Robust identification of flame frequency response via multi-fidelity Gaussian process approach

Accurate, robust, and efficient identification of flame frequency response (FFR) plays a crucial role in thermoacoustic instability prediction, analysis and control. In order to extract the FFR from high-fidelity numerical simulation time series data, two methods are currently used in the community, which are based on harmonic excitation or broadband excitation, respectively. The former can produce quite accurate FFR estimates even in the presence of significant noise, but only at discrete frequencies; the latter method, which combines broadband forcing and system identification techniques, provides the complete FFR over the frequency range of interest, but may introduce increased levels of uncertainties in the identified results. The present study aims to fully exploit the respective strengths, while avoiding the weaknesses of the two aforementioned methods by proposing a multi-fidelity approach that merges FFR identification results from a short time broadband excitation (low-fidelity) and harmonic excitations at a few select frequencies (high-fidelity). The proposed approach is realized via a machine-learning technique called “Multi-fidelity Gaussian Process.” Our case study demonstrates that the proposed multi-fidelity approach can effectively assimilate the global trend provided by the low-fidelity results and local estimates provided by the high-fidelity results, thus leading to a globally accurate and robust FFR identification even in the presence of strong noise. In addition, we investigate the impact of the number and locations of harmonic forcing frequencies on the performance of the proposed approach. Finally, we employ the proposed multi-fidelity framework to identify the FFR of a turbulent premixed swirl burner test rig based on previously published data, which further highlights the capability and flexibility of the proposed approach in real applications.