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

本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。我们的主要目标是在这些参数中找到有效的方法来产生准确的函数近似（元模型、代理模型、代理模型、响应面），这些参数将支持不同的不确定性描述，如概率、信念函数和不精确概率。这将通过对不确定性进行适当的最优重新参数化，使其与观测数据一致，符合物理定律，并且最适合于可分离的低秩张量近似来实现。与自适应函数近似算法一起，这种表示将使快速代理模型能够轻松地调整到特定的结构问题。一旦发现，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，或者在以后的项目阶段从精细模型升级到粗糙模型。此外，正、逆问题的求解可以看作是一个完整的自适应过程。

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.