## 5 Results and Discussion
### Effect of Smaller Training Dataset Size  
The results presented in the previous section are obtained using full-size training datasets (each containing 75 data points). Thought this dataset size is relatively small, it is important to find out the effect of the assisted approach as the size of the training datasets gets even smaller. Thus, three progressively reduced training dataset sizes are also investigated. The three reduced training dataset sizes are: reduced-1 (48 data points), reduced-2 (35 data points) and reduced-3 (22 data points). For the reduced size datasets investigation, only the BR learning algorithm is used since it gives the best performance. Table 3 lists the values of the three performance metrics obtained using the reduced training dataset sizes for the traditional and the four assisted scenarios. From the table, it can be seen that for the three reduced training dataset sizes, the MAE\({}_{\text{P}}\), RMSE\({}_{\text{P}}\) and R\({}^{2}\) values for the four assisted scenarios are clearly superior to those of the traditional approach. Closer inspection of the results listed in the table shows that for reduced-1 and reduced-2 dataset sizes, the accuracy gradually improves as the assistance level gets higher; whereas, for reduced-3 dataset size, the results associated with assisted 1, 2 and 3 scenarios are fairly close to each other. The general trend for accuracy improvement for the different training dataset sizes can be better observed by referring to Figure 5. Similar to Figure 3, the upper part of Figure 5 shows MAE\({}_{\text{P}}\) values obtained using the traditional and assisted scenarios associated with the different dataset sizes, while the lower part of the figure shows the error reduction of the assisted scenarios relative to the traditional approach. The data presented in the figure for the full-size dataset are obtained from Table 2. As expected, the figure shows that, in general, as the size of the training dataset gets smaller, the ANN predictions become less accurate. From the figure, it can be seen that for all dataset sizes, except reduced-3, the accuracy of the ANN predictions gradually improves as the assistance level increases. It can also be seen that the relative error reduction increases as the dataset size gets smaller. This observation clearly indicates that the proposed assisted-ANN approach is more effective in improving the accuracy for smaller size training datasets. For the reduced-3 training dataset size, the figure shows that the situation is slightly different  
Figure 4: The experimental residual strength values along with the predictions obtained by the ANN model for the traditional and assisted approaches (assisted 3 and 4 only) for one of the testing datasets using the BR algorithm (**top**), together with the residual strength prediction errors (**bottom**). The shown ANN predictions are for the best one of the 80 random combinations of the testing datasets. than the larger dataset sizes. In this case, all the four assisted scenarios give clearly better accuracy than the traditional approach; however, the relative error reduction resulting from assisted scenarios 1, 2 and 3 is relatively high, and the error reduction values for the three scenarios are fairly close to each other. It is probably worth mentioning here that for the reduced-3 training dataset size, all the data points are manually selected; while for the larger dataset sizes (reduced-1 and reduced-2), some of the data points are chosen randomly. As mentioned previously, the manually selected data points are all at either the upper or lower limit values of the different inputs (lead crack length, ligament length, etc. ), and do not include intermediate values. Most likely, this difference in the nature of the data points for reduced-3 is what caused the difference in relative error reduction trend.