ABSTRACT Deep learning has shown strong potential for diagnosing faults in planetary gearboxes, which are critical components in wind and gas turbines, electric drives, and hybrid vehicle powertrains. However, industrial deployment remains constrained by reliance on initial labels, single-step contrastive objectives, limited modelling of cluster structure, and difficulty detecting previously unseen faults. To address these issues, we propose a stagewise framework, Hierarchical Multi-Granularity Prototype-Contrastive Learning (HMPCL), which maximises the value of limited known-class data by organising representation learning across instance-, subcluster-, and class-level granularities. The framework adopts a multi-stage objective (Stages 0–3), progressing from coarse instance discrimination to refined prototype-guided alignment, while jointly improving intra-cluster compactness and inter-cluster separability under both over-clustered and standard clustering settings. A prototype bank with Sinkhorn-Knopp balanced assignments is introduced to stabilise representation learning, prevent collapse, and strengthen novel fault detection. This hierarchical prototype-based strategy accelerates convergence, improves generalisation, and yields a robust classification system for gearbox fault diagnosis. Experimental results on planetary gearbox datasets across two case studies demonstrate consistently strong diagnostic performance and practical effectiveness.

C-GAN-VAE: Causal Generative Adversarial Variational Autoencoder for few shot fine grained cross domain fault diagnosis for planetary gearbox

Investigation of spatial coupling entropy in quantifying the coupling relationship of information flow in multi-stage planetary gearboxes

As key transmission components in mechanical systems, gearboxes often operate under harsh environments and heavy-load conditions, making them susceptible to various types of damage. In recent years, built-in encoder signals have attracted increasing attention for rotating machinery health monitoring due to their low cost, ease of acquisition, and direct correlation with rotational motion. However, fault-related features in encoder signals are usually weak and easily submerged by strong harmonic interference and noise, posing significant challenges for accurate fault identification and feature extraction. To address this issue, this article proposes a weighted bi-domain sparse decomposition (WBSD) model for encoder signal analysis and fault diagnosis of gearboxes. The proposed WBSD model exploits the distinct morphological characteristics of fault-induced impulses and interference components in both the time and frequency domains. Specifically, two dedicated nonconvex regularization terms are constructed to enforce periodic group sparsity of fault impulses in the time domain and spectral sparsity of harmonic interference in the frequency domain by introducing weighted coefficients, periodic binary vectors, and nonconvex penalty functions, thereby enabling accurate separation and sparse representation of fault features. Furthermore, an efficient iterative solving algorithm is developed for the WBSD model by integrating the alternating direction method of multipliers with the majorization–minimization method. Experimental results obtained from both simulated signals and real encoder signals collected from a planetary gearbox test platform demonstrate that the proposed WBSD model consistently outperforms comparative methods in extracting weak fault impulses under strong noise and interference, confirming its effectiveness and practical applicability for fault diagnosis of gearboxes.

Abstract As a critical component of wind turbines, planetary gearboxes are susceptible to interference from complex environments and transmission path effects, which often mask fault characteristics in vibration signals and compromise diagnostic accuracy. To address these challenges, this paper proposes a time–frequency dual-branch network with dual-level gated fusion (TFDN-DLGF). The model first employs a collaborative preprocessing mechanism that integrates dual-dimensional quality scoring with an improved complete ensemble empirical mode decomposition with adaptive noise signal-to-noise separation method to enhance signal quality and reinforce fault signatures. A dual-branch architecture then extracts complementary features: the time-domain branch utilizes impact-perceptive convolution, ResNext-based dense blocks, and BiGRU to effectively resist broadband noise interference while capturing multi-scale impact characteristics; the frequency-domain branch adopts convolutional neural network, frequency-channel dual attention, and BiGRU to extracts fault-sensitive frequency bands and their evolutionary patterns stably under noisy backgrounds. Finally, the DLGF module achieves adaptive integration at both feature and decision levels, significantly improving noise robustness. Experimental results demonstrate that the proposed method achieves accuracies of 93.75% and 94.50% under strong noise conditions and approaches near-perfect performance under noise-free conditions, substantially outperforming existing methods and providing a reliable solution for gearbox fault diagnosis in high-noise industrial environments.

