## 4 Interpretable Analysis of Prediction Model Based on SHAP  
### Partial Interpretation Based on SHAP  
The purpose of local interpretation is to analyze and interpret the prediction results of a single sample. In this study, three samples were selected for local interpretation, taken from A3 (28-day age, 0.5% volume fraction of steel fiber), A5a (28-day age, 1.5% volume fraction of steel fiber), and A5b (90-day age, 1.5% volume fraction of steel fiber) in Reference [17]. The specific data are shown in Table 5. From Formula (2), the final prediction of compressive strength is the result of the SHAP values of each input feature offsetting each other at the reference value. Here, the process of visual offsetting is visualized by the force plot, where the red and blue strips represent the positive and negative effects on the compressive strength, respectively. The length of the color strip represents the SHAP value of the feature, that is, the corresponding influence degree. Figure 5 is the force diagram of the three sample specimens. For sample 1, the predicted compressive strength of the DNN model is 77.33 MPa, which is in good agreement with the test result of 78.2 MPa. As shown in Figure 5a, the final compressive strength is the positive and negative superposition of SHAP values of each input feature based on the reference value of 101.7 MPa. Features located in the blue region indicate a negative contribution relative to the baseline value, while those in the red region indicate a positive contribution. The longer the feature's band, the greater its contribution and the more significant its influence. It can be seen from the figure that the cement content, coarse aggregate content, and the steel fiber length are the main characteristics of negative effect, while the dosage of high-range water reduc \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Evaluation Indicators**} \\ \cline{2-4}  & **MAPE/\%** & **RMSE/MPa** & **MAE/MPa** \\ \hline DNN & 8.16 & 9.41 & 6.62 \\ GB 50010 & 69.32 & 81.10 & 57.00 \\ ACI 544.4R & 58.10 & 58.10 & 56.00 \\ CEB-FIP & 453.12 & 820.90 & 391.28 \\ \hline \end{tabular}
\end{table} 
Table 4: Model performance evaluation of the DNN model with these three classical strength formulas. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{1}{c}{**Feature Parameter/Unit**} & **Sample1 (A3)** & **Sample2 (A5a)** & **Sample3 (A5b)** \\ \hline Cement content/kg\(\cdot\)m\({}^{-3}\) & 400 & 400 & 400 \\ Fly ash content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Slag content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Silicon powder content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Nano-silica content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Limestone powder content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Sand content/kg\(\cdot\)m\({}^{-3}\) & 751 & 740 & 740 \\ Coarse aggregate content/kg\(\cdot\)m\({}^{-3}\) & 1127 & 1111 & 1111 \\ Quartz powder content/kg\(\cdot\)m\({}^{-3}\) & 0 & 0 & 0 \\ Water content/kg\(\cdot\)m\({}^{-3}\) & 140 & 140 & 140 \\ Dosage of high-range water & 24.42 & 24.15 & 24.15 \\ reducer/kg\(\cdot\)m\({}^{-3}\) & 24.42 & 24.15 & 24.15 \\ Steel fiber content/\% & 0.5 & 1.5 & 1.5 \\ Steel fiber diameter/mm & 0.55 & 0.55 & 0.55 \\ Steel fiber length/mm & 35 & 35 & 35 \\ Age/d & 28 & 28 & 90 \\ Compressive strength/MPa & 78.2 & 81 & 89.3 \\ \hline \end{tabular}
\end{table} 
Table 5: Data of test samples. the main characteristics of positive effect. Cement content exhibits the strongest negative impact, whereas the dosage of high-range water reducer shows the most pronounced positive effect.