# Similarity Analysis for Time Series-Based 2D Temperature Measurement of Engine Exhaust Gas in TDLAT
## 5 Conclusions  
The results of this study are summarized as follows: (_i_) the paired \(t\) test for 18 candidate cycles indicated that, in most cases, \(T_{Rec}\) was not the same in each cycle. This implies that \(T_{Rec}\) might vary depending on the cycle set during CT analysis. Therefore, a standard for proper cycle setting is needed. (_ii_) Three types of similarity analysis yielded different results. First, the Two-sample \(t\) test showed that the \(T_{Rec}\) for 71 cycles was not the much different from that of \(T_{T{Rec}}\). Second, the results from RMSE showed that the \(T_{Rec}\) of the 601 cycles was most similar to that of the \(T_{T{Rec}}\). Finally, TMD results show that the \(T_{Rec}\) for 201 cycles was most similar to that of \(T_{T{Rec}}\). (_iii_) The reason for different results is that all three methodologies have different characteristics. For a more visualized description, a comparison of \(T_{T{Rec}}\) and \(T_{Rec}\) was provided based on the similarity analysis result. Figures 9-11 show a comparison of the \(T_{T{Rec}}\) with the \(T_{Rec}\) for each 71, 601, and 201 cycles, respectively. The movement of \(T_{T{Rec}}\) and \(T_{Rec}\) over time shows that \(T_{Rec}\) for 601 and 201 cycles moved closely with \(T_{T{Rec}}\). However, a closer look at the temperature change pattern shows that \(T_{Rec}\) of 201 cycles was moving similarly to \(T_{T{Rec}}\). On the other hand, for 71 cycle, the range of \(T_{Rec}\) changes over time was observed to be much larger than \(T_{T{Inc}}\). (_iv_) For the Two-sample \(t\)-test, it was difficult to determine similarity by sensitively reflecting changes in temperature as the difference in the mean of the overall temperature data in a given period was taken into account. Likewise, the RMSE was purely an indicator of the mean of distance between \(T_{T{Rec}}\) and \(T_{Rec}\), which made it difficult to analyze, including the correlation between changes in T_{T{Inc}}\)and T_{Rec}._ TMD was a suitable indicator for this study because it considers both the distance and correlation between T_{T{Inc}}\) and T_{Rec}\). Therefore, if the engine used in this study is in idle mode, setting it to 201 cycles in the CT analysis will increase the accuracy of the analysis while minimizing the analysis time and effort. Figure 12 shows the 2D reconstruction temperature distribution in 201 cycles in time from 1.0 to 9.0 s. The temperature of the peak area of the 2D distribution in each time was equal to that of the corresponding time at the 201 cycle reconstruction temperature in Figure 11. As illustrated in Figure 12, it can be seen that the maximum temperature was continuously distributed in the central area. For example, Figure 12b,h show a reconstruction temperature of approximately 410 K and 408 K \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cycles**} & \multicolumn{8}{c}{**Time (s)**} & \multicolumn{8}{c}{**Total**} \\ \cline{2-11}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & \\ \cline{2-11}  & & & & & **TMD** & & & & **TMD** & **Rank** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 6: Results of time-based Mahalanobis distance (TMD) analysis between \(T_{T{Inc}}\) and \(T_{Rec}\) for 18 candidate cycles. in the central area, and Figure 10 shows also the same temperature at that time. This was the same in other times. This study presented the statistical analysis procedure and the appropriate cycle to improve TDLAT performance when measuring time series-based 2D temperature in idle mode of engine. To the best of our knowledge, this is the first attempt to present the criteria for cycle selection through the similarity analysis when based on signal stabilization technique. This signal stabilization technique was more effective in error reduction than the conventional polynomial reduction method when converting signals into absorption spectra.