## 5 Results and Discussion
### Machine Learning Model
#### 5.2.2 Analysis of Time-Frequency Domain Model  
As mentioned in Section 4.3.1, the second-order scattering coefficient shows strong classification capability. The high values compared to the non-fault state in the second-order scattering scattergram (Figure 6(c)) indicate that the analytical scattering coefficient values can be used as the characteristics of the fault state of the propeller fault.  
The labels were set on the zeroth-order scattering coefficients graph, the first-order scattering coefficients graph, and the second-order scattering coefficients graph of the propeller fault signals. Then, the kNN model was built using the labeled features which contain non-fault and fault states. Among the three kNN machine learning model parameter settings, the first type of parameter setting achieved the highest accuracy for the damaged propeller state. The accuracy was 98.77 percent and the running time was 112 s (Table 4).  
The single fault kNN models of the time-frequency domain data have better classification effects, but the results of the two models both achieved an accuracy rate of over 88.5 percent as shown in Tables 5 and 6. It can also be found that the loosening of the motor  
\begin{table}
\begin{tabular}{c c c c} \hline  & **1** & **2** & **3** \\ \hline Tie-Breaking Algorithm & Nearest Point Search & Nearest Point Search & Nearest Point Search \\ \hline Distance Metric & Euclidean distance & Cosine similarity & Cosine similarity \\ \hline Distance Weighted & Same weight on each point & Same weight on each point & Inverse square on each point \\ \hline Nearest Neighbor Search & Brute-force search & Brute-force search & Brute-force search \\ \hline Number Of Nearest Neighbor & 3 & 3 & 7 \\ \hline Standardize & Yes & Yes & Yes \\ \hline Running Time & 112 s & 108 s & 108 s \\ \hline Accuracy & 98.77\% & 97.77\% & 98.04\% \\ \hline \end{tabular}
\end{table}
Table 4: Comparison table of model parameters used by the time-frequency domain for the propeller fault.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **1** & **2** & **3** \\ \hline Tie-Breaking Algorithm & Nearest Point Search & Nearest Point Search & Nearest Point Search \\ \hline Distance Metric & Euclidean distance & Cosine similarity & Cosine similarity \\ \hline Distance Weighted & Same weight on each point & Same weight on each point & Inverse square on each point \\ \hline Nearest Neighbor Search & Brute-force search & Brute-force search & Brute-force search \\ \hline Number Of Nearest Neighbor & 3 & 3 & 7 \\ \hline Standardize & Yes & Yes & Yes \\ \hline Running Time & 1.18 s & 1.32 s & 0.63 s \\ \hline Accuracy & 87\% & 91\% & 90\% \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of parameters of models trained using the time-domain feature when the propeller is damaged.  
screw had a lower accuracy rate because the fault is relatively slight and does not produce a visible change in the data. Regarding the running time, the model built using time-domain data had a faster solution speed due to less computational load. Other models used a large amount of data, resulting in a longer running time, and the wavelet scattering transform also needed considerable computation time.