Prediction of thermoacoustic instabilities is a critical issue for both design and operation of combustion systems. Sustained high-amplitude pressure and temperature oscillations may cause stresses in structural components of the combustor, leading to thermomechanical damage. Therefore, the design of combustion systems must take into account the dynamic characteristics of thermoacoustic instabilities in the combustor. From this perspective, there needs to be a procedure, in the design process, to recognize the operating conditions (or parameters) that could lead to such thermoacoustic instabilities. However, often the available experimental data are limited and may not provide a complete map of the stability region(s) over the entire range of operations. To address this issue, a Bayesian nonparametric method has been adopted in this paper. By making use of limited experimental data, the proposed design method determines a mapping from a set of operating conditions to that of stability regions in the combustion system. This map is designed to be capable of (i) predicting the system response of the combustor at operating conditions at which experimental data are unavailable and (ii) statistically quantifying the uncertainties in the estimated parameters. With the ensemble of information thus gained about the system response at different operating points, the key design parameters of the combustor system can be identified; such a design would be statistically significant for satisfying the system specifications. The proposed method has been validated with experimental data of pressure time-series from a laboratory-scale lean-premixed swirl-stabilized combustor apparatus.

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