Modelling Non-Linear Rendering Processes - Real-Time Rendering: Computer Graphics with Control Engineering - page 53

Inputs

Layer 1 Layer 2

W 2

W 1

y

+

F 2

d 2

+

F 1

d 1 U

x 2

X´ 1

x 1

B 2

B 1

FIGURE 4.2 Two-layer distributed time delay neural network with time delays at inputs of
each layer. The notations with their respective meaning or representative are:

U , the input layer
d , the delay
Wn , where W is the weight and n represents the n th layer
Bn where B is the bias and n represents the n th layer
Fn , where F is the firing function and n represents the n th layer
y , the output of the network

Second, the ANN's layered network structure makes it easy to extend by cascading
ANNs together for modelling modular systems. For example, to model a compli-
cated system it may be possible to break down the process into modelling individual
subsystems using simple ANNs and then joining them together. This is certainly
applicable in the context of computer software since modern programming para-
digms emphasise modularity and object-oriented principles.

4.2.2 s ystems m odelling with f uzzy l logic
Fuzzy set theory and fuzzy control have been implemented successfully in many
technical fields. The primary benefit offered by the fuzzy control paradigm is its
ability to emulate human control based on linguistic variables and a set of intuitive
expert rules used as a decision or inference system. In comparison to conventional
control techniques, the advantages of the fuzzy control paradigm are twofold.
First, it imposes no requirement for a mathematical model of the system to be
controlled. This is especially important and useful as it may be difficult to derive
certain process models due to their complex dynamics and some systems cannot
be modelled using first principles. Second, the fuzzy controller works on relatively
straightforward computation and can be developed to handle non-linear processes
empirically in practice without the need for complicated mathematics.
In addition, fuzzy logic is tolerant of imprecise data. Systems with reliable perfor-
mance can be built using fuzzy logic that leverages the experiences of experts. In direct
contrast to neural networks that use training data and generate system models, fuzzy
logic allows a user to rely on the experiences of humans who understand the system.
Furthermore, fuzzy logic can be blended with conventional control techniques.
In many cases, fuzzy systems augment them and simplify other implementations.
Finally, fuzzy logic is based on natural language that provides a strong basis for human
communication. As a result, fuzzy logic is easy to use. These advantages translate to its
appeal as a practical solution to real world control problems involving implementation.