Rotating machinery are present in many engineering applications. Such rotor systems often subjected to high vibration loads that can be at the origin of noise or failure. For these reasons, it is of main importance to predict with accuracy the critical speeds and the dynamic response amplitude of such structures. However, they are often subjected to many potential uncertainties that may rise from environmental variations or manufacturing tolerances. These uncertain parameters, often described as random, are often numerous and must be taken into consideration during the design stage. For this, some design parameters are usually adjusted to propose a robust design of the rotor, considering the possible variation of the random parameters. Performing such studies require to be able to deal with a high number of uncertain parameters and with parameters of different nature, namely parametric and random.

This work proposes to illustrate the efficiency of advanced kriging-based surrogate modelling in order to achieve such a goal. The proposed hybrid surrogate-model combines polynomial chaos expansion and kriging to deal with both parameter natures, to consider nine varying parameters of a full finite element model of the rotating system under study. For the first time, this hybrid surrogate model is applied to perform rotordynamics analysis and more specifically the prediction of critical speeds and the associated unbalance responses for a complex rotor system with uncertainties. Compared to previous works, the kriging performances are significantly increased by integrating some physical properties of the rotor directly in its construction. Finally, the hybrid surrogate model gives a direct access to the Sobol indices which makes it possible to carry out without additional computation costs an extensive sensitivity analysis.

旋转机械存在于许多工程应用中。这种转子系统经常承受高振动载荷，这可能是噪音或故障的根源。由于这些原因，准确预测此类结构的临界速度和动态响应幅度非常重要。然而，它们经常受到许多潜在的不确定性的影响，这些不确定性可能源于环境变化或制造公差。这些不确定的参数，通常被描述为随机的，通常数量众多，必须在设计阶段加以考虑。为此，考虑到随机参数的可能变化，通常会调整一些设计参数以提出转子的稳健设计。

这项工作旨在说明先进的基于克里金法的代理建模的效率，以实现这一目标。所提出的混合代理模型结合多项式混沌展开和克里金法来处理这两种参数性质，以考虑所研究的旋转系统的完整有限元模型的九个不同参数。这种混合替代模型首次应用于执行转子动力学分析，更具体地说是预测具有不确定性的复杂转子系统的临界速度和相关的不平衡响应。与以前的工作相比，通过将转子的一些物理特性直接集成到其结构中，克里金性能显着提高。最后，