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Technical Brief

Detection of Thermoacoustic Instabilities Via Nonparametric Bayesian Markov Modeling of Time-Series Data

[+] Author and Article Information
Sihan Xiong

Mechanical Engineering Department,
Pennsylvania State University,
University Park, PA 16802-1412
e-mail: sux101@psu.edu

Sudeepta Mondal

Mechanical Engineering Department,
Pennsylvania State University,
University Park, PA 16802-1412
e-mail: sbm5423@psu.edu

Asok Ray

Fellow ASME
Mechanical Engineering Department,
Pennsylvania State University,
University Park, PA 16802-1412
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 March 15, 2017; final manuscript received June 29, 2017; published online September 20, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 140(2), 024501 (Sep 20, 2017) (7 pages) Paper No: DS-17-1153; doi: 10.1115/1.4037288 History: Received March 15, 2017; Revised June 29, 2017

Real-time detection and decision and control of thermoacoustic instabilities in confined combustors are challenging tasks due to the fast dynamics of the underlying physical process. The objective here is to develop a dynamic data-driven algorithm for detecting the onset of instabilities with short-length time-series data, acquired by available sensors (e.g., pressure and chemiluminescence), which will provide sufficient lead time for active decision and control. To this end, this paper proposes a Bayesian nonparametric method of Markov modeling for real-time detection of thermoacoustic instabilities in gas turbine engines; the underlying algorithms are formulated in the symbolic domain and the resulting patterns are constructed from symbolized pressure measurements as probabilistic finite state automata (PFSA). These PFSA models are built upon the framework of a (low-order) finite-memory Markov model, called the D-Markov machine, where a Bayesian nonparametric structure is adopted for: (i) automated selection of parameters in D-Markov machines and (ii) online sequential testing to provide dynamic data-driven and coherent statistical analyses of combustion instability phenomena without solely relying on computationally intensive (physics-based) models of combustion dynamics. The proposed method has been validated on an ensemble of pressure time series from a laboratory-scale combustion apparatus. The results of instability prediction have been compared with those of other existing techniques.

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Figures

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Fig. 1

Graphical representation of the Bayes network: xj={xj,t}t=D+1T; y={yt}t=D+1T; and zj={zj,t}t=D+1T. Rectangle ≡ deterministic hyperparameter; shaded ellipse ≡ observed random variable; and transparent ellipse ≡ unobserved random variable.

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Fig. 2

Schematic diagram of the combustion apparatus

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Fig. 3

Profile of the average mutual information

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Fig. 4

MCMC results for histograms of pressure measurements under stable operation: (a) histogram of the maximal order (i.e., depth D), (b) inclusion proportions of different lags, (c) histogram of the number of clusters of the tensor λs1,…,sD, and (d) histogram of combinations of realizations (s1,… , sD)

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Fig. 5

MCMC results for histograms of pressure measurements under unstable operation: (a) histogram of the maximal order (i.e., depth D), (b) inclusion proportions of different lags, (c) histogram of the number of clusters of the tensor λs1,…,sD, and (d) histogram of combinations of realizations (s1,… , sD)

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Fig. 6

Posterior probabilities for an unstable test sequence

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Fig. 7

ROC curves with different test data lengths

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Fig. 8

ROC curves with test data length = 20

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