A Gaussian-process-based framework for high-dimensional uncertainty quantification analysis in thermoacoustic instability predictions

Abstract

When combining a flame model with acoustic tools to predict thermoacoustic instability, uncertainties embedded in the flame model and acoustic system parameters propagate through the thermoacoustic model, inducing variations in calculation results. Therefore, uncertainty quantification (UQ) analysis is essential for delivering a reliable prediction of thermoacoustic instability. The present paper proposes a general, surrogate-based framework to efficiently perform UQ analysis in thermoacoustic instability predictions that (1) can handle large variational ranges and flexible statistical descriptions of the uncertain parameters, (2) takes into account uncertainties from both acoustic system parameters and high-dimensional flame response models (e.g. the finite impulse response model (FIR), the flame describing function (FDF), etc.), (3) quantifies uncertainties in modal frequency and linear growth rate for linear thermoacoustic analysis, or (4) quantifies uncertainties in limit cycle frequency and amplitude for nonlinear thermoacoustic analysis. The framework is built upon Gaussian process (GP) surrogate models. An active learning strategy from the machine learning community has been adopted to significantly enhance the efficiency of GP model training, thus achieving a significant reduction in computational cost. The effectiveness of the proposed UQ framework is demonstrated by two case studies: one linear case with an uncertain FIR model and acoustic system parameters, and one nonlinear case with an uncertain FDF dataset and acoustic system parameters. Compared with reference Monte Carlo simulations, the case studies reveal UQ analyses that are, respectively, 20 and 15 times faster, but nevertheless highly accurate. The proposed GP-based framework also forms an efficient foundation on which to address other types of studies, in which repetitive thermoacoustic calculations are required, such as parametric investigations, sensitivity analyses, nonlinear bifurcation studies and robust design.