The present study aims at arming an operator of fielded turbulent combustors with a repertoire of mathematical measures for real-time monitoring to forewarn the onset of impending combustion instability. In turbulent combustors, the route to high-amplitude, periodic, combustion-driven oscillations from conditions of low-amplitude, chaotic, combustion noise happens through an intermediate regime in flow conditions where the measured pressure fluctuations display bursts of intermittent, high-amplitude, periodic oscillations that appear in a near-random manner amidst chaotic fluctuations. This loss of chaos from combustion noise to combustion instability can be quantified to serve as a precursor to impending instability. The recurrence properties of intermittent burst oscillations can be quantified using dynamical systems theory by tracking the distribution of the aperiodic segments in the measured signals. Several statistical measures may be constructed through such recurrence quantification that provide robust early warning signals to an impending instability. Further, the transition to combustion driven oscillations leads to a collapse of the number of relevant time scales involved in the problem. This collapse in time scales can be quantified using generalized Hurst exponents which serve as an additional measure that captures the onset of an impending combustion instability well in advance. The various patent pending measures illustrated in this paper serve as precursors due to the inevitable presence of an intermittent regime of burst oscillations in turbulent combustors.

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