Analytical Modeling and Data-Driven Uncertainty Analysis of the Vibration Response of Partially Liquid-Filled Rotors Under Lateral Excitation.

Partially liquid-filled rotor systems subjected to lateral excitation exhibit pronounced fluid-structure interaction, leading to complex and highly sensitive vibration responses. To enable efficient probabilistic prediction under parametric uncertainty, this study develops a deterministic-data-driven framework for a rigid hollow rotor partially filled with liquid. Based on small-perturbation flow theory, the liquid-induced feedback forces are analytically derived and incorporated into the coupled rotor-liquid dynamic equations, yielding a closed-form steady-state solution. The results reveal that lateral excitation in one direction induces coupled vibration in the orthogonal direction, resulting in an elliptical whirl trajectory of the rotor center. The vibration characteristics depend jointly on excitation frequency and rotor angular velocity, and for a given angular velocity, two critical excitation frequencies are identified at which the response amplitude increases sharply. Surrogate models based on a backpropagation neural network (BPNN) and a support vector machine (SVM) are constructed and validated, with the BPNN demonstrating superior predictive accuracy. Uncertainty analysis further shows that the maximum vibration amplitude exhibits asymmetric, non-Gaussian distributions even under normally distributed inputs, and excessive amplification may occur beyond certain uncertainty levels. The proposed framework provides a robust tool for probabilistic vibration assessment and uncertainty-informed design of partially liquid-filled rotor systems.