Lean Blowout Detection Techniques for Partially Premixed Flames in a Dump Combustor - Novel Combustion Concepts for Sustainable Energy Development - page 216

alphabet. When data from the time series sequence fall in a particular region, it is
coded with the symbol associated with that region. Thus, the time series data are
converted to a sequence of symbols, referred to as symbolic time series. There are
different approaches for partitioning the range of data into regions. The most
intuitive approach generates the partitions such that the region rich in data is
divided into partitions of smaller size and region with sparse data has partitions of
large size. In this work, the entire region is partitioned in such a way that each
region contains equal number of data. This maximizes the information entropy
associated with the data and is known as maximum entropy partitioning. To achieve
this, the elements of time series data are sorted in ascending order. Starting from the

first data in the sorted list, every consecutive data segment of length N = jb c
constitutes a distinct element of the partition where N and R represent the total
number of data and number of symbols used and

represents the greatest integer
less than or equal to x. Once the partitions are generated, the time series data are
converted into symbol sequence and the number of data in each segment is cal-
culated. The array containing numbers of data in all the partitions constitutes the
state vector. For detection of LBO, a condition away from the blowout limit where
combustion is stable is identi

bc

ed as the nominal state. The partitions are generated
using maximum entropy partitioning of this nominal time series data. In other
words, at the nominal state, the number of data in each partition is same. Once the
partitions are generated, the same partitions are used for all subsequent operating
conditions. As the equivalence ratio is reduced, new time series data are obtained.
Each time series data are partitioned using the same partitions as the nominal state,
and the number of data in each region is calculated. A new state vector containing
the number of data in all the partitions for the new operating condition is computed.
Some measure of deviation of the new state vector from the nominal state vector is
considered as an anomaly measure. The objective of the present research is to use
this anomaly measure for predicting LBO. For this, two methods of generating
partitions are used. In one approach, the time series data are directly used. This has
been referred to as simple partitioning (simple P). In the other approach, complex
analytic functions are generated by Hilbert transform of the time series data. Given
the Hilbert transform of a real-valued signal x ð t Þ , the corresponding complex-

valued analytic signal is de ned as A½ ð t Þ ¼x ð t Þþ ix ð t Þ where

x ð t Þ

is the Hilbert

transform of x ð t Þ (Subbu and Ray 2008 ). The partitioning is generated using both

the amplitude and the phase of the complex analytic function. This method of
STSA, referred to as analytic signal space partitioning (ASSP), is more effective
than simple partitioning and computationally very ef

cient. The algorithms for
simple partitioning and ASSP are given below. Further details could be found in
Mukhopadhyay et al. ( 2013 ).
Simple Partitioning (Simple P)
Generation of partitions
1. Generate time series data of length N, x(i) for the nominal state
2. Select number of states, N 1 , and assign one symbol to each partition (alphabet)