Mistuning breaks the cyclic symmetry of bladed disks, leading to localized vibrations and accelerated high-cycle fatigue. To efficiently quantify reliability metrics under mistuning-induced uncertainties, this study develops a cyclic-equivariant B-life active learning (CEBAL) framework for predicting reliability-oriented life quantiles. The surrogate produces two outputs: a scalar log-life prediction and a residual-quantile head that defines a calibrated lower confidence bound (LCB) for conservative candidate ranking during active learning. Final reliability metrics, including life quantiles (e.g., B10/B50), failure probability, and reliability index, are computed exclusively from the orbit-averaged point predictor through Monte Carlo integration. Cyclic symmetry of the 12-sector bladed disk is enforced through a sector-circulant network architecture, sector-rotation data augmentation, and resonance-weighted training. Validation results show accurate LCB calibration, sector-level frequency localization accuracy of 92.8% within +/- 6 Hz, and disk-level accuracy of 95.5% within +/- 6 Hz. Extended validation from engine order 3 (EO = 3) to engine order 2 (EO = 2) further supports transferability in the tested neighboring-EO setting. The framework therefore offers a symmetry-consistent and sample-efficient surrogate approach for reliability assessment of mistuned bladed disks under limited finite element budgets.

Boundary-layer ingestion (BLI) fans operate under severe three-dimensional, non-axisymmetric inlet distortion that induces low engine-order excitations and multi-harmonic blade vibration, posing major challenges for prediction and health monitoring. We develop a probabilistic digital twin (PDT) that embeds physics-consistent cyclic harmonic response synthesis (CHRS) into neural surrogates for (i) forward full-field stress prediction, (ii) inverse identification from sparse multi-harmonic measurements, and (iii) online drift tracking. Physics labels are generated from a reusable database of prestressed cyclic-symmetry finite-element models combined with CHRS, enabling low-cost multi-harmonic modal-superposition evaluations in resonance-critical regimes. A dual-path network learns a shared latent stress manifold that unifies parameter-to-field mapping, sensor-to-parameter inference, and sensor-to-field reconstruction. Manifold-alignment regularization ties the sensor embedding to the physical-parameter manifold, improving identifiability. To stabilize learning in sharply varying resonant regimes, stochastic weight averaging (SWA) is adopted, while conformalized quantile regression (CQR) provides calibrated prediction intervals with near-nominal 95% coverage under independent and identically distributed conditions. On a representative BLI fan case, the PDT predicts peak stress accurately (R2=0.9997) and improves inverse identification across parameters (average MAPE=0.22%, mean R2=0.9936). Drift tests track time-varying parameters (R2 up to 0.94) and peak-stress history (R2 up to 0.74), motivating drift-aware recalibration to sustain coverage for uncertainty-aware integrity monitoring.

Mistuning in bladed disks can cause significant amplification and localization of vibration responses, particularly under unsteady loads, thereby posing serious challenges to structural reliability and service life. This study proposes a hybrid prediction framework that integrates a cyclic-shift (CS) equivariance-consistent physics-informed neural network with deep reinforcement learning (CS-PINN-DRL) to overcome the limitations of conventional methods under small-sample and uncertainty conditions. By embedding rotation-equivariance under coherent sector relabeling (cyclic shifts) together with physical constraints into the neural network and adaptively optimizing the loss-function weighting, the model achieves improvements in both accuracy and stability. Numerical validation shows that the surrogate attains a test-set coefficient of determination (R2 approximate to 0.997) with typical pointwise mean absolute percentage error near 1-2% and reliably identifies the critical blade. Predictions of sectoral peaks and the global resonant frequency show a tight concentration (most deviations within approximately +/- 1 Hz). Uncertainty propagation and variance decomposition indicate that the displacement amplification factor (DAF) and displacement localization factor (DLF) are highly sensitive to parameter variations, whereas resonance metrics remain robust. Furthermore, the total uncertainty is found to be dominated by aleatoric components, with only a minor contribution from epistemic sources. The framework offers an efficient and accurate surrogate for mistuned bladed-disk response prediction, supporting vibration safety assessment and health monitoring.

