# Examining the Optimization of Spray Cleaning Performance for LiDAR Sensor
## 3 Results and Discussion
### Optimization Results and Reproducibility Examination  
As shown in Table 7, the optimal conditions of four factors were obtained based on the number of sprays for LiDAR cleaning. All four sprays met suitability, and the second spray showed the highest explanatory power. The target points were identical (10 mm), whereas the spray angles were approximately 30\({}^{\circ}\), excluding that of the third spray. For the third and fourth sprays, the optimal conditions of time and pressure were similar, whereas the spray angle and cleaning rate were different. When experiments were performed under the calculated optimal conditions to examine reproducibility, the second spray model exhibited the smallest difference relative to the highest explanatory power of the model.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Response** & **R-Squared** & **Adj.** & **Adeq.** & **F-Value** & **_p-Value_** \\ \hline Fourth spray & 0.9147 & 0.8822 & 14.573 & 28.16 & \textless{}0.0001 ** \\ \hline \hline \end{tabular}  
* \(p<0.05\).  
\end{table}
Table 6: Variance analysis results of the fourth spray model.  
Figure 11: Three-dimensional graphs of the cleaning rate of the third spray to **(a)** washer pressure and spray time, **(b)** spray angle and spray time, **(c)** target point and spray time, **(d)** spray angle and washer pressure, **(e)** target point and washer pressure, and **(f)** target point and spray angle.  
In this study, all cases were not tested by DOE. However, the optimized spray time and number of sprays were compared and the correlation between the two factors was obtained, as listed in Table 8. The cleaning rate was observed to increase with the spray time and number of sprays.  
When the total spray time was 1 s, the cleaning rate was higher for two sprays at an interval of 0.5 s compared with one spray for 1 s. When the total spray time was 1.5 s, the cleaning rate was higher for three sprays at an interval of 0.5 s compared with one spray for 1.5 s. Thus, the cleaning rate was higher when the spray time was shorter and the spray was repeated under the same pressure and flow rate conditions, indicating the effectiveness of repeated sprays when compared with the spray time for a high cleaning rate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optimal Factor** & **1 st Spray Model** & **2 nd Spray Model** & **3 rd Spray Model** & **4 th Spray Model** \\ \hline Spray time & 1.41275 & 1.46406 & 1.5 & 1.5 \\ Spray angle & 27.2456 & 23.8065 & 20.0002 & 31.7463 \\ Washer pressure & 8.93588 & 8.18167 & 7.72457 & 7.60159 \\ Target point & 8.13383 & 11.5988 & 10.4796 & 10.1625 \\ Adj. R-squared & 0.8158 & 0.8902 & 0.8655 & 0.8822 \\ Predicted cleaning rate & 47.5398 & 61.0655 & 72.5963 & 77.7102 \\ Actual cleaning rate & 39.34 & 62.9 & 70.31 & 74.69 \\ Diff (predicted-actual) & 8.20 & 1.8345 & \(-\)2.2863 & \(-\)3.0202 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Optimization factors according to the number of sprays.  
Figure 12: Three-dimensional graphs of the cleaning rate of the fourth spray to (**a**) washer pressure and spray time, (**b**) spray angle and spray time, (**c**) target point and spray time, (**d**) spray angle and washer pressure, (**e**) target point and washer pressure, and (**f**) target point and spray angle.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Spray** & **1 st Spray** & **2 nd Spray** & **3 rd Spray** & **4 th Spray** \\
**Time (s)** & **Result (\%)** & **Result (\%)** & **Result (\%)** & **Result (\%)** \\ \hline
0.5 & 38.37072 & 48.55307 & 59.09963 & 63.75687 \\
1.0 & 43.3935 & 55.04252 & 65.84797 & 70.73354 \\
1.5 & 48.41628 & 61.53196 & 72.5963 & 77.7102 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of cleaning rates according to spray time and number of sprays.