Thresholdless Classification of chaotic dynamics and combustion instability via probabilistic finite state automata. (1st February 2022) - Bhattacharya, Chandrachur; Ray, Asok
Abstract: 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. Highlights: Extension of standard PFSA using geometric properties of state transition matrices Performance of the proposed p-PFSA validated on data generated from chaotic systems Method used for the real-life problem of combustion instability detection p-PFSA compares well to methods like HMMs and NNs in accuracy/time complexity