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Self-sustained oscillations are ubiquitous in nature and engineering. In thispaper, we propose a novel output-only system-identification framework foridentifying the system parameters of a self-sustained oscillator affected byGaussian white noise. A Langevin model that characterizes the self-sustainedoscillator is postulated, and the corresponding Fokker--Planck equation isderived from stochastic averaging. From the drift and diffusion terms of theFokker--Planck equation, unknown parameters of the system are identified. Wedevelop a numerically efficient algorithm for enhancing the accuracy ofparameter identification. In particular, a modified Levenberg--Marquardtoptimization algorithm tailored to output-only system identification isintroduced. The proposed framework is demonstrated on both numerical andexperimental oscillators with varying system parameters that develop intoself-sustained oscillations. The results show that the computational costrequired for performing the system identification is dramatically reduced byusing the proposed framework. Also, system parameters that were difficult to beextracted with the existing method could be efficiently computed with thesystem identification method developed in this study. Pertaining to therobustness and computational efficiency of the presented framework, this studycan contribute to an accurate and fast diagnosis of dynamical systems understochastic forcing.

A numerically efficient output-only system-identification framework for stochastically forced self-sustained oscillators