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Abstract

This work proposes a data-driven parameter identification approach for a two-degree-of-freedom airfoil system with cubic nonlinearity and stochasticity, where the random turbulent flow is quantified by non-Gaussian Lévy colored noise. The joint identification of the parameters controlling the flow velocity, airfoil geometry and structural stiffness is shaped as a unified machine learning task that includes three stages. (1) The first stage extracts local deep learning features from measurement data. (2) Next, the local features are fused to construct fixed-length global features representing the whole sample trajectory. (3) The global features are mapped to the parameter estimates and the accuracy indicators for uncertainty quantification. The numerical studies show that the obtained parameter estimation neural network can identify the system parameters from a sample trajectory with partially observed state measurements, namely, system parameters can be fully identified if only one or two of the pitch and plunge degrees of freedom are available. The intermediate deep features extracted by the PENN are compact representations of the stochastic system, as they carry key information of the system parameters. Suitable rules for information fusion are further designed, adapting the PENN to identify the system parameters from multiple short trajectories or time-varying parameters from a sample trajectory. The results suggest that the proposed deep learning approach is a flexible and versatile computation device for information extraction and fusion from limited data of stochastic nonlinear systems.