The Development of Neural Network Based System Identification ...

5.2 OFF-LINE BASED SYSTEM IDENTIFICATION FOR MLP NETWORK 127
17
16
15
h=2
h=3
h=4
h=5
h=6
h=7
14
RMSE (%)
13
12
11
10
9
1−1(4regs) 2−1(6regs) 2−2(8regs) 3−1(8regs) 3−2(10regs) 3−3(12regs)
Lag Space
Figure 5.5 The percentage of Root Mean Square Error (RMSE) of MLP network model for each
network structure and number of hidden neurons. The neural network training was carried out using
off-line Levenberg-Marquardt (LM) algorithm.
plot, network structure with 3 past outputs and 1 past input (regression vector with
dimension size of 8) gives the lowest RMSE value for neurons size, h = 4. Despite the
fact that the neuron size h = 7 → 8 gives a comparable low RMSE value, it does not
indicate that the prediction displays good generalisation performance since neuron size
h = 5, has a sudden increase in RMSE value. The noise has affected the error calculation
for the neuron size h = 7 → 8. However, the validity test is still useful in aiding the
selection of an appropriate network structure [Billings et al., 1992]. Furthermore, it is
not advisable to use an excessive number of neurons which may lead to an over-fitting
problem. Finally, we arrive at the following network specifications (Table 5.1) that
adequately represent the attitude dynamics of a model scaled helicopter.
Table 5.1
The MLP neural networks model parameters.
MLP Network Specifications for Attitude Dynamics
Number of past outputs 3
Number of past inputs 1
Number of neurons in hidden layer 4
Activation function at hidden layer Tanh
Activation function at output layer Linear
Number of regressors 8
Total number of weights 46
Weight decay 0.0001