Thresholdless Classification of chaotic dynamics and combustion instability via probabilistic finite state automata

The objective of the work reported in this paper is to make decisions on the current state of a dynamical system for pattern classification and anomaly/fault detection, which is often achieved by time series analyses of pertinent measured signals. In this context, one of the most commonly used methods is hidden Markov model (HMM), while yet another popular method is neural networks (NN) in their various configurations; however, both of these methods may require large training data and computational time. An alternative feasible method is probabilistic finite state automata (PFSA), which is much faster for training and also for testing. In its current state-of-the-art, the standard PFSA, called s-PFSA, has certain shortcomings that this paper attempts to remedy. Therefore, s-PFSA is modified into the proposed projection-based PFSA, abbreviated as p-PFSA, to yield better classification accuracy and robustness. Efficacy of p-PFSA is first demonstrated on four different models of chaotic dynamical systems by comparison with s-PFSA, HMM and NN, which are used to serve as baseline methods for validation of classification performance; the NN models consist of two vanilla NNs and another NN with long short term memory (LSTM). Then, these results of comparison are extended to assess the relative performance of p-PFSA for a real-life application in terms of accuracy, robustness, and computational complexity on a laboratory-scale apparatus that emulates the essential characteristics of industrial-scale combustion systems.