in the training phase; finally, the actual target class, that is known, and the class predicted by the model are compared to assess the accuracy of the prediction. Among the most adopted classifiers for diagnostics, there are k-Nearest Neighbour (k-NN), Naive Bayes Classifiers, Artificial Neural Networks (ANNs) [47], Support Vector Machines (SVMs) [48; 49], and Deep Learning models, such as Deep Belief Networks (DBNs) [35], Deep Boltzmann Machine (DBM) [50], Convolutional Neural Networks (CNNs), and Recurrent Neural Networks (RNNs) [51]. There is no definite guide to a priori choose one method over another. However, in many cases, the SVM outperforms the ANN regarding the accuracy and the generalization capability [48] and requires fewer training observations. Clustering is an unsupervised learning approach. It can reveal hidden structures in the data without relying on a target class that guides the algorithm training. In a clustering task, a set of unlabeled data is grouped into clusters so that observations belonging to the same cluster are similar between each other and dissimilar to observations belonging to the remaining clusters. The first distinction separates hard clustering techniques from fuzzy techniques. In hard clustering, the membership of elements in a cluster is assessed in binary terms, meaning that an element either belongs to a cluster or not. On the contrary, the membership of elements in fuzzy clustering is described by a membership function valued in [0, 1], meaning that elements can belong to more clusters with a certain degree [52]. The most common unsupervised clustering algorithms adopted for fault diagnosis are Adaptive Resonance Theory (ART) [53], Self-Organizing Maps (SOM) [54], and Affinity Propagation [55]. Classification is for labeled data, i.e., when each observation is associated with a categorical target value.