## 4 Experimental Results and Analysis  
### Experimental Datasets  
For the experiment of the proposed model, signals were collected from a fault-free bearing (FFB) and faulty bearings at various shaft speeds. In this study, six fault modes are considered: A 3-mm crack on the outer raceway (BCO 3 mm), a 3-mm crack on the inner raceway (BCI 3 mm), a 3-mm crack on the roller (BCR 3 mm), a 12-mm crack on the outer raceway (BCO 12 mm), a 12-mm crack on the inner raceway (BCI 12 mm), and a 10-mm crack on the roller (BCR 12 mm). Signals are collected for different rotational speeds (300 rpm to 500 rpm). Finally, AE data are divided into five datasets based on the shaft rotational speed, where each dataset contains a total of 630 AE signals of 5 s duration each (i.e., 90 AE signals for FFB and 90 for each of the six bearing faults). Table 1 presents the details of the experimental dataset.  
To validate the proposed model, five test cases are defined to progressively introduce new faults (small or big cracks) into the system, as shown in Table 2. Actually, to diagnosis the continues growth of different faults, the data acquisition process should run for a long time (several years) during operation of a bearing, which is very difficult. Thus, to validate the proposed online baring fault and identify new faults, faulty signals of different faults are incorporate in progressive test cases. Finally, the proposed model is validated by five considered datasets. Each dataset is divided into two halves, one for analysis and the other for evaluation. The analysis dataset, containing 45 of 90 signals from each class, is used to detect fault modes and update the DSK. The evaluation dataset, also containing 45 samples from each class, is used for diagnosis. It is considered that the system only starts with the diagnostic knowledge of a healthy machine, originating from 30 FFB signals, where each signal is represented by a 22-dimensional feature vector. Each test case uses 30 randomly-selected samples from the corresponding fault class in the analysis dataset to evaluate the unknown fault mode detection process and update the system. For evaluation, we randomly select 30 samples from each candidate fault class in the evaluation dataset.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Dataset 1** & **Dataset 2** & **Dataset 3** & **Dataset 4** & **Dataset 5** \\ \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} Average RPM \\ \end{tabular} } & 300 rpm & 350 rpm & 400 rpm & 450 rpm & 500 rpm \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Fault \\ Severity \\ \end{tabular} } & \multirow{2}{*}{Small crack} & Crack length: 3 mm, width: 0.35 mm, depth: 0.3 mm on outer raceway, inner \\  & & & raceway, and roller \\ \cline{2-6}  & \multirow{2}{*}{Big crack} & Crack length: 12 mm on outer and inner raceways and 10 mm on roller, width: 0.49 mm, depth: 0.5 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Various datasets with the crack severity specifications considered in this study.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & **Initial** & **Test Case 1** & Update & **Test Case 2** & Update & **Test Case 3** & No & **Test Case 4** & Update System & **Test Case 5** & Update System & **Final** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} System \\ Condition \\ \end{tabular} } & & & \multirow{4}{*}{FFB} & & & & & & & & & & & \\  & & & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & \\ \hline Unknown & \multirow{4}{*}{FFB} & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Organization of different test cases.