Efficient functional representation of the structural mechanical response dependent on polymorphic uncertain parameters and uncertaintiesx

取决于多态不确定参数和不确定性的结构机械响应的有效函数表示x

• 批准号: 341531955
• 负责人: Professor Dr. Hermann Georg Matthies
• 金额: --
• 依托单位: Institut für Wissenschaftliches Rechnen
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/341531955?language=en
• 关键词: Efficient; functional; representation; structural; mechanical

The purpose of this project is to build an efficient computationalframework for the treatment of various polymorphic uncertainty descriptions for large scale structural problems characterized by a large number of uncertain parameters. Our main goal is to find efficient ways to produce accurate functional approximations (meta-, proxy-, surrogate-models, response surface) in these parameters which will support different uncertainty descriptions, such as probabilistic, belief functions, and imprecise probabilities. This will be achieved by a suitable optimal re-parametrization of uncertainties to the forms which are consistent with the observation data and adherent to the physical laws, and are most suitable for separable low-rank tensor approximations. Together with the adaptive functional approximation algorithms such representations will enable fast surrogate models easily tuned to the particular structural problem.Once found, parameterised models can be combined with low-rank procedures for the purpose of reducing uncertainty in the model, or for upscaling from a fine to a coarse model in a later project phase. In addition, the solution of both the forward and inverse problems can be considered as one whole adaptive process.

该项目的目的是建立一个有效的计算框架，用于处理以大量不确定参数为特征的大规模结构问题的各种多态不确定性描述。我们的主要目标是找到有效的方法来在这些参数中产生准确的函数近似（元模型、代理模型、代理模型、响应面），这将支持不同的不确定性描述，例如概率、置信函数和不精确概率。这将通过对不确定性进行适当的最佳重新参数化来实现，其形式与观测数据一致并符合物理定律，并且最适合可分离的低秩张量近似。与自适应函数逼近算法一起，这种表示将使快速代理模型能够轻松调整到特定的结构问题。一旦找到，参数化模型可以与低秩过程相结合，以减少模型中的不确定性，或者从在稍后的项目阶段将精细化为粗略模型。此外，正向问题和逆向问题的求解都可以被认为是一个完整的自适应过程。