Symbolic recurrence for the analysis of thermoacoustic instability

Thermoacoustic instability in gas turbine engines is caused by the interaction of unsteady heat release and the acoustic field. Recurrence plots (RPs) provide a versatile framework for the time-series analysis of thermoacoustic instability. In this work, the sensitivity of recurrence analysis (RA) to the threshold parameter ( ϵ ) is examined, demonstrating that different ϵ threshold values generate different recurrence structures, which can complicate the characterization of combustion dynamics. The onset and extent of changes in dynamics are shown to be sensitive to the choice of ϵ - threshold value. To address the challenges associated with ϵ threshold selection, this work presents a proof-of-concept application of symbolic recurrence analysis (SRA), a qualitative trend based and ϵ independent approach, for the analysis of thermoacoustic instability. Using two representative operating conditions exhibiting intermittent changes in dynamics, the proposed framework illustrates that SRA can effectively analyze the dynamics without requiring ϵ threshold. The results suggest that symbolic recurrence plots (SRPs) provide a robust, ϵ independent complement to conventional recurrence analysis for thermoacoustic diagnostics. Furthermore, this proof-of-concept establishes a framework for relating symbolic recurrence patterns to physically interpretable flame behavior, offering a basis for linking time-series diagnostics with spatial flame dynamics. Novelty and significance statement Recurrence analysis (RA) is a widely used tool to analyze the different dynamics regimes and to characterize the temporal behavior of thermoacoustic instability. However, different threshold values ( ϵ ) result in different structures in the recurrence plot, leading to difficulties in the interpretation of the temporal dynamics of the system. The onset and extent of the changes in dynamics are very sensitive to the selection of threshold values ( ϵ ). There is no unique quantitative method for selecting the appropriate threshold values ( ϵ ) and the requirement of subjective selection of the ϵ threshold parameter introduces user dependence. ϵ threshold independent frameworks have not been systematically explored for thermoacoustic applications in TARS nozzle. Symbolic recurrence analysis (SRA), which is a ϵ -threshold parameter free framework and complements the recurrence analysis, is presented to demonstrate its capability to characterize instability dynamics in TARS configuration without the ϵ threshold selection ambiguity inherent to conventional recurrence analysis. Qualitative and quantitative comparison of recurrence and symbolic recurrence analysis is demonstrated. A framework is proposed that establishes a direct connection between symbolic recurrence patterns and physically interpretable flame behavior, offering a new avenue for linking time-series diagnostics with spatial flame dynamics. This work demonstrates symbolic recurrence as a robust and powerful tool for effectively distinguishing and understanding the characteristics of dynamics regimes in thermoacoustic instability.