Measurement of behavioral uncertainties in mechanical vibration systems: A symbolic dynamics approach

Shalabh Gupta, Dheeraj Singh, Abhishek Srivastav, Asok Ray

    Research output: Chapter in Book/Report/Conference proceedingChapter

    1 Citation (Scopus)

    Abstract

    Maturity of engineering and scientific theories in recent decades has facilitated creation of advanced technology of human-engineered complex (e.g., electro-mechanical, transportation, and power generation) systems. A vast majority of these systems are often subjected to mechanical vibration. A possible consequence is performance degradation and structural damage that may eventually lead to widespread catastrophic failures. This chapter presents a recently reported technique of data-driven pattern recognition, called Symbolic Dynamic Filtering (SDF), for online detection of slowly evolving anomalies (i.e., deviation from the nominal characteristics) and the associated behaviorial uncertainties. The underlying concept of SDF is built upon the principles of Statistical Mechanics, Symbolic Dynamics and Information Theory, where time series data from selected sensor(s) in the fast time scale of the process dynamics are analyzed at discrete epochs in the slow time scale of anomaly evolution. Symbolic dynamic filtering includes preprocessing of time series data using the Hilbert transform. The transformed data is partitioned using the maximum entropy principle to generate the symbol sequences, such that the regions of the data space with more information are partitioned finer and those with sparse information are partitioned coarser. Subsequently, statistical patterns of evolving anomalies are identified from these symbolic sequences through construction of a (probabilistic) finite-state machine that captures the system behavior by means of information compression. The concept of SDF has been experimentally validated on a special-purpose computer-controlled multi-degree of freedom mechanical vibration apparatus that is instrumented with two accelerometers for identification of anomalous patterns due to parametric changes.

    Original languageEnglish (US)
    Title of host publicationMechanical Vibrations
    Subtitle of host publicationMeasurement, Effects and Control
    PublisherNova Science Publishers, Inc.
    Pages331-357
    Number of pages27
    ISBN (Electronic)9781614702313
    ISBN (Print)9781606920367
    StatePublished - Jan 1 2009

    Fingerprint

    Time series
    Statistical mechanics
    Information theory
    Finite automata
    Accelerometers
    Pattern recognition
    Power generation
    Uncertainty
    Entropy
    Degradation
    Sensors

    All Science Journal Classification (ASJC) codes

    • Engineering(all)

    Cite this

    Gupta, S., Singh, D., Srivastav, A., & Ray, A. (2009). Measurement of behavioral uncertainties in mechanical vibration systems: A symbolic dynamics approach. In Mechanical Vibrations: Measurement, Effects and Control (pp. 331-357). Nova Science Publishers, Inc..
    Gupta, Shalabh ; Singh, Dheeraj ; Srivastav, Abhishek ; Ray, Asok. / Measurement of behavioral uncertainties in mechanical vibration systems : A symbolic dynamics approach. Mechanical Vibrations: Measurement, Effects and Control. Nova Science Publishers, Inc., 2009. pp. 331-357
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    Gupta, S, Singh, D, Srivastav, A & Ray, A 2009, Measurement of behavioral uncertainties in mechanical vibration systems: A symbolic dynamics approach. in Mechanical Vibrations: Measurement, Effects and Control. Nova Science Publishers, Inc., pp. 331-357.

    Measurement of behavioral uncertainties in mechanical vibration systems : A symbolic dynamics approach. / Gupta, Shalabh; Singh, Dheeraj; Srivastav, Abhishek; Ray, Asok.

    Mechanical Vibrations: Measurement, Effects and Control. Nova Science Publishers, Inc., 2009. p. 331-357.

    Research output: Chapter in Book/Report/Conference proceedingChapter

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    Gupta S, Singh D, Srivastav A, Ray A. Measurement of behavioral uncertainties in mechanical vibration systems: A symbolic dynamics approach. In Mechanical Vibrations: Measurement, Effects and Control. Nova Science Publishers, Inc. 2009. p. 331-357