# Fault Diagnosis Method Based on Time Series in Autonomous Unmanned System
## 5 Experimental Results and Analysis
### Test Results and Analysis  
(1)  
Experiment results of time series symbolization  
Each value of all time series is taken as a sample to train the Gaussian mixture clustering model, and the clustering label of each sample is successively obtained as its corresponding symbol thus each time series is symbolized, as shown in the figure below:  
The series is symbolized, as shown in Figure 3 below:  
Figures 4 and 5 respectively compress a time series in the data set with the traditional symbolic representation method of time series and the symbolic representation method of time series based on Gaussian mixture clustering proposed in this paper. These two algorithms use the same compression ratio, and it can be seen that the symbolic representation method of time series based on Gaussian mixture clustering proposed in this paper can better describe the fluctuation of the original time series. Figure 3: Original time series. We used the above formula to calculate 408 time series in the data set for experiments, and the results are shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**The Serial Number**} & **Traditional Symbolic** & **A Symbolic Representation** \\  & **Representation of Time Series** & **Method of Time Series Based on** \\  & & **Gaussian Mixture Clustering** \\ \hline
1 & 0.006521201 & 0.002199259 \\
2 & 0.002446704 & 0.015722783 \\
3 & 8.02 \(\times\) 10\({}^{-7}\) & 8.02 \(\times\) 10\({}^{-7}\) \\
4 & 0.00701202 & 0.000718564 \\
5 & 0.002896344 & 0.002896344 \\
6 & 0.002338207 & 0.009036553 \\
7 & 0.005271108 & 0.009092318 \\
8 & 0.004497003 & 0.001726509 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between the symbolic representation method of time series based on Gaussian mixture clustering and the traditional method. Figure 4: Time series after SAX dimensionality reduction compression. Figure 5: Time series of SAX dimensionality reduction compression based on gaussian mixture clustering. It can be observed that the discrimination between the samples based on the improved Markov chain feature engineering is more prominent, which is conducive to the following clustering analysis. The DBI indices of different clustering algorithms based on the Markov feature engineering and the improved Markov feature engineering are obtained by calculation, as shown in Figure 8:  
In general, when the number of clusters exceeds 5, the DBI of the improved Markov feature engineering under any clustering method is much smaller than the DBI before the improvement. The effect is more apparent when the number of clusters increases. The DI of different clustering algorithms based on the Markov feature engineering and the improved Markov feature engineering is obtained by calculation, as shown in Figure 9.  
It can be found from the figure that when the number of clusters is between 2 and 7, the DI increases, but after that, the DI starts to decrease. When the number of clusters is greater than 11, the DI of the improved feature engineering is still relatively stable. In contrast, the DI of the pre-improvement feature engineering is very small under any algorithm, and the clustering effect becomes generally poor. Figure 8: Comparison diagram of clustering DBI index before and after improvement. Figure 7: Sample distribution based on the improved Markov chain feature engineering. The sample anomaly rate is defined as follows in this paper:  
\[\text{ACC(S)}=\frac{\text{n}_{\text{S}}}{\text{N}} \tag{16}\]  
N is the total number of samples, \(\text{n}_{\text{S}}\) is the number of elements in the cluster where the current sample is located.