# A Tutorial for Feature Engineering in the Prognostics and Health Management of Gears and Bearings
## 2 PHM Framework and Datasets for the Tutorial  
The PHM framework can be divided into several steps as shown in Figure 1. After the data acquisition, the signal processing step is performed which aims to remove noise from the raw signal to obtain only the necessary information for the diagnosis and prognosis. Discrete signal separation techniques remove the periodic signals that are not related to the fault such as the ones transmitted from nearby equipment. Residual fault signals are then enhanced by signal enhancement techniques. If necessary, the signals, whether in their raw form or after processing, can also be decomposed into various components to facilitate the exploration of fault information. Detailed information about the techniques is addressed in the previous tutorial study [13]. Once the signal processing is done, the feature engineering process is conducted next, where the features that represent the fault or degradation of the system can be extracted, evaluated, and selected as shown in Figure 1. Finally, by exploiting these features, fault diagnosis is performed to classify the state of the target system or failure prognosis is performed to predict when the failure will occur in the future. Note that feature engineering requires substantial skills and expertise, which is the key to the success of the subsequent steps: diagnosis and prognosis. Recently, there is a new trend that takes advantage of deep learning-based neural network approaches to avoid the feature engineering process  
Figure 1: Framework of Prognostics and health management (PHM). as illustrated in Figure 2[11]. The deep learning-based method utilizes the raw data directly in the diagnosis right after the signal processing, as opposed to the traditional data-driven method that underlies the feature engineering process. However, since the deep learning-based method is not mature yet and poses several challenges to be addressed in the future, this tutorial presents the traditional feature engineering method, aided by Matlab implementations. In the PHM study of gears and bearings, the general method of data acquisition is to measure vibration by attaching an accelerometer to the housing of gears or bearings. Gathering the data is, however, too expensive, requiring a test rig, sensors, and time-consuming tests. To avoid this, several universities and research institutions have released their data to the public, which are summarized in reference [13]. They are classified into diagnostic and prognostic data. Diagnostic data are obtained by running the components under normal and fault conditions, respectively. Prognostic data are obtained by running the components constantly from the normal to the failure state. Among them, the data used in this paper are presented in Table 1 and the details are as follows: HS (High speed) gear dataset [14] is the vibration data obtained for 6 s with a sampling frequency of 97,656 Hz from the 3 blades upwind V90 wind generator, which produces an output of 3 MW and operates at 30 Hz. The gear has 32 teeth and the gear mesh frequency (GMF) is 960 Hz. The data are collected in the normal and fault conditions, in which the natural faults are applied in the pinion gear. Among 17 files, 11 are fault and 6 are normal. The next dataset is KAUG (Korea Aerospace University Gear), obtained from the gearbox testbed made by the authors. The encoder signals are acquired from the testbed at a 10 kHz sampling rate. There are 31 data files, of which 10 are normal, 10 spall, and 11 crack. The KAUG datasets are given on the authors' homepage www.kau-sdol.com. The CWRU bearing dataset is provided by Case Western Reverse University [15]. Two bearings are installed at the motor drive- and fan- end, which are operated under various motor loads and speeds. Among the many cases, this study considers the fault data at the inner and outer race of the drive-end with the hole diameter of 0.021 inches. The operating load is 3 HP, speed is 1730 rpm, and sampling frequency is 12 kHz.