## 3 Results and Discussion
### Prediction of Ultimate Damage Load
#### 3.2.1 Prediction of Artificial Neural Network of Acoustic Emission Single-Parameter Data  
In this four-point bending test, nine crumb rubber concrete specimens were used: three specimens in which the rubber content was 5%, 10%, and 15% for each. The specific  
Figure 14: Average frequency distribution: (**a**) cluster 1; (**b**) cluster 3. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Name of** & **Rise Time** & **Count** & **Energy** & **Duration** & **Amplitude** & **Average** & **RMS 1** \\
**Cluster** & **(ms)** & **Count** & **(ms\(\times\)****μv)** & **(ms)** & **Amplitude** & **Frequency** & **RMS 1** \\ \hline Cluster 1 & 6.98 & 1.46 & 0.26 & 16.29 & 41.43 & 42.25 & 398.91 \\ Cluster 3 & 9.57 & 2.50 & 0.57 & 31.11 & 42.65 & 95.81 & 38.18 \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 3: Average AE parameters of cluster 1 and cluster 3.  
dimensions of the experimental specimens can be seen in the experimental part. In predicting the damage ultimate load of crumb rubber concrete using the artificial neural network, the AE signals and load data of one specimen from each of the three sets of specimens with different rubber contents were extracted as the prediction set, and the AE signals and load data of the other two specimens from the same set were used as the training set to predict the damage ultimate load of the specimens. This operation was repeated three times with different specimens, and the predicted and true values of the three sets of results were averaged and analyzed for errors. In this section, 10 acoustic emission parameters--rise time (1), count (2), energy (3), duration (4), amplitude (5), RMS (6), ASL (7), signal strength (8), center frequency (9), and peak frequency (10)--predict the damage ultimate load of three different crumb rubber concretes, and compare the prediction results with their true values to calculate the prediction error. The Matlab 10 Neural Network Toolbox was used to train the networks. The Levenberge-Marquardt algorithm was used for back propagation during training. At the same time, the learning rate was set to 0.9 in the calculation process. In the process of obtaining the prediction results shown in Tables 4-13, the input data are a matrix composed of the single acoustic emission parameter column vectors of the six crumb rubber concrete specimens, and the hidden layer is composed of nine neurons, and the output end is the predicted value of the ultimate load of the crumb rubber concrete. The prediction result of the artificial neural network with a single parameter of rise time follows: when the number of iterations reaches 80, the average error (MSE) reaches the minimum value (Figure 15a); that is, the optimal number of training iterations is 80 times. At the same time, the best iteration numbers of the other nine acoustic emission parameters can also be determined from Figure 15b-j. Table 4 shows that the maximum prediction error of the specimens with three different rubber contents is -2.39%. It is concluded that the single-parameter neural network with rise time predicts that the damage ultimate load error of crumb rubber concrete is small, and the results using different acoustic emission parameters is different from what is shown in Tables 4-13. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rubber Content** & **Actual Value (kN)** & **Predictive Value (kN)** & **Prediction Error** \\ \hline
5\% & 16.24 & 16.48 & 1.46\% \\
10\% & 15.27 & 14.39 & \(-5.78\%\) \\
15\% & 11.32 & 12.12 & 7.04\% \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Peak frequency (10) single-parameter neural network prediction results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rubber Content** & **Actual Value (kN)** & **Predictive Value (kN)** & **Prediction Error** \\ \hline
5\% & 16.24 & 16.57 & 2.07\% \\
10\% & 15.27 & 14.90 & \(-2.45\%\) \\
15\% & 11.32 & 10.97 & \(-3.12\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: RMS (6) single-parameter neural network prediction results.