The Development of Neural Network Based System Identification ...

30 CHAPTER 2 LITERATURE REVIEW
prediction and past input and output measurements [Norgaard, 2000].
In the NNARX model structure, the variables to be estimated and other influencing
variables including their time lags are typically fed into a static feed-forward network
such as the multi-layer perceptron (MLP) network [Samarasinghe, 2007]. Studies have
shown that the NN based approach using the NNARX architecture is effective in
modelling the dynamic response of the helicopter based UAS [Suresh et al., 2002, Samal
et al., 2008, San Martin et al., 2006, Rimal et al., 2011, Chetouani, 2010]. Another
interesting finding following the work of Rahideh et al. [2008] suggests that the NNARX
networks trained with Levenberg-Marquardt (LM) algorithm is capable to exceed the
prediction performance of first principle model.
Different neural network structures such as Radial Basis Function (RBF) and
Recurrent Neural Networks (RNN) have been used in past research works with success
in identifying the helicopter dynamics [Ahmad et al., 2002, Kumar et al., 2010, Pedro
and Kantue, 2011]. An example of RBF network application for system identification of
a twin rotor helicopter system was proposed in Ahmad et al. [2002]. The RBF network
typically uses the orthogonal least square (OLS) algorithm to systematically find a set
of weights and radial basis centres to ensure that the desired input-outputs mapping is
performed [Chen et al., 1991]. However, the RBF network usually requires more hidden
neurons compared with the conventional NNARX network with sigmoid or tangent
hyperbolic activation functions in the hidden layer. The reason behind such an increase
in the number of neurons used in the RBF network contributes to the fact that the
outputs of the radial basis neurons only cover a relatively small input space compared
to the outputs of typical activation functions in the NNARX networks [Shaheed, 2005].
Thus, in order to adequately represent broader input space, a much larger number
of neurons need to be included in the network to achieve more reliable identification
results.
Many parameters in a RBF network such as the network weights, biases, centre
vectors and spread constant need to be optimised compared with a much simpler
NNARX network that only require optimisation of weights and biases [Shaheed and
Tokhi, 2002]. In terms of generalisation performance, NNARX network produces a much