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.

In the three-roll planetary rolling process, excessively high surface temperature of the rolls can easily lead to copper adhesion, deterioration of roll surface quality, shortened rolling lifespan, and severely affect the quality of copper tube products as well as production efficiency. To improve the cooling efficiency of the roll cooling system, this study developed a fluid–solid–heat coupled model and validated it experimentally to investigate the effects of nozzle diameter, spray angle, and axial position of the spray ring on the cooling performance of the roll surface. Given the low computational efficiency of finite element simulations, three machine learning models—Random Forest (RF), Gradient Boosting Decision Tree (GBDT), and Support Vector Machine (SVM)—were introduced and evaluated to identify the most suitable predictive model. Subsequently, the Particle Swarm Optimization (PSO) algorithm was employed to optimize the geometric parameters of the spray ring. The results show that the maximum deviation between the coupled model predictions and experimental data was 4.36%, meeting engineering accuracy requirements. Among the three machine learning models, the RF model demonstrated the best performance, achieving RMSE, MAE, and R² values of 1.7336, 1.3203, and 0.9082, respectively, on the test set. The combined RF-PSO optimization approach increased the heat transfer coefficient by 44.72%, providing a robust theoretical foundation for practical process parameter optimization and precision tube manufacturing.

During the three-roll planetary rolling process, the cooling efficiency of conventional nozzle structures is insufficient, which can easily lead to copper adhesion on the roll surface, product quality degradation, and shortened roll lifespan, thereby limiting both the quality of copper tubes and overall production efficiency. To enhance the performance of the cooling system, this study proposes a novel elliptical nozzle structure and develops a multiphysics coupled model to reveal the effects of nozzle inclination angle and gas–liquid pressure ratio on cooling behavior. An independently constructed experimental platform was used to measure jet flow patterns and the surface temperature of alloy steel plates under various parameter conditions, thereby validating the accuracy and reliability of the numerical model. The results indicate that, under the same effective outlet area, the elliptical nozzle significantly increases jet exit velocity and overall cooling efficiency. To address the issues of high computational cost and low efficiency during optimization using finite element simulations, a high-accuracy surrogate model based on a Random Forest (RF) algorithm was introduced, and the geometric parameters of the nozzle were globally optimized using a Particle Swarm Optimization (PSO) algorithm. Ultimately, the combined RF-PSO strategy improved the average heat transfer coefficient by 55.57%, markedly enhancing the roll cooling performance and providing a solid theoretical basis and methodological reference for high-performance cooling system design and precision copper tube manufacturing.