A fault sample generation method for planetary gearbox based on GA-ICDM

Abstract The knowledge distillation algorithm in incremental learning enables the intelligent diagnosis model for planetary gearboxes to gradually expand the diagnosable fault classes. However, the standard knowledge distillation method still faces two primary challenges. One is that it is difficult to effectively suppress semantic drift, and the other is that it overlooks the mutual interference among highly similar faults in adjacent learning phases. To overcome the above challenges, we propose a novel method called hybrid knowledge distillation. To improve the diagnosis performance of planetary gearboxes under the scenario of continuously expanding fault classes. First, we propose memory proofreading to constrain semantic drift, thereby avoiding the exacerbation of catastrophic forgetting. Then, we introduce feature distillation to learn finer-grained features, reducing confusion among highly similar fault classes, and alleviating catastrophic forgetting caused by them. Finally, we propose advantage distillation to enhance the plasticity of the model. The effectiveness of the proposed method is verified by 10 fault classes of planetary gearboxes. The average incremental accuracy is 96.99%, and the average incremental forgetting is only 2.73%. Compared with the representative continual learning methods learning without forgetting, synaptic intelligence and incremental classifier and representation learning, the proposed method has the best performance and a large increase. It also adapts well to different class-incremental scenarios. The results show that proposed method can effectively alleviate catastrophic forgetting and well balance the stability and plasticity of the model.

Background: Panchagavya, a traditional bio-formulation prepared from cow-derived ingredients (milk, curd, ghee, urine and dung), is valued for its ability to enhance soil fertility and plant growth. However, the conventional preparation method requires labor-intensive, repeated manual stirring for proper fermentation, leading to inconsistent quality and limited scalability. Mechanization is needed to produce Panchagavya efficiently and uniformly for wider adoption in organic farming. Methods: A motor-operated mixer was designed and fabricated using a 230 V AC single-phase motor (0.186 kW) coupled with a 10:1 planetary gearbox to drive a helical ribbon-type blade inside a 100 L HDPE container. Torque and power requirements were calculated to ensure adequate mixing without damaging microbial integrity. Performance was evaluated at batch sizes of 50, 75 and 100 L by measuring mixing time, homogeneity of total soluble solids, energy consumption and labor effort. Statistical analysis was performed using one-way ANOVA. Result: The motorized mixer achieved 98.3%±0.7 homogeneity, significantly higher than crank-operated (91.2%±1.5) and manual (83.4%±2.1) methods (p less than 0.05). Mixing time was reduced to 5-10 min, more than 60 % faster than manual practice. Energy consumption ranged from 0.0155 to 0.0310 kWh per batch, costing only ₹ 0.12-0.25 per cycle. Operator involvement was limited to less than two minutes, translating to potential labor savings of about ₹ 1,000 per month for a farmer preparing Panchagavya every other day. Thermal tests showed motor temperatures remained below 45oC, confirming mechanical stability.

Abstract Planetary gearboxes in wind turbines operate under complex conditions, while labeled fault data from large-scale systems are often scarce or unavailable, making conventional data-driven and transfer learning–based fault diagnosis methods impractical due to their reliance on target-domain fault samples or restrictive domain assumptions. To address this issue, this paper proposes a sample-free cross-domain fault diagnosis framework that integrates a digital twin–driven feature generation strategy with a multi-scale category-aligned convolutional neural network (MSCA-CNN) and amplitude-sensitive permutation entropy (ASPE). A high-fidelity aggregate-parameter digital twin dynamic model of a wind turbine planetary gearbox is first constructed to generate labeled vibration responses under different fault conditions. Representative fault features, including kurtosis, envelope spectral peak, and ASPE, are then extracted to form source-domain feature vectors. Based on these data, the proposed MSCA-CNN is trained using category-conditioned domain adversarial learning to build a transfer learning fault diagnosis model capable of reducing the distribution discrepancy between simulated and measured signals. The trained model is finally evaluated on multiple publicly available planetary gearbox datasets with different structural configurations. Experimental results demonstrate that the proposed framework enables reliable cross-domain fault diagnosis without requiring real fault samples from wind turbines, exhibiting strong robustness and generalization performance.

Abstract Reliable fault diagnosis of wind turbine planetary gearboxes is crucial for ensuring operational stability and minimizing maintenance costs. However, in practical industrial environments, vibration signals are often contaminated by noise, and the scarcity of fault samples severely constrains the effectiveness of conventional deep learning-based fault diagnosis methods. To address these challenges, this paper proposes a novel hybrid multi-scale and dilated convolutional attention network (MCAN) specifically designed for intelligent fault diagnosis of wind turbine planetary gearboxes under the combined conditions of noise and limited samples. The model incorporates multi-scale and dilated convolution branches to synergistically model both local transient features and long-range dependencies. Concurrently, a self-attention-based feature fusion module is designed to adaptively enhance discriminative key features while suppressing redundant noise. Comprehensive experiments conducted on the wind turbine planetary gearboxes dataset demonstrate that MCAN outperforms mainstream methods, including LiConvFormer, WDCNN, ResNet, TCN-BiLSTM, and MCNN-LSTM, across various noise levels and sample sizes. Ablation studies and attention visualization further validate the effectiveness of the model's architecture. Notably, even under extreme conditions (e.g., SNR = 2 dB and minimal samples), MCAN maintains a high diagnostic accuracy, showcasing exceptional robustness and generalization capability. This research provides an effective solution for the intelligent monitoring of wind power equipment under complex operating conditions, holding significant promise for broad engineering applications.

