## 6 Conclusions and Findings  
In this study, an ANN classifier was developed for the real-time quality estimation of HMA compaction. Some conclusions and findings are listed as follows.  
(1) To investigate the effect of hidden layer structure on the performance of the ANN model, four ANN models with different hidden layer setups were considered. The double-hidden-layer networks showed the best performance.  
(2) The compaction quality was estimated by the ANN classifier based on the vibration signals. The results showed the validity of the ANN classifier for the real-time quality estimation of HMA compaction.  
(3) A classifier was developed in this study, but not an estimator. This is due to the limitation of the accuracy of the non-nuclear density gauge. The range of degree of compaction was considered in this study, this was a kind of compromise. To develop the ANN estimator, an accurate measurement of the degree of compaction is necessary.  
(4) It should be noted that although this study focused on the compaction of AC-25 asphalt mixture, it is not clear whether the ANN classifier developed in this study can be used for other asphalt mixes, such as AC-20 and SMA-13. Different materials may lead to different vibration patterns, thus ANNs may need to be re-designed and re-trained for different specified materials. Furthermore, different materials and different training dataset sizes may lead to different optimal network designs; the network in this study (Network 3) may not be suitable if the material is not AC-25, or if the amount of training data is very large.  
In addition, the amount of training data is limited in this study. Collecting more training data may improve the performance of the ANN model. However, ANN still shows a huge potential for the problem of compaction quality control.  
Conceptualization, W.C. and F.R.; methodology, F.R.; formal analysis, W.C. and S.L.; investigation, W.C., F.R. and Q.W.; resources, Z.X. and S.L.; data curation, S.L. and Q.W.; visualization, F.R.; validation, W.C. and Z.X.; writing--original draft preparation, F.R., W.C. and Q.W.; writing--review and editing, W.C., S.L. and F.R.; project administration, Z.X.; supervision, W.C.; funding acquisition, Z.X. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Target Class** & **Degree of Compaction (\%)** & **Number of Signals** \\ \hline class 1 & \textless{}95 (Level 1) & 850 \\ class 2 & 95\textless{}96 (Level 2) & 1000 \\ class 3 & 96\textless{}97 (Level 3) & 1040 \\ class 4 & \textgreater{}97 (Level 4) & 1040 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Number of the collected signals for the validation test.  
Figure 11: Output accuracy of ANN classifier.  
**Funding:** This work was supported by the Science and Technology Plan of Shandong Transportation Department (No. 2019B48), and the authors would like to acknowledge their financial support.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to them forming part of an ongoing study.  
**Conflicts of Interest:** The authors declare no conflict of interest.