Combustion instabilities have been a plaguing challenge in lean-conditioned propulsion systems. An open-loop control system was developed using machine learning to suppress pressure fluctuations and NO x emissions simultaneously. The open-loop control is realized by regulating the solenoid valve to modulate the methane supply. Control laws comprising the multi-frequency forcing are generated via the linear genetic programming (LGP), before being converted into square waves with different frequencies and duty cycles to activate the solenoid valve. The cost function is intended to evaluate and rank individuals of each generation, so as to select candidates for evolution. Optimized periodic forcing (OPF) with different duty cycles ( d ) and frequencies ( f P ) is set to provide a comparison with the superiority of multifrequency forcing of LGP. Three stages of pressure oscillations and NO x emissions have been found as d increases from 0.5 to 1.0: high level, transition, and low level, revealing the transition of the combustion mode. After ten generations of development, the pressure amplitude and NO x emissions are reduced by 67.1% and 36.9% under the optimal control law identified by LGP, respectively. The flame structure images and Rayleigh index maps indicate that the convective movement of the flame, which may be the key factor driving combustion instabilities, can be suppressed by the optimal control law. Furthermore, the proximity graph of the similarity between control laws is introduced to depict the machine learning process, with the steepest descent lines visualizing its ridgeline topology. With the evolution process, individuals are found moving closer to the top right-hand corner of the map, and two main search pathways gradually become clear. (c) 2023 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
