Symbolic dynamic filtering (SDF) has been recently reported in literature as a pattern recognition tool for early detection of anomalies (i.e., deviations from the nominal behavior) in complex dynamical systems. Accurate and computationally tractable modeling of such complex system dynamics, solely based on fundamentals of physics, is often infeasible. Hence, it might be necessary to learn the behavior of the system through times series data obtained from sensors. Symbolic dynamics provide a useful tool for time series analysis. Symbolic dynamics attempts to model a continuous time signal by a corresponding symbolized sequence.;This dissertation presents a review of SDF and its performance evaluation relative to other classes of pattern recognition tools, such as Bayesian Filters and Artificial Neural Networks, from the perspectives of: (i) anomaly detection capability, (ii) decision making for failure mitigation and (iii) computational efficiency. The evaluation is based on analysis of time series data generated from a nonlinear active electronic system.;This dissertation also addresses statistical estimation of multiple parameters that may vary simultaneously but slowly relative to the process response in nonlinear dynamical systems. The estimation algorithm is sensor-data-driven and is built upon this concept of SDF for real-time execution on limited-memory platforms, such as local nodes in a sensor network. In this approach, the behavior patterns of the dynamical system are compactly generated as quasi-stationary probability vectors associated with the probabilistic finite-state automata in the symbolic dynamic setting. The estimation algorithm is validated on nonlinear electronic circuits that represent externally excited Duffing and unforced van der Pol systems. It is also evaluated on the NASA C-MAPSS model of an aircraft engine and the simulation of a permanent magnet synchronous motor. Confidence intervals are obtained for statistical estimation of two parameters in these systems.;A framework is also presented for sensor-information fusion. In a complex system such as an aircraft gas-turbine engine, the patterns generated from a single sensor may not carry sufficient information to identify multiple parameters/faults because different combinations of component faults may generate similar signatures in a particular sensor observation. Low dimensional pattern vectors are identified for the purpose of feature level sensor fusion. The current framework attempts to fuse information from different sensors at the feature level as opposed to the frameworks of data level or decision level fusion.
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