## 2 PHM: Reference Methodologies, Frameworks, and Architectures
### Fault Diagnosis Assessment Function
#### 2.2.2 Novelty Detection  
Novelty detection aims to discover new patterns in the data. Two approaches can be used to perform the novelty detection task. The first group includes Evolving Intelligent Systems (EIS), which can handle streaming data and adapt both their structure and parameters depending on the input data. EISs can be seen as an evolution of the Fuzzy Rule-Based models (FRB), i.e., sets of linguistic statements in the form IF-THEN, where conditions and consequences are associated with fuzzy concepts, i.e., linguist terms [59]. Evolving FRB classifiers can classify the data from scratch. Thus, they can start building the model sample by sample from the first input data. For the fuzzy partitioning of the input feature space, i.e., the identification of the antecedent part of the evolving FRB classifier, evolving clustering algorithms can be used [60]. Evolving clustering algorithms rely on the idea that multiple clusters correspond to different system modes. As new input data arrive, the system integrates these data into existing clusters if the data are compatible with the existing model structure and adapts the local parameters of the corresponding cluster (parameter adaptation); otherwise, the algorithm creates a new cluster (structure evolving) [61]. In [62], a recursive clustering algorithm incorporating a drift detection method is proposed, in which the clustering updating process depends not only on the similarity measure but also on the monitoring changes in the input data flow, which gives the algorithm greater robustness with respect to the presence of outliers and noise. However, these methods require the membership function to be determined a priori. In [63], a new way of determining the antecedent part for FRB has been introduced. The antecedent part is called the AnYa system and is non-parametric. The membership function is directly extracted from the data and represents their density and distribution. Hence, the concept of the cluster is replaced by the concept of cloud, which has no boundaries, could assume any shape, and is not represented by any centers or prototypes. Therefore, in contrast to traditional clustering methods, in AnYa there is no need to use a particular kind of distance; local and global density, which can be calculated recursively as new input arrives, are the only variables affecting the cloud shape and the point assignment process. Based on AnYa fuzzy systems, an evolving system is proposed in [64], which can protect from the addition of new clouds based on outliers and allows removing less active and informative clouds. The second group of approaches relies on novelty detection and diagnosis models to discover new scenarios, starting from data related to a healthy condition and some known fault conditions. In [65], an ensemble-based classifier for novelty detection and an evolving classifier for diagnosis are separately performed for a different set of features and then integrated into a unique methodology to discover new patterns in case only data related to a healthy condition are available. In that work, a measurement labeled as 'unknown' can represent an outlier, a new fault, or a new operating condition. Thus, machine user intervention is required to verify which of the above cases the detected novelty refers to. In [66], a hybrid approach for multi-modal signal analysis, novelty detection, and diagnosis, is presented. It aims at detecting and incrementally including newly discovered scenarios based on time-frequency features. In [67], a new scenario named Initially Labeled Streaming Environment (ISLE) is defined. It is characterized by an infinite verification latency, meaning that no labeled data are received after initialization. In this context, the authors developed a new algorithm, named COMPOSE, which learns drifting concepts from a streaming and non-stationary environment that provides only unlabeled data after initialization. An application to fault diagnosis of COMPOSE is introduced in [68].