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

Abstract

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.