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.

As a key component of pure electric vehicles, the reducer plays a vital role in power transmission and overall drive system performance. This study investigates the nonlinear dynamic characteristics of helical gears with tooth root crack faults in high-speed reducers. A coupled bending–torsional–shaft dynamic model is developed, in which the time-varying mesh stiffness of cracked helical gears is calculated using an improved potential energy method. The system’s nonlinear dynamic responses under varying mesh error excitation, gear backlash, and damping ratio are numerically obtained via the variable-step Runge–Kutta method. The results reveal that under high input speed conditions, the motion of the faulted system evolves from single-period to quasi-periodic motion as bifurcation parameters change. In the stable state, fault characteristic signals are apparent, whereas under strong nonlinear vibrations and chaotic motion, they become difficult to distinguish in traditional time- and frequency-domain analyses. To address this limitation, the DBSCAN clustering algorithm is introduced, which applies machine learning to cluster the Poincaré cross-sections of the system under different motion states. This approach enables the effective classification and identification of crack-induced and fault-related noise, thereby improving the accuracy of fault detection in nonlinear dynamic gear systems.

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.

The drive system of pure electric vehicles is characterized by high transmission efficiency and a rapid torque response, with the centralized drive configuration being the most commonly adopted. To improve the dynamic performance and reliability of such systems, this study investigates the nonlinear dynamic characteristics of high-speed helical gear reducers used in electric vehicles. A coupled bending–torsional–shaft dynamic model is established, in which the time-varying mesh stiffness is calculated using an improved potential energy method. The system responses under varying mesh errors, backlash, and damping ratios are obtained through numerical integration via the variable-step Runge–Kutta method. The results demonstrate that at high input speeds, the helical gear system exhibits complex nonlinear behavior. Small backlash and minor manufacturing errors lead to stable periodic or quasi-periodic motion, whereas increasing these parameters induces dynamic instability. Moreover, enhancing the mesh damping ratio effectively suppresses chaotic responses and improves overall system stability.

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.

Rub-impact is a critical failure mode in high-speed rotor systems that heavily complicates fault diagnosis. While traditionally studied in aero-engines due to its severe risks of blade damage and thermal-induced rotor instability, rub-impact has increasingly emerged as a crucial concern in modern electric vehicle (EV) traction motors characterized by high speeds, slender shafts, and ultra-narrow rotor–stator air gaps. Since rub-impact rarely occurs in isolation, this study establishes a dynamic model of an EV motor rotor system experiencing compound rub-impact and bearing faults based on Jeffcott rotor theory and the lumped-mass method. The influences of key fault parameters on system dynamics are comprehensively investigated through analyses of time histories, phase trajectories, Poincaré sections, frequency spectra, and envelope spectra. The results show that increasing the rub-impact stiffness (from 1.0 × 10¹⁰ N/m to 3.0 × 10¹⁰ N/m) significantly enhances the non-linear impulsive behavior of the system while reducing the rotor unbalance vibration amplitude by 20.0%. Under compound fault conditions with a local bearing defect width of 3 mm, the disk response is mainly governed by global rub-impact behavior, whereas the bearing-end response is more sensitive to local bearing defects. Under compound fault conditions, although widening the localized bearing defect (from 1 mm to 3 mm) significantly exacerbates the local fault severity at the bearing end, the disk’s phase trajectories, Poincaré maps, and spectra remain virtually uninfluenced. This is attributed to the fact that the relative signature intensity of the bearing fault characteristic frequency $f_i$ attenuates by more than 99% during structural transmission, causing the global non-linear dynamics of the rotor disk to be exclusively governed by global rub-impact behavior and completely insensitive to the localized defect propagation. These quantitative findings provide a precise theoretical basis for the diagnosis and identification of compound faults in rotor systems.