This paper presents a nonparametric regression model of categorical time series in the setting of conditional tensor factorization and Bayes network. The underlying algorithms are developed to provide a flexible and parsimonious representation for fusion of correlated information from heterogeneous sources, which can be used to improve the performance of prediction tasks and infer the causal relationship between key variables. The proposed method is first illustrated by numerical simulation and then validated with two real-world datasets: (1) experimental data, collected from a swirl-stabilized lean-premixed laboratory-scale combustor, for detection of thermoacoustic instabilities and (2) publicly available economics data for causal inference-making.
Real-time detection and decision and control of thermoacoustic instabilities in confined combustors are challenging tasks due to the fast dynamics of the underlying physical process. The objective here is to develop a dynamic data-driven algorithm for detecting the onset of instabilities with short-length time-series data, acquired by available sensors (e.g., pressure and chemiluminescence), which will provide sufficient lead time for active decision and control. To this end, this paper proposes a Bayesian nonparametric method of Markov modeling for real-time detection of thermoacoustic instabilities in gas turbine engines; the underlying algorithms are formulated in the symbolic domain and the resulting patterns are constructed from symbolized pressure measurements as probabilistic finite state automata (PFSA). These PFSA models are built upon the framework of a (low-order) finite-memory Markov model, called the D-Markov machine, where a Bayesian nonparametric structure is adopted for: (i) automated selection of parameters in D-Markov machines and (ii) online sequential testing to provide dynamic data-driven and coherent statistical analyses of combustion instability phenomena without solely relying on computationally intensive (physics-based) models of combustion dynamics. The proposed method has been validated on an ensemble of pressure time series from a laboratory-scale combustion apparatus. The results of instability prediction have been compared with those of other existing techniques.
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