## 3 Proposed Method
### Hybrid-Based Feature Calculation  
The proposed method supports different or multiple physical magnitudes, despite vibration signals being the most preferred physical magnitude to diagnose the fault occurrence in bearings. In this proposal, the processing of different signals to achieve an improved characterization of the electromechanical system condition is considered, which, in turn, is related to the bearing condition. Thus, in the first stage, the three available signals (two vibration signals and one stator current) are characterized with the aim of computing a meaningful set of hybrid features. Subsequently, the processing of the available signals is carried out in two domains, that is, the time-domain (TD) and frequency-domain (FD). During the characterization procedure, the acquired signals are segmented into equal parts of one second; the consideration of this temporal period guarantees sufficient statistical consistency in most of the practical applications. In this regard, for the TD analysis, the available signals are characterized by estimating a set of \(T=15\) statistical features, and as a result, two representative \(T\)-dimensional feature matrices are obtained from the considered signals. Thereby, the characteristic feature matrix in the TD for the vibrations signals is \(M^{T_{V}}\) and for the stator current is \(M^{T_{C}}\), where \(T\in\mathbb{R}T\). On the other side, for the FD analysis, from each segmented part of the available signals, its corresponding frequency spectrum is computed through the classical application of the FFT technique. Subsequently, from each achieved frequency spectrum for each considered signal, a set of \(F=14\) statistical features is estimated aiming to obtain a numerical representation of the previously estimated frequency spectra. After applying the FD analysis, two significant \(F\)-dimensional feature matrices are obtained separately for the vibration signals and the stator current. The characteristic feature matrices in the FD are \(M^{F_{V}}\) for vibrations and \(M^{T_{C}}\) for stator current, where \(F\in\mathbb{R}F\). The characterization of signals by means of its processing through different domain analyses, such as TD and FD, allows improving the characterization of the fault-related patterns because it has been proved to ensure that promising results are achieved in the condition assessment when a meaningful set of hybrid features is estimated. Regarding the statistical features that are proposed to be estimated during the processing of the vibration and stator current signals in TD and FD analyses, the corresponding mathematical equations of the proposed sets of statistical features are summarized in Tables 1 and 2; these proposed sets of features have been usually considered in several condition monitoring approaches [33; 34; 35]. Thus, the statistical features computed in the TD are represented by Equations (3)-(17), while those computed in the FD are represented by Equations (18)-(30). The estimation of these sets of statistical features provides several advantages in condition  
Figure 2: A flow chart of the proposed condition monitoring method for the diagnosis and detection of multiple fault severities that may occurred in the outer race of bearings in IM’s. monitoring strategies, that is, high-performance signal characterization due to its ability of modeling trends and changes in signals when its estimation is performed in TD, whereas the calculation of statistical features in FD allows modeling changes in the main frequency components with a high convergence to the power spectrum. Furthermore, in regard to the computational burden, the easy computation of statistical features shows an advantage over other complex signal processing, such as DWT and MUSIC, among others [10; 21].