Depth estimation in Markov models of time-series data via spectral analysis

Devesh K. Jha, Abhishek Srivastav, Kushal Mukherjee, Asok Ray

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

Symbol sequences are generated from observed time series data to construct probabilistic finite state automata (PFSA) models that capture the evolution of the dynamical system under consideration. One of the key challenges here is to estimate the relevant history or depth (i.e., the size of temporal memory) of the symbol sequences; in this context, spectral decomposition of the one-step transition matrix has been recently proposed for depth estimation. This paper compares the performance of depth estimation by spectral analysis with that of other commonly used metrics (e.g., log-likelihood, entropy rate and signal reconstruction) for analysis of symbolic dynamic systems. For experimental validation of the proposed concept, time-series data of fatigue damage evolution in a polycrystalline alloy, collected on a laboratory apparatus, have been discretized to generate symbol sequences. The depths, estimated by the spectral decomposition method, are then compared with those obtained by other metrics, and the results are found to be in close agreement. Furthermore, unsupervised clustering of time-series data, obtained for a number of test specimens in the fatigue-test experiments, demonstrates the efficacy of the proposed depth estimation method as well as the accuracy of depth estimation via spectral analysis and PFSA model construction.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5812-5817
Number of pages6
ISBN (Electronic)9781479986842
DOIs
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
Volume2015-July
ISSN (Print)0743-1619

Other

Other2015 American Control Conference, ACC 2015
CountryUnited States
CityChicago
Period7/1/157/3/15

Fingerprint

Spectrum analysis
Time series
Finite automata
Dynamical systems
Decomposition
Signal reconstruction
Fatigue damage
Entropy
Fatigue of materials
Data storage equipment
Experiments

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Jha, D. K., Srivastav, A., Mukherjee, K., & Ray, A. (2015). Depth estimation in Markov models of time-series data via spectral analysis. In ACC 2015 - 2015 American Control Conference (pp. 5812-5817). [7172250] (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7172250
Jha, Devesh K. ; Srivastav, Abhishek ; Mukherjee, Kushal ; Ray, Asok. / Depth estimation in Markov models of time-series data via spectral analysis. ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 5812-5817 (Proceedings of the American Control Conference).
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Jha, DK, Srivastav, A, Mukherjee, K & Ray, A 2015, Depth estimation in Markov models of time-series data via spectral analysis. in ACC 2015 - 2015 American Control Conference., 7172250, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 5812-5817, 2015 American Control Conference, ACC 2015, Chicago, United States, 7/1/15. https://doi.org/10.1109/ACC.2015.7172250

Depth estimation in Markov models of time-series data via spectral analysis. / Jha, Devesh K.; Srivastav, Abhishek; Mukherjee, Kushal; Ray, Asok.

ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 5812-5817 7172250 (Proceedings of the American Control Conference; Vol. 2015-July).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Jha DK, Srivastav A, Mukherjee K, Ray A. Depth estimation in Markov models of time-series data via spectral analysis. In ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc. 2015. p. 5812-5817. 7172250. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2015.7172250