Reduced order online and offline data-driven modeling to investigate the nonlinear dynamics of laminate structures under multiparametric uncertainties

Manufacturing processes of composites involve a margin of parameter variability (e.g., geometric, mechanical, loading) which results in an inaccurate prediction of their dynamics when considered with exact assumptions. Real-time calculation of such structures confronts engineers with several challenges (e.g., dimension of finite element model, size of parameter space, uncertainty level, nonlinearity). To guarantee accuracy while saving computing time, a double-process Reduced Order Model (ROM) is proposed. It allows reducing both offline data acquisition and online data interpolation for real-time calculation. The learning phase is gradually becoming one of the most critical part of data-driven models. To overcome this problem, a set of reduced bases are built using the Proper Orthogonal Decomposition (POD) from a set of solutions computed using a regression-based Polynomial Chaos Expansion for a properly chosen Design of Experiments. In the online phase, the POD bases are interpolated on a Grassmann manifold using the Inverse Distance Weighting at a non-sampled set of the uncertain parameters’ values. The proposed double-process ROM allows to accurately approximate the nonlinear dynamics of a laminate plate with uncertain thickness and fiber orientation of two layers, with a drastically reduced computing time compared to a Full Order Model solving based on classical statistical data-sampling and postprocessing.