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Technical Brief

Hidden Markov Modeling-Based Decision-Making Using Short-Length Sensor Time Series

[+] Author and Article Information
Najah F. Ghalyan

Department of Mechanical Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: nfg103@psu.edu

Sudeepta Mondal

Department of Mechanical Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: sbm5423@psu.edu

David J. Miller

Professor
Department of Electrical Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: djmiller@engr.psu.edu

Asok Ray

Distinguished Professor
Fellow ASME
Department of Mechanical Engineering and Mathematics,
The Pennsylvania State University,
University Park, PA 16802
e-mail: axr2@psu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received October 11, 2018; final manuscript received March 28, 2019; published online May 8, 2019. Assoc. Editor: Youngsu Cha.

J. Dyn. Sys., Meas., Control 141(10), 104502 (May 08, 2019) (6 pages) Paper No: DS-18-1459; doi: 10.1115/1.4043428 History: Received October 11, 2018; Revised March 28, 2019

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.

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Figures

Grahic Jump Location
Fig. 1

The electrically heated Rijke tube apparatus

Grahic Jump Location
Fig. 2

Unsteady pressure signals showing the transience from stable (nominal) to unstable limit cycle (anomalous) behavior: (a) Ein abruptly increased to 1800 W with Q =210 LPM and (b) Ein abruptly increased to 2000 W with Q =250 LPM

Grahic Jump Location
Fig. 3

ROC curves for combustion instability detection having |A|=2, D =2, and L =200

Grahic Jump Location
Fig. 4

ROC curves for combustion instability detection having |A|=2, D =2, and L =50

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Fig. 5

ROC curves for combustion instability detection having |A|=2, D =3, and L =50

Grahic Jump Location
Fig. 6

ROC curves for combustion instability detection having |A|=2, D =4, and L =50

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