A method is developed for propagation of model parameter uncertainties into frequency response functions based on a modal representation of the equations of motion. Individual local surrogate models of the eigenfrequencies and residue matrix elements for each mode are trained to build a global surrogate model. The computational cost of the global surrogate model is reduced in three steps. First, modes outside the range of interest, necessary to describe the in-band frequency response, are approximated with few residual modes. Secondly, the dimension of the residue matrices for each mode is reduced using principal component analysis. Lastly, multiple surrogate model structures are employed in a mixture. Cheap second-order multivariate polynomial models and more expensive Gaussian process models with different kernels are used to model the modal data. Leave-one-out cross-validation is used for model selection of the local surrogate models. The approximations introduced allow the method to be used for modally dense models at a small computational cost, without sacrificing the global surrogate model’s ability to capture mode veering and crossing phenomena. The method is compared to a Monte Carlo based approach and verified on one industrial-sized component and on one assembly of two car components.

开发了一种基于运动方程的模态表示将模型参数不确定性传播到频率响应函数中的方法。训练每个模式的特征频率和残差矩阵元素的各个局部替代模型以构建全局替代模型。全局代理模型的计算成本分三步降低。首先，描述带内频率响应所必需的感兴趣范围之外的模式用很少的残余模式进行近似。其次，使用主成分分析降低了每种模式的残差矩阵的维数。最后，在混合中使用多个代理模型结构。廉价的二阶多元多项式模型和更昂贵的具有不同内核的高斯过程模型用于对模态数据进行建模。留一法交叉验证用于局部代理模型的模型选择。引入的近似允许该方法以较小的计算成本用于模态密集模型，而不会牺牲全局代理模型捕获模式转向和交叉现象的能力。该方法与基于蒙特卡罗的方法进行了比较，并在一个工业尺寸的组件和两个汽车组件的一个组件上进行了验证。在不牺牲全局代理模型捕获模式转向和交叉现象的能力的情况下。该方法与基于蒙特卡罗的方法进行了比较，并在一个工业尺寸的组件和两个汽车组件的一个组件上进行了验证。在不牺牲全局代理模型捕获模式转向和交叉现象的能力的情况下。该方法与基于蒙特卡罗的方法进行了比较，并在一个工业尺寸的组件和两个汽车组件的一个组件上进行了验证。