###### Abstract  
Extracting representative feature sets from raw signals is crucial in Prognostics and Health Management (PHM) for components' behavior understanding. The literature proposes various methods, including signal processing in the time, frequency, and time-frequency domains, feature selection, and unsupervised feature learning. An emerging task in data science is Feature Construction (FC), which has the advantages of both feature selection and feature learning. In particular, the constructed features address a specific objective function without requiring a label during the construction process. Genetic Programming (GP) is a powerful tool to perform FC in the PHM context, as it allows to obtain distinct feature sets depending on the analysis goal, i.e., diagnostics and prognostics. This paper adopts GP to extract system-level features for machinery setting recognition and component-level features for prognostics. Three distinct fitness functions are considered for the GP training, which requires a set of statistical time-domain features as input. The methodology is applied to vibration signals extracted from a test rig during run-to-failure tests under different settings. The performances of constructed features are evaluated through the classification accuracy and the Remaining Useful Life (RUL) prediction error. Results demonstrate that GP-based features classify known and novel machinery operating conditions better than feature selection and learning methods. prognostics and health management; feature construction; genetic programming +
Footnote †: journal: Medical  
approach consists of dividing the signal into segments of defined length and computing one or more features for each signal segment. Depending on the failure propagations, features may assume different trends, e.g., strictly monotonic, constant, mixed, or constant with discontinuities [4]. Thus, a deep knowledge of the system is required to identify relevant features representing specific failure propagations. Alternatively, dimensionality reduction methods, including feature selection and feature learning, can be implemented to extract relevant features from a large original set according to a specific object and, at the same time, to reduce the eventual redundancy [5; 6]. Methods for feature selection extract relevant features from the original set without any transformation [7]. In particular, filter methods rank the features in the original set according to one or more evaluation criteria and select the features with the highest score [8; 9]. Wrapper and embedding feature selection approaches use ML algorithms' performances to select the optimal subset of features [10; 11]. On the other side, feature learning methods project the original feature set into a new feature space with a lower dimension, losing the physical meaning of the original features [12]. Deep Learning (DL), which allows extracting a relevant and non-redundant feature set automatically and in an unsupervised way, represents a breakthrough in feature learning methods. DL allows the construction of end-to-end diagnostics and prognostics models to learn features directly from raw data and recognize and predict the health state of machines [13; 14]. The major problem with DL-based feature learning is that it requires many calculations during the training process and many hyperparameters to set [15]. An emerging task in data science is Feature Construction (FC), which aims to construct higher-level features from the original feature set to increase the classification performance and eventually reduce the dimensionality of features [16]. Like feature learning, FC may provide a combination of the original features in output and, therefore, the resulting features may not have a clear physical meaning. However, FC may also work just as feature selection when the original feature set contains a feature that already describes the failure propagation.