Sequential hypothesis tests for streaming data via symbolic time-series analysis

This paper addresses sequential hypothesis testing for Markov models of time-series data by using the concepts of symbolic dynamics. These models are inferred by discretizing the measurement space of a dynamical system, where the system dynamics are approximated as a finite-memory Markov chain on the discrete state space. The study is motivated by time-critical detection problems in physical processes, where a temporal model is trained to make fast and reliable decisions with streaming data. Sequential update rules have been constructed for log-posterior ratio statistic of Markov models in the setting of binary hypothesis testing and the stochastic evolution of this statistic is analyzed. The proposed technique allows selection of a lower bound on the performance of the detector and guarantees that the test will terminate in finite time. The underlying algorithms are first illustrated through an example by numerical simulation, and are subsequently validated on time-series data of pressure oscillations from a laboratory-scale swirl-stabilized combustor apparatus to detect the onset of thermo-acoustic instability. The performance of the proposed sequential hypothesis tests for Markov models has been compared with that of a maximum-likelihood classifier with fixed sample size (i.e., sequence length). It is shown that the proposed method yields reliable detection of combustion instabilities with fewer observations in comparison to a fixed-sample-size test.