The training process for FFNN and LRNN models was carried out using the Levenberg–Marquardt algorithm (Samarasinghe 2006). The least square method (Tsay 2005) was used for the calibration of the MLR model. The single objective of minimizing MSE was used in the training process of all models. The remaining two performance indicators (i.e., E and MAPE) were then computed using the training (i.e., combination of training and validation) and testing outcomes. A suitable number of hidden neurons for FFNN and LRNN models was selected using trial and error. The results are presented in Table 2 only for the testing performances.
Performances of the MLR and ANN models for the testing dataset with the different inputs
. | . | Data #1 . | Data #2 . | ||||||
---|---|---|---|---|---|---|---|---|---|
Models . | Inputs . | hn . | MSE . | MAPE . | E . | hn . | MSE . | MAPE . | E . |
MLR | Original inputs | – | 0.052 | 119.3 | 0.567 | – | 0.030 | 26.2 | 0.769 |
PLC-selected inputs | – | 0.047 | 106.7 | 0.570 | – | 0.024 | 25.5 | 0.770 | |
PLC-Wavelet inputs | – | 0.026 | 85.1 | 0.702 | – | 0.011 | 16.7 | 0.914 | |
FFNN | Original inputs | 12 | 0.034 | 86.3 | 0.589 | 2 | 0.020 | 22.3 | 0.873 |
PLC-selected inputs | 10 | 0.030 | 79.0 | 0.632 | 6 | 0.018 | 20.8 | 0.884 | |
PLC-Wavelet inputs | 16 | 0.022 | 77.8 | 0.732 | 6 | 0.009 | 16.8 | 0.944 | |
LRNN | Original inputs | 12 | 0.035 | 104.2 | 0.580 | 2 | 0.021 | 24.1 | 0.867 |
PLC-selected inputs | 12 | 0.033 | 65.1 | 0.604 | 2 | 0.018 | 21.9 | 0.882 | |
PLC-Wavelet inputs | 16 | 0.018 | 71.6 | 0.787 | 6 | 0.009 | 16.7 | 0.940 |
. | . | Data #1 . | Data #2 . | ||||||
---|---|---|---|---|---|---|---|---|---|
Models . | Inputs . | hn . | MSE . | MAPE . | E . | hn . | MSE . | MAPE . | E . |
MLR | Original inputs | – | 0.052 | 119.3 | 0.567 | – | 0.030 | 26.2 | 0.769 |
PLC-selected inputs | – | 0.047 | 106.7 | 0.570 | – | 0.024 | 25.5 | 0.770 | |
PLC-Wavelet inputs | – | 0.026 | 85.1 | 0.702 | – | 0.011 | 16.7 | 0.914 | |
FFNN | Original inputs | 12 | 0.034 | 86.3 | 0.589 | 2 | 0.020 | 22.3 | 0.873 |
PLC-selected inputs | 10 | 0.030 | 79.0 | 0.632 | 6 | 0.018 | 20.8 | 0.884 | |
PLC-Wavelet inputs | 16 | 0.022 | 77.8 | 0.732 | 6 | 0.009 | 16.8 | 0.944 | |
LRNN | Original inputs | 12 | 0.035 | 104.2 | 0.580 | 2 | 0.021 | 24.1 | 0.867 |
PLC-selected inputs | 12 | 0.033 | 65.1 | 0.604 | 2 | 0.018 | 21.9 | 0.882 | |
PLC-Wavelet inputs | 16 | 0.018 | 71.6 | 0.787 | 6 | 0.009 | 16.7 | 0.940 |
hn, number of hidden neurons.