Fast and Unbiased Determination of Dominant Frequencies and Amplitude of Thermoacoustic Oscillations

Reported is a three-step procedure (also referred to as the observer) for fast and unbiased determination of the dominant frequencies and amplitude of thermoacoustic oscillations. The first step is to determine the rang of the dominant frequency by computing the amplitude at frequency bins uniformly distributed from the lowest possible frequency to the Nyquist frequency (i.e., one-half of the sampling frequency) with a strategically specified, widely spaced frequency-bin separation. The other steps are to refine the estimation. The frequency estimation becomes unbiased after step 2, and the error (or uncertainty) is insensitive to the signal-to-noise ratio. The computational complexity can be orders-of-magnitude lower than the discrete Fourier transform and the fast Fourier transform, and the accuracy is no longer limited by Fs/N, where Fs and N refer to the sampling frequency and the data length, respectively. This Paper recommends that the frequencies and amplitude be estimated every two pressure cycles. Cycle-to-cycle (or short-term) variations in the frequencies and amplitude are well resolved for thermoacoustic oscillations in three different real devices exhibiting quasi-steady oscillations before the onset of combustion instabilities and spontaneous instabilities (i.e., linearly unstable oscillations) with different levels of nonlinearities, respectively.