# Data-Driven Fault Detection and Diagnosis: Challenges and Opportunities in Real-World Scenarios
## 4 Experimental Design
### Experimental Scenario  
For each case study, two main tasks are carried out: feature extraction and fault/novelty detection. Because features have to be extracted from streaming data in real time, only time-domain features have been considered. In particular, the peak, peak-to-peak, mean, root mean square, crest factor, kurtosis, skewness, shape factor, and impulse factor are computed over batches of different lengths depending on the specific case. Then, two methods for feature selection and learning, i.e., the Pearson correlation analysis (PC) and the principal component analysis (PCA) have been used to reduce the dimensionality of the dataset. Finally, the AAD and ADP algorithms for anomaly and novelty detection are applied from scratch or after a pretraining phase to detect novel faults (improper conditions) or novel machinery settings. The mathematical background of feature extraction and selection (PC and PCA) methods and the clustering-based novelty detection approach (AAD + ADP) used in this paper are provided in Appendices A and B, respectively.  
In particular, two approaches have been adopted for different case studies, i.e., clustering-based with pretraining and clustering-based from scratch. The schemes of the two approaches are depicted in Figure 6.  
In the clustering-based with pretraining approach, the dataset is divided into two sets, named training and testing sets, including 70% and 30% of observations, respectively. The training set is first used to extract and select the relevant features revealing the health condition of monitored components. Then, the AAD + ADP (described in Appendix B) is applied to the selected features, and the local parameters of created clusters, i.e., the number of observations and the clouds' centers, are stored. Finally, the remaining observations  
Figure 5: Raw signals produced by the sealing group during the nominal condition and the three fault conditions.  
Figure 6: Experimental scenario.  
are used to test the effectiveness of the algorithm to (1) assign the 30% of observations corresponding to the conditions included in the training test to the correct clusters among the initialized ones and (2) to detect the change towards a novel condition and create a new cluster.  
In the clustering-based from scratch approach, no cluster is initialized. The algorithm starts from the first data creating a cluster; then, it creates a new cluster each time it recognizes a novel condition.  
Note that the testing phase of the approaches is applied to streaming data. Hence, the algorithm reads data batches of a certain length, extracts one or more features, and creates a label corresponding to the assigned cluster.  
According to the framework proposed in [19], novelty detection is also applied at a system level to discover novel operating conditions of the machinery. Therefore, some of the case studies deal with the operating recognition problem.  
Table 2 summarizes the goal (fault detection or operating condition recognition), the approach, the method, and the feature engineering method adopted for each case study.