Output-only parameter identification of a colored-noise-driven Van-der-Pol oscillator: Thermoacoustic instabilities as an example.

The problem of output-only parameter identification for nonlinear oscillators forced by colored noise is considered. In this context, it is often assumed that the forcing noise is white, since its actual spectral content is unknown. The impact of this white-noise forcing assumption upon parameter identification is quantitatively analyzed. First, a Van-der-Pol oscillator forced by an Ornstein-Uhlenbeck process is considered. Second, the practical case of thermoacoustic limit cycles in combustion chambers with turbulence-induced forcing is investigated. It is shown that in both cases, the system parameters are accurately identified if time signals are appropriately band-pass-filtered around the oscillator eigenfrequency.