Measure invariance of ergodic symbolic systems for low-delay detection of anomalous events

• The spectral properties of ergodic measure symbolic systems are investigated for applications to signal processing, pattern recognition, and anomaly detection in real-time uncertain dynamical systems. underlying algorithm is built upon the concept sequences measure-preserving transformations (MPTs) on probability spaces construction non-stationary probabilistic finite state automata (PFSA) by using short-length windows time-series measurements. MPT-based methodology has been validated with experimental data generated from a laboratory apparatus that deals thermoacoustic instabilities combustion processes, which known have chaotic characteristics time scale milliseconds. This paper investigates (MPT) spaces, where constructed resulting PFSA non-homogeneous Markov, MPT depend several parameters include window length. also develops an metric quantify divergence evolving nominal PFSA; this information then used classification low-delay tolerance. In application, concepts ergodicity develop novel series analysis (STSA)-based method, whose performance comparison two well-known techniques, namely, hidden Markov model (HMM) cumulative sum (CUSUM), same data. results consistently show superior proposed STSA.