Efficient statistical parameter calibration for complex structural dynamics systems underconsideration of model uncertainty

增加工业产品开发过程的虚拟化需要精确的数学模型来描述结构系统的动态行为。与此同时，越来越短的开发周期、越来越多的产品召回以及由此带来的经济损失，对提高数学模型在决策中的表达能力提出了挑战。因此，考虑模型固有的数据不确定性和模型不确定性变得越来越重要。通过统计参数定标，可以降低模型参数的不确定性，同时量化模型参数的不确定性，从而提高模型的预测精度。统计参数校准方法假定计算成本低廉的模型或使用可评估数千倍的复杂模型的快速替代模型。新颖的多保真度方法将廉价的低保真度模型的大量评估与昂贵的、更精确的高保真度模型的少量评估结合起来。因此，可以减少统计参数校准的计算工作量，同时确保结果的高精度。因此，复杂的结构模型也可以有效地校准。然而，现有的方法忽略了模型的不确定性，导致校准有偏差，物理参数丧失其意义。因此，该项目的目标是开发一种多保真度方法，在考虑模型不确定性的情况下，对计算成本高的模型进行有效的统计参数校准。该方法在CRC 805的演示器上进行测试，该演示器已被设计为具有与飞机起落架相似的要求，将能够在可比结构系统上实现可转移性。利用所开发的方法，可以量化计算密集型模型的数据不确定性和模型不确定性。

Increasing the virtualization of the industrial product development process requires accurate mathematical models for the description of the dynamical behavior of structural systems. At the same time, ever-shorter development cycles as well as an increasing number of product recalls and the resulting economic damage pose a challenge for the industry to improve the expressiveness of mathematical models in the decision-making. The consideration of the data uncertainty and model uncertainty inherent to the models is therefore getting more and more important. By means of a statistical parameter calibration, the uncertainty of the model parameters can be reduced and quantified simultaneously in order to increase the predictive accuracy of the model. Methods for statistical parameter calibration presume computationally inexpensive models or use fast surrogate models of complex models that can be evaluated thousand fold. Novel multi-fidelity methods combine the numerous evaluations of an inexpensive low-fidelity model with a few evaluations of an expensive, more precise high-fidelity model. Thus, the computational effort for a statistical parameter calibration can be reduced while at the same time ensuring a high precision of the results. Consequently, also complex structural models can be calibrated efficiently. However, existing approaches neglect the model uncertainty, resulting in the calibration to be biased and the physical parameters to forfeit its meaning. Therefore, the goal of the project is the development of a multi-fidelity method for the efficient statistical parameter calibration of computationally expensive models under consideration of model uncertainty. The testing of the method on the demonstrator of the CRC 805, which has been designed with similar requirements as an airplane landing gear will enable the transferability on comparable structural systems. By means of the developed method, it will be possible to quantify the data uncertainty as well as model uncertainty for computationally intensive models.