# Constructing Condition Monitoring Model of Harmonic Drive
## 3 The Proposed Approach
### Data Preprocessing  
The sound samples may have contained unnecessary sounds, such as environmental noise and factory noise; therefore, the method of separating the sound of machinery from the original samples was an essential step in the monitoring model. In this study, discrete wavelet transforms were used to process sound samples and discard some audio components to remove undesirable noises. The filter used in this research was the Sym10 wavelet shown in Figure 2, which belongs to the Symlet wavelet family. The Symlet wavelet has the advantage of fast calculation, and is exactly reversible without edge effect problems and memory-saving [15]. The process of the wavelet transforms is shown in Figure 3. In the first step, the sample was decomposed into 15-level discrete wavelet decompositions to obtain 15 detail coefficients and 1 approximation coefficient, representing higher frequency audio components and the lowest frequency audio components. In the second step, after the wavelet decomposition was completed, the coefficients generated in the previous step were reconstructed through the wavelet reconstruction. The reconstructed sounds were the corresponding audio component of the original sound sample in each frequency interval. The wavelet decomposition process is shown in Figure 4. For example, considering the two-level one-dimensional wavelet decomposition, the original audio signal X was a one-dimensional input signal, which was passed through a low pass filter g[k] of length K and high pass filter h[k], thus separating the low-frequency and high-frequency components of the signal. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Normal** & **Abnormal** \\ \hline The number of samples & 7 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of original samples. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Normal** & **Abnormal** \\ \hline Number of samples in one second & 285 & 171 \\ Number of samples in three seconds & 95 & 57 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of cutting samples. Figure 2: The Sym10 wavelet function. The signal through the down-sampling filter obtained the high-frequency detail coefficient cD1 and the approximate coefficient cA1 of low frequency. Then, cA1 was used as the subsequent input, and the same decomposition steps were performed to obtain the detail coefficient cD2 and the approximate coefficient cA2. The corresponding equations, Equations (3)-(6), are as follows:  
This research used 15-level wavelet decomposition to obtain the coefficients set S = {cD1, cD2, cD3, cD4, cD5, cD6, cD7, cD8, cD9, cD10, cD11, cD12, cD13, cD14, cD15, cA15}  
\[\text{cD1}[n]=\sum_{k=0}^{K-1}\text{ X }[n+1-k]h[k] \tag{3}\]  
\[\text{cA1}[n]=\sum_{k=0}^{K-1}\text{ X }[n+1-k]g[k] \tag{4}\]  
\[\text{cD2}[n]=\sum_{k=0}^{K-1}\text{cA1}[n+1-k]h[k] \tag{5}\]  
\[\text{cA2}[n]=\sum_{k=0}^{K-1}\text{ cA1}[n+1-k]g[k] \tag{6}\]  
Since this research only required the audio components of each coefficient, except for the detail coefficients of the audio components slated for reconstruction, the remaining  
Figure 4: The wavelet decomposition process. Figure 3: The wavelet transform process. coefficients were replaced by 0 arrays. The audio components were obtained after one or more reconstructions. Taking the cD1 audio component as an example, the 0 arrays and the high-frequency coefficients cD1 were passed through the low-pass reconstruction filter \(g^{\star}[k]\) and the high-pass reconstruction filter \(h^{\star}[k]\), respectively, then two signals were added to obtain the cD1 audio component, as shown in Figure 5.  
After obtaining the audio components at each frequency interval, this research adopted different audio components for each machinery type. Removing unnecessary noise improves the prediction performance of the neural network. The audio components selected for each category are shown in Tables 4 and 5.