The Development of Neural Network Based System Identification ...

LIST OF FIGURES
xix
3.13 Overview of the measurement system setup. 73
4.1 Different types of NN modelling architectures: (a) Single-layer perceptron;
(b) Linear neuron; (c) Multi-layer perceptron (MLP); (d) Competitive
network; (e) Self-organising feature map (SOFM); and (f) Recurrent
networks 79
4.2 The artificial neuron model with multiple inputs and single output:
(a) The output is represented in compact mathematical form as ŷ h =
( ∑m
f h j=1 W hjX j + b 1
). The term h represents the number of neurons
in the network and m is the number of inputs entering the neuron; and
(b) The detailed working mechanism of a single neuron. Figure adapted
from Samarasinghe [2007]. 81
4.3 Different types of activation function for NN modelling: (a) Linear
function; (b) Sigmoid function; (c) Hyperbolic Tangent function; (d)
Step; (e) Sign function; and, (f) Gaussian function with real constant
a, b, c > 0 82
4.4 A fully connected, feed-forward multi-layered perceptron (MLP) with
m-inputs, h-hidden neurons and n-outputs. 83
4.5 The hybrid multi-layered perceptron (HMLP). The dashed lines indicate
extra linear connections in the network. 85
4.6 The structure and operation of Elman network. (a) The basic Elman
Network (b) The modified version of Elman network with self-connections
in the context units; and (c) The modified version of Elman network
with reduced weight connections. 88
4.7 Overview of neural network based system identification procedure. 91
4.8 Offset distance of the IMU with respect to centre of gravity. 93