Environmental Engineering Reference
In-Depth Information
P Crt R
(
( )
=
High
))
=
0 6
,
;
P Crt
(
(R)
=
Medium
))
r
r
...
...
r
11
12
1
n
=
0 3
,
;
P Crt R
(
( )
=
Low
))
=
0,
1
r
r
r
21
22
2
n
M
=
,
P
...
...
r
...
ij
The choice of reactor safety assessment is made
according to the
maximum probability criterion
.
Reactor condition assessment is a complex and
costly task. Fukushima-1 accident proved the
importance of the need for the reliable operation
of monitoring systems (detectors). These risks
can lead to a situation, when the operator can
completely loose the sense of what is happening
to the reactor. For support and decision making
in case of station black-out it is necessary to use
all the information (including indirect informa-
tion) for reactor state assessment. Consequently,
it is important to solve the problem of predicting
reactor components condition without any mea-
surement and using additional information. This
task is solved in the fuzzy backward chaining
block. A primary importance of fuzzy backward
chaining is that it considers parameters, which are
essential for safety, though physical measurement
of which is substantially limited.
r
r
...
r
m
1
m
2
mn
where
r
ij
- an element of matrix expressing the
expert's confidence level in existence of cause-
and-effect relations between a component input
parameter and a corresponding output parameter
describing safety of the system.
Considering BBN block the following distribu-
tion was obtained:
P Crt R
(
( )
=
High
))
=
0 7
,
;
P Crt
(
(R)
=
Medium
))
=
0 1
, ;
P Crt R
(
( )
=
Low
))
=
0,
2
Introduce parameters conditions vector y
1
,
y
2
, y
3
. These parameters are values of the vector
of the criticality probability distribution (BBN
output parameters).
State this vector in the following form:
B
=
0 7
,
y
+
0 1
,
y
+
0 2
,
y
.
Fuzzy Backward Chaining
Block for Prediction of Reactor
Components Condition Parameters
1
2
2
In the fuzzy backward chaining block the
expression, for example,
0 1
,
y
means that the
level of the expert's confidence that the system is
in a certain condition
Crt S
2
The problem of fuzzy backward chaining lies in
evaluation of input parameters describing reactor
components condition, provided that the matrix of
knowledge and reactor safety and output estima-
tions are known.
In terms of input A and output B sets link
between them can be represented in the following
form
B A R
(
1
=
Medium
is equal
to 0.1.
It is necessary to find such a fizzy set
t h a t
would correspond to fuzzy set B. Fuzzy set A can
be represented as a vector
a
A
=
{ (
µ
x
)
x
,
µ
(
x
)
x
, ..., (
µ
x
)
x
},
1
1
2
2
n
n
= ,
where А(В) - a fuzzy set of
input (output) parameters specified in space X(Y).
Matrix of knowledge R can be represented as
,
where а
n
- corresponding value of membership
degree
µ
(
=
( ,
a a
, ....,
a
n
)
1
2
x
n
of the reactor components condition
)
parameter.
In this example reactor components are fuel
elements S
11
and circuit S
12
. Two parameters a
1
-
fuel element temperature and a
2
- pressure in the
circuit are considered.
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