Skip to main content
SpringerLink
Log in

A variance-estimation-based stopping rule for symbolic dynamic filtering

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

As an alternative to the batch means (BM) method in the stopping rule for symbolic dynamic filtering, this short paper presents an analytical procedure to estimate the variance parameter and to obtain a lower bound on the length of symbol blocks for constructing probabilistic finite state automata (PFSA). If the modulus of the second largest eigenvalue of the PFSA’s state transition matrix is relatively small or if the symbol block length is not too large, then the performance of the proposed stopping rule is superior to that of the stopping rule based on BM method. The algorithm of the proposed stopping rule is validated on ultrasonic data collected from a fatigue test apparatus for damage detection in the polycrystalline alloy 7075-T6.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wen Y., Ray A.: A stopping rule for symbolic dynamic filtering. Appl. Math. Lett. 23, 1125–1128 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ray A.: Symbolic dynamic analysis of complex systems for anomaly detection. Signal Process. 84(7), 1115–1130 (2004)

    Article  MATH  Google Scholar 

  3. Flegal J., Haran M.: Markov chain Monte Carlo: can we trust the third significant figure. Stat. Sci. 23(2), 250–260 (2008)

    Article  MathSciNet  Google Scholar 

  4. Jones G., Haran M., Caffo B., Neath R.: Fixed-width output analysis for Markov chain Monte Carlo. J. Am. Stat. Assoc. 101, 1537–1547 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Flegal, J., Jones, G.: Batch means and spectral variance estimators. In Markov chain Monte Carlo. technical report, University of Minnesota, Department of Statistics (2008)

  6. Berman A., Plemmons R.: Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1997)

    Google Scholar 

  7. Bapat R., Raghavan T.: Nonnegative Matrices and Applications. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  8. Gupta S., Ray A.: Statistical mechanics of complex systems for pattern identification. J. Stat. Phys. 134(2), 337–364 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bhattacharya R., Waymire E.: Stochastic Processes with Applications. Wiley-Interscience, New York (1990)

    Google Scholar 

  10. Garren S.T., Smith R.L.: Estimating the second largest eigenvalue of a Markov transition matrix. Bernoulli 6, 215–242 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rosenthal J.: Convergence rates for Markov chains. Soc. Ind. Appl. Math. J. 37(3), 387–445 (1995)

    MATH  Google Scholar 

  12. Gupta S., Ray A., Keller E.: Symbolic time series analysis of ultrasonic data for early detection of fatigue damage. Mech. Syst. Signal Process. 21(2), 866–884 (2007)

    Article  Google Scholar 

  13. Rajagopalan V., Ray A.: Symbolic time series analysis via wavelet-based partitioning. Signal Process. 86(11), 3309–3320 (2006)

    Article  MATH  Google Scholar 

  14. Schervish M.: p-values: what they are and what they are not. Am Stat. 50, 203–206 (1996)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Yicheng Wen & Asok Ray

  2. Mathematics Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Qiang Du

Authors
  1. Yicheng Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asok Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asok Ray.

Additional information

Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsoring agencies.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wen, Y., Ray, A. & Du, Q. A variance-estimation-based stopping rule for symbolic dynamic filtering. SIViP 7, 189–195 (2013). https://doi.org/10.1007/s11760-011-0215-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-011-0215-y

Keywords

Search

Navigation