The Development of Neural Network Based System Identification ...

120 CHAPTER 5 NN BASED SYSTEM IDENTIFICATION: RESULTS AND DISCUSSION
5.2 OFF-LINE BASED SYSTEM IDENTIFICATION FOR MLP
NETWORK
In this section, the off-line system identification proposed in Section 4.3.4 is implemented
to identify the attitude dynamics of the UAS helicopter model. The identification process
is conducted using real flight test data obtained from different flight manoeuvres. The
flight test data were divided into training, validation and test data sets. The training and
validation data sets were used for purpose of NN training and model structure selection.
The test data set was used for the final evaluation of the NN model prediction accuracy
and reliability. In each manoeuvre, only a certain input command was used to excite
the dynamic of interest. During the experiment, all control inputs and all UAS state
measurements were recorded and sampled at 100 Hz. Figure 5.1 shows the recorded
data during lateral and longitudinal cyclic swept for 100 s. The data were filtered
using a low pass filter at a cut-off frequency 15 Hz to remove the undesirable structural
vibrations effect. Using the collected data, the suitable regression vector (network
structure) and hidden neurons size were determined using the Lipschitz coefficient and
k-fold cross validation technique previously discussed. To avoid over-fitting problem,
the adaptability of the NN weights during training was reduced using the regularisation
method.
5.2.1 Improving Generalisation of Neural Network through Regularisation
The NN training used in this research work employed regularisation term in the error
criterion to improve generalisation performance of the NN model. For a relatively small
sized network model, a trial and error approach was adopted to select the appropriate
weight decay parameter α to minimise the generalisation error. Figure 5.2 shows the
effect of varying weight decay values on the training error, validation error and training
iteration using attitude dynamic data set (y = [p q] T ; y = [δ lon δ lat ] T ). The result
was obtained using the NN model trained with Levenberg-Marquardt (LM) algorithm
using 5 hidden neurons and 8 regressors (n y = 3 and n u = 1). As the value of weight