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

## TL;DR

This paper investigates output-only parameter identification of nonlinear oscillators driven by colored noise, demonstrating that accurate parameter estimation is possible with proper filtering, using Van der Pol oscillators and thermoacoustic systems as examples.

## Contribution

It introduces a method for accurate parameter identification of nonlinear oscillators under colored noise forcing, challenging the white noise assumption.

## Key findings

- Parameter identification is accurate with band-pass filtering.
- Colored noise forcing impacts are mitigated by filtering.
- Method applies to thermoacoustic instabilities in combustion chambers.

## Abstract

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.