# Temporal Convolutional Network-Based Axle Load Estimation from pavement Vibration Data
## 5 Conclusions and Future Work  
Accurately measuring vehicle axle loads is a vital component in weight enforcement and pavement condition assessment. Existing WIM technologies are costly, impractical for high-speed vehicle detection due to inadequate time for pressure change registration, and susceptible to installation challenges. The goal of this paper was to develop an inexpensive but accurate DOVS-based WIM system. The vibration of concrete pavement contains valuable information that can identify vehicle load characteristics. But it is difficult to ensure the accuracy of the process, which typically requires complicated mathematical modeling and formula derivation. The proposed method, characterized by an extended sensing range, high temporal sampling rate, and dense spatial sampling rate, demonstrates promising results in field tests under diverse conditions. The TCN model, trained with over 6000 samples of vibration data and corresponding ground truth of axle loads, exhibits the ability to learn the intricate inverse mapping between pavement structure inputs and outputs. The method achieves estimated axle loads within an 11.5% error margin, showcasing its efficacy in weight enforcement and pavement condition assessment. Furthermore, the approach aligns closely with specified standards such as those set by LTPP and Cost-323 [41], reinforcing its potential to offer valuable support in assessing and making decisions related to pavement structure conditions. The collection of pavement vibration data involves privileged data and is only used for traffic data analysis. The data have been desensitized and do not involve personal privacy. Future work in this research avenue could focus on several aspects to further enhance the proposed method. Firstly, refining the deep learning-based load reconstruction method to accommodate variations in load conditions and pavement types would contribute to increased robustness. Secondly, exploring the application of the proposed methodology to asphalt pavements, which may present distinct challenges in coordination with fiber optic technology, could broaden its scope. Lastly, considering the potential integration of real-time monitoring capabilities into the proposed method would provide a dynamic approach to pavement assessment and management. Addressing these aspects would contribute to the continual improvement and applicability of the presented vibration-based method for axle load estimation in diverse pavement scenarios. Conceptualization, Z.B., M.Z. and H.Z. ; methodology, Z.B. and M.Z. ; validation, Z.B. ; investigation, Z.B. and M.G. ; resources, Z.B. ; data curation, Z.B. and J.C.; writing--original draft preparation, Z.B. ; writing--review and editing, Z.B., M.Z. and H.Z; visualization, Z.B. and M.G. ; supervision, Z.B. and M.Z. ; project administration, Z.B. and M.Z. ; funding acquisition, H.Z. and M.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Nature Science Foundation of China (Grant No: 52278457 and Grant No: 52308462) and Shanghai Pujiang Programme (23 PJD043). Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. The authors thank the editor and anonymous reviewers for their numerous constructive comments and encouragement that have improved our paper greatly. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods for Axle Load Estimation** & **Annual Life Cycle Cost (5)** & **Error** & **Expected Life (Years)** \\ \hline DOVS-based (presented) & 1000 & \(\pm\)11.5\% & 15 \\ Bending plate & 5000 & \(\pm\)15\% & 4 \\ Strip WIM (piezoelectric) & 6000 & \(\pm\)10\% & 6 \\ Single load cell & 8000 & \(\pm\)6\% & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The axle configurations of vehicles. Conflicts of Interest: Author [PERSON] was employed by the company Shanghai Research Institute of Building Sciences Co., Ltd.