Abstract Surrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic response of structural dynamics systems. In linear structural dynamics problems, the system response can be described by the frequency response function. It is well known that standard polynomial chaos expansions of the frequency response present slow convergence around system eigenfrequencies, due to the highly nonlinear nature of the frequency response for low damping. To overcome this issue, we develop a rational approximation that expresses the system response as a rational of two polynomials with complex coefficients. To estimate the latter, we propose a regression approach that is non-intrusive and can be easily coupled with existing deterministic solvers. We demonstrate the effectiveness of the proposed method with two examples, a two-degree-of-freedom system and a finite element model of a cross laminated timber plate.

中文翻译：

---

具有参数不确定性的线性结构动力学中基于多项式混沌的有理逼近

摘要 代理模型能够在物理系统的计算要求高的模型中有效地传播不确定性。我们使用基于多项式的替代模型来模拟结构动力学系统的随机响应。在线性结构动力学问题中，系统响应可以用频率响应函数来描述。众所周知，由于低阻尼频率响应的高度非线性特性，频率响应的标准多项式混沌展开在系统特征频率附近呈现缓慢收敛。为了克服这个问题，我们开发了一种有理近似，将系统响应表示为具有复系数的两个多项式的有理数。估计后者，我们提出了一种非侵入性的回归方法，可以轻松地与现有的确定性求解器结合使用。我们通过两个例子证明了所提出方法的有效性，一个二自由度系统和一个交叉层压木板的有限元模型。