Toyota Central R&D Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi, 480-1192, Japan.
Sci Rep. 2023 Jul 11;13(1):11241. doi: 10.1038/s41598-023-38393-2.
We present a construction method for reduced-order models (ROMs) to explore alternatives to numerical simulations. The proposed method can efficiently construct ROMs for non-linear problems with contact and impact behaviors by using tensor decomposition for factorizing multidimensional data and Akima-spline interpolation without tuning any parameters. First, we construct learning tensor data of nodal displacements or accelerations using finite element analysis with some representative parameter sets. Second, the data are decomposed into a set of mode matrices and one small core tensor using Tucker decomposition. Third, Akima-spline interpolation is applied to the mode matrices to predict values within the data range. Finally, the time history responses with new parameter sets are generated by multiplying the expanded mode matrices and small core tensor. The performance of the proposed method is studied by constructing ROMs for airbag impact simulations based on limited learning data. The proposed ROMs can accurately predict airbag deployment behavior even for new parameter sets using the Akima-spline interpolation scheme. Furthermore, an extremely high data compression ratio (more than 1000) and efficient predictions of the response surfaces and Pareto frontier (2000 times faster than that of full finite element analyses using all parameter sets) can be realized.
我们提出了一种构建降阶模型 (ROM) 的方法，以探索替代数值模拟的方法。所提出的方法可以通过张量分解对具有接触和冲击行为的非线性问题进行有效建模，而无需调整任何参数。首先，我们使用有限元分析构建节点位移或加速度的学习张量数据，并使用一些代表性的参数集。其次，数据通过 Tucker 分解分解为一组模态矩阵和一个小核张量。第三，应用 Akima 样条插值对模态矩阵进行内插，以预测数据范围内的值。最后，通过乘以扩展的模态矩阵和小核张量来生成具有新参数集的时程响应。通过基于有限学习数据的气囊冲击模拟来研究所提出方法的性能。即使使用 Akima 样条插值方案，所提出的 ROM 也可以准确预测气囊展开行为，即使对于新的参数集也是如此。此外，可以实现极高的数据压缩比（超过 1000）和响应曲面和 Pareto 前沿的高效预测（使用所有参数集的全有限元分析快 2000 倍）。
