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

工业产品开发过程的日益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，不断缩短的开发周期以及越来越多的产品召回和由此造成的经济损失对该行业提出了挑战，即提高数学模型在决策中的表达能力。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。通过对模型参数进行统计校正，可以同时降低模型参数的不确定性，并将其量化，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较低的模型，或者使用复杂模型的快速替代模型，这些模型可以被评估数千倍。新的多保真方法结合了对廉价的低保真模型的大量评估和对昂贵的、更精确的高保真模型的一些评估。因此，可以减少统计参数校准的计算量，同时确保结果的高精度。因此，也可以有效地校准复杂的结构模型。然而，现有的方法忽略了模型的不确定性，导致了标定的偏差和物理参数的丧失意义。因此，该项目的目标是开发一种多保真方法，用于在考虑模型不确定性的情况下对计算昂贵的模型进行有效的统计参数校准。在CRC805的演示器上对该方法进行了测试，该演示器的设计要求与飞机起落架类似，将使该方法能够在类似的结构系统上移植。通过所开发的方法，将有可能量化数据不确定性以及计算密集型模型的模型不确定性。

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.