非线性多尺度结构动力学模型的原位自适应降阶
In-situ adaptive reduction of nonlinear multiscale structural dynamics models
摘要：
常规的在参数空间的预定区域中的降阶基的离线训练导致易受外推影响的参数降阶模型。只要查询的参数点位于参数空间的未探索区域中，就会出现此漏洞。本文解决了这个问题，提出了一个原位，自适应框架的非线性模型减少计算默认在线执行，并根据需要转移离线。该框架是基于本地降阶基（ROBs）的数据库的概念，其中本地定义在参数空间的兴趣。它通过实时更新预先计算的ROB，并使用一系列最合适的局部ROB沿其轨迹逼近动力系统的解来实现精度。它通过管理局部ROB的维度，并在过程中引入超约简来实现效率。虽然足够全面，框架中描述的背景下，在固体力学的动态多尺度计算。在这种情况下，即使在宏观问题的非参数设置中，并且当考虑到所有离线、在线和自适应开销成本时，所提出的计算框架也可以将单个三维、非线性、多尺度计算加速一个数量级。数量级，而不影响准确性。
英文摘要：
Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried parameter point lies in an unexplored region of the parameter space. This paper addresses this issue by presenting an in-situ, adaptive framework for nonlinear model reduction where computations are performed by default online, and shifted offline as needed. The framework is based on the concept of a database of local Reduced-Order Bases (ROBs), where locality is defined in the parameter space of interest. It achieves accuracy by updating on-the-fly a pre-computed ROB, and approximating the solution of a dynamical system along its trajectory using a sequence of most-appropriate local ROBs. It achieves efficiency by managing the dimension of a local ROB, and incorporating hyperreduction in the process. While sufficiently comprehensive, the framework is described in the context of dynamic multiscale computations in solid mechanics. In this context, even in a nonparametric setting of the macroscale problem and when all offline, online, and adaptation overhead costs are accounted for, the proposed computational framework can accelerate a single three-dimensional, nonlinear, multiscale computation by an order of magnitude, without compromising accuracy.
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