# Measurement and Analysis of Vibration Levels for Truck Transport Environment in Korea
## 3 Results and Discussion
### Statistical Characteristics of the Measured Truck Transport Vibration Events  
The blue bars in Figures 8 and 9 show the PDF and the cumulative distribution function (CDF), respectively, for the rms G of vertical transport vibration events. The green line in the figures represents the standard normal distribution, and the red line represents the log-logistics distribution Equations (5) and (6), which is the best-fit result for the measurement data based on the R-square and RMSE. Figure 8: PDF of the vertical rms G for all data recorded (**a**) leaf-spring 5-ton truck (**b**) air-ride 5-ton truck (**c**) leaf-spring 11-ton truck. Figure 7: PSD plots of the vertical vibration levels according to pavement type. The kurtosis and skewness for this PDF were analyzed (Table 7). The kurtosis values for all recorded data were more significant than 3 for all trucks of this study, which indicates a heavy-tailed distribution; therefore, the vibration events measured in Korea's truck transport environment do not follow a normal distribution [41]. However, the kurtosis for the lower 70% of data recorded was much closer to 3 and thus closer to normal distribution because the high-amplitude events included in the measured vibration signal, which exist outside normal distribution, were excluded. Figure 9 shows the CDF for each condition. These values coincide with the log-logistics calculated values in 90% of the experimental data under all experimental conditions, but show some differences from the normal distribution values. The heavy-tailed distribution characteristics of the vibration events measured in this study are also well illustrated by the normal quantile-quantile (Q-Q) analysis shown in Figure 10. The normal Q-Q plot provides a diagnostic check on whether the data originate from a normal distribution and involve a plot of empirical quantiles against the corresponding quantile of normal distribution. A straight-line relationship suggests that the data are normally distributed. Q-Q plots are displayed in a curved shape, indicating that the distribution is skewed or has heavier tails than those in a normal distribution. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Kinds of Truck**} & \multicolumn{3}{c}{**Skewness**} & \multicolumn{3}{c}{**Kurtosis**} & \multicolumn{3}{c}{**Log-Logistics Distribution Function**} \\ \cline{2-10}  & **Top 30\%** & **Lower 0\%** & **All data** & **Top 30\%** & **Lower 70\%** & **All data** & \(\mathbf{\alpha}\) & \(\mathbf{\beta}\) & **R-Square** & **RMSE** \\ \hline Leaf-spring 5-ton truck & 2.21 & \(-0.99\) & 1.77 & 9.69 & 4.92 & 9.17 & 4.9948 & 0.1736 & 0.999 & 0.0083 \\ Air-ride 5-ton truck & 1.78 & \(-0.12\) & 2.21 & 6.98 & 2.96 & 10.31 & 2.6593 & 0.0560 & 0.999 & 0.0121 \\ Leaf-spring 11-ton truck & 1.30 & \(-0.34\) & 0.96 & 3.97 & 1.75 & 4.47 & 5.7276 & 0.3083 & 0.998 & 0.0197 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistic analysis results for vertical rms G of the data recorded. Figure 9: CDF of the vertical rms G for all data recorded (**a**) leaf-spring 5-ton truck (**b**) air-ride 5-ton truck (**c**) leaf-spring 11-ton truck. Moreover, the skewness values for all data recorded were 1-2.2 for all trucks. This indicates that the transport vibration events measured in the study were skewed to the right to cause, and many vibrations events with values higher than the mean. However, the kurtosis for the lower 70% of the data recorded was close to zero and thus close to symmetric distribution. The CDF represents the percentage of events below a certain level of the data such as the rms G. The values for the parameters \(\alpha\) (scale) and \(\beta\) (shape) that characterize this log-logistics distribution are shown in Table 7 [41].