TY - JOUR
T1 - Symbolic time series analysis for anomaly detection in measure-invariant ergodic systems
AU - Ghalyan, Najah F.
AU - Ray, Asok
N1 - Funding Information:
The first author would like to thank the Higher Committee for Education Development (HCED) in Iraq for their financial support. The work reported in this paper has been supported in part by U.S. Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-15-1-0400 in the area of dynamic data-driven application systems (DDDAS). Any opinions, findings, and conclusions in this paper are those of the authors and do not necessarily reflect the views of the sponsoring agencies. Higher Committee for Education Development (HCED) (Funder ID: 10.13039/501100009928). U.S. Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-15-1-0400; Funder ID: 10.13039/100000181).
Publisher Copyright:
Copyright © 2020 by ASME
PY - 2020/6
Y1 - 2020/6
N2 - This paper presents a novel framework of symbolic time series analysis (STSA) for anomaly detection in dynamical systems. The core concept is built upon a property of measure-preserving transformation (MPT) sequence, acting on a probability space with ergodic measure, that the eigenfunctions of these transformations would be time-invariant. As a result, unlike a standard STSA that is required to generate time-homogeneous Markov chains, the proposed MPT-based STSA is allowed to have time-inhomogeneous Markov chains, where the (possibly time-varying) state transition probability matrices have time-invariant eigenvectors. Such a time-invariance facilitates analysis of the dynamical system by using short-length time series of measurements. This is particularly important in applications, where the underlying dynamics and process anomalies need fast monitoring and control actions in order to mitigate any potential structural damage and/or to avoid catastrophic failures. The MPT-based STSA has been applied for low-delay detection of fatigue damage, which is a common source of failures in mechanical structures and which is known to have uncertain dynamical characteristics. The underlying algorithm has been validated with experimental data generated from a laboratory apparatus that uses ultrasonic sensors to detect fatigue damage in polycrystalline-alloy specimens. The performance of the proposed MPT-based STSA is evaluated by comparison with those of a standard STSA and a hidden Markov model (HMM) on the same experimental data. The results consistently show superior performance of the MPT-based STSA.
AB - This paper presents a novel framework of symbolic time series analysis (STSA) for anomaly detection in dynamical systems. The core concept is built upon a property of measure-preserving transformation (MPT) sequence, acting on a probability space with ergodic measure, that the eigenfunctions of these transformations would be time-invariant. As a result, unlike a standard STSA that is required to generate time-homogeneous Markov chains, the proposed MPT-based STSA is allowed to have time-inhomogeneous Markov chains, where the (possibly time-varying) state transition probability matrices have time-invariant eigenvectors. Such a time-invariance facilitates analysis of the dynamical system by using short-length time series of measurements. This is particularly important in applications, where the underlying dynamics and process anomalies need fast monitoring and control actions in order to mitigate any potential structural damage and/or to avoid catastrophic failures. The MPT-based STSA has been applied for low-delay detection of fatigue damage, which is a common source of failures in mechanical structures and which is known to have uncertain dynamical characteristics. The underlying algorithm has been validated with experimental data generated from a laboratory apparatus that uses ultrasonic sensors to detect fatigue damage in polycrystalline-alloy specimens. The performance of the proposed MPT-based STSA is evaluated by comparison with those of a standard STSA and a hidden Markov model (HMM) on the same experimental data. The results consistently show superior performance of the MPT-based STSA.
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U2 - 10.1115/1.4046156
DO - 10.1115/1.4046156
M3 - Article
AN - SCOPUS:85091295740
VL - 142
JO - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME
JF - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME
SN - 0022-0434
IS - 6
M1 - 142-6_A3_03
ER -