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：

---

降阶在线和离线数据驱动建模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），这会导致在考虑精确假设时对其动力学的预测不准确。这种结构的实时计算给工程师带来了一些挑战（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）。为了保证精度并节省计算时间，提出了双进程降阶模型（ROM）。它可以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，使用正确正交分解（POD）从一组解决方案中构建了一组简化基，这些解决方案是使用基于回归的多项式混沌展开计算的，以进行正确选择的实验设计。在在线阶段，POD 基使用非采样的一组不确定参数值的反距离加权在格拉斯曼流形上进行插值。所提出的双处理 ROM 可以精确地近似具有不确定的厚度和两层纤维取向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，大大减少了计算时间。