Optimizing Thermoacoustic Characterization Experiments for Identifiability Improves Both Parameter Estimation Accuracy and Closed-Loop Controller Robustness Guarantees

ABSTRACT

This article examines the degree to which optimizing a Rijke tube experiment can improve the accuracy of thermoacoustic model parameter estimation, thereby facilitating robust stability control. We use a one-dimensional thermoacoustic model to describe the combustion dynamics in a Rijke tube. This model contains two unknown parameters that relate velocity perturbations to heat release rate oscillations, namely, a time delay $\tau$ and amplification factor $\beta$. The parameters are estimated from experiments where the system input is the acoustic excitation from a loudspeaker and the output is the pressure response captured by a microphone. Our work is grounded in the insight that optimizing an experiment’s design for higher Fisher identifiability leads to more accurate parameter estimates. The novel goal of this paper is to apply this insight in the laboratory using a flame-driven Rijke tube setup. For comparison purposes, we conduct a benchmark experiment with a broadband chirp signal as the excitation input. Next, we excite the Rijke tube at two frequencies optimized for Fisher identifiability. Repeats of both experiments show that the optimal experiment achieves parameter estimates with uncertainties at least one order of magnitude smaller than the benchmark. With smaller parameter estimate uncertainties, an LQG controller designed to attenuate combustion instabilities is able to achieve stronger robustness guarantees, quantified in terms of closed-loop structured singular values that account for parameter estimation uncertainty.

KEYWORDS:

• Optimal experimental design
• Fisher identifiability
• uncertainty quantification
• linear quadratic Gaussian
• robustness guarantees

Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. CMMI-1728307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation [CMMI-1728307].