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Lean combustion is increasingly employed in both ground-based gas turbines and aircraft engines for minimizing NOx emissions. Operating under lean conditions increases the risk of Lean Blowout (LBO). Thus LBO proximity sensors, combined with appropriate blowout prevention systems, have the potential to improve the performance of engines. In previous studies, atmospheric pressure, swirl flames near LBO have been observed to exhibit partial extinction and re-ignition events called LBO precursors. Detecting these precursor events in optical and acoustic signals with simple non-intrusive sensors provided a measure of LBO proximity. This thesis examines robust LBO margin sensing approaches, by exploring LBO precursors in the presence of combustion dynamics and for combustor operating conditions that are more representative of practical combustors, i.e., elevated pressure and preheat temperature operation. To this end, two combustors were used: a gas-fueled, atmospheric pressure combustor that exhibits pronounced combustion dynamics under a wide range of lean conditions, and a low NOx emission liquid-fueled lean direct injection (LDI) combustor, operating at elevated pressure and preheat temperature. In the gas-fueled combustor, flame extinction and re-ignition LBO precursor events were observed in the presence of strong combustion dynamics, and were similar to those observed in dynamically stable conditions. However, the signature of the events in the raw optical signals have different characteristics under various operating conditions. Low-pass filtering and a single threshold-based event detection algorithm provided robust precursor sensing, regardless of the type or level of dynamic instability. The same algorithm provides robust event detection in the LDI combustor, which also exhibits low level dynamic oscillations. Compared to the gas-fueled combustor, the LDI events have weaker signatures, much shorter durations, but considerably higher occurrence rates. The disparity in precursor durations is due to a flame mode switch that occurs during precursors in the gas-fueled combustor, which is absent in the LDI combustor. Acoustic sensing was also investigated in both the combustors. Low-pass filtering is required to reveal a precursor signature under dynamically unstable conditions in the gas-fueled combustor. On the other hand in the LDI combustor, neither the raw signals nor the low-pass filtered signals reveal precursor events. The failure of acoustic sensing is attributed in part to the lower heat release variations, and the similarity in time scales for the precursors and dynamic oscillations in the LDI combustor. In addition, the impact of acoustic reflections from combustor boundaries and transducer placement was addressed by modeling reflections in a one-dimensional combustor geometry with an impedance jump caused by the flame. Implementing LBO margin sensors in gas turbine engines can potentially improve time response during deceleration transients by allowing lower operating margins. Occurrence of precursor events under transient operating conditions was examined with a statistical approach. For example, the rate at which the fuel-air ratio can be safely reduced might be limited by the requirement that at least one precursor occurs before blowout. The statistics governing the probability of a precursor event occurring during some time interval was shown to be reasonably modeled by Poisson statistics. A method has been developed to select a lower operating margin when LBO proximity sensors are employed, such that the lowered margin case provides a similar reliability in preventing LBO as the standard approach utilizing a more restrictive operating margin. Illustrative improvements in transient response and reliabilities in preventing LBO are presented for a model turbofan engine. In addition, an event-based, active LBO control approach for deceleration transients is also demonstrated in the engine simulation.