## 5 Results and Discussions
In this sense, the whole resulting feature matrices, considering all supply frequencies and all bearing conditions, are concatenated, as shown in Table 3. From Table 3, it must be noted that all considered conditions, HC, S1, S2, S3, S4, and S5, are concatenated as row elements, where each condition includes its corresponding feature matrices achieved by analyzing the vibration signals in TD and FD, \(M^{T_{V}}\) and \(M^{F_{V}}\), respectively, and also includes its corresponding feature matrices achieved by analyzing the stator current signature in TD and FD, \(M^{T_{C}}\) and \(M^{F_{C}}\), respectively. In regard to the domain of analysis, the resulting feature matrices are concatenated as column elements, as shown in Table 3. Additionally, for the different values of supply frequency, each tested condition includes the corresponding feature matrices that are particularly estimated from the vibrations and stator current signals when the frequencies in the VFD are set to 5 Hz, 15 Hz, and 50 Hz. Such supply frequencies are addressed in Table 3 as @5 Hz, @15 Hz and @50 Hz, respectively. Subsequently, the LDA technique is applied over all concatenated matrices, aiming to perform the fusion of information, that is, the fusion of statistical features estimated from multiple signals analyzed in both domain analyses, DT and DF. The information fusion stage is achieved because the LDA is based on a linear transformation that projects the information of the original feature space (87-dimensional space) into a new and reduced feature space (2-dimensional space). The resulting projection symbolizes the linear combination, in different weights, of the original set of features (high-dimensional set of hybrid features), where the most representative information of all considered features is retained. In fact, those features that have a high weight, in the linear combination, have a high influence over the resulting projection. In contrast, those insignificant features may have a lower influence and a low weight that does not have significant influence over the resulting projection. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **HC** & \(M^{T_{V}}\)\({}_{\text{@5 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@5 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@5 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@5 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@15 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@15 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@15 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@15 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@5 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@5 HzHz}}\) & \(M^{T_{C}}\)\({}_{\text{@5 HzHz}}\) & \(M^{F_{V}}\)\({}_{\text{@5 HzHz}}\) & \(M^{F_{C}}\)\({}_{\text{@5 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@50 Hz}}\) \\ \cline{3-6}  & & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@5 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@5 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@5 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@5 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@15 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@15 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@15 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@15 Hz}}\) \\ \cline{3-6}  & & \(M^{T_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{T_{C}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{V}}\)\({}_{\text{@50 Hz}}\) & \(M^{F_{C}}\)\({}_{\text{@50 Hz}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The arrangement of feature matrices that are subjected to the feature extraction and fusion domain procedure. After applying the LDA technique over the hybrid set of features of all considered conditions, the original 87-dimensional feature space is projected into a 2-dimensional space, where the projected features belong to the new set of extracted features.