High-performance geared turbofan engines generate significant heat within the planetary power gearbox. This study presents the thermal design of an integrated fan guide vane heat exchanger aimed at recovering gearbox heat losses with minimal pressure loss and converting them into useful propulsive energy via the Junkers–Meredith Effect. Hot gearbox oil is routed through hollow fan static guide vanes, enabling heat transfer to the bypass airflow while simultaneously reducing oil temperature and augmenting thrust. A comprehensive analytical framework is applied, incorporating heat transfer modeling, guide vane geometry reconstruction, lubrication flow sizing, and propulsion performance evaluation for both take-off and cruise flight conditions, using the PW1127G-JM geared turbofan as the reference engine. The results indicate that the proposed system can achieve a thrust increase of up to 6.4% at the end of take-off and deliver a thrust-specific fuel consumption reduction of up to 5.6% during take-off and approximately 2% during cruise. While sufficient heat dissipation is achieved under cruise conditions, take-off operation requires a higher transient oil temperature. Overall, this study demonstrates that integrating heat recovery into existing engine structures offers a promising pathway to enhance propulsion efficiency, reduce fuel consumption, and support more sustainable aircraft engine designs.

Cracks in planetary gearbox casings generate additional vibration responses, which may be used for monitoring structural degradations. This paper provides a signal processing framework to effectively track casing crack-related features in planetary gearboxes using the carrier synchronous signal average (C-SSA). The proposed algorithm is based on processing the hunting-tooth synchronous signal average (H-SSA) to extract the C-SSA which contains the cyclic interaction between the gear loadings and the corresponding casing response. The root mean square (RMS) of the C-SSA signal can then serve as a health condition indicator (CI) to track crack propagation. Further enhancement can be achieved by applying the Hilbert transform (HT) on the C-SSA using the full bandwidth to derive squared envelope signal, which enhances the trending capability. To remove cyclic temperature influences observed in the trends, singular spectrum analysis technique (SSAT) has been used to ensure that the trend reflects the changes purely due to the damage progression. Experiments using three casing-mounted sensors show good capability to track crack progression. Tests under 100%, 125%, and 150% load levels show consistent performance across these operating conditions, with better results seen at higher loads. The results demonstrate that C-SSA and its squared envelope signal effectively enhance the sensitivity and reliability of vibration-based casing crack detection, providing a practical tool for long-term structural health monitoring of planetary gearboxes.

Gearboxes are essential mechanical components for power transmission. Among them, planetary gearboxes stand out for their compact design and high reduction ratio, making them particularly advantageous in various sectors such as energy generation, transportation, and robotics. Like all mechanical components under load, they are susceptible to different types of degradation, including wear, cracks, chipping, and even broken teeth. Such defects can negatively impact transmission quality, potentially leading to system shutdowns and endangering operators. This necessitates an autonomous monitoring solution that can respond in real-time. This paper presents a robust monitoring methodology for diagnosing faults in planetary gearboxes. The approach begins with filtering the monitoring signals using Variational Mode Decomposition (VMD). The filtered signal is then transformed into a time–frequency image using Wavelet Transform (WT). These images are subsequently used to train a transfer learning network. To ensure the robustness of the proposed intelligent solution, a data augmentation step is included to address issues of data scarcity and imbalanced datasets. Experimental validation demonstrates the effectiveness of the proposed methodology under different operating conditions. • Autonomous, intelligent fault diagnosis methodology for planetary gearboxes. • Signal filtering using variational mode decomposition for noisy environments. • Solutions to data scarcity and dataset imbalance in intelligent diagnosis.

Improved vibration separation technique for planetary gearbox fault diagnosis based on resonance demodulation and initial phase optimization

The distribution discrepancy metrics are the core foundation of achieving domain confusion. Therefore, they mainly determine the performance of deep transfer diagnosis models. However, their effectiveness relies on the stability of data local distributions, making them unsuitable for cross-domain machine diagnosis tasks under continuous time-varying conditions. Hence, a new integrated-dispersion manifold distance (IDMD) is proposed to enhance the discrepancy representation capability in dynamic data structures. The maximum entropy-based local distribution (MELD) selection mechanism is designed to represent the global distribution information of time-varying monitoring signals adaptively. Furthermore, the ensemble Grassmann manifold geodesic (EGMG) measurement is constructed to characterize the intrinsic distribution discrepancy information due to complex nonlinear structures of high-dimensional data. The proposed IDMD distribution discrepancy metric is validated against two fault transfer diagnosis experiments under time-varying conditions, including laboratory planetary gearboxes and actual wind turbine bearings. The experimental results demonstrate its effectiveness and advantage over the existing advanced methods.

