## 4 Result and Discussion
### Statistical Evaluation  
This subsection presents the distribution function of the sensors for every test. It is essential for every researcher who works on structural system identification methods to model measurement data in their research. As indicated by many scholars (such as those of [13; 14]), these standard deviation functions are usually assumed without being measured. This section can further enrich the current literature with actual data by proving the standard deviation functions of various noncontact distance sensors in different ambient situations. These functions can help advance structural system identification applications and noise-canceling functions without learning the required electronic engineering skills for setting up low-cost distance sensors. In order to show an overall distribution of each type of sensor for each performed laboratory experiment, the normal distribution function for averaged results for each kind of sensor (like the data in Figure 9) was calculated in Excel. The normal distribution check of the estimated data as then calculated through SPSS software using the Shapiro-Wilk \(p\)-value and Kurtosis Z-value methods. Many scholars indicate that a distribution is normal as long as the Z-value is \(+/-1.96\) and the \(p\)-value is higher than 0.05. Figures 12-16 show the normal distribution functions for VL53L0X, VL53L1X, and HC-SR04 sensors for all of the experiments presented in this study. The horizontal axes of all graphs are the averaged estimated data of all sensors in millimeters, and the vertical axes are the normal distribution function. Tables 4-8 investigate the normal distribution of the estimation. Figure 12: The normal distribution function of VL53L0X for tests with ambient light. Figure 13: The normal distribution function of VL53L0X for tests with no excessive ambient light. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Steel** & & & & \\
**Measurement** & **Mean** & **Variance** & **Standard** & **Shapiro–Wilk** & **Kurtosis** \\
**Pattern** & & & & **Deviation** & **\(p\)**-Value** & **Z-Value** \\ \hline
290 & 320 & 2.61 & 1.61 & 0.75 & 0.18 \\
340 & 368 & 4.61 & 2.15 & 0.05 & \(-\)0.43 \\
440 & 475 & 14.54 & 3.81 & 0.43 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical analysis of VL53L0X for tests with ambient light. Figure 14: The normal distribution function of VL53L1X for tests with ambient light. Figure 15: The normal distribution function of VL53L1X for tests with no excessive ambient light. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Steel** & & & & & \\
**Measurement** & **Mean** & **Variance** & **Standard** & **Shapiro–Wilk** & **Kurtosis** \\
**Pattern** & & & & & \\ \hline
290 & 319 & 2.11 & 1.45 & 0.36 & \(-\)0.22 \\
340 & 367 & 3.29 & 1.81 & 0.19 & 2.02 \\
440 & 472 & 6.82 & 2.61 & 0.79 & \(-\)0.15 \\
540 & 575 & 13.43 & 3.67 & 0.82 & \(-\)0.51 \\
640 & 679 & 23.27 & 4.82 & 0.21 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical analysis of VL53L0X for tests with no excessive ambient light. Figure 16: The normal distribution function of HC-SR04 for various distance measurements. Analyzing Figures 12-15 shows that the distribution function value for ToF sensors decreases when the target object is located further away from the distance sensor. The area under the graph increases with the target object locating further away. The presence of ambient light makes this area even bigger. These indicators mean that the probability of estimating the right answer by the ToF sensors decreases as the distance increases, or when ambient light exists.