  Self-sustained oscillations are ubiquitous in nature and engineering. In this
paper, we propose a novel output-only system-identification framework for
identifying the system parameters of a self-sustained oscillator affected by
Gaussian white noise. A Langevin model that characterizes the self-sustained
oscillator is postulated, and the corresponding Fokker--Planck equation is
derived from stochastic averaging. From the drift and diffusion terms of the
Fokker--Planck equation, unknown parameters of the system are identified. We
develop a numerically efficient algorithm for enhancing the accuracy of
parameter identification. In particular, a modified Levenberg--Marquardt
optimization algorithm tailored to output-only system identification is
introduced. The proposed framework is demonstrated on both numerical and
experimental oscillators with varying system parameters that develop into
self-sustained oscillations. The results show that the computational cost
required for performing the system identification is dramatically reduced by
using the proposed framework. Also, system parameters that were difficult to be
extracted with the existing method could be efficiently computed with the
system identification method developed in this study. Pertaining to the
robustness and computational efficiency of the presented framework, this study
can contribute to an accurate and fast diagnosis of dynamical systems under
stochastic forcing.