A methodology has been developed for creating a fundamentally new high-speed planetary gearbox for an electric vehicle drive with double-crown planetary gears mounted in central bearing supports mounted on the periphery of a three-lobed flange integral with the planet carrier. Functional relationships have been established that enable the determination of rational parameters for a high-speed gearbox with improved dynamic performance. The use of alloyed materials for gears, whose performance criterion is contact strength, with high mechanical properties has enabled significant material savings, reduced weight and dimensions, and improved the technical and economic performance of the electric vehicle gearbox. The selection of gear material is based on loading conditions and cost effectiveness. The developed planetary gearbox has a simpler design, smaller dimensions and weight, increased efficiency, and improved speed and power characteristics compared to similar products.

The rapid expansion of offshore wind energy underscores the critical need for reliable gearbox monitoring, especially for failure-prone planetary gearboxes in harsh marine environments. To address this, we propose two novel, physics-informed diagnostic parameters: the Filtered Root Mean Square (FRMS) and the Normalized Summation of the positive amplitudes of the Difference Spectrum (NSDS). These parameters enhance fault detection by isolating fault-related vibrations from healthy gearbox modulation. Furthermore, an integrated, real-time diagnosis system implementing these parameters is developed using LabVIEW. Experimental validation on a dedicated test bench demonstrates the system's effectiveness, achieving a diagnostic accuracy of 95.4 % and outperforming traditional methods. This work provides a practical and efficient solution for condition monitoring of offshore wind turbine gearboxes.

Effectively reducing the distribution discrepancy between domains is essential for enhancing the accuracy of multichannel fault diagnosis under cross-domain conditions. When extracting domain-invariant features from multichannel data, existing transfer learning methods struggle to minimize the conditional distribution discrepancy between different class-level subdomains while preserving intrinsic structural information. To address the above issue, this article proposes a novel tensor transfer learning approach termed multilinear joint distribution adaptation (MJDA). Specifically, inspired by JDA, we extend the JDA model into tensor space and formulate a corresponding optimization problem, which is efficiently solved by an alternating iterative algorithm. By estimating a set of transformation matrices without vectorization, MJDA directly minimizes the joint distribution discrepancy to extract domain-invariant features. Furthermore, twin support higher-order tensor machines are embedded as a tensor classifier, which not only provides pseudo labels for the target domain but also performs fault pattern recognition on the testing data. Extensive transfer experiments on planetary gearbox datasets demonstrate that the proposed MJDA consistently outperforms other typical tensor transfer learning models.

The traditional deconvolution method can filter out the interference caused by the propagation path and noise from the complex vibration signal to restore the fault excitation characteristics. In order to solve the influence of the initial filter coefficients on the convergence results of the algorithm and improve the accuracy of fault identification, this paper designed filter optimized minimum entropy deconvolution (FOMED) method. Firstly, the method of mode location and initial filter coefficient construction based on spectrum trend is studied to achieve the rough estimation of frequency domain mode. Then, the filter coefficients based on Meyer wavelet are introduced to update the initial filter banks. Simulation results show that the new iterative updating method has better robustness. Finally, through kurtosis of unbiased autocorrelation of square envelope (AC), the fault information in the filtering results is screened and diagnosed. The experimental data verify that the proposed FOMED is suitable for fault detection of planetary gearbox in wind turbine transmission system and rolling bearing in rotating machinery equipment.

Abstract Aero-engines have complex structures and operate under harsh conditions, making the rotating components of their power transmission units prone to failures that compromise operational safety. While existing intelligent fault diagnosis algorithms primarily address single-condition challenges, such as variable operating conditions or class imbalance, few can stably handle compound conditions where these issues coexist. To resolve this problem, this manuscript proposes a comprehensive solution: (1) a decision-constrained class weighting strategy is adaptively applied to class imbalance to enhance diagnostic performance under class imbalance; (2) multi-classifier consensus constraints are then integrated to ensure diagnostic reliability through voting-based result alignment; (3) furthermore, an inter-class separation and intra-class aggregation strategy is used to amplifies feature discriminability to further improve model performance; (4) Wasserstein distance minimization is employed to reduce cross-domain distribution discrepancies, strengthening domain adaptation capability. Validated on planetary gearbox and ultra-high-speed aerospace bearing test bench datasets, the method achieves consistent fault classification accuracy above 92%, demonstrating robust and high-precision transfer diagnosis for rotating components under composite conditions. This establishes a solid foundation for intelligent aero-engine health management.