System Identification Technique and Neural Networks for Material Lifetime Assessment Application - Complex System Modelling and Control Through Intelligent Soft Computations - page 764

Inputs Hidden layer Output layer

n 1 1 a 1 1

w 1 1,1

p 1

w 2 1,

b 1 1

1

n 1 2

a 1 2 p 2

a o = n o = t n o

p 3

b 1 2

.
.
.

.
.
.

b o

.
.
.

1 1

w 2 1, S 1

n 1 S 1

a 1 S 1

p R

w 1 S 1 ,

b 1 S 1

1

Fig. 2 MLP with one hidden layer and single output

Furthermore, for convenience P and T will be referred to as the sets of input and
variable output, respectively. Given the observation set O, learning in NN for
realization of the estimate f means adjusting to vector of parameters weight w and
biases b using a set of learning rule or learning algorithm in such a way that f
minimizes the objective function or empirical error de

ned as:

X

Q

2

t q f

E ð w Þ ¼ p q ; w ð 1 Þ

q¼1

and generalizes well or outputs properly when a novel input vector p test never seen
before is fed into the network.
The estimate f realized by the MLP shown in Fig. 2 given the training set O can
be written as:

X

s
i¼1 w

f

2 1

ð p ; w Þ ¼

1 ; i s w i ; j p þ b i

þ b o ð 2 Þ

where (.) is a sigmoidal function used in the nodes of hidden layer.

In addition, by keeping in mind that learning in NN is principally updating the
network weights based on the given set of examples so that the network will give
proper response to new examples, below are two limiting factors of the NN

τ