# An ANN Model for Predicting the Compressive Strength of Concrete
## 4 The Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & \(i\) & & & & \\  & & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline \multirow{9}{*}{\(j\)} & 1 & 0.6144 & 0.8055 & 0.1110 & 0.8372 & 1.7008 & \(-0.3427\) & 0.6209 & 0.5749 \\  & 2 & 1.3936 & 1.0523 & 1.4664 & 0.1982 & \(-0.4601\) & \(-0.5712\) & 0.5264 & 3.1878 \\  & 3 & 0.5066 & \(-1.7844\) & 0.0736 & \(-1.7298\) & \(-1.0940\) & 0.0095 & \(-0.9082\) & 1.1462 \\  & 4 & \(-1.3016\) & 0.8221 & 1.3503 & 0.2557 & 0.0471 & 2.0145 & \(-1.1131\) & 1.5552 \\  & 5 & \(-0.4564\) & 0.0257 & \(-1.7657\) & 2.7258 & \(-1.7268\) & \(-1.9379\) & 0.2811 & 1.4361 \\  & 6 & \(-0.0404\) & 0.1909 & 1.1077 & 2.3484 & \(-0.5073\) & 2.2264 & \(-0.1963\) & 1.4299 \\  & 7 & 0.7199 & \(-0.0957\) & 0.2010 & \(-0.1656\) & 2.5119 & \(-0.2500\) & 0.0705 & \(-0.1386\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The thresholds of the hidden neurons and the synaptic weights from the input layer to the hidden layer (\(w_{i,j}^{(1)}\)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \(j\) & & & \\
**0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline \(-1.0706\) & \(-0.2102\) & 2.0741 & 2.3526 & \(-1.2642\) & \(-1.3384\) & 2.2950 & \(-1.5356\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The threshold of the output neuron and the synaptic weights from the hidden layer to the output neuron (\(w_{j}^{(2)}\)). Figure 2: The result of the training: (**a**) 3 neurons in the hidden layer, (**b**) 7 neurons in the hidden layer, (**c**) 12 neurons in the hidden layer. After the number of neurons in the hidden layer and all the thresholds and synaptic weights are determined, we use our ANN to predict the compressive strengths of the 12 mix designs in [16] and compare the results with the data observed in their laboratory. The results are listed in Table 4. The predicted compressive strengths in [16] are also listed in the same table. The comparisons of the predicted and the actual compressive strengths are plotted in Figure 4. Note that the range shown in this figure is from 0 to 100 due to the range of the compressive strength in the database is from 5.66 to 95.3 MPa. It is found in Figure 4 that the circular dots are more focused to the central inclined line. This implies that our ANN model outperforms the ANN model of [16] in the verification. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Ingredients (kg/m3)**} & \multicolumn{4}{c}{**Compressive Strength (MPa)**} \\ \hline \multirow{2}{*}{**Water**} & \multirow{2}{*}{**Cement**} & \multirow{2}{*}{**Fine**} & \multirow{2}{*}{**Coarse**} & \multirow{2}{*}{**Agreeate**} & **Blast** & \multirow{2}{*}{**Fly Ash**} & **Super-** & \multirow{2}{*}{**Actual**} & **Predicted** & **Predicted** & **by Present** \\  & & & & & & & & & **Model** \\  & & & & & & & & & **Model** \\ \hline
194 & 223 & 669 & 1040 & 76 & 72 & 0.74 & 44.10 & 34.43 & 40.20 \\
184 & 244 & 649 & 1104 & 105 & 19 & 0.79 & 47.99 & 32.26 & 42.87 \\
187 & 194 & 650 & 1072 & 171 & 22 & 0.81 & 49.75 & 34.85 & 42.60 \\
189 & 272 & 670 & 1040 & 121 & 14 & 0.70 & 52.87 & 35.60 & 47.14 \\
191 & 346 & 549 & 1136 & 38 & 41 & 0.73 & 46.70 & 45.96 & 43.99 \\
189 & 261 & 619 & 1072 & 93 & 57 & 0.88 & 47.06 & 39.04 & 45.78 \\
204 & 331 & 457 & 1136 & 99 & 54 & 0.77 & 54.52 & 54.55 & 44.53 \\
191 & 280 & 555 & 1104 & 121 & 46 & 0.68 & 47.61 & 50.16 & 46.91 \\
210 & 300 & 535 & 1040 & 131 & 51 & 0.54 & 46.06 & 52.05 & 47.60 \\
207 & 430 & 604 & 960 & 20 & 61 & 0.76 & 54.30 & 40.08 & 52.32 \\
190 & 329 & 516 & 1104 & 112 & 52 & 0.87 & 54.98 & 55.07 & 50.83 \\
208 & 351 & 554 & 960 & 52 & 121 & 0.72 & 55.13 & 40.91 & 52.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The predicted and actual compressive strengths of the experimental concrete mixtures in [16]. Figure 3: The comparison of the outputs of ANN with their target values in which the ANN has seven neurons in the hidden layer and is trained after 12,040 times of iteration.