Parameter identification and nonlinear growth analysis of time-delay thermoacoustic instabilities in Rijke tubes

The Rijke tube is widely used as an experimental platform for studying thermoacoustic instability. However, environmental changes in the experiment may affect model parameter settings, complicating accurate control design. To tackle this challenge, this paper proposes an ODE-based modeling and parameter identification method for the Rijke tube. Using a sinusoidal sweep signal as the excitation input, we propose a parameter identification method based on the linearized transfer function structure of the ODE model, employing a nonlinear least squares approach. The output of the identified model is compared with that of the original system. Moreover, to address the mismatch between the nonlinear amplitude growth of the system’s output and the limitations of the linear model, a nonlinear growth analysis based on the Sigmoid-Prony approach is developed, in which the exponential envelope of classical Prony is replaced by a sigmoid function to capture the full amplitude saturation dynamics with physical interpretability. It can be applied to analyze the output of the nonlinear DDE system, extracting the effects of time delay and heat release parameters on system behavior. The simulation results indicate that the linear model identification method is limited to address the system uncertainty, whereas the Sigmoid-Prony method effectively captures the nonlinear amplitude growth dynamics lost due to linearization, as well as the impact of time delay and nonlinear heat release on the system’s parameters.