The Development of Neural Network Based System Identification ...

5.4 OFF-LINE BASED SYSTEM IDENTIFICATION FOR ELMAN NETWORK 139
10 3 Self Connection Strengh, α
10 2
RMSE (%)
10 1
10 0
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Figure 5.14 The self connection α strength selection results using modified Elman network with
reduced connection. The Elman network training are repeated 10 times and validated on a test set.
The training is carried out using 6 hidden neurons.
from 0 to 1 to investigate the prediction performance of basic Elman network (α = 0)
and modified Elman network. Finding from the plot shows that the self connection
values between 0.3 to 0.5 produced satisfactory prediction performance before RMSE
values increase beyond α = 0.6. The lowest RMSE value is found at α = 0.5 with
14.24 ± 1.26% and this is used throughout the analysis.
The result of neurons size selection is reproduced here for the modified Elman
network using the k-fold cross validation method. The result of the hidden neurons
selection for 1 past output and 1 past input (4 regressors) network structure is given in
Figure 5.15. From the plot, the network structure with 1 past input and 1 past output
measurement produces an acceptable RMSE percentage between hidden neuron sizes
h = 4 → 10, thus it is logical to select the optimum neuron size at h = 4. Finally, we
arrive at the following network specifications (Table 5.7) that adequately represent the
attitude dynamics of a model scaled helicopter. Note that the total number of weights
in the optimum Elman network is lesser than the optimum MLP and HMLP network.
The corresponding one-step ahead prediction of the angular rate responses that are