The operational reliability of aero-engines is critically dependent on the health of rolling element bearings, while incipient fault diagnosis remains particularly challenging under small-sample conditions. Although multiscale entropy methods are widely used for complexity analysis, conventional coarse-graining strategies suffer from severe information loss and unstable estimation when data are extremely limited. To address this, the primary objective of this study is to develop a robust diagnostic framework that ensures feature consistency and classification stability even with minimal training samples. Specifically, this paper proposes an integrated approach combining Refined Time-shifted Multiscale Rating Entropy (RTSMRaE) with an Animated Oat Optimization (AOO)-optimized Extreme Learning Machine (ELM). By introducing a refined time-shift operator and a dual-weight fusion mechanism, RTSