Integrated blisk–shaft rotors represent a critical advancement in aero-engine design, offering enhanced structural integrity and weight reduction. However, their complex dynamic behavior under inherent material uncertainties poses significant challenges for reliable vibration prediction. This study presents a novel stochastic uncertainty analysis framework combining reduced-order finite element modeling and artificial neural networks (ANNs) to efficiently and accurately quantify the modal variability of integrated blisk–shaft rotors. A high-fidelity finite element model is first developed, followed by the construction and validation of a reduced-order model (ROM) to substantially decrease computational costs while preserving modal accuracy. Material parameter uncertainties are introduced, and corresponding natural frequencies are computed using the ROM. Subsequently, an ANN surrogate model is trained to capture the nonlinear mapping between uncertain input parameters and modal frequencies, enabling rapid prediction across the stochastic parameter space. The proposed approach is employed to perform comprehensive uncertainty propagation and global sensitivity analyses, identifying the dominant parameters influencing each modal frequency. Results demonstrate that the combined ROM-ANN methodology achieves high predictive accuracy with significantly reduced computational effort, offering an effective tool for uncertainty-aware dynamic analysis and design optimization of integrated blisk–shaft rotors. This work advances the integration of machine learning techniques with classical structural dynamics for robust aero-engine rotor design under uncertainty.

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.

Integrated blisk–shaft rotors are susceptible to low-cycle fatigue (LCF) under complex operating conditions and parameter uncertainties, rendering direct finite-element-based probabilistic assessment computationally demanding. This study develops a surrogate-assisted fatigue-reliability framework integrating dominant-cycle identification, an improved cat swarm optimization-assisted artificial neural network (ICSO-ANN), and Monte Carlo simulation. Elastoplastic finite-element analysis is first performed to identify the fatigue-critical region and dominant fatigue cycle. Subsequently, 1000 finite-element samples are generated using Latin hypercube sampling. Four independent assessments are conducted, each using 200 samples for model development and 50 held-out samples for independent testing. The ICSO-ANN achieves a MAPE of 0.77%, demonstrating high accuracy in fatigue life prediction. Probabilistic analysis against a normally distributed design life requirement with a mean of 11,000 cycles yields a reliability of approximately 98.6%. On an identical 10³-sample basis, the surrogate-assisted analysis achieves an approximately 69-fold computational speedup over direct finite-element-based Monte Carlo analysis. Sensitivity analysis further identifies fatigue strength parameters and rotational speed as the dominant contributors to fatigue life uncertainty. The proposed framework provides a computationally efficient approach for the uncertainty propagation and probabilistic LCF reliability assessment of integrated blisk–shaft rotors.