Symbolic time series analysis (STSA) of complex systems for anomaly detection has been recently introduced in literature. An important feature of the STSA method is extraction of relevant information, imbedded in the measured time series data, to generate symbol sequences. This paper presents a wavelet-based partitioning approach for symbol generation, instead of the currently practiced method of phase-space partitioning. Various aspects of the proposed technique, such as wavelet selection, noise mitigation, and robustness to spurious disturbances, are discussed. The waveletbased partitioning in STSA is experimentally validated on laboratory apparatuses for anomaly/damage detection. Its efficacy is investigated by comparison with phase-space partitioning.
This paper presents symbolic time series analysis (STSA) of multi-dimensional measurement data for pattern identification in dynamical systems. The proposed methodology is built upon concepts derived from Information Theory and Automata Theory. The objective is not merely to classify the time series patterns but also to identify the variations therein. To achieve this goal, a symbol alphabet is constructed from raw data through partitioning of the data space. The maximum entropy method of partitioning is extended to multi-dimensional space. The resulting symbol sequences, generated from time series data, are used to model the dynamical information as finite state automata and the patterns are represented by the stationary state probability distributions. A novel procedure for determining the structure of the finite state automata, based on entropy rate, is introduced. The diversity among the observed patterns is quantified by a suitable measure. The efficacy of the STSA technique for pattern identification is demonstrated via laboratory experimentation on nonlinear systems.
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