Despite significant research, self-excited thermoacoustic oscillations continue to hinder the development of lean-premixed gas turbines, making the early detection of such oscillations a key priority. We perform output-only system identification of a turbulent lean-premixed combustor near a Hopf bifurcation using the noise-induced dynamics generated by inherent turbulence in the fixed-point regime, prior to the Hopf point itself. We model the pressure fluctuations in the combustor with a van der Pol-type equation and its corresponding Stuart–Landau equation. We extract the drift and diffusion terms of the equivalent Fokker–Planck equation via the transitional probability density function of the pressure amplitude. We then optimize the extracted terms with the adjoint Fokker–Planck equation. Through comparisons with experimental data, we show that this approach can enable prediction of (i) the location of the Hopf point and (ii) the limit-cycle amplitude after the Hopf point. This study shows that output-only system identification can be performed on a turbulent combustor using only pre-bifurcation data, opening up new pathways to the development of early warning indicators of thermoacoustic instability in practical combustion systems.

尽管进行了大量研究，但自激热声振荡继续阻碍稀薄预混燃气轮机的发展，这使得尽早检测此类振荡成为关键任务。我们使用霍普夫点本身之前的定点状态中固有湍流产生的噪声感应动力学，对霍普夫分叉附近的湍流稀薄预混燃烧器进行仅输出的系统识别。我们用范德波尔型方程及其相应的斯图尔特-兰道方程对燃烧室中的压力波动进行建模。我们通过压力振幅的过渡概率密度函数提取等效Fokker-Planck方程的漂移项和扩散项。然后，我们使用伴随的Fokker-Planck方程优化提取的项。通过与实验数据进行比较，我们证明了这种方法可以预测（i）Hopf点的位置和（ii）Hopf点之后的极限循环幅度。这项研究表明，仅使用分叉前的数据就可以在湍流燃烧器上进行仅输出的系统识别，从而为开发实际燃烧系统中热声不稳定性预警指标提供了新的途径。