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.

中文翻译：

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降阶在线和离线数据驱动建模，以研究多参数不确定性下层合板结构的非线性动力学


复合材料的制造过程涉及参数可变性（例如，几何、机械、载荷），当使用精确假设考虑时，这会导致对其动力学的预测不准确。实时计算此类结构使工程师面临多项挑战（例如，有限元模型的尺寸、参数空间的大小、不确定性水平、非线性）。为了保证准确性，同时节省计算时间，提出了一种双进程降阶模型 （ROM）。它允许减少离线数据采集和在线数据插值以进行实时计算。学习阶段正逐渐成为数据驱动模型最关键的部分之一。为了克服这个问题，使用适当的正交分解 （POD） 从一组解中构建一组约化基，这些解使用基于回归的多项式混沌展开计算，以正确选择实验设计。在在线阶段，POD 基数在 Grassmann 流形上使用反距离加权在一组不确定参数值的非采样处进行插值。所提出的双过程 ROM 可以准确近似两层厚度和纤维取向不确定的层压板的非线性动力学，与基于经典统计数据采样和后处理的全阶模型求解相比，大大缩短了计算时间。