A novel method for characterising and propagating system uncertainty in structures subjected to dynamic actions is proposed, whereby modal shapes, frequencies and damping ratios constitute the random quantities. The latter, defined in the modal subspace rather than the full geometrical space, reduce the number of the random variables and the size of the dynamic problem. A numerical procedure is presented for their identification by calibrating their probabilistic definition in line with the geometrical space. A high-order perturbation technique is proposed for the multi-fidelity response quantification by means of an ad hoc extension of the conventional perturbation method. The approach involves a set of auxiliary deterministic differential equations to be adaptively solved with the piecewise exact method, and moment-cumulant relationships are employed to approximate high-order moments. Finally, a polynomial chaos expansion approach is adopted to complement the second-moment analysis for spectral quantification with the modal subspace reduction. Demonstrated on a multi-storey steel frame with semi-rigid connections and a simply supported bridge subjected to a moving load, the proposed variants exhibit improved performance with respect to the conventional second-order and improved perturbation, as well as increased flexibility, enabling the analyst to decide, on-demand, the level of fidelity, balancing accuracy and computational effort.

提出了一种表征和传播受动力作用的结构中系统不确定性的新方法，其中模态形状、频率和阻尼比构成随机量。后者定义在模态子空间而不是整个几何空间中，减少了随机变量的数量和动态问题的规模。通过根据几何空间校准它们的概率定义，提出了一种用于识别它们的数值程序。由的装置提出了多保真度响应量化的高阶扰动技术特设常规微扰方法的扩展。该方法涉及一组辅助确定性微分方程，可使用分段精确方法自适应求解，并采用矩-累积关系来逼近高阶矩。最后，采用多项式混沌展开方法来补充谱量化的二阶矩分析和模态子空间缩减。在具有半刚性连接的多层钢框架和承受移动载荷的简支桥上展示，所提出的变体表现出相对于传统二阶和改进扰动的改进性能，以及增加的灵活性，使分析师按需决定保真度、平衡准确性和计算工作量。