The Development of Neural Network Based System Identification ...

94 CHAPTER 4 NEURAL NETWORK BASED SYSTEM IDENTIFICATION
4.3.2 Neural Network Model Structure Selection
The primary objective of system identification process is to create a model describing
the underlying relationships between input-output variables. There are two types of
NN model structure that have been successfully used for system identification and timeforecasting
tasks: a) NNARX model structure or also known as time lagged feed-forward
networks; b) dynamically driven recurrent networks.
In a neural network based ARX (NNARX) model structure, the variable to be
estimated and other influencing variables including their time lags are typically fed into
a static feed-forward network such as multi-layer perceptron (MLP) network [Norgaard,
2000]. The reason to include extra variables from the time lags is to enable the model to
extract information from the time lags that are not included in the current measurement
and the lags of the variables of interest [Samarasinghe, 2007]. This would subsequently
improve the prediction accuracy. In contrast to NNARX model structure, a dynamically
driven recurrent network such a Elman network learns the dynamics of a time series
through internal feedback connections that remember the past state of the series.
The black box based modelling approach such as NNARX is usually used to deduce
the dynamic model of a system by taking into account the relationship between all
inputs and outputs of the system. Generally, we represent the n th order discrete time
helicopter non-linear with m inputs, p outputs as follows:
x (t + 1) = h [x(t), u(t)]
y(t) = g [x(t)] (4.16)
where x ∈ R p is the state vector, y ∈ R n is output vector and u ∈ R m is input vector at
discrete time step t with assumption that the dynamic system has m inputs, p states
and n outputs.
The model structure for neural network modelling used in this research was adapted
from standard ARX (Autoregressive structure with extra inputs) model structure
reported in Ljung [1999]. Using this approach, the measurement data are sampled in
discrete time step, t and the sampled values between input and output measurements