## 4 Experiments
### Fault Diagnosis of gearbox
#### 4.2.2 Results  
The gearbox datasets were still processed as the structure of the SDAE fault diagnosis scheme (see Figure 3). A total of 120 samples are inputted into the system for training the model, with the outputting of four target values. After the optimization of the parameters in the model, another 120 samples are tested for the fault pattern recognition. Figure 10 shows the input signals and their frequency spectra. Each sample contains 1000 data points and the frequency spectra of the sample have 501 Fourier coefficients. The SDAE architecture is required to be determined again due to the change of objects. The number of data units in a gear sample is 1000 and the spectra length is 501; thus, the size of input is 501. After the grid search runs, the selected architecture remains (500, 500, 500). For this dataset, the parameters and structure are similar with the bearing fault dataset, thereby demonstrating the generalization ability of the proposed method to the different datasets. After selecting the appropriate structure, the training samples are inputted to train an SDAE network. The classification result can be viewed in detail after the testing process. Figure 11 shows the testing results of the four gear pattern recognition for dataset II. The training and testing samples are correctly recognized with 100% accuracy (see Figure 11). However, an evident output value floating exists for the slight wear condition recognition. Table 7 shows the recognition accuracy of each health status of the gearbox dataset for the proposed and DBN methods. The training set is correctly recognized; however, one sample of the testing set is misjudged. The contribution of the proposed method is the denoising ability to deal with random noises. To further attest to the superiority of the proposed method, signals of the dataset are combined with different levels of artificially random noises in the time domain and converted to frequency signals thereafter. Figure 12 shows the example of the noise mixed signals of bearing fault in different levels, and Figure 13 shows the example of noise mixed signals of gearbox fault. These artificially added noise dataset led to additional experiments being conducted to validate the proposed method and the comparison method DBN and SAE. Table 8 shows the recognition accuracy on different levels of noise interference. From Table 8, as the level of noises increases, the superiority of the proposed method becomes evident. Compared with DBN, the proposed method can consistently achieve a high accuracy above 90%, thereby indicating that the proposed method is robust to a range of noise levels. Figure 10: Example signals and their spectra of four health status patterns: (**a**) slight wear; (**b**) medium wear; (**c**) broken tooth; and (**d**) normal wear signals. Figure 11: (**a**) Training results and (**b**) testing results of gearbox dataset by SDAE. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Noise Level**} & \multicolumn{2}{c}{**SDAE Accuracy (\%)**} & \multicolumn{2}{c}{**DBN Accuracy (\%)**} & \multicolumn{2}{c}{**SAE Accuracy (\%)**} \\ \cline{3-8}  & & **Training** & **Testing** & **Training** & **Testing** & **Training** & **Testing** & **Training** & **Testing** \\ \hline \multirow{3}{*}{\begin{tabular}{l} Bearing \\ Dataset I \\ \end{tabular} } & 0.1 & 100 & 100 & 100 & 99.5 & 100 & 100 \\  & 0.2 & 100 & 100 & 100 & 99.5 & 100 & 100 \\  & 0.3 & 100 & 97 & 100 & 92.5 & 100 & 95 \\ \hline \multirow{3}{*}{\
\begin{tabular}{l} Bearing \\ Dataset II \\ \end{tabular} } & 0.1 & 100 & 100 & 100 & 98.5 & 100 & 98.5 \\  & 0.2 & 100 & 97 & 100 & 90.5 & 100 & 95 \\  & 0.3 & 100 & 91 & 100 & 84.5 & 98.5 & 82.5 \\ \hline \multirow{3}{*}{
\begin{tabular}{l} Gearbox \\ \end{tabular} } & 0.1 & 100 & 100 & 100 & 99.17 & 100 & 99.5 \\  & 0.2 & 100 & 95 & 100 & 93.34 & 100 & 86.7 \\  & 0.3 & 100 & 93.4 & 100 & 87.5 & 100 & 77.5 \\ \hline \hline \end{tabular}
\end{table}