## 5 Numerical Results
### PCA and Clustering  
Figure 4 represents PCA and \(K\)-means clustering results for data on a certain illustrative day, 25 May 2018. The distribution of the data points in the reduced space defined by the first and the second principal components are shown; the left plot is based on the RTK-GPS data and the right plot is based on the INS data. The dimension is reduced to principal component axes with a rate of cumulative dispersion of at least 90% through the PCA process, and the clusters are identified by \(K\)-means clustering. The two plots in Figure 5 depict the distribution of data points in the reduced space defined by the first and the second principal components. It can be seen in both plots that the data for one drone (x76) is distributed in a significantly different way from those for the other drones. Thus, it can be conjectured that data from x76 are likely to contain the time series that exhibits anomaly. However, it is not directly apparent how the clustering result is related to an anomaly, as it is not likely that all the data from a potentially faulty vehicle belong to a single cluster. Figure 5 represents what portion of data of each drone belong to a particular cluster. It can be seen that most of data from all the drones belong to Clusters 1 and 5, but the distributions between x76 and the others are different. According to the ratio of data belonging to Clusters 1 and 5, x76 behaves differently from the others--significantly more data belong to Cluster 1 than 5, as opposed to the other drones. Another noticeable observation is that any data from x76, potentially a problematic drone, do not belong to Clusters 4, 6, 7, and 8. As such, it can be conjectured that although the clustering does not clearly indicate which drone may have behaved abnormally, the distribution of data across the clusters may \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Input** & **Output** & **Operation** \\ \hline Input & (\(n\), timestamp, 6) & (\(n\), 160, 6) & Standardization \\ \hline Hidden 1 & (\(n\), 160, 6) & (\(n\), 80, 12) & 1D Convolution (strides 2, kernel size 3), 1D Batch normalization, Rectified Linear Unit (ReLU) [53] \\ \hline Hidden 2 & (\(n\), 80, 12) & (\(n\), 40, 24) & 1D Convolution (strides 2, kernel size 3), 1D Batch normalization, ReLU \\ \hline Hidden 3 & (\(n\), 40, 24) & (\(n\), 20, 48) & 1D Convolution (strides 2, kernel size 3), 1D Batch normalization, ReLU \\ \hline Hidden 4 & (\(n\), 20, 48) & (\(n\), 10, 96) & 1D Convolution (strides 2, kernel size 3), 1D Batch normalization, ReLU \\ \hline Hidden 5 & (\(n\), 10, 96) & (\(n\), 5, 128) & 1D Convolution (strides 2, kernel size 3), 1D Batch normalization, ReLU \\ \hline Hidden 6 & (\(n\), 5, 128) & (\(n\), 5, 128) & 1D Convolution (strides 1, kernel size 3), 1D Batch normalization, ReLU \\ \hline Hidden 7 & (\(n\), 5, 128) & (\(n\), 128) & Global Average Pooling (GAP) [54] \\ \hline Hidden 8 & (\(n\), 128) & (\(n\), 64) & Dense, Batch normalization, ReLU \\ \hline Output & (\(n\), 64) & (\(n\), 2) & Dense, Sigmoid \\ \hline \hline \multicolumn{4}{c}{Hyper-parameters for learning model} \\ \hline Batch size & Time length & Epoch number & Learning rate \\
128 & 160 & 50 & 0.00004 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Neural network parameters and learning parameters (\(n\): batch size). be an indicator of anomaly in the data. Clusters 1, 2, and 3 are the indicators for abnormal data and Clusters 4, 5, 6, 7, and 8 indicate normal data. Along this line, data from each drone in Clusters 1-3 are labeled \"TA\" and the other data in Clusters 4-8 are labeled \"TN\" for the further procedure. In case of indistinct data such as Cluster 0 and uncertain data like as x56 in Cluster 3, a human expert may check the flight data to use as labeled data. Figures 6 and 7 represent equivalent results for the data obtained from a flight test on another date, 5 June 2018.