Identification of Nonlinear Feedback Parameters of a Noise-Driven Limit-Cycling Combustion System

We present a procedure for estimating nonlinear feedback parameters obtained from time series data (power spectral density (PSD), and probability density function (pdf)) with application to the identification of the unsteady heat-release coupling of a limit-cycling thermoacoustic system. The limit cycling and Gaussian components are identified from the pdf of the output signal. The respective describing function gains, along with a phase-shifting element are fit to a nominal acoustic oscillator model by using the PSD. The nonlinear feedback parameters are determined from the describing function gains and their Gaussian and harmonic inputs. The estimation procedure is demonstrated on a benchmark oscillator problem and is applied to time-series data obtained from a limit-cycling combustor rig. Relations between the feedback parameters and the equivalence ratio are discussed