Optimal experimental design and optimal modeling for parameter identification of inhomogeneousproblems

非齐次问题参数识别的优化实验设计和优化建模

• 批准号: 516711743
• 负责人: Dr.-Ing. Ismail Caylak, since 3/2024
• 金额: --
• 依托单位: Lehrstuhl für Technische Mechanik (LTM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/516711743?language=en
• 关键词: Optimal; experimental; design; optimal; modeling

The reliable prediction of numerical simulations requires not only physically based mathematical modeling but also determination of the associated model constants based on experimental data. However, deficiencies of experimental data as well as model deficiency may have an impact on the stability of the identified parameters. This application is based on the following working hypothesis: Stable material parameters are a prerequisite for a reliable prediction and in this way for the validation of a model. The overall aim of this proposal is therefore an optimal experimental design as well as an optimal model design for stable identification of material parameters for models with partial differential equations for hyperelasticity and plasticity. The assessment of stability and thus reliability of the identified parameters is based on a confidence matrix and an associated design function. The design function is intended to give the goodness of the estimation in terms of a real number, which allows to compare different estimations and thus provides the opportunity for optimization. In this research project, three design functions known from the literature on optimal experimental design are used. Initially, control variables will be used as design variables to control load, geometry as well as position of the measuring points. Regarding the confidence matrix, three options are considered. For confidence matrices calculated by aid of statistics, the required experiments are usually time consuming and cost intensive. One way to artificially increase the number of experiments is to generate synthetic data using a stochastic model. It has to be noted, that only aleatory but no epistemic uncertainties are taken into account. To represent the synthetic data, an existing method based on B-splines for spatial dependencies is extended to time dependencies. Another aim of the research project is to estimate the reliability of stable parameter identification with respect to the model structure, whereby material parameters are now also variables of the design function. The main result of the project will be material parameters for models of hyperelasticity and plasticity with optimized confidence ranges with respect to experimental and model design. Final investigations are intended to verify the above working hypothesis.

数值模拟的可靠预测不仅需要基于物理的数学建模，还需要根据实验数据确定相关的模型常数。然而，实验数据的缺陷以及模型的缺陷可能会对所识别的参数的稳定性产生影响。该应用基于以下工作假设：稳定的材料参数是可靠预测的先决条件，并以这种方式验证模型。因此，本建议的总体目标是一个最佳的实验设计，以及一个最佳的模型设计的材料参数的稳定识别模型与偏微分方程的超弹性和塑性。稳定性的评估，从而确定的参数的可靠性是基于一个置信矩阵和相关的设计功能。设计函数旨在根据真实的数给出估计的优度，这允许比较不同的估计，从而提供优化的机会。在这个研究项目中，三个设计函数已知的文献中的最优实验设计。最初，控制变量将被用作设计变量，以控制载荷、几何形状以及测量点的位置。关于置信矩阵，考虑了三个备选方案。对于通过统计学计算的置信矩阵，所需的实验通常是耗时且成本密集的。人为增加实验数量的一种方法是使用随机模型生成合成数据。必须指出的是，只有偶然的，但没有认识上的不确定性考虑在内。为了表示合成数据，现有的方法基于B样条的空间依赖性扩展到时间依赖性。该研究项目的另一个目的是估计模型结构的稳定参数识别的可靠性，其中材料参数现在也是设计函数的变量。该项目的主要成果将是超弹性和塑性模型的材料参数，并在实验和模型设计方面具有优化的置信范围。最后的调查旨在验证上述工作假设。