Pattern identification in dynamical systems via symbolic time series analysis

Abstract

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.

Different Methods of Partitioning the Phase Space of a Dynamic System

“…The selection of optimal is an area of active research. An entropy rate approach has been adopted for selecting the alphabet size [23]. Let h(M (k) ) denote the entropy rate of the transition matrix for iteration k [4].…”

Review and comparative evaluation of symbolic dynamic filtering for detection of anomaly patterns

“…This section presents the underlying concepts and salient features of SDF for anomaly detection in complex dynamical systems. While the details are reported as pieces of information in previous publications [1][2][3][4][5], the essential concepts of space partitioning, symbol generation, and construction of a finite-state machine from the generated symbol sequence are succinctly explained in this section for completeness of this paper.…”

“…Therefore, symbolic sequences as representations of the system dynamics should be generated by alternative methods because phase-space partitioning might prove to be a difficult task in the case of high dimensions and presence of noise. The wavelet transform [25] largely alleviates these shortcomings and is particularly effective with noisy data from highdimensional dynamical systems [4]. A comparison of wavelet partitioning and other partitioning methods, such as SFNN, is reported in recent literature [5], where wavelet partitioning has been shown to yield comparable performance with several orders of magnitude smaller execution time.…”

“…For many human-engineered complex systems, early detection of anomalies with low false alarm rates mitigates the risk of forthcoming failures. Recently, Ray and coworkers [1][2][3][4] have developed a novel pattern identification technique, called symbolic dynamic filtering (SDF). This tool has been used early detection of anomaly patterns in dynamical systems, possibly due to parametric or non-parametric changes.…”

“…(1) A unified review of the underlying theories of SDF based on the work reported in a scattered manner in previous publications [1][2][3][4][5] (2) Comparative evaluation of SDF performance relative to other pattern recognition techniques in terms of:…”