# Vibration Signal Classification Using Stochastic Configuration Networks Ensemble
## 4 Performance Evaluation
### Results and Discussion  
In the experiments, the vibration data provided by the Jiangnan University (JNU) [37], the Southeast University (SEU) [38] and the University of Connecticut (UoC) [39] are used for performance comparison. The JNU dataset is collected under different rotating speeds, and there are four operating modes for each speed. The JNU dataset has twelve categories with a total of 8790 samples. The SEU dataset is also collected under different rotating speeds and load conditions, and has twenty categories with a total of 2040 samples. Similarly, the UoC dataset has nine categories with a total of 3238 samples. Then, the corresponding frequency spectrum data \((1\times 512)\) and time-frequency images \((33\times 33)\) are obtained via Fourier transform and STFT. For each dataset, the samples are randomly selected, with 80% as the training dataset and the remaining 20% as the testing dataset. In the algorithm implementation, the weights in NNRW and NNRW2D are randomly assigned from \([-1,1]^{512}\) and \([-1,1]^{33}\), respectively, while the biases for them are randomly assigned from \([-1,1]\). For the SCNs, the parameters \(\lambda,T_{max}\) and \(r\) are the same as those set on the CWRU dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Damage Size** & **Samples** & **Fault Mode** & **Label** \\ \hline \(\sim\) & 238 & Normal & 0 \\ \hline
0.007 in. & 118 & Inner ring & 1 \\
0.014 in. & 119 & Inner ring & 2 \\
0.021 in. & 119 & Inner ring & 3 \\ \hline
0.007 in. & 118 & Rolling element & 4 \\
0.014 in. & 118 & Rolling element & 5 \\
0.021 in. & 118 & Rolling element & 6 \\ \hline
0.007 in. & 119 & Outer ring & 7 \\
0.014 in. & 119 & Outer ring & 8 \\
0.021 in. & 119 & Outer ring & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The description of the CWRU dataset. Figure 5: Performance comparison of different samples on the CWRU dataset. In the stochastic configuration algorithm, the output weight parameter \(\beta\) is calculated via the optimal model, i.e., Equation (16). For the regularization factor \(\alpha\in[0,1]\), first we take \(\alpha=\{0:0.2:1\}\) with other parameters fixed. The difference in the classification rate under different \(\alpha\) values is small. As shown in Figure 6, \(\alpha\) is reset to some smaller values \(\{0.0001,0.001,0.005,0.01,0.05,0.08\}\). For the JNU dataset, the optimal model is insensitive to the factor \(\alpha\) and obtains close values, which indicates that the parameter \(\beta\) itself calculated by the stochastic configuration algorithm is sparse and the regular term has a weak effect. For the SEU and UoC dataset, there is no obvious trend in the recognition rate with different regularization factor values. According to the comparison results, \(\alpha\) is set to 0.05 in the following discussion. To show the results of the visual comparison, set the maximum number of hidden modes \(L_{max}=\{100:100:1400\}\) for the JNU dataset and \(L_{max}=\{20:20:240\}\) for the SEU dataset, and the other parameters are fixed. For the randomized algorithms, the SCN-D and NNRW are built with frequency spectrum signal \(\mathbf{D}\), the SCN-X and NNRW2D are built with time-frequency image data \(\mathbf{X}\), and the SCN-H is built with hybrid data \(\mathbf{Z}\). As shown in Figures 7 and 8, the recognition rates of the comparison models increase with the increase in the number of hidden layer nodes L. The results show that the SCN-H model built with the hybrid data obtains the highest accuracy values. Meanwhile, the SCN-D and SCN-X methods obtain higher accuracy than the NNRW and NNRW2D methods under the same training data, respectively. Compared with SCN-X, the SCN-D can be built with fewer hidden nodes to obtain the same recognition rate, and more fault features can be extracted from the frequency spectrum data. To demonstrate the effectiveness of the proposed model, for the SCN-based models, we set the parameter \(L_{max}=5000\), \(T_{max}=100\), \(r=\{0.9,0.99,0.999,0.9999,0.9999\}\), \(\lambda=\{0.5,1,5,30,50,100\}\), \(\epsilon=0.00001\).