An Auto-Framing Method for Stochastic Process Signal by using a Hidden Markov Model based Approach

다국어 초록 (Multilingual Abstract)

In this paper, an “auto-framing” method, an algorithmic method to divide stochastic time-series process data into appropriate intervals, is developed based on the approach of hidden Markov model (HMM). While enormous amounts of process time-series data are being measured and collected today, their use is limited by the high costs to gather, store, and analyze them. “Data-framing” refers to the task of dividing stochastic signal data into time frames of distinct patterns so that the data can be stored and analyzed in an efficient manner. Data-framing is typically carried out manually, but doing so can be both laborious and ineffective. For the purpose of automating the data-framing task, stochastic signals of switching patterns are modeled using a hidden Markov model (HMM) based jump linear system (JLS), which switches the stochastic model probabilistically in accordance with the underlying Markov chain. Based on the model, an estimator is constructed to estimate from the collected signal data the state sequence of the underlying Markov chain, which is subsequently used to decide on the framing points. An Expectation Maximization (EM) algorithm, which is composed of two optimal estimators, fixed interval Kalman smoother and Viterbi algorithm, is used to estimate for the state estimation. We demonstrate the effectiveness of the HMM-based approach for auto-framing using simulated data constructed based on real industrial data.

참고문헌 (Reference)

1 J. H. Hu, "Research on signal framing for frame number optimization in automotive embedded networked control system" 4748-4753, 2009

2 W. C. Wong, "Realistic disturbance modeling using hidden Markov models : applications in model-based process control" 19 (19): 1438-1450, 2009

3 G. M. de Almeida, "Process monitoring in chemical industries - a hidden Markov model approach" 2008

4 T. -J. Ho, "Novel extended Viterbi-based multiple-model algorithms for state estimation of discrete-time systems with Markov jump parameters" 54 (54): 393-404, 2006

5 A. P. Dempster, "Maximum likelihood from incomplete data via the EM algorithm" 39 (39): 1-38, 1977

6 E. Mazor, "Interacting multiple model methods in target tracking : a survey" 34 (34): 103-123, 1998

7 B. Juang, "Hidden Markov models for speech recognition" 33 (33): 251-272, 1991

8 A. Logothetis, "Expectation maximization algorithms for MAP estimation of jump Markov linear systems" 47 (47): 2139-2156, 1999

9 Y. Bar-Shalom, "Estimation and Tracking: Principles, Techniques, and Software" Artech House 1993

10 A. Viterbi, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm" 13 (13): 260-269, 1967

11 O. Costa, "Discrete-time Markov Jump Linear Systems(Probability and Its Applications)" Springer 2004

12 J. Tugnait, "Comments on an approximation coefficient proposed in ‘stochastic model simplification" 27 (27): 1002-1004, 1982

13 S. Jaisimha, "Bandwidth extension of narrow band speech using cepstral linear prediction" 3 : 1404-1407, 2003

14 U. Orguner, "Analysis of single Gaussian approximation of Gaussian mixtures in Bayesian filtering applied to mixed multiple-model estimation" 80 (80): 9520967-, 2007

15 S. E. Levinson, "An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition" 62 (62): 1035-1074, 1983

16 L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition" 257-286, 1989

17 W. Liu, "A novel suboptimal algorithm for state estimation of Markov jump linear systems" 9 (9): 148-154, 2011