## 4 Experimental Results and Analysis
### New Fault Mode Detection and System Update for Online Fault Diagnosis  
Initially, we assume that the system only has knowledge of a healthy machine. Thus, the DSK includes 22 features of each of the 30 FFB signals. For each test case, the system extracts an optimal number of features from unknown signals and adds those features to the DSK to form the analysis set. The new fault mode detection module detects \(k_{opt}\), which represents the number of fault modes in the analysis set. If \(k_{opt}\) is greater than \(F_{dsk}\), the number of features in the current DSK, the new fault signatures are added to the DSK.  
Here, system knowledge is represented as \(C_{dsk}\times N_{dsk}\times F_{dsk}\),  
As a central part of the online diagnosis system, the DSK updating process extracts a heterogeneous feature pool from the signals of all detected fault modes. The hybrid feature selection algorithm selects the discriminant fault signatures and constructs a DSK, which is used in the evaluation process. Table 3 summarizes the optimal feature subsets for different test cases with different datasets. After completing each test case, the DSK is represented as \(C_{dsk}\times N_{dsk}\times F_{dsk}\), where \(C_{dsk}\) is the number of emerging fault classes, \(N_{dsk}\) is the number of samples in each class, and \(F_{dsk}\) is the number of discriminant fault signature variables.  
Figure 13: (**a–e**) Sample distribution of different datasets and optimal \(k_{opt}\) (blue big circle) selection using the compactness and separation measure of (**f–j**) clusters (COSES) method, (**k–o**) silhouette coefficient, and (**p–t**) the proposed MPDFCDF cluster evaluation method.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{2}{c}{**Initial**} & \multicolumn{2}{c}{**Test Case 1**} & \multicolumn{2}{c}{**Test Case 2**} & \multicolumn{2}{c}{**Test Case 3**} & \multicolumn{2}{c}{**Test Case 4**} & \multicolumn{2}{c}{**Test Case 5**} \\ \cline{2-13}  & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Knowledge**} \\  & & & & & & & & & & & & & \\ \hline
1 & f1-22 & \(1\times 30\times 22\) & f1, f12, f13, f15 & \(2\times 30\times 4\) & f2, f9, f10 & \(4\times 30\times 3\) & f2, f9, f10 & \(4\times 30\times 3\) & f2, f9 & \(5\times 30\times 2\) & f2, f9, f13 & \(7\times 30\times 3\) \\ \hline
2 & f1-22 & \(1\times 30\times 22\) & f2, f9, f14 & \(2\times 30\times 3\) & f2, f9, f22 & \(4\times 30\times 3\) & f2, f9, f22 & \(4\times 30\times 3\) & f2, f9, f13 & \(5\times 30\times 3\) & f2, f9, f11, f22 & \(7\times 30\times 4\) \\ \hline
3 & f1-22 & \(1\times 30\times 22\) & f2, f15, f16, f20 & \(2\times 30\times 4\) & f2, f16 & \(4\times 30\times 2\) & f2, f16 & \(4\times 30\times 2\) & f2, f11, f15, f16 & \(5\times 30\times 4\) & f2, f9, f11 & \(7\times 30\times 3\) \\ \hline
4 & f1-22 & \(1\times 30\times 22\) & f2, f9, f13 & \(2\times 30\times 3\) & f2, f9, f20, f21 & \(4\times 30\times 4\) & f2, f9, f20, f21 & \(4\times 30\times 4\) & f2, f9 & \(5\times 30\times 2\) & f2, f9, f13 & \(7\times 30\times 3\) \\ \hline
5 & f1-22 & \(1\times 30\times 22\) & f2, f9 & \(2\times 30\times 2\) & f2, f9, f20, f21 & \(4\times 30\times 4\) & f2, f9, f20, f21 & \(4\times 30\times 4\) & f2, f9, f22 & \(5\times 30\times 3\) & f2, f9, f11 & \(7\times 30\times 2\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimal feature vector for different test cases of different datasets.