## 5 Results and Discussion
### Assisted-ANN Performance for Different Learning Algorithms  
The ANN optimization procedure, described previously in Section 4.4, is carried out for the five modeling scenarios (traditional and the four assistance levels) used in this investigation. For each scenario, 80 ANNs are developed using the 80 random training datasets, and the optimum ANN configuration is identified based on the MAE\({}_{\text{P}}\) value (averaged value for the 80 different random combinations) for the validation datasets. When using the testing datasets for evaluating the performance of the ANN, in addition to the MAE\({}_{\text{P}}\), two additional performance metrics (RMSE\({}_{\text{P}}\) and R\({}^{2}\)) are also taken into consideration for determining the goodness of the residual strength predictions. For the traditional and all four assistance levels, the BR learning algorithm, along with the Elliot symmetric sigmoid (elliotsig) activation function, gives the best prediction performance. As for the optimum number of nodes in the hidden layer, it varies from case to case. The LM and SGC learning algorithms are ranked second and third, respectively, in terms of prediction accuracy. Thought, the BR learning algorithm results in the best prediction performance and will be adopted henceforth; however, it is also important to observe the effect of the assisted approach when used along with the different learning algorithms. Table 2 lists the values of the three performance metrics obtained using the BR, LM and SGC algorithms for the traditional and the four assisted scenarios. In each case, the shown values are for the optimum configuration (best activation function and number of hidden nodes), and each value is the average for the 80 random combinations of the testing dataset. As can be seen from the table, improvement can be clearly observed in the MAE\({}_{\text{P}}\), RMSE\({}_{\text{P}}\) and R\({}^{2}\) values for the four assisted scenarios as compared to the traditional scenario. Also, this improvement can be observed for the three learning algorithms. The improved results associated with the assisted scenarios indicate that, though dependency may exist between the direct independent input parameters and assistance parameters; the developed ANN model did not trap into local optima nor did it hide important input-output relationships. Also, the results show that the addition of the assistance parameters did not add significant noise into the model. Furthermore, the highly accurate results obtained using the testing dataset, also indicate that the ANN model did not experience overfitting during the learning process; on the contrary, it has learned to generalize to new situations. To further illustrate the accuracy improvement resulting from using the assisted approach, Figure 3 is developed using the MAE\({}_{\text{P}}\) values given in Table 2. From the figure, it can be seen that for any of the five scenarios, the BR gives the best accuracy followed by the LM then the SGC. The figure also shows that, for all three learning algorithms, the accuracy gradually improves as the assistance level increases (from assisted 1 to assisted 4). This gradual accuracy improvement is consistent with the logic of assigning the assistance parameters being used at the different assistance levels, where at each level, a higher-order assistance parameter is used (as previously explained in Section 4.2). In order to quantify the accuracy improvement obtained using the four assistance levels, the error (MAE\({}_{\text{P}}\)) reduction relative to the traditional approach is calculated and shown in the bottom part of Figure 3.  
By inspecting the relative error reduction values, it can be clearly observed that, in general, the heights values of error reduction are associated with the SGC algorithm, followed by the LM and BR algorithms, respectively. For instance, at assistance level 4, the relative error reduction for the SGC, LM and BR are \(-46.1\%\), \(-40.9\%\) and \(-21.8\%\), respectively.