## 4 Results and Discussion
### Results Evaluation  
#### 4.2.1 Predicting Model for Compressive Strength  
The compressive strength ANN model developed in this study was adopted to evaluating the effects of steel fibers on the compressive strength of UHPFRC. Comparisons between the predicted and the experimental values for the training and testing data of the compressive strength ANN model were shown in Figure 3. It was evident that the predicted values from the training and testing data, as calculated by the ANN model, were closed to the target values. This phenomenon demonstrated that the ANN model could successfully learn the nonlinear relationship between the input and output variables. Therefore, the ANN model possessed potential in estimating the effects of steel fibers on the compressive strength of UHPFRC.  
The input layer weights (ILW), input layer bias (ILB), hidden layer weights (HLW), and hidden layer bias (HLB) of the compressive strength ANN model are given by Equations (14)-(17), respectively.  
Figure 3: Comparison of predicted values from compressive strength ANN model with experimental results: (**a**) Training data, (**b**) Testing data. The figures show that the comparison between the target values and predicted values of testing and training data from experiments and compressive strength ANN model, the horizontal axis denotes number of training or testing data, and the vertical axis denotes the compressive strength. It was obvious that the predicted values accord with the target values.  
\[\text{ILW}=\left[\begin{array}{cccccc}1.5393&-0.2127&-0.0696&-1.4878&0.2019&0.9149 \\ 0.4685&0.8877&-0.0434&1.2903&-1.2371&1.0505\\ 0.9528&-0.4423&0.3086&1.0429&0.6903&-1.7290\\ 1.0738&0.4441&-1.5045&0.4403&0.5282&-1.1052\\ -0.3691&0.5837&0.7369&-1.7350&1.1595&0.0825\\ -0.8850&-1.3132&1.1989&1.2757&-0.6270&-1.0193\\ 0.5121&0.5669&1.4762&1.6028&-0.0071&-0.7542\\ -1.1525&-0.3260&-0.5873&1.3268&-1.2193&-0.4579\\ 0.1460&-0.7018&-0.5530&-0.1367&-0.1684&-2.0212\\ 0.5865&-0.3549&0.1205&2.1009&0.9361&-0.8912\\ 0.8419&-1.6760&0.4490&0.3753&-1.4686&1.2215\\ 1.0630&-1.0899&-0.5704&-1.4019&1.1772&0.5639\\ 1.3647&-0.8022&-0.9620&-0.6018&-0.8654&0.0328\\ 0.8870&-0.7126&1.1355&-0.8674&1.3638&0.9118\\ 0.3813&-0.7026&-1.6491&-2.4456&-0.4511&-0.7444\\ 0.3807&-1.1086&-1.0983&1.5312&0.5930&0.8901\\ 0.7989&0.5241&-1.0421&-0.9141&0.8343&1.2352\\ -2.5278&-0.8382&-0.7985&0.4525&-0.3999&0.4810\\ -1.6123&0.2212&0.7569&-0.5385&-0.1606&-1.2508\\ 2.6458&1.4649&0.8273&0.0796&-0.1915&-0.5157\\ \end{array}\right] \tag{14}\]  
\[\text{ILB}=\left[\begin{array}{cccccc}-2.2307&\\ -2.1048&\\ -1.7769&\\ -2.1635&\\ -1.0505&\\ 0.6502&\\ 0.6618&\\ -0.3364&\\ -0.7205&\\ 0.7212&\\ 0.1701&\\ 0.5343&\\ 0.4370&\\ 0.6864&\\ 1.7985&\\ -1.9737&\\ -1.7898&\\ 2.0694&\\ \end{array}\right] \tag{15}\]  
\[\text{HLW}=\left[\begin{array}{cccccc}-0.6653&-0.8688&-0.6540&1.3721&-1.3609& \ldots\\ -1.2337&-1.1160&0.1162&-0.5726&0.0664&\ldots\\ -0.7506&-0.3342&0.4221&-0.2911&-1.5284&\ldots\\ 0.6934&0.5566&-1.0555&0.5285&-0.8820&\end{array}\right] \tag{16}\]  
\[\text{HLB}=\left[\begin{array}{cccccc}-0.6960&\\ \end{array}\right] \tag{17}\]  
The performance indicators of the compressive strength ANN model for training and testing data, including \(RMS\), \(R^{2}\), and \(IAE\), were listed in Table 5. In Table 5, the indicators show that the proposedmodel produced good results. Thus, the ANN model studied in this paper had high-precision and it was suitable for predicting the compressive strength of UHPFRC.