Venkatesh Rajagopalan

Symbolic time series analysis for anomaly detection: a comparative evaluation

Recent literature has reported a novel method for anomaly detection in complex dynamical systems, which relies on symbolic time series analysis and is built upon the principles of automata theory and pattern recognition. This paper compares the performance of this symbolic-dynamics-based method with that of other existing pattern recognition techniques from the perspectives of early detection of small anomalies. Time series data of observed process variables on the fast time-scale of dynamical systems are analyzed at slow time-scale epochs of (possible) anomalies. The results are derived from experiments on a nonlinear electronic system with a slowly varying dissipation parameter.

Pattern identification in dynamical systems via symbolic time series analysis

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.

Estimation of slowly varying parameters in nonlinear systems via symbolic dynamic filtering

This paper introduces a novel method for real-time estimation of slowly varying parameters in nonlinear dynamical systems. The core concept is built upon the principles of symbolic dynamic filtering (SDF) that has been reported in literature for anomaly detection in complex systems. In this method, relevant system outputs are measured, at different values of a critical system parameter, to generate an ensemble of time series data. The space of wavelet-transform coefficients of time series data is partitioned to generate symbol sequences that, in turn, are used to construct a special class of probabilistic finite state automata (PFSA), called the D-Markov machine. The parameter is estimated based on the statistical information derived from the PFSA. The bounds and statistical confidence levels, associated with parameter estimation, are also computed. The proposed method has been validated in real time for two nonlinear electronic systems, governed by Duffing equation and van der Pol equation, on a laboratory apparatus.

Wavelet-based Space Partitioning for Symbolic Time Series Analysis

Recent literature has reported symbolic time series analysis of complex systems for real-time anomaly detection. A crucial aspect in this analysis is symbol sequence generation from the observed time series data. This paper presents a wavelet-based partitioning, instead of the currently practiced method of phase-space partitioning, for symbol generation. The partitioning algorithm makes use of the maximum entropy method. The wavelet-space and phase-space partitioning methods are compared with regard to anomaly detection using experimental data.

Wavelet Space Partitioning for Symbolic Time Series Analysis

A crucial step in symbolic time series analysis (STSA) of observed data is symbol sequence generation that relies on partitioning the phase-space of the underlying dynamical system. We present a novel partitioning method, called wavelet-space (WS) partitioning, as an alternative to symbolic false nearest neighbour (SFNN) partitioning. While the WS and SFNN partitioning methods have been demonstrated to yield comparable performance for anomaly detection on laboratory apparatuses, computation of WS partitioning is several orders of magnitude faster than that of the SFNN partitioning.

Failure precursor detection in complex electrical systems using symbolic dynamics

Failures in a plants electrical components are a major source of performance degradation and plant unavailability. In order to detect and monitor failure precursors and anomalies early in electrical systems, we have developed a signal processing method that can detect and map patterns to an anomaly measure. Application of this technique for failure precursor detection in electronic circuits resulted in robust detection. This technique was observed to be superior to conventional pattern recognition techniques such as neural networks and principal component analysis for anomaly detection. Moreover, this technique based on symbolic dynamics offers superior robustness due to averaging associated with experimental probability calculations. It also provided a monotonically increasing smooth anomaly plot which was experimentally repeatable to a remarkable accuracy.

Wavelet-based symbolic analysis for detection of broken rotor bars in inverter-fed induction motors

This paper presents a wavelet based symbolic approach for detecting small signature faults. Wavelet transform allows adaptive usage of Windows to extract pertinent information. This is critical for detecting faults whose signatures are significantly smaller compared to dominant frequencies in the signal. Rotor bar breakage, in an inverter-fed induction motor, is considered for validating the effectiveness of the proposed technique

Incipient fault detection in mechanical power transmission systems

This paper presents a novel method for anomaly detection in a helical gear box, where the objective is to predict incipient faults before they become catastrophic. The anomaly detection algorithm relies on symbolic time series analysis and is built upon concepts from automata theory, information theory, and pattern recognition. Early detection of slow time-scale anomalous behavior is achieved by observing time series data at the fast time-scale of machine operation.

Early detection of voltage imbalances in three-phase induction motors

Online monitoring of induction motor health is of increased interest, as the industrial processes that depend on the motors become more complex and as performance to cost ratio of monitoring technology (e.g. sensors, microprocessors) has increased dramatically. Much efforts have been directed towards developing methods that use conventional signal processing and pattern classification techniques. This paper proposes a novel technique for early detection of stator voltage imbalances in three-phase induction motors, which is built upon the theories of wavelet transforms and symbolic time series analysis.

Prognosis of Failure Precursor in Complex Electrical Systems Using Symbolic Dynamics

Failures in a plants electrical components are a major source of performance degradation and plant unavailability. In order to detect and monitor failure precursors and anomalies early in electrical systems, we have developed signal processing capabilities that can detect and map patterns in already existing and available signals to an anomaly measure. Toward this end, the language measure theory based on real analysis, finite state automaton, symbolic dynamics and information theory has been deployed. Application of this theory for electronic circuit failure precursor detection resulted in a robust statistical pattern recognition technique. This technique was observed to be superior to conventional pattern recognition techniques such as neural networks and principal component analysis for anomaly detection because it exploits a common physical fact underling most anomalies which conventional techniques do not. Symbolic dynamic technique resulted in a monotonically increasing smooth anomaly plot which was experimentally repeatable to a remarkable accuracy. For the Van der Pol oscillator circuit board experiment, this lead to consistently accurate predictions for the anomaly parameter and its range.