## 4 Conclusions  
Based on the response surface method, this research adopted the Box-Behnken design method to carry out a three-factor, three-level design. Density, air voids, Marshall stability, flow value, VMA, and VFA values were used as response indicators, while the asphalt-aggregate ratio, NTC, and fiber contents were taken as influencing factors. This method is more logical and predictable when determining the optimal content of various factors. This paper draws the following conclusions through experimental analysis:  
(1) Through the Box-Behnken design method, a three-factor function was fitted to each response indicator. It is concluded that the relationship between density, air voids, Marshall stability, VMA, VFA, and the three influencing factors is a quadratic function, and the relationship between the flow value and the three influencing factors is linear;  
(2) Through analysis of variance and testing of the fitted model, it is concluded that the fitted model has a higher significance level. Comparing the predicted value with the measured value, it is found that the difference between them is small. This shows that the model has high fitting \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fiber** & **NTC** & **Asphal–Aggregate** & **Density** & **Air** & **Marshall** & **Flow** & **VMA** & **VFA** \\
**Content (\%)** & **Content (\%)** & **Ratio (\%)** & **(g/cm\%)** & **Voids (\%)** & **Stability (\%)** & **Value (mm)** & **(\%)** & **(\%)** \\ \hline
3.9 & 5.1 & 5.67 & 2.4237 & 3.4 & 13.29 & 2.7 & 14.9 & 73.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Model optimization factor and prediction index values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Project** & **Density (g/cm\({}^{3}\))** & **Air Voids (\%)** & **Marshall Stability (kN)** & **Flow Value (mm)** & **VMA (\%)** & **VFA (\%)** \\ \hline
1 & 2.431 & 3.436 & 17.22 & 1.8 & 16.7 & 56.9 \\ \hline
2 & 2.399 & 4.516 & 12.59 & 2.3 & 14.6 & 84.2 \\ \hline
3 & 2.497 & 4.593 & 16.13 & 2.9 & 13.9 & 80.1 \\ \hline
4 & 2.428 & 5.22 & 15.62 & 1.9 & 12.3 & 71.6 \\ \hline
5 & 2.429 & 1.384 & 11.75 & 3.8 & 15.6 & 77.3 \\ \hline
6 & 2.396 & 1.413 & 11.71 & 4.7 & 13.9 & 67.3 \\ \hline Average Value & 2.430 & 3.427 & 14.17 & 2.9 & 14.5 & 72.9 \\ \hline Standard Deviation & 0.033 & 1.527 & 2.223 & 1.050 & 1.392 & 9.018 \\ Prediction Data & 2.424 & 3.43 & 13.29 & 2.7 & 14.9 & 73.2 \\ Error (\%) & 0.270 & 0.096 & 6.620 & 6.960 & 2.759 & 0.370 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Accuracy rate of the response surface methodology. accuracy and prediction ability, and can accurately reflect the relationship between each input index and output index;  
(3) Through comprehensive consideration of the response index values, the three influencing factors are optimized and predicted, and the optimal content of NTC, BF, and the optimal asphalt-aggregate ratio are 5.1%, 3.9%, and 5.67%, respectively. The response index value is obtained through model test prediction, while the measured data is compared with the predicted value to obtain a minimum relative error of 0.096% and a maximum error of 6.960%. This shows that the response surface method can be used to design, analyze, optimize, and predict the mix ratio of the asphalt mixture. Conceptualization, H.B. ; formal analysis, [PERSON], H.B., and J.S. ; investigation, Y.G. ; data curation, H.B. and J.S. ; writing--original draft preparation, [PERSON] and Z.T. ; writing--review and editing, Y.G. and Z.T. ; project administration, Y.G. and J.S. ; funding acquisition, Y.G. and Z.T. All authors have read and agreed to the published version of the manuscript. This work was supported by the Transportation Technology Program of Jilin Province of China (Grant No. 2018 ZDXC-16, 2018--1--9), the Education Department's \"13 th Five-Year\" Science and Technology Program of Jilin Province (Grant No. JKH20190015 KJ), the Fundamental Research Funds for the Central Universities and the Scientific and Technological Developing Scheme Program of Jilin Province (Grant No.