Lean Blowout Detection Techniques for Partially Premixed Flames in a Dump Combustor - Novel Combustion Concepts for Sustainable Energy Development - page 218

ASSP
Generation of partitions

1. Generate time series data of length N, x(i) for the nominal state
2. Generate complex analytic function using Hilbert transform,

x0 ðÞ ¼Hilbert x ððÞ
3. Arrange abs ð x0 Þ and angle ð x0 Þ in ascending orders and store the sorted series as

x1(i) and x2(i)
4. Select number of states, N 11 and N 12 for x1 and x2, respectively, and assign one
symbol to each partition (alphabet)
5. Assign N 21 ¼

N jk N jk where

N N

denotes nearest lower integer
6. Assign partition1(1) = x1(1) and partition1(i +1)=x1(i * N 2 ) for 1

b and N 22 ¼ bc

i ð N 11 1 Þ

and partition (N 11 +1)=x1(N)
7. Assign partition2(1) = x2(1) and partition2(i +1)=x2(i * N 2 ) for 1

i ð N 12 Þ

1

and partition (N 12 +1)=x2(N)
Construction of state probability vector for nominal state

1. Initialize state probability vector p(i) = 0 for 1 ≤ i ≤ N

11 *

N

12

2. for j = 1 : N

for i 1 = 1 : N

11 −

1

for i 2 = 1 : N − 1

12

x 1 j ) ≥ partition 1 i 1 & x 1 j ) < partition 1 i 1 + 1 &

if ,

x 2 j ) ≥ partition 2 i 2 & x 2 j ) < partition 2 i 2 + 1 ))

p (( i 1 − 1 * ( N − 1 + i 2 = p (( i 1 − 1 * ( N − 1 + i 2 + 1

12 12

end

end
end

3. p0(i)=p(i)/N, for 1 ≤ i ≤ N

11 *

N

12

Construction of state probability vector for other states
1. Generate time series data of length N 0 , x(i) for the non-nominal state
2. Generate complex analytic function using Hilbert transform, x0(i) = hilbert (x(i))
3. Arrange abs ð x0 Þ and angle ð x0 Þ in ascending orders and store the sorted series as

x1(i) and x2(i)
4. Initialize state probability vector p(i) = 0 for 1

i N 11 N 12