## 4 Experimental Studies
### Results and Comparative Analysis
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Full Time Series Sliding**} & \multicolumn{6}{c}{**Monte Carlo Search Method**} \\ \cline{2-10}
**Water Fatoes** & \multicolumn{3}{c}{**Search Method**} & \multicolumn{3}{c}{**0.5a**} & \multicolumn{3}{c}{**0.5a**} \\ \cline{2-10}  & **Run Time** & **Optimal Sliding** & **Run Time** & **Optimal Window** & **Run Time** & **Optimal Window** & **Run Time** & **Optimal Window** & **Run Time** & **Optimal Window** \\  & **(to)** & **Window Size** & **(to)** & **Accuracy (\%)** & **(to)** & **Accuracy (\%)** & **(to)** & **Accuracy (\%)** & **(to)** & **Accuracy (\%)** \\ \hline
**pH** & 1,0508 & 14 & 0.9500 & 62 & 0.6023 & 65 & 0.6949 & 70 & 0.8867 & 77.5 \\ \hline
**Dissolved Oxygen** & 1,001 & 12, 14 & 0.5687 & 65 & 0.6527 & 72.5 & 0.8605 & 77.5 & 0.9302 & 80 \\ \hline
**Electronic Conductivity** & 1,1270 & 16 & 0.6674 & 62.5 & 0.7332 & 67.5 & 0.7504 & 75 & 1.0313 & 85 \\ \hline
**Turbidity** & 1,1163 & 16, 17, 18 & 0.6113 & 60 & 0.6648 & 67.5 & 0.8070 & 72.5 & 0.9176 & 80 \\ \hline
**Ch chlorophyll-1** & 1,1410 & 17 & 0.5352 & 57.5 & 0.7680 & 65 & 0.8770 & 67.5 & 0.9316 & 75 \\ \hline
**Algol Density** & 1,1251 & 14 & 0.6649 & 55 & 0.6754 & 65 & 0.7352 & 72.5 & 0.9437 & 75 \\ \hline
**Femmangate Index** & 0.2066 & 9 & 0.1445 & 57.5 & 0.1728 & 62.5 & 0.1899 & 68 & 0.1984 & 75 \\ \hline
**Ammoni-Nitrogen** & 0.2058 & 8 & 0.1574 & 52.5 & 0.1789 & 60 & 0.1816 & 67.5 & 0.2242 & 70 \\ \hline
**Total Phosphorus** & 0.2426 & 12 & 0.1418 & 55 & 0.1637 & 57.5 & 0.1703 & 65 & 0.2039 & 67.5 \\ \hline
**Total Nitrogen** & 0.2586 & 14 & 0.1262 & 60 & 0.1477 & 62.5 & 0.1723 & 65 & 0.1906 & 72.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical information table of experimental calculation results. Figure 3 shows the rate of computation time increase histogram calculated by Equation (2). It can be seen from Figure 3 and Table 4 that the time series of water quality factors with the highest rate of computation time increase was the Chl-a observation series. When the random sampling scale was \(i=0.5n\), the maximum rate of computation time increase was 53.09%, and the optimal window accuracy was 57.5%. The time series of the water quality factor with the lowest rate of computation time increase was the EC observation series. When the random sampling scale was \(i=0.8n\), the rate of the computation time increase was 8.49%, and the optimal window accuracy was 80%. The statistical results show that, when the random sampling scale was \(i=0.5n\), the average rate of computation time increase with all water quality factors was 45.53%; when the random sampling scale was \(i=0.6n\), the average rate was 37.11%; when the random sampling scale was \(i=0.7n\), the average rate was 29.51%; and when the random sampling scale was \(i=0.8n\), the average rate was 17.09%. Taking the turbidity time series data as an example, the results in Figure 4 show the statistical characteristics of MCSM and FTSSSM under different sampling scales. The curve results of FTSSSM show that the outlier detection rate showed a rising trend first and then declined (red line in Figure 4a). The optimal window sizes of the turbidity time series data were 16, 17 and 18, under which 5.99% of the outlier data could be detected. The average outlier detection rate curve of the new algorithm proposed in this paper was basically consistent with the red line under different sampling scales. Because the scale of random sampling did not include all the data of the sequences, the outlier detection rate was lower than the red line. It should be noted that the goal of the new algorithm was to determine the optimal window size, and after the optimal window size was determined, the sliding detection of the whole sequence was still achieved through the optimal window size. The detailed data in Figure 4b shows that when \(i=0.5n\), a total of seven optimal window sizes were obtained, which were 14, 15, 16, 17, 18, 19 and 20.