# Weigh-in-Motion Method Based on Modular Sensor System and Axle Recognition with Neural Networks
## 5 Conclusions  
This paper proposes a modular WIM system, including an axle recognition algorithm based on the Transformer-GRU model and a weighing algorithm under the new sensor module, which realizes whole-vehicle-load weighing with multiple vehicles traveling through platforms simultaneously. It offers the advantages of high weighing accuracy,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle Type**} & \multirow{2}{*}{**Weather**} & \multirow{2}{*}{**Number**} & \multicolumn{3}{c}{**The Proportion of Error Is Less Than the Parameter**} \\ \cline{3-6}  & & & **Less Than 1\%** & **Less Than 2\%** & **Less Than 5\%** \\ \hline \multirow{2}{*}{2-axle} & Sunny & 1722 & 0.9617 & 0.9768 & 0.9925 \\  & Rainy & 1895 & 0.9820 & 0.9937 & 0.9979 \\ \hline \multirow{2}{*}{3-axle} & Sunny & 116 & 1.0000 & 1.0000 & 1.0000 \\  & Rainy & 79 & 0.9747 & 0.9747 & 0.9873 \\ \hline \multirow{2}{*}{4-axle} & Sunny & 213 & 0.9390 & 0.9718 & 0.9906 \\  & Rainy & 151 & 0.9470 & 0.9603 & 0.9801 \\ \hline \multirow{2}{*}{5-axle} & Sunny & 128 & 0.8906 & 0.9375 & 0.9531 \\  & Rainy & 87 & 0.8966 & 0.9195 & 0.9540 \\ \hline \multirow{2}{*}{6-axle} & Sunny & 431 & 0.9536 & 0.9861 & 0.9884 \\  & Rainy & 295 & 0.9559 & 0.9762 & 0.9864 \\ \hline \multirow{2}{*}{Total} & Sunny & 2610 & 0.9567 & 0.9770 & 0.9900 \\  & Rainy & 2507 & 0.9737 & 0.9864 & 0.9936 \\ \cline{1-1}  & Total & 5117 & 0.9650 & 0.9816 & 0.9918 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Highway toll station weighing results.  
high traffic efficiency, and strong anti-cheating capabilities, enabling highway free-flow toll collection and overload management. Furthermore, the accuracy of the axle recognition algorithm based on Transformer-GRU achieves a very high level in both the test set and field test, offering advantages in reducing costs and enhancing system reliability. The verification of the five-platform modular system at the test site and toll station entrance shows excellent accuracy, consistency, and robustness. At present, modular sensor systems have passed the measurement organization evaluation test, and have been actually operated at toll stations in Guangxi, Yunnan, and Shaanxi, and the weighing results are accurate and reliable.  
Conceptualization, X.L., Z.Y. and B.S.; methodology, Z.Y. and B.S.; software, Z.Y. and B.S; validation, X.L., Z.Y. and B.S.; formal analysis, Z.Y. and B.S.; investigation, Z.Y. and B.S.; resources, X.L.; data curation, Z.Y. and B.S.; writing--original draft preparation, Z.Y. and B.S.; writing--review and editing, Z.Y.; visualization, X.L.; supervision, X.L.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The partial dataset can be downloaded at the website [[https://github.com/jiongjiongxj/weigh-in-motion-based-on-Neural-Network-Axle-Recognition](https://github.com/jiongjiongxj/weigh-in-motion-based-on-Neural-Network-Axle-Recognition)]([https://github.com/jiongjiongxj/weigh-in-motion-based-on-Neural-Network-Axle-Recognition](https://github.com/jiongjiongxj/weigh-in-motion-based-on-Neural-Network-Axle-Recognition)) uploaded on 12 November 2024.  
The authors declare no conflicts of interest.