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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.

Table 2

Performances of the MLR and ANN models for the testing dataset with the different inputs

  Data #1
Data #2
ModelsInputshnMSEMAPEEhnMSEMAPEE
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 0.020 22.3 0.873 
PLC-selected inputs 10 0.030 79.0 0.632 0.018 20.8 0.884 
PLC-Wavelet inputs 16 0.022 77.8 0.732 0.009 16.8 0.944 
LRNN Original inputs 12 0.035 104.2 0.580 0.021 24.1 0.867 
PLC-selected inputs 12 0.033 65.1 0.604 0.018 21.9 0.882 
PLC-Wavelet inputs 16 0.018 71.6 0.787 0.009 16.7 0.940 
  Data #1
Data #2
ModelsInputshnMSEMAPEEhnMSEMAPEE
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 0.020 22.3 0.873 
PLC-selected inputs 10 0.030 79.0 0.632 0.018 20.8 0.884 
PLC-Wavelet inputs 16 0.022 77.8 0.732 0.009 16.8 0.944 
LRNN Original inputs 12 0.035 104.2 0.580 0.021 24.1 0.867 
PLC-selected inputs 12 0.033 65.1 0.604 0.018 21.9 0.882 
PLC-Wavelet inputs 16 0.018 71.6 0.787 0.009 16.7 0.940 

hn, number of hidden neurons.

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