# Measurement and Analysis of Vibration Levels for Truck Transport Environment in Korea
## 2 Experiment Design
### Data collection and Analysis  
The vibration data were filtered to remove all undesirable events from the analysis, such as non-vibration related movement caused by stopping or slow traveling speeds. That is, events below 0.05 rms G were filtered out [34; 35].  
The recorded time-domain vibration data are presented as frequency-domain PSD with the FFT based on Saver Xware software (Lansmont Corp.). In this study, PSD levels from 1 to 250 Hz are shown. A PSD profile is a plot of the energy (vibration strength) versus the frequency and is commonly used to measure and compare vibration levels. The square root of the integral of the PSD over the total frequency range is the overall rms G, which represents the vibration levels for the entire spectrum [36; 37].  
The PSD for any band of frequencies can be calculated as follows [14; 15; 22; 29; 32]:  
\[PSD=\frac{1}{BW}\sum_{i=1}^{N}\bigl{(}rms\;G_{i}^{2}\bigr{)}/N \tag{1}\]  
where \(rms\;G\) is the sampled root-mean-square acceleration measured within a bandwidth of frequencies, and \(N\) is the total sample number of vibration signals for a given segment of vibration history.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Characteristics** & **Daegu**\(\rightarrow\) & **Sangju**\(\rightarrow\) & **Seongju**\(\rightarrow\) & **Jinju**\(\rightarrow\) & **Masan** \\ \hline Classification of roads & national road & highway & national road & highway \\ Pavement & mostly asphalt & mostly concrete & mostly asphalt & mostly asphalt \\ Distance (km) & 77.6 & 60.9 & 113.7 & 49.7 \\ Travel speed (km/h) & 60–90 & 90–100 & 60–90 & 90–100 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pre-planned test route and driving conditions.  
Figure 3: Installation of data recorder at the center position at the rear end of the load platform.  
The corresponding PDs were then plotted against the center frequency of the bandwidth to develop the PDS for the data set. In this study, 1 Hz was selected for the bandwidth. To use vibration testing in a lab-based simulation test and to identify the distribution characteristics of the vibration events measured in Korea's truck transport environment, the kurtosis (_K_), and skewness (_S_) of probability distribution functions (PDF) using a confidence interval of 95% were analyzed. The kurtosis and skewness show the peakedness and asymmetry of data distribution compared with the Gaussian normal distribution, respectively. That is, when the standard normal distribution has a kurtosis of 0, a positive kurtosis indicates a heavy-tailed rather than normal distribution. A skewness of 0 shows indicates symmetric distribution, in which the deviation from 0 indicates asymmetric distribution [38]:  
\[S=\frac{1}{N}\sum_{i=1}^{N}\left\{\frac{x_{i}-\mu}{\sigma}\right\}^{3} \tag{2}\]  
\[K=\frac{1}{N}\sum_{i=1}^{N}\left\{\frac{x_{i}-\mu}{\sigma}\right\}^{4} \tag{3}\]  
where \(N\) is the number of data points (vibration events) within the analysis time, \(\mu\) is the mean, and \(\sigma\) is the standard deviation (\(\sigma=\sqrt{\sum\left(x_{i}-\mu\right)^{2}/N}\)).  
In the statistical analysis of measurement data, the use of acceleration G measured directly by an accelerometer is difficult to handle in statistical programs because the amount of data is too large. Therefore, in this study, a method for significantly reducing the amount of data was applied by calculating rms G at a specific time interval from the time-domain acceleration G [13; 18; 21]. The moving _rms G_ of each vibration record was computed by using Equation (4) with a particular window length:  
\[rms\ G=\sqrt{\frac{1}{N}\sum_{i=1}^{N}a_{i}^{2}} \tag{4}\]  
where \(N\) is the window length [\(N\) = 2000, where the sampling rate \(f_{\text{s}}\) = 1000 Hz, and the time length of the window (\(N\)/\(f_{\text{s}}\)) is 2 s], and \(a_{i}\) is the acceleration G measured directly by the accelerometer.