The Development of Neural Network Based System Identification ...

5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP NETWORK 133
5.3 OFF-LINE BASED SYSTEM IDENTIFICATION FOR HMLP
NETWORK
In this section, the results of the model structure and hidden neurons size selection of
HMLP network are presented. The identification of UAS helicopter attitude dynamics
was carried out using the off-line Levenberg-Marquardt training as in Section 4.3.4. The
flight data sets was obtained by performing different flight manoeuvres to excite the
dynamic of interest. Using the collected data, the suitable regression vector (network
structure) and hidden neurons size were determined using the k-fold cross validation
technique as previously discussed. The method for minimising the over-fitting effect in
the HMLP network training is similar to regularisation method used in MLP network.
The results of cross validation for HMLP network with different network structures
(input nodes) are given in Figure 5.10. Six different network structures were tested and
compared with each other. The plot indicates that the simple HMLP network structure
with 1 past output and 1 past input (4 regressors) gives the highest percentage of RMSE,
which is similar to cross validation trend in MLP, and it is not fit for predicting the
non-linear dynamics of the helicopter UAS. As the number of regressors or inputs to
the network increases, the RMSE value decreases and stabilises after 2 past outputs
and 1 input (6 regressors) structure. Hence, the neural network model structure can be
selected as a total of 6 regressors with 2 past output and 1 past input observation. This
cross validation procedure was repeated for different hidden neuron sizes and an overall
RMSE trend points out to the same sharp breakpoint at 2 past outputs and 1 input (6
regressors) network structure.
The result of neurons size selection is reproduced here for the HMLP network using
the k-fold cross validation method. The result of the hidden neurons selection for 2 past
outputs and 1 past input (6 regressors) network structure is given in Figure 5.11. From
the plot, the network structure with 2 past outputs and 1 past input (regression vector
with dimension size of 6) yield the lowest RMSE value (9.82 %) for neurons size, h = 3.
Finally, we arrive at the following network specifications (Table 5.4) that adequately
represent the attitude dynamics of a model scaled helicopter. By examining the RMSE