Environmental Engineering Reference
In-Depth Information
consistent semantics for representing causes and
effects (and likelihoods) via an intuitive graphical
representation. An important fact to realize about
Bayesian belief networks is that they are not de-
pendent on knowing exact historical information
or current evidence.
According to approach it is suggested to con-
struct BBN for each type of influence. Each node
of BBN is represented by criticality matrix. Nodes
are connected by links, which represent the dif-
ferent types of influence. We consider six types
of influence among power grid systems.
Fragments of six BBNs are shown in Figure 12.
Hence, BBNs, which describe the PG system
safety, consist of set of nodes. For each node the
set of state is introduced. As mentioned above the
state of node is characterized by value of its
criticality calculated according to (12).
Every node also has a conditional probability
table, or CPT, associated with it. Conditional
probabilities represent likelihoods based on prior
information or past experience. A conditional
probability is stated mathematically as, i.e. the
probabilities of the power grid system (child
node), being at state characterized by expressions
“Criticality is High (Medium, Low)” considering
all possible combinations of other PG systems (par-
ents' nodes) criticalities (High, Medium, Low).
Let us consider the fragment of BBN related
to the informational influence between systems
S
1
S
2
S
3
, where the criticality of S
3
(child node) is
conditioned by criticalities both of S
2
S
3
(parents'
nodes).
Probability of S
3,
being at one of the established
state
Ω
S3
depending on the states of parents nodes,
could be determined as:
probability for PG system S
3
to be at
k
-th state
provided system
S
1
being at
i
th state and system
S
2
being at
j
-th state;
P S
i
( )
1
- the probability
for S
1
being at
i
-th state determined by expert
taking into account value (12);
P S
j
(
)
(
( )
2
)
- the
probability for S
2
being at
j
-th state determined
by expert taking into account value (12); .
In this case the probability for system S
1
being
at the state described by expression “Criticality -
High” is calculated as presented in Box 1.
The probabilities of S
1
being at the states de-
scribed by expressions “Criticality - Medium”
and “Criticality-High” are determined similarly.
The power grid system S
i
state conditioned
by the given type of influence is determined on
the criterion:
Crt S
(
)
=
argmax( (
P Crt S
(
)
=
High
),
i
i
(17)
P Crt S
(
(
)
=
Medium P Crt S
),
(
(
)
=
Low
),
i
i
where
P Crt S
( ( )
=
) - the probability of
the power grid system of being at the state de-
s c r i b e d by
High
i
l i ngu i s t i c va l u e Hi gh ;
( ( )
=
- the probability of the
power grid system of being at the state described
by linguistic value Medium;
P Crt S
P Crt S
Medium
i
)
=
Low
(
(
i
- the probability of the power grid system of being
at the state described by a linguistic value Low.
Similarly for each power grid system all criti-
calities, determined by different types of influence,
are calculated and represented as power grid
system criticality tuple shown in Table 6.
Analysis of the Linguistic
Computational Models
∑
∑
P S
(
( )
k
)
=
P S
(
( )
k
/
S
( )
i
,
S
( )
j
)
∗
P S
(
( )
i
)
∗
P S
(
( )
j
),
3
3
1
2
1
2
i
j
(15)
The CWW is used to evaluate the total criticality
for each power grid system.CWW procedure uses
the linguistic assessments and make computa-
tions with them. Foundations and applications
providing the current status of theoretical and
where
P S
k
( )
3
- the probability for S
3
being at
k
-th state;
P S
(
)
( )
k
( )
i
( )
j
(
/
S
,
S
)
- conditional
3
1
2
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