Real-time decision-making (e.g., monitoring and active control of dynamical systems) often requires feature extraction and pattern classification from short-length time series of sensor data. An example is thermoacoustic instabilities (TAI) in combustion systems, caused by spontaneous excitation of one or more natural modes of acoustic waves. The TAI are typically manifested by large-amplitude self-sustained pressure oscillations in time scales of milliseconds, which need to be mitigated by fast actuation of the control signals, requiring early detection of the forthcoming TAI. This issue is addressed in this technical brief by hidden Markov modeling (HMM) and symbolic time series analysis (STSA) for near-real-time recognition of anomalous patterns from short-length time series of sensor data. An STSA technique is first proposed, which utilizes a novel HMM-based partitioning method to symbolize the time series by using the Viterbi algorithm. Given the observed time series and a hidden Markov model, the algorithm generates a symbol string with maximum posterior probability. This symbol string is optimal in the sense of minimizing string error rates in the HMM framework. Then, an HMM likelihood-based detection algorithm is formulated and its performance is evaluated by comparison with the proposed STSA-based algorithm as a benchmark. The algorithms have been validated on a laboratory-scale experimental apparatus. The following conclusions are drawn from the experimental results: (1) superiority of the proposed STSA method over standard methods in STSA for capturing the dynamical behavior of the underlying process, based on short-length time series and (2) superiority of the proposed HMM likelihood-based algorithm over the proposed STSA method for different lengths of sensor time series.

References

References
1.
Rawung
,
R.
, and
Putrada
,
A.
,
2014
, “
Cyber Physical System: Paper Survey
,”
International Conference on ICT for Smart Society
(
ICISS
),
Bandung, Indonesia
,
Sept. 24–25
, pp. 273–278.
2.
Darema
,
F.
,
2004
, “
Dynamic Data Driven Applications Systems: A New Paradigm for Application, Simulation and Measurements
,” Computational Science-(
ICCS
), Kraków, Poland, June, pp.
662
669
.https://link.springer.com/chapter/10.1007/978-3-540-24688-6_86
3.
Lieuwen
,
T. C.
, and
Yang
,
V.
,
2005
,
Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling
,
American Institute of Aeronautics and Astronautics
, Reston, VA, pp.
3
26
, Chap. 1.
4.
Matveev
,
K.
,
2003
, “
Thermoacoustic Instabilities in the Rijke Tube: Experiments and Modeling
,”
Ph.D. thesis
, California Institute of Technology, Pasadena, CA.https://thesis.library.caltech.edu/859/
5.
Sarkar
,
S.
,
Chakravarthy
,
S. R.
,
Ramanan
,
V.
, and
Ray
,
A.
,
2016
, “
Dynamic Data-Driven Prediction of Instability in a Swirl-Stabilized Combustor
,”
Int. J. Spray Combust. Dyn.
,
8
(
4
), pp.
235
253
.
6.
Ray
,
A.
,
2004
, “
Symbolic Dynamic Analysis of Complex Systems for Anomaly Detection
,”
Signal Process.
,
84
(
7
), pp.
1115
1130
.
7.
Mukherjee
,
K.
, and
Ray
,
A.
,
2014
, “
State Splitting and Merging in Probabilistic Finite State Automata for Signal Representation and Analysis
,”
Signal Process.
,
104
, pp.
105
119
.
8.
Mondal
,
S.
,
Ghalyan
,
N. F.
,
Ray
,
A.
, and
Mukhopadhyay
,
A.
,
2018
, “
Early Detection of Thermoacoustic Instabilities Using Hidden Markov Models
,”
Combust. Sci. Technol.
(epub).
9.
Hajek
,
B.
,
2015
,
Random Processes for Engineers
,
Cambridge University Press
,
Cambridge, UK
.
10.
Rabiner
,
L.
, and
Juang
,
B.-H.
,
1993
,
Fundamentals of Speech Recognition
,
Prentice Hall
,
Upper Saddle River, NJ
.
11.
Daw
,
C. S.
,
Finney
,
C. E. A.
, and
Tracy
,
E. R.
,
2003
, “
A Review of Symbolic Analysis of Experimental Data
,”
Rev. Sci. Instrum.
,
74
(
2
), pp.
915
930
.
12.
Graben
,
P. B.
,
2001
, “
Estimating and Improving the Signal-to-Noise Ratio of Time Series by Symbolic Dynamics
,”
Phys. Rev. E
,
64
(
5 Pt. 1
), p.
051104
.
13.
Gupta
,
S.
, and
Ray
,
A.
,
2007
, “
Symbolic Dynamics Filtering for Data-Driven Pattern Recognition
,”
Pattern Recognition: Theory and Applications
,
Nova Science Publishers
, Hauppauge, NY, pp.
17
71
.
14.
Wen
,
Y.
,
Mukherjee
,
K.
, and
Ray
,
A.
,
2013
, “
Adaptive Pattern Classification for Symbolic Dynamic Systems
,”
Signal Process.
,
93
(
1
), pp.
252
260
.
15.
Bahrampour
,
S.
,
Ray
,
A.
,
Sarkar
,
S.
,
Damarla
,
T.
, and
Nasrabadi
,
N.
,
2013
, “
Performance Comparison of Feature Extraction Algorithms for Target Detection and Classification
,”
Pattern Recognit. Lett.
,
34
(
16
), pp.
2126
2134
.
16.
Chattopadhyay
,
P.
,
Mondal
,
S.
,
Bhattacharya
,
C.
,
Mukhopadhyay
,
A.
, and
Ray
,
A.
,
2017
, “
Dynamic Data-Driven Design of Lean Premixed Combustors for Thermoacoustically Stable Operations
,”
ASME J. Mech. Des.
,
139
(
11
), p.
111419
.
17.
Murphy
,
K.
,
2012
,
Machine Learning: A Probabilistic Perspective
,
1st ed.
,
The MIT Press
, Cambridge, MA.
18.
Ghalyan
,
N. F.
,
Miller
,
D. J.
, and
Ray
,
A.
,
2018
, “
A Locally Optimal Algorithm for Estimating a Generating Partition From an Observed Time Series and Its Application to Anomaly Detection
,”
Neural Comput.
,
30
(
9
), pp.
2500
2529
.
19.
McDonough
,
R. N.
, and
Whalen
,
A. D.
,
1995
,
Detection of Signals in Noise
,
2nd ed.
,
Academic Press
, Boston, MA.
20.
Rigas
,
G.
,
Jamieson
,
N.
,
Li
,
L.
, and
Juniper
,
M.
,
2016
, “
Experimental Sensitivity Analysis and Control of Thermoacoustic Systems
,”
J. Fluid Mech.
,
787
, p. R1.
21.
Jamieson
,
N. P.
,
Rigas
,
G.
, and
Juniper
,
M. P.
,
2017
, “
Experimental Sensitivity Analysis Via a Secondary Heat Source in an Oscillating Thermoacoustic System
,”
Int. J. Spray Combust. Dyn.
,
9
(
4
), pp.
230
240
.
You do not currently have access to this content.