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Goal-oriented model adaptivity in stochastic elastodynamics: simultaneous control of discretisation, surrogate model and sampling errors
International Journal for Uncertainty Quantification ( IF 1.5 ) Pub Date : 2020-01-01 , DOI: 10.1615/int.j.uncertaintyquantification.2020031735
Pedro Bonilla-Villalba , S. Claus , A. Kundu , Pierre Kerfriden

The presented adaptive modelling approach aims to jointly control the level of renement for each of the building-blocks employed in a typical chain of nite element approximations for stochastically parametrized systems, namely: (i) nite error approximation of the spatial elds (ii) surrogate modelling to interpolate quantities of interest(s) in the parameter domain and (iii) Monte-Carlo sampling of associated probability distribution(s). The control strategy seeks accurate calculation of any statistical measure of the distributions at minimum cost, given an acceptable margin of error as only tunable parameter. At each stage of the greedy-based algorithm for spatial discretisation, the mesh is selectively rened in the subdomains with highest contribution to the error in the desired measure. The strictly incremental complexity of the surrogate model is controlled by enforcing preponderant discretisation error integrated across the parameter domain. Finally, the number of Monte-Carlo samples is chosen such that either (a) the overall precision of the chain of approximations can be ascertained with sucient condence, or (b) the fact that the computational model requires further mesh renement is statistically established. The eciency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted nite element solutions converge faster than those obtained using uniformly rened grids.

中文翻译:

随机弹性动力学中面向目标的模型适应性:同时控制离散化、替代模型和采样误差

所提出的自适应建模方法旨在共同控制随机参数化系统的典型有限元近似链中使用的每个构建块的修正水平,即:(i)空间场的有限误差近似(ii)代理建模以在参数域中插入感兴趣的数量和 (iii) 相关概率分布的蒙特卡罗采样。控制策略寻求以最小成本准确计算分布的任何统计量度,给定可接受的误差范围作为唯一的可调参数。在用于空间离散化的基于贪婪的算法的每个阶段,网格在对所需度量中的误差贡献最大的子域中被选择性地重整。代理模型的严格增量复杂性是通过强制执行在参数域中集成的优势离散化误差来控制的。最后,选择蒙特卡罗样本的数量,以便 (a) 可以充分自信地确定近似链的整体精度,或者 (b) 统计建立计算模型需要进一步网格重修的事实。针对具有前向不确定性传播的频域振动结构动力学问题讨论了所提出方法的效率。结果表明,局部适应的有限元解比使用均匀重整网格获得的解收敛得更快。选择蒙特卡洛样本的数量,以便 (a) 可以充分自信地确定近似链的整体精度,或者 (b) 统计建立计算模型需要进一步网格重修的事实。针对具有前向不确定性传播的频域振动结构动力学问题讨论了所提出方法的效率。结果表明,局部适应的有限元解比使用均匀重整网格获得的解收敛得更快。选择蒙特卡洛样本的数量,以便 (a) 可以充分自信地确定近似链的整体精度,或者 (b) 统计建立计算模型需要进一步网格重修的事实。针对具有前向不确定性传播的频域振动结构动力学问题讨论了所提出方法的效率。结果表明,局部适应的有限元解比使用均匀重整网格获得的解收敛得更快。针对具有前向不确定性传播的频域振动结构动力学问题讨论了所提出方法的效率。结果表明,局部适应的有限元解比使用均匀重整网格获得的解收敛得更快。针对具有前向不确定性传播的频域振动结构动力学问题讨论了所提出方法的效率。结果表明,局部适应的有限元解比使用均匀重整网格获得的解收敛得更快。
更新日期:2020-01-01
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