Symbolization of dynamic data-driven systems for signal representation

Abstract

The underlying theory of symbolic time series analysis (STSA) has led to the development of signal representation tools in the paradigm of dynamic data-driven application systems (DDDAS), where time series of sensor signals are partitioned to obtain symbol strings that, in turn, lead to the construction of probabilistic finite state automata (PFSA). Although various methods for construction of PFSA from symbol strings have been reported in literature, similar efforts have not been expended on identification of an appropriate alphabet size for partitioning of time series, so that the symbol strings can be optimally or suboptimally generated in a specified sense. The paper addresses this critical issue and proposes an information-theoretic procedure for partitioning of time series to extract low-dimensional features, where the key idea is suboptimal identification of boundary locations of the partitioning segments via maximization of the mutual information between the state probability vector of PFSA and the members of the pattern classes. Robustness of the symbolization process has also been addressed. The proposed alphabet size selection and time series partitioning algorithm have been validated by two examples. The first example addresses parameter identification in a simulated Duffing system with sinusoidal input excitation. The second example is built upon an ensemble of time series of chemiluminescence data to predict lean blowout (LBO) phenomena in a laboratory-scale swirl-stabilized combustor apparatus.