The detrended fluctuation analysis, a technique for detecting long-range correlations in fractal time series, is used to characterize thermoacoustic oscillations of impending combustion instabilities. The slope of the linear regime of the structure function with respect to the time scale in a logarithmic plot, referred to as the Hurst exponent, takes a different value across a critical time scale corresponding to one pressure cycle. The slope for pressure oscillations over one pressure cycle, termed as the intercycle Hurst exponent, is a power-law scaling parameter for long-range oscillations; however, the slope for pressure oscillations within one pressure cycle, termed as the “intracycle Hurst exponent,” is no longer a power-law scaling parameter but resultant from the nonstationary, local average of highly nonlinear (as a function of time), seemingly sinusoidal, nearly periodic pressure oscillations. Both parametric studies and analyses of experimental data show that the intracycle Hurst exponent consistently increases with the signal-to-noise ratio and peaks at 1.6, thus having potentials for assessments of the safety margin to the onset of combustion instabilities. Given the same observation window, the measurement error (or uncertainty) of the intracycle Hurst exponent is significantly lower than that of the intercycle Hurst exponent.

去趋势波动分析是一种检测分形时间序列中远距离相关性的技术，用于表征即将发生的燃烧不稳定性的热声振荡。在对数图中，结构函数的线性形式相对于时间尺度的斜率（称为赫斯特指数）在对应于一个压力循环的关键时间尺度上采用不同的值。一个压力周期内压力振荡的斜率，称为周期间Hurst指数，是长距离振荡的幂律定标参数。但是，一个压力周期内压力振荡的斜率（称为“周期内赫斯特指数”）不再是幂律定标参数，而是高度非线性（作为时间的函数）的非平稳局部平均值得出的，看起来是正弦的，几乎是周期性的压力振荡。参数研究和实验数据分析均表明，循环内赫斯特指数随信噪比的增加而不断增加，并在1.6处达到峰值，因此具有评估燃烧不稳定开始的安全裕度的潜力。给定相同的观察窗口，周期内赫斯特指数的测量误差（或不确定性）显着低于周期内赫斯特指数的测量误差（或不确定性）。