The Development of Neural Network Based System Identification ...

140 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION
Table 5.7
The modified Elman network parameters.
Elman Network Specifications for Attitude Dynamics
Number of past outputs 1
Number of past inputs 1
Number of neurons 4
Activation function at hidden layer
Tanh
Activation function at output layer Linear
Number of regressors 4
Total number of weights 34
Weight decay 0.0001
Self connection strength α 0.5
10 3 Hidden Neurons Size
10 2
RMSE (%)
10 1
10 0
1 2 3 4 5 6 7 8 9 10
Figure 5.15 The validation RMSE comparison for different hidden neuron sizes. The k-cross validation
process was conducted for modified Elman network with network structure of 4 regressors (n y = 1 and
n u = 1). The neural network training was carried out using the off-line Levenberg-Marquardt (LM)
algorithm.
estimated from the off-line trained modified Elman network is shown in Figure 5.16 and
Figure 5.17. The off-line LM training is carried out using training data set from 16 s
to 28 s, and the prediction performance is validated on roll rate and pitch rate data
(test data) from 36 s to 37 s. The network is trained using the nearly optimal structure
from Table 5.7. These predicted responses from modified Elman network are overlaid
with the measured helicopter responses from the test data set. The results indicate
that one-step ahead modified Elman network prediction overlap the test data almost