Symbolic identification and anomaly detection in complex dynamical systems

Symbolic dynamic filtering (SDF) has been reported in recent literature for early detection of anomalies (i.e., deviations from the nominal behavior) in complex dynamical systems. In this context, instead of solely relying on physics- based modeling that may be difficult to formulate and validate, this paper proposes data-driven modeling and system identification based on the concept of symbolic dynamics, automata theory, and information theory. For anomaly detection in inter-connected complex dynamical systems, with or without closed loop control, the input excitation to an individual component is likely to deviate from the nominal condition as a result of deterioration of some other component(s) or to accommodate disturbance rejection by feedback control actions. This paper presents a formal-language-based syntactic method of anomaly detection to account for deviations in the pertinent input excitation. A training algorithm is formulated to generate an automaton model of the underlying subsystem or component from a set of input-output combinations for different classes of inputs, where the objective is to detect (possibly gradually evolving) anomalies under different input conditions. The proposed method has been validated on a test apparatus of nonlinear active electronics.