Development and Analysis of Methods for the Identification of Correlated Parameters in Multifield Problems

由于不同领域的相互作用，对受水文、温度和机械载荷影响的建筑物（如水坝）的安全性评估是一个要求很高的问题。对这类建筑物寿命的估计往往与目前的损坏状况有关。对于现有结构，问题是如何在基于模型的方法中高精度地识别存在的裂缝或损伤。一种可能的情况是，对于新建的建筑物，已经推导出一个经过验证和校准的模型。经过几年的使用，特别是在地震等极端事件之后，结构内部可能会出现裂缝或损坏。这些应通过相对较短的时间间隔（例如一个月）的测量和与现有模型的比较来确定。提出的项目的目标是开发和分析方法，可以在识别过程中考虑多场系统中主要参数（例如用于模拟损伤的参数）的可能相关性。例如，在大坝损坏的情况下，可以预期局部的水力渗透性增加和局部的机械刚度降低是并行的。在逆分析期间可以明确地考虑这种相关性，以提高对检测量的置信度。针对所提出的问题，将采用扩展有限元法（XFEM）来描述损伤识别、裂纹和损伤。XFEM已成为一种有用的工具，特别是对于逆问题，因为在识别例程期间不需要重新划分域。开发的方法是通用的，可以应用于工程和自然科学中的几个多领域识别问题，其中输入参数之间的相关性是已知的，或者至少可以估计，例如压电，磁电学或热力学。拟议的研究项目包括开发和分析用于在多领域背景下识别参数的数学模型，并通过实际建筑物的现有测量验证派生方法。

The evaluation of the safety of buildings, which suffer from hydrological, temperature and mechanical loads, e.g., dams, is a highly demanding problem due to the interaction effects of the different fields.The estimation of the lifetime of such building is often linked to the question of the current state of damage.For existing structures the question arises, how existent cracks or damages can be identified with a high precision in a model-based approach. A possible scenario might be, that for a newly constructed building a validated and calibrated model has been derived. After some years of usage, and in particular after extreme events like earthquakes, cracks or damages might have occurred inside the structures.Those shall be identified by measurements of a relatively short time interval (e.g. one month) and the comparison with the existing model. The goal of the proposed project is the develop and analyze methods, which can consider during identification procedures possible correlations of main parameters (e.g. those to model damage) in a multi-field system. For example, in case of a damage in a dam one can expect in parallel a local increase of the hydraulic permeability and a local reduction of the mechanical stiffness.Such correlations can be considered explicitly during an inverse analysis, in order to improve the confidence in the detected quantities. For the proposed problem, the damage identification, cracks and damages will be described with the eXtended Finite Element Methode (XFEM). XFEM has established as a useful tool, in particular for inverse problems, as during the identification routines no re-meshing of the domain is necessary.The method to develop is of general character and might be applied to several multi-field identification problems in engineering and natural sciences, where correlations between the input parameters are known or can at least be estimated, e.g. piezoelectricity, magneto-electronics or thermo-mechanics. The proposed research project includes the development and analysis of mathematical models for the identification of parameters in a multi-field context and the validation of the derived methods with existing measurements of real buildings.