Bayesian methods are employed for model calibration to enhance the accuracy of combustion chamber predictions in the preliminary design phase. This study integrates the DREAM algorithm with performance parameter estimation methods to develop a calibration model for preliminary combustion chamber design. Indicators such as the total pressure recovery coefficient, outlet temperature distribution factor, and combustion efficiency are employed to calibrate the preliminary combustion chamber design. Ultimately, while preserving the total pressure recovery and combustion efficiency performance, the outlet temperature distribution factor is optimized by 62.2 % in underperforming combustion chambers.

ObjectiveAiming at the low dynamic solution efficiency caused by the complex structure, numerous substructures and connections, and a large number of nodes in the finite element model of aero-engine magazine, a super-element condensation method for the dynamic model of magazine structure with connections was proposed to achieve efficient and accurate solution.MethodsFirstly, a bolt-connected magazine was taken as the research object, and super-element substructures and residual structure were divided based on its physical connection structure. Secondly, external nodes on the connection surface were defined, and the super-element substructures were condensed to the connection surface of the residual structure. Then, each structure was assembled to obtain the condensed model. Finally, the effectiveness of the method was verified by a modal test using the hammering method.ResultsThe modal solution time of the condensed model was reduced from 623 s to 21 s, the maximum error of the simulation frequency before and after condensation was 0.79%, and the average error compared with the test frequency was 0.35%, which greatly improved the computational efficiency while ensuring high modeling accuracy.

Boundary layer ingestion (BLI) improves propulsive efficiency but introduces circumferential inflow distortion that complicates early resonance assessment of fan blades under uncertainty. In this setting, a key challenge is not only accurate prediction of local frequency response functions (FRFs), but also reliable discrimination of resonance-peak identity when posterior FRF realizations compete within a local resonance neighborhood. This study therefore formulates BLI resonance assessment as an uncertainty-aware screening problem for resonancecritical engine-order (EO)-mode neighborhoods in preliminary fan-blade design. Physics-semantic entropy (PSE) is introduced to quantify peak-identity ambiguity, and the area under the risk-coverage curve (AURC) is used for confidence ranking, selective prediction, and active sampling. To support efficient screening, a cyclic travelingwave response synthesis (CTRS) procedure is used to generate high-fidelity local FRFs and normalized peak stresses from a single cyclic-symmetric sector, and a windowed principal component analysis-Gaussian process surrogate is constructed on local normalized FRFs for prediction. Across two retained resonance neighborhoods under the present combined multi-harmonic loading setting, the surrogate achieves held-out coefficients of determination of approximately 0.97-0.99 for peak frequency and normalized peak stress amplitude. Repeated pool-based active-learning replays further reduce the average convergence sample count by approximately 11% relative to random sampling. These results indicate that the proposed framework provides accurate, confidenceinformed resonance screening and enables more targeted use of expensive high-fidelity verification in preliminary BLI fan-blade design.

Model validation for complex simulation models with multivariate functional responses poses significant challenges, as it involves the dual coupling of physical correlations among variables and field correlations in time-series data. A novel Autoencoder-based Dual-Layer Feature Extraction (AE-DLFE) method is proposed. The first layer uses joint principal component analysis to decouple physical correlations, while the second layer develops an Autoencoder-improved Feature Selective Validation (AE-FSV) method that adaptively extracts features of time-series data and measures feature discrepancies via deep representation learning. On this basis, a new validation metric named U-PCDM (Uncertainty Principal Component Difference Measure) is developed to quantify the discrepancies between simulation and experiment under uncertainty. Theoretical analysis confirms the boundedness and unique temporal permutation sensitivity of the proposed metric. Case study results demonstrate that the proposed AE-FSV enhances the evaluation accuracy of traditional FSV on transient data. Furthermore, compared to benchmark methods such as MD-pooling, the U-PCDM metric significantly improves computational efficiency—especially in high-dimensional scenarios—while maintaining consistent model rankings. This work effectively addresses the heterogeneous correlation coupling issue, offering a robust quantitative tool for model validation.

