Model order reduction in space and parameter dimension - towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability

空间和参数维度的模型降阶 - 在鲁棒性和可靠性的背景下实现基于损伤的多态不确定性建模

• 批准号: 312911604
• 负责人: Professorin Dr.-Ing. Stefanie Reese
• 金额: --
• 依托单位: Rektor der Universität Siegen
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/312911604?language=en
• 关键词: Model; order; reduction; space; parameter

The evaluation of robustness and reliability of realistic structures in the presence of polymorphic uncertainty involves numerical simulations with a very high number of degrees-of-freedom as well as parameters. Some of these parameters are certain in the way that they are a priori known. However, the second group of parameters is imprecise, vague, uncertain or based on incomplete information. In this group are many parameters which crucially influence the damage and failure behavior and as such have a strong influence on the load bearing capacity of a structure. It is of pivotal importance to include their uncertainty and fuzziness into the modelling. The main goal of the project is to develop a modeling framework for this purpose which uses extended model order reduction and hierarchical tensor approximation, together with a recently developed method of data-driven mechanics to significantly reduce the computational effort. The idea is to combine an adaptive method of proper orthogonal decomposition with hierarchical tensor approximation and intelligent data mechanics in such a way that the uncertain or fuzzy quantities of interest can be computed by simple functional evaluation. Quantities of interest are e.g. certain stress or deformation levels which shall not be exceeded. It is also conceivable to require the damage level going below a certain prescribed value.Although the focus of the project is on civil engineering structures, it is intended to make the method relatively generally applicable and in this way generate multiple cooperation possibilities within the priority program 1886. Therefore, the new combined tool of model reduction and hierarchical tensor approximation shall be open to several material models, various types of geometry description and finally also different notions of uncertainty and fuzziness. The flexibility with respect to the latter aspect is firstly given by the possibility to set up the original parameter space in many different ways. Secondly the evaluation of uncertainty or fuzziness is majorly simplified by the functional representation of the quantities of interest.

在存在多态不确定性的情况下，评估现实结构的稳健性和可靠性涉及到具有非常高的自由度和参数的数值模拟。这些参数中的一些是确定的，因为它们是先验已知的。然而，第二组参数是不精确、模糊、不确定或基于不完全信息的。在这一组中，有许多参数对损伤和破坏行为有至关重要的影响，因此对结构的承载能力有很大的影响。将它们的不确定性和模糊性纳入建模是至关重要的。该项目的主要目标是为此目的开发一个建模框架，该框架使用扩展的模型降阶和分层张量近似，以及最近开发的数据驱动力学方法，以显著减少计算工作量。其思想是将适当的正交分解的自适应方法与分层张量近似和智能数据力学相结合，以便通过简单的函数评估来计算感兴趣的不确定或模糊量。感兴趣的数量是例如不应超过的某些应力或变形水平。尽管该项目的重点是土木工程结构，但它的目的是使该方法相对普遍适用，并以这种方式在优先方案1886内产生多种合作可能性。因此，新的模型降阶和层次张量近似的组合工具应该对多种材料模型、各种类型的几何描述以及不同的不确定性和模糊性概念开放。关于后一方面的灵活性首先是通过以许多不同的方式建立原始参数空间的可能性来给予的。其次，将不确定性或模糊性的评价主要简化为对兴趣量的泛函表示。