# An FCM-GABPN Ensemble Approach for Material Feeding Prediction of Printed Circuit Board Template
## 4 Experimental Results and Discussions
The testing samples were taken to evaluate the performance of the approaches, and the average _MSE_, _MAE_, _MAPE_, _Surpr_Pd_, and _Suprf Pd_ of five runs for BPN, MSC-ANN, FCM-GABPN-w/o aggregation, FCM-BPN, and FCM-GABPN is given in Table 5. The improvement of different approaches comparing to the manual feeding (actual results of the factory) according to the performance indicators are also given, and the following discussions are made:  
(1) The prediction accuracy (measured with _MSE_, _MAE_, and _MAPE_) of the FCM-GABPN approach was significantly better than those of the other approaches, in most cases by achieving a 95.91%, 83.03%m and 89.57% reduction in _MSE_, _MAE_, and _MAPE_, respectively, over manual feeding. Meanwhile, the proposed FCM-GABPN exhibited superiority in the reduction of surplus and/or supplemental feeding in most of the case comparing to other methods by reducing 70.16% _Surpr_Pd_ and 31.03% _Suprf Pd_ over manual feeding. (2) The advantages of FCM-GABPN over BPN without performing pre-classification were 5.28%, 34.77%, 51.17%, 29.30%, and 1.29% by reduction in _MSE_, _MAE_, _MAPE_, _Surpr_Pd_, and _Suprf Pd_, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Approaches** & _MSE_ & _MAE_ & _MAPE_ & _Surpr_Pd_(\(\star\)) & _Suprf Pd_(\(\%\)) \\ \hline Manual feeding & 22.862 & 1.467 & 29.161 & 28.49 & 18.53 \\ \hline BPN & 2.143 (\(-\)90.63\%) & 0.759 (\(-\)48.26\%) & 17.962 (\(-\)38.40\%) & 16.85 (\(-\)40.86\%) & 13.02 (\(-\)29.74\%) \\ \hline MSC–ANN & 1.272 (\(-\)94.44\%) & 0.396 (\(-\)73.01\%) & 5.542 (\(-\)81.00\%) & 12.25 (\(-\)57.00\%) & 12.78 (\(-\)31.03\%) \\ \hline FCM–GABPN-w/o aggregation & 1.031 (\(-\)95.49\%) & 0.364 (\(-\)75.19\%) & 4.537 (\(-\)84.44\%) & 11.88 (\(-\)58.30\%) & 11.34 (\(-\)38.81\%) \\ \hline FCM–BPN & 0.984 (\(-\)95.70\%) & 0.305 (\(-\)79.21\%) & 3.423 (\(-\)88.26\%) & 9.05 (\(-\)68.23\%) & 13.86 (\(-\)25.20\%) \\ \hline FCM–GABPN & 0.935 (\(-\)95.91\%) & 0.249 (\(-\)83.03\%) & 3.041 (\(-\)89.57\%) & 8.50 (\(-\)70.16\%) & 12.78 (\(-\)31.03\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Improvement of different approaches comparing to comparison basis—manual feeding. Figure 7: Regression of predicted feeding panel versus least feeding panel. respectively, and the superiority of MSC-ANN over BPN was 3.79%, 24.75%, 42.60%, 16.14 %, and 1.29%. The advantages of FCM-GABPN-w/o aggregation over BPN were 4.86%, 26.93%, 46.04%, 17.44%, and 9.07%, and the FCM-BPN over BPN were 5.28%, 30.95%, 49.86%, and 27.37% by reduction in _MSE_, _MAE_, _MAPE_, and _Surpr_Pd_, but with only a 4.54% increase in _Supfr_. Pre-classification and critical attribute selection for each category before prediction model establishment seem to have significant effect on the performance of material feeding prediction. (3) The superiority FCM-GABPN-w/o aggregation, FCM-BPN, and FCM-GABPN over MSC-ANN according to the _MSE_, _MAE_, _MAPE_, and _Surpr_Pd_ with only 5.83% inferiority in _Supfr Pd_ for FCM-BPN approach and the same value for FCM-GABPN indicates that the pre-classification by clustering, which considers many attributes, surpassed the MSC classification, which considers only one attribute. In addition, the FCM-GABPN-w/o aggregation, FCM-BPN and FCM-GABPN only established three BPNs for the three categories of samples, while MSC-ANN pre-classified the samples into six categories and trained a prediction model for each category. (4) FCM-BPN and FCM-GABPN achieved lower _MSE_, _MAE_, _MAPE_, and _Surpr_Pd_ in comparison to FCM-GABPN-w/o aggregation, which indicates that applying the aggregator BPN to derive the representative value by considering the membership degree of each sample facilitates the prediction improvement for the four performance indicators. The 13.61% and 7.78% increase in _Surpr_Pd_ for FCM-BPN and FCM-GABPN may be brought by the 9.07% and 11.86% reduction in _Supfr Pd_, respectively. In practice, the reduction of surplus feeding and supplemental feeding is conflicted because it is difficult to obtain the minimum value for both of them in the factory.