Excessive resonance of aeroengine blades threatens airworthiness, making accurate frequency-domain prediction of vibration responses (frequency response functions, FRFs) imperative. We propose a resonance-aware hybrid surrogate-frequency-domain physics-informed neural network-physics-informed Gaussian process regression (PINN-PIGPR)-for FRFs under multi-source uncertainty. The PINN enforces frequency-domain physical constraints at discrete frequencies and outputs the FRF in one shot. A resonance-window strategy identifies the dominant peak and focuses learning on nearby frequencies, improving accuracy in the resonance band. The PINN prediction then serves as the prior mean of a Gaussian process (GP); a residual GP, trained with a composite kernel over the joint (frequency x parameter) space, achieves cross-frequency coherence and per-frequency corrections. The resulting surrogate supports uncertainty propagation via Monte Carlo simulation (MCS). Validation on a 3-DOF mass-spring benchmark and a dovetail-connected blade shows consistent gains over standalone PINN and GPR: lower peak-frequency and peak-amplitude errors, reduced FRF-normalized root-meansquare error (nRMSE), and sustained accuracy in resonance bands. Before uncertainty propagation, we validate the surrogate's reliability via MCS, where PINN-PIGPR yields reliability estimates closest to the MCS benchmark among the methods compared. These results indicate a physics-consistent, resonance-aware frequency-domain approach suitable for blade health monitoring and frequency-domain safety assessment.

Piezoelectric metastructures offer high adaptability for vibration control in aerospace engineering. Under supersonic flow conditions, aeroelastic effects significantly impact elastic wave properties and thus the vibration suppression performance of piezoelectric metastructures. Nevertheless, comprehensive investigations of their aeroelastic dynamics remain absent. To fill this gap, we develop an analytical framework for an aero-elasto-electric coupled metastructure in this study, and investigate its elastic wave propagation and vibration suppression properties. A non-Hermitian effect is observed through analyzing the dispersion relations of cells and the frequency response functions of finite metastructures. It leads to the amplification of vibration transmission in the flow direction (forward direction), while causing attenuation in the direction against the flow (backward direction), with the phenomenon particularly evident at low frequencies. Nevertheless, the non-Hermitian effect could not enhance the backward vibration attenuation within the local-resonance bandgap. With bandgaps located in low-frequency ranges, the backward attenuation performance may even vanish. In contrast, the forward bandgap attenuation is consistently maintained under supersonic flows with varying dynamic pressure. Distinct nonreciprocal patterns may emerge within and outside the low-frequency bandgap. If the bandgap is designed to lie in a relatively high-frequency range, it can still prohibit vibration transmission effectively in all directions. These findings on the aeroelastic dynamics of piezoelectric metastructures provide useful design guidelines for their applications in supersonic aircraft.

The continuous advancement of modern aero engines places higher demands on fan blades, requiring lighter weight without compromising mechanical properties, such as bird strike resistance. The triply periodic minimal surface (TPMS) structure, a lattice structure, has garnered significant attention due to its lightweight, controllable, and excellent mechanical properties. The progress of additive manufacturing (AM) technology has made it possible to use TPMS structures as fillers for fan blades. This study addresses the challenge of impact resistance in wide-chord hollow fan blades and, for the first time, proposes the use of TPMS structures as the filling layer for such blades. Using a multi-level filling structure impact analysis framework, the blade designs are categorized into three levels of simulation and experimental verification, namely, the material-level, the element-level, and the component-level. To reduce the computational cost of numerical simulations, homogenization models were developed for element-level and component-level specimens. The experimental and simulation results show good consistency between the two, while revealing some unique properties of TPMS as the fan blade filling layer. The research demonstrates that TPMS structure has great potential as a new filling core layer for wide-chord hollow fan blades.

Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used method for investigating the mechanical behavior of such lattice structures through finite element simulations. This study proposes a two-parameter voxel method that incorporates joint control of element size and minimum Jacobian (MJ). Numerical results indicate that the simulation outcomes tend to stabilize when the MJ reaches 0.3. The grid convergence index (GCI), based on Richardson extrapolation, is introduced to systematically assess the numerical convergence behavior of both voxel models and the proposed two-parameter voxel models. This provides a systematic and objective framework for evaluating discretization errors and mesh convergence in TPMS modeling. Compared with traditional voxel method, the proposed method exhibits superior mesh convergence, solution accuracy, and computational efficiency. Furthermore, the two-parameter voxel method also shows excellent applicability in the analysis of graded TPMS structures, exhibiting even better convergence behavior than in uniform structures.

