The Development of Neural Network Based System Identification ...

128 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION
10 2 Hidden Neurons Size
RMSE (%)
10 1
10 0
1 2 3 4 5 6 7 8 9 10
Figure 5.6 The percentage of Root Mean Square Error (RMSE) comparison of MLP network trained
with different hidden neuron sizes. The k-cross validation process was conducted for network structure
with 8 regressors (n y = 3 and n u = 1). The neural network training was carried out using off-line
Levenberg-Marquardt (LM) algorithm.
An example of the one-step ahead prediction of the angular rate responses that
are estimated from the off-line neural network system identification is shown in Figure
5.7 and Figure 5.8. The off-line LM training is carried out using the training data set
from 16 s to 28 s recording, 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 5.1. These predicted responses from neural network
identification (NNID) are overlaid with the measured helicopter responses. The results
indicate that one-step ahead NNID predictions overlap the test data almost perfectly
as indicated by the magnitude order of the prediction error plot. This usually happens
when the sampling frequency of the data collected is high compared with the frequency
of the dynamic system as suggested in Norgaard [2000]. The small prediction error
from one-step ahead prediction does not necessarily indicate that the model is sufficient
without further checks.
The quality of the fitted model is further inspected by running k-step ahead
prediction to check if there is a possibility of a significant discrepancy between prediction