## 5 Results and Discussions  
To validate the effectiveness of the proposed method in front of the diagnosis and detection of the different severities of bearing faults, the method is applied to the available signals that are acquired from the pulley-belt electromechanical system; such signals are the two vibration signals and the stator current signature. Hence, as described in Section 3.1, these signals were acquired during 150 s of the continuous operation of the IM, and its processing is carried out under Matlab, which is a dedicated software used in a great deal of engineering applications. According to the proposed method, each one of the acquired signals is segmented into equal 1-second parts to generate a consecutive set of samples; afterward, the multi-domain analysis is performed over each one of the segmented parts of the signals to perform the signal characterization in two different domains, that is, DT and DF. Moreover, the proposed multi-domain analysis leads to achieve high-performance characterization of the electromechanical system operation, which, in turn, is associated with the different bearing conditions. In this regard, for the TD analysis, the set of 15 statistical features is computed from each segment of each available signal; thus, for both vibration signals, a feature matrix with 30 statistical features and 150 samples (dim(\(M^{T_{V}}\)) = (150 \(\times\) 30)) is achieved; meanwhile, the feature matrix achieved from the stator current consists of 15 statistical features with 150 samples (dim(\(M^{T_{C}}\)) = (150 \(\times\) 15)). On the other hand, in the FD analysis, from each segmented part of each available signal, the corresponding frequency spectrum is estimated by means of applying the FFT technique, and then, from each resulting spectrum, the set of 14 statistical features is calculated to characterize each corresponding spectrum into a set of representative numerical values. Thereby, for both vibrations signals analyzed in FD, a feature matrix with 28 statistical features and 150 samples (dim(\(M^{F_{V}}\)) = (150 \(\times\) 28)) is computed; whereas, for the analysis in FD of the stator current signature, a characteristic feature matrix that contains 14 statistical features with 150 samples (dim(\(M^{F_{C}}\)) = (150 \(\times\) 14))  
Figure 5: The set of damaged bearings experimentally tested in the IM of an electromechanical systems. The damaged bearings are damaged in their outer race with a severity of damage of 1 mm (S1), 2 mm (S2), 3 mm (S3), 4 mm (S4), and 5 mm (S5). is achieved. Consequently, for each evaluated condition, a high-dimensional set of hybrid features that contain the characteristic patterns is computed. The high-dimensional set of hybrid features includes the four representative feature matrices: \(M^{T_{V}}\), \(M^{T_{C}}\), \(M^{F_{C}}\), and \(M^{F_{C}}\), which are estimated after analyzing each one of the available signals in two different domains (TD and FD). Hence, the resulting dimension by concatenating the features matrices consist of 87 statistical features in TD and FD with 150 consecutive samples (dim([\(M^{T_{V}}\), \(M^{T_{C}}\), \(M^{F_{C}}\), \(M^{F_{C}}\)] ) = (150 \(\times\) 87)). Additionally, it should be clarified that these representative feature matrices are estimated for each one of the considered conditions that is experimentally tested under the considered supply frequencies fixed in the VFD (5 Hz, 15 Hz, and 50 Hz). In order to carry out the information fusion and data compression, the high-dimensional set of hybrid features are subjected to the feature extraction procedure by means of applying the LDA technique.