A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics
A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics
复制标题
用于非线性结构动力学超简化的精益高效快照生成技术
DOI：
10.1016/j.cma.2017.06.009
复制
发表时间：
2017
影响因子：
7.2
通讯作者：
D. Rixen
中科院分区：
文献类型：
--
作者：
J. Rutzmoser;D. Rixen
基于子空间投影的模型降阶可以带来令人印象深刻的加速，因为自由度的数量可以大大减少。然而，非线性力的计算，这是在未约化的物理域进行，成为非线性系统的主要瓶颈。Hyper-Reduction是一种在简化的基础模型中近似但廉价地计算非线性力的方法，它需要训练集，而训练集通常是通过对完整的、未简化的模型进行训练模拟来获得的，这导致了巨大的离线成本。为了降低离线训练的代价，本文提出了非线性随机Krylov训练集（NSKTS）。这些训练集是通过解决一些非线性静力学问题，其中的力是由Krylov力子空间的随机加权力构成的。NSKTS作为训练集的能量守恒网格采样和加权（ECSW）超约简方法的可行性证明了几何非线性橡胶靴子的例子表现出优异的结果，在精度，加速比和鲁棒性。
Model Order Reduction based on subspace projection can lead to impressive speedups, as the number of dofs can be drastically reduced. However, the computation of the nonlinear forces, which is performed in the unreduced physical domain, becomes the dominating bottleneck for nonlinear systems. This issue is addressed by Hyper-Reduction, which is the approximate but inexpensive computation of the nonlinear forces in a reduced basis model.The established Hyper-Reduction methods require training sets which are usually obtained by a training simulation of the full, unreduced model resulting in immense offline costs. To reduce the offline-costs, so-called Nonlinear Stochastic Krylov Training Sets (NSKTS) are proposed in this paper. These training sets are obtained by solving a number of nonlinear static problems where the force is constructed by stochastically weighted forces of a Krylov force subspace. The feasibility of NSKTS as training sets for the Energy Conserving Mesh Sampling and Weighting (ECSW) Hyper-Reduction method is demonstrated on a geometrically nonlinear rubber boot example exhibiting excellent results in terms of accuracy, speedup and robustness.