Remote sensing change detection (RSCD) is essential for monitoring surface changes, requiring features that capture both categorical and fine boundary details at high resolution. Deep learning methods typically fuse upsampled coarse features from deep layers with high-resolution shallow features to form comprehensive semantic representations. However, the fixed grid structure in Euclidean space limits the handling of irregular boundaries and edges, often resulting in blurred boundaries, especially near ambiguous thresholds. To overcome these limitations, we propose a graph neural network (GNN)-based feature fusion method that integrates high- and low-frequency information with a mutual information-driven semantic enhancement module. Specifically, we leverage non-Euclidean space to enable flexible spatial transformations during feature extraction. In our framework, low-frequency extraction captures global structure and background features for intraclass consistency, while high-frequency extraction preserves edge details for boundary clarity. After fusing these complementary features, we further optimize their mutual information to suppress background noise and irrelevant changes, enabling the model to focus on true change regions and thereby improving detection accuracy and overall performance. The code is available at https://github.com/sundaobo/GFMNet

Conventional balancing methods for high-speed flexible rotors typically necessitate costly and potentially hazardous balancing tests conducted near their critical speeds. This paper first demonstrates the feasibility of achieving multi-mode balancing using measurements taken below the first critical speed, based on traditional modal balancing methods and rotor modal parameters. However, while theoretically viable, this approach is highly susceptible to measurement noise, complicating its practical implementation. To address this issue, we propose an innovative resonance-avoiding modal balancing (RAMB) method specifically designed for multi-mode balancing. In RAMB, balancing is performed mode by mode in a forward manner, effectively integrating the correction weights of lower modes into the balancing equation. This strategy eliminates the need to operate the rotor at unbalanced critical speeds, enhancing the effectiveness of multi-mode balancing while ensuring measurement safety. The effectiveness of both the conventional method and the RAMB approach is validated through numerical simulations and experimental tests as well. The results show that RAMB significantly enhances the vibration suppression over the entire operating speed range while avoiding resonance measurements and exhibits comparable robustness to noise, confirming the validity and superiority of the proposed balancing method.

Boundary Layer Ingestion (BLI) is a novel propulsion technology that enhances thrust by introducing airflow through the fan blades. However, predicting fan blades high-cycle fatigue (HCF) life for such design is challenging due to uncertainties from factors such as airflow. To address this difficulty, a fan blade HCF life prediction method based on aleatory and epistemic uncertainty with random damage is proposed, aimed at accurately assessing the fatigue life of blades under uncertain conditions. The method combines sparse polynomial chaos expansion-Monte Carlo simulation (SPCE-MCS) with finite element analysis (FEA) to establish the relationship between uncertainty parameters and stress responses. Random damage sequences are constructed by sampling the damage cumulative distribution function (CDF). The expectation-maximization Gaussian mixture distribution (EM-GMD) is then used to quantify the epistemic uncertainty and optimize the normal distribution of fatigue life. The results show that, compared to the traditional method (without considering random damage), the proposed method reduces the confidence interval of fatigue life prediction by over 95 %, with errors in the characteristic parameters of the fatigue life distribution below 3 %, confirming the reliability of the fatigue life distribution. Overall, this study provides an effective solution for reliability assessment of BLI blades.

A planetary gear train involves multiple components and has more complex kinematic relationships than a parallel gear train. Consequently, the fault characteristics extraction is more complicated. To ensure safe operation, it is necessary to properly understand the fault behavior of the planetary gear train. In the previous kinematic modeling, the relationship between the faulty tooth meshing location and the fault impact response phase is not fully considered. However, the fault impact response phase variation plays an important role in accurately characterizing the fault characteristics in the planetary gear train. To solve this problem, we analyze the relationship between the faulty tooth location variation and the fault impact response phase variation and then a novel fault response model is established. Based on this model, a revised planetary damage detection scheme is formulated. Through the simulated data analysis, it is revealed that the faulty tooth location variation not only affects the fault impact response phase, but also reallocates the sideband distributions in the response spectrum. Finally, using a laboratory planetary gear set, it is validated that the proposed model is able to reflect the real damage response better. Therefore, using the proposed model, more accurate damage features are able to be extracted from the measured vibration responses.

Bird strikes pose one of the most significant threats to aviation safety, often leading to substantial loss of life and economic damage. Many bird strike incidents involve multiple birds. However, in previous bird strike studies, the problem of multiple bird strikes has often been neglected. In this paper, the bird slicing process of a rotating engine fan is examined, and a probability model is introduced to assess the risk of multiple impacts on the fan blades. In addition, this paper utilized an implicit–explicit calculation method. The parameters of blade root stress, tip displacement, plastic deformation, and energy were selected to investigate the effects of the time interval and strike position of a bird strike on the dynamic response of and damage to the blades. The results indicated that the position of bird strikes has a more pronounced effect on blade damage compared to the time interval between impacts. Damage to a blade is most severe when the blade root is struck multiple times. Multiple bird strikes may not always lead to a significant increase in maximum blade tip displacement, and may even have a dampening effect.

The health condition of low-speed rolling bearing, such as the main bearing in wind turbines which bears the heavy dead weight and operates under variable speeds, has a big impact on the safe operation of the machinery. Therefore, damage detection of low-speed bearings plays a key role in the health management of large-scale rotating machinery. However, in popular vibration based bearing damage detection algorithms, due to the fact that the additional vibration features incurred by the low-speed operated bearing damage are typically weak in amplitude and low in frequency contents, the additional responses caused by damage are difficult to be isolated by conventional algorithms. Especially, in the cases of variable speed operations, the smearing effect caused by Fourier transform makes it more difficult to extract the damage features by spectrum analysis based methods. To deal with these issues, we developed a damage detection procedure specially designed for bearings operated at low and variable speeds. According to the dynamic properties of the vibration signals incurred by a low-speed bearing with damage, an envelope analysis method based on synchronous averaging with sliding narrow band-pass filters is designed and developed for extracting damage features in the low frequency range. The fundamental theory used in the method is derived first. Then, a damage detection signal processing procedure is constructed based on the elaborated theory. The feasibility and advantages of the proposed methodology are validated by numerical simulations as well as the measured data from a wind turbine field example.

Synchronous analysis is one of the most effective and practical techniques in rotating machinery diagnostics, especially in cases with variable speed operations. A modern analog-to-digital convertor (ADC) usually digitizes an analog signal to an equal time interval data series. Synchronous resampling converts the data series from an equal time interval data series to an equal shaft rotation angle interval data series. This conversion is usually achieved in the digital domain with the aid of shaft speed information, through either direct measurement or identification from a measured vibration signal, which is a time-consuming process. In order to improve the computational efficiency as well as the data processing accuracy, in this paper, a fast synchronous time-point calculation method based on an inverse function interpolation procedure is proposed. By identifying the inverse function of the instantaneous phase with respect to time, the calculation process of synchronous time points is optimized, which results in improved calculation efficiency and accuracy. These advantages are demonstrated by numerical simulations as well as experimental verifications. The numerical simulation results show that the proposed method can improve calculation speed by about five times. The synchronous analysis based on the proposed method was applied to a bearing fault detection in a high-speed rail carriage, which demonstrated the advantages of the proposed algorithm in improving the signal-to-noise ratio (SNR) for bearing damage feature extraction.

To establish a high-fidelity model of engineering structures, this paper introduces an improved Bayesian model updating method for stochastic dynamic models based on frequency response functions (FRFs). A novel validation metric is proposed first within the Bayesian theory by using the normalized half-power bandwidth frequency transformation (NHBFT) and the principal component analysis (PCA) method to process the analytical and experimental frequency response functions. Subsequently, traditional Bayesian and approximate Bayesian computation (ABC) are improved by integrating NHBFT-PCA metrics for different application scenarios. The efficacy of the improved Bayesian model updating method is demonstrated through a numerical case involving a three-degrees-of-freedom system and the experimental case of a bolted joint lap plate structure. Comparative analysis shows that the improved method outperforms conventional methods. The efforts of this study provide an effective and efficient updating method for dynamic model updating based on the FRFs, addressing some of the existing challenges associated with FRF-based model updating.