The Development of Neural Network Based System Identification ...

5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP NETWORK 135
14
12
10
RMSE (%)
8
6
4
2
0
1 2 3 4 5 6 7 8 9 10
Hidden Neurons Size
Figure 5.11 The percentage of Root Mean Square Error (RMSE) comparison for different hidden
neurons selection. The k-cross validation process was conducted for HMLP network with network
structure of 6 regressors (n y = 2 and n u = 1). The neural network training was carried out using off-line
Levenberg-Marquardt (LM) algorithm.
The corresponding one-step ahead prediction of the angular rate responses that are
estimated from the off-line HMLP neural network model is shown in Figure 5.12 and
Figure 5.13. 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 set) from 36 s to 37 s. The network is trained using the nearly optimal structure
from Table 5.4. These predicted responses from HMLP network are overlaid with the
measured helicopter responses from the test data set. The results indicate that one-step
ahead HMLP network prediction overlaps the test data almost perfectly as indicated by
the magnitude order of the prediction error plot. Again, this usually happens due to
the effect of high sampling frequency of the data collected.
The corresponding error statistics of one-step and k-step ahead predictions are
given in Table 5.5. From the error statistics, we can conclude that the discrepancy
between the one step or k-step ahead prediction (k = 5) and the measured data is
insignificant. Overall, we can conclude that the trained HMLP neural network model
predictions are close to the measured values and that the neural network is properly
trained to mimic the rigid body dynamics of the helicopter.