Environmental Engineering Reference
In-Depth Information
3. Arrange the time series data in ascending order and store the sorted series as x1
(i)
4. Assign N
2
¼
N
jk
where
N
denotes nearest lower integer
5. Assign partition(1) = x1(1) and partition (i +1)=x1(i * N
2
) for 1
bc
i
ð
N
1
1
Þ
and partition (N
1
+1)=x1(N)
Construction of state probability vector for nominal state
1.
Initialize state probability vector p(i) = 0 for
1
≤
i
≤
N
1
2.
for
j
=
1
:
N
for
i
=
1
N
1
if
x
(
j
)
≥
partition
(
i
)
&
x
(
j
)
<
partition
(
i
+
1
,
p
(
i
)
=
p
(
i
)
+
1
end
end
end
≤
Construction of state probability vector for other states
1
i
≤
N
3.
p0(i)=p(i)/N, for
1
1.
Generate time series data of length
N
′ , x(i) for the non-nominal state
2.
Initialize state probability vector p(i) = 0 for
1
≤
i
≤
N
1
for
j
=
1
:
N
′
for
i
=
1
N
1
if
,
x
(
j
)
≥
partition
(
i
)
&
x
(
j
)
<
partition
(
i
+
1
p
(
i
)
=
p
(
i
)
+
1
end
end
end
3.
p1(i)=p(i)/N, for
1
≤
i
≤
N
1
Use the same partitions for all the states
Determination of Anomaly Measure
p
0
p
1
p
kk
p
kk
1. Compute anomaly measure, M ¼
cos
1
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