Casestudie Breakdown prediction Contell PILOT - Transumo

clustering as well as an analysis of historical data is often done by the use of artificial
neural networks ([Blasig95], p. 3-4).
The succeeding subsections will introduce artificial neural networks and will review
their applicability to sensor based temperature monitoring data. A positive review
would allow the usage of automated clustering and classification.
5.9.2 Artificial Neural Networks
Artificial neural networks are based on the functioning of a human brain. Every brain
consists of neurons. These neurons are stimulated from neighbored neurons by
chemical impulses, the so called neurotransmitters. Neurons transform incoming
chemical impulses to electrochemical signals and relay them to the neighbored
neurons. A regular exchange of these signals between two neurons leads to a high
activation of this connection. By contrast, sparse communication leads to a low
activation or even a loss of connection. ([Martin98], p. 262-263)
The underlying basic principal is learning from failures. A connection that represents
an error is assigned to a low activation level after recognition. By contrast, generally
valid facts are represented by a highly activated connection. ([Lusti02], p. 316)
Artificial neural networks adopt this functioning. They are defined by a tuple (N, V, F).
N is a set of neurons. A neuron n i is defined by Formula 5-19. V and F represent a
set of directed connections between neurons and a set of learning functions
respectively, which are defined by Formula 5-20. ([Hagen97], p.6-7)
n
i
= ( x(
t),
w ( t),
a ( t),
f , g,
h)
i
i
with
x(
t)
= ( x ( t),
K,
x
w ( t)
= ( w
a ( t)
∈ R as activation level at time t
i
i
h : R
n
1
× R
i1
n
( t),
K,
w
( t))
∈ R
→ R with s ( t)
= h(
x(
t),
w ( t))
as propagation
g : R×
R → R with a ( t)
= g(
s ( t),
a ( t −1))
as activation
f : R → R with y ( t)
=
n
i
in
i
( t))
∈ R
i
n
as input vector at time t
as weighting vector at time t
f ( a ( t))
as output
i
n
i
i
i
function to provide the input signal s ( t)
function to calculate the activation level a ( t)
function to calculate the output y ( t)
i
i
i
Formula 5-19: Definition of Neurons
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