# Comparative Accuracy Analysis of Truck Weight Measurement Techniques
## 3 Results  
The collected vehicle measurements from static and dynamic scales were compared to determine the weighing systems' accuracy. The statistical analysis was conducted to find evidence to claim if there was a difference in considered weighing methods. The vehicle attributes such as GVW, single, and tandem axle weight were verified.  
The analysis compares measured vehicles' mean and standard deviation to determine the measurement techniques' divergences. The multiple \(t\)-tests for paired means were conducted to determine the mean difference between the truck weigh station and other measurement techniques, that is, the certified portable scales and the rest of the considered weighing systems. The mean difference for a 95% confidence interval was checked; according to ASTM 1318E-09 requirements [29]. This is the primary US standard used for weigh-in-motion performance requirements. The 95% compliance of measurements is needed to be within specified tolerances. The \(t\)-test analysis was to check if there was a difference in the measured weight by considered measurements for GVW, axle, and tandem axle weights.  
Additionally, the measurement tolerances established by [29] were verified for vehicle attributes. Table 2 summarizes the ASTM E1318 requirements for WIM systems. There are four WIM types Type I-Type IV. The Type I and Type II were used for regular data collection, where Type I has more rigorous tolerances in comparison to Type II. Type III is used to collect data about overloaded vehicles. Type IV is not yet approved in the US. In this analysis, WIM Type I's tolerance requirements are used to validate the accuracy of analyzed weighing systems.  
Moreover, the linear correlation between vehicle attributes measured by the considered weighing system is examined using the correlation coefficient. The statistical analysis is used to determine if there is enough evidence to prove a difference between considered measuring systems.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Measurement Type \(\rightarrow\)** & **\#1** & **\#2** & **\#3** & **\#4** \\ \(\downarrow\)**Attributes** & **WIM** & **Static Scales** & **Portable Scales** & **B-WIM System** \\ \hline Timestamp of weighing & \(\bigvee\) & \(\bigvee\) & \(\bigvee\) & \(\bigvee\) \\ GVW (kip) & \(\bigvee\) & \(\bigvee\) & \(\bigvee\) & \(\bigvee\) \\ W1 (kip)\(\rightarrow\)\#1 axle weight & \(\bigvee\) & & \(\bigvee\) & \(\bigvee\) \\ W2 (kip)\(\rightarrow\)\#2 axle weight & \(\bigvee\) & & \(\bigvee\) & \(\bigvee\) \\ W3 (kip)\(\rightarrow\)\#3 axle weight & \(\bigvee\) & & \(\bigvee\) & \(\bigvee\) \\ W4 (kip)\(\rightarrow\)\#4 axle weight & \(\bigvee\) & & \(\bigvee\) & \(\bigvee\) \\ W5 (kip)\(\rightarrow\)\#5 axle weight & \(\bigvee\) & & \(\bigvee\) & \(\bigvee\) \\ AG\_1 (kip)—Tandem axle \#1 & \(\bigvee\)* & \(\bigvee\) & \(\bigvee\)* & \(\bigvee\)* \\ AG\_2 (kip)—Tandem axle \#2 & \(\bigvee\)* & \(\bigvee\) & \(\bigvee\)* & \(\bigvee\)* \\ S1 (ft)—spacing axle \#1 and \#2 & \(\bigvee\) & & & \(\bigvee\) \\ S2 (ft)—spacing axle \#1 and \#2 & \(\bigvee\) & & & \(\bigvee\) \\ S3 (ft)—spacing axle \#3 and \#4 & \(\bigvee\) & & & \(\bigvee\) \\ S4 (ft)—spacing axle \#4 and \#5 & \(\bigvee\) & & & \(\bigvee\) \\ Vehicle class & \(\bigvee\) & & & \(\bigvee\) \\ Vehicle speed (mph) & \(\bigvee\) & & & \(\bigvee\) \\ Number of axles & \(\bigvee\) & \(\bigvee\)** & \(\bigvee\)** & \(\bigvee\) \\ Plate number & \(\bigvee\) & \(\bigvee\)** & \(\bigvee\)** & \(\bigvee\) \\ US DOT number & \(\bigvee\) & \(\bigvee\)** & \(\bigvee\)** & \(\bigvee\) \\ \hline \end{tabular}  
* tandem axle is considered if the spacing between axles does not exceed 6 ft, it is calculated as a sum of axle weights: AG_1 = W2 + W3 and AG_2 = W4 + W5, ** tandem axle is considered if the spacing between axles does not exceed 6 ft, it is calculated as a sum of axle weights: AG_1 = W2 + W3 and AG_2 = W4 + W5.  
\end{table}
Table 1: Attributes considered during measurements.