## 7 Experimental Results  
The CWRU dataset was chosen to test the recommended scheme [38]. To test the quality of the proposed AMRXU-AVSPMI technique, the method was compared with state-of-the-art techniques, including AMRXU-VSPMI and AMRXU-PMI. All simulations \begin{table}
\begin{tabular}{c c} \hline \hline
**Classes** & **(NORM, ROLF, INRF, OURF)** \\ \hline Number of samples per class & 100 \\ Number of training samples per class & 75 \\ Number of testing samples per class & 25 \\ Number of samples per test & 400 \\ Number of training samples per test & 300 \\ Number of testing samples per test & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the dataset for training and testing based on the SVM. \begin{table}
\begin{tabular}{c c} \hline \hline
**Steps** & **Explanation, with Equation Number(s) in Parentheses** \\ \hline
1 & Resampling and RMS feature extraction (1). \\
**RMS Signal Modeling** \\
2 & Signal modeling using AR technique (2-4). \\
3 & Increase the accuracy and robustness of AR using the combination of AR and ARXU (5-8). \\
4 & Improve the performance of ARXU under nonlinear conditions using the combination of ARXU and MBR that is called AMRXU (16-19). \\
**RMS Signal Estimation** \\
5 & Signal estimation using the AMRXU-PI technique (20-23). \\
6 & Increasing the accuracy of AMRXU-PI using the AMRXU-PMI method (24-27). \\
7 & Increasing the robustness of the AMRXU-PMI method using the AMRXU-VSPMI technique (28-31). \\
8 & Increasing the reliability, flexibility, and accuracy of AMRXU-AVSPMI using the proposed SNFS scheme that is called AMRXU-AVSPMI (39-42). \\
9 & Determination of residual signals (45). \\
10 & Classification and identification of the signal states (faults) using the SVM. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the proposed scheme’s implementation. are performed in MATLAB 2015a software with the system configuration of Intel (R) core TM i7-8700U, 8 GB RAM, 3.2 GHz processor, and 64-bit Windows 10 operating system. Figure 2 illustrates the original vibration signals in bearings under all conditions. As seen in the figure, when crack sizes are 0.007, 0.014, and 0.021 inches, the ROLF, INRF, and OURF overlap, causing misclassifications in fault diagnosis. Based on Figure 2, it can be seen that the classification of the original raw signals is very difficult because these signals are overlapped in abnormal conditions. To address this issue, the proposed algorithm is recommended. The normal Raw signal of bearing and the resampled RMS signal for the normal condition is illustrated in Figure 3.  
Figure 3: RAW signals and resample signals: (**a**) the normal raw signal of a bearing, and (**b**) the resampled RMS signal extracted from the raw signal. Figure 2: Bearing vibration signals for normal bearings and for ball, inner, and outer faults. Figure 4 shows the error in signal modeling using the AR technique, the ARXU method, and the proposed AMRXU algorithm for resampled RMS signals in a normal state. In Figure 4, the accuracy of the normal resampled RMS signal modeled using AR is around 51.33%; by ARXU, it is around 85.5%, and based on AMRXU, the accuracy is 98.5%. Thus, the linear AR and ARXU approaches are not accurate enough to model the nonlinear and nonstationary signals. To address this issue, the nonlinear signal modeling approach using proposed AMRXU is suggested in this work. The mean square error (MSE) of the RMS resampled normal signal modeling using the AMRXU for training, validation, and testing is presented in Figure 5. From the figure, we can observe that MSE curves sharply decrease within the first 7 epochs until they reach the MSE level of near 0.01. Then, for the next 17 epochs, some oscillations can be approximated, and these curves converge to an MSE level of around 0.0079. The AMRXU-PMI and AMRXU-VSPMI methods are inherently linear estimators and the most significant advantage for them is that we can perform model structure and parameter identification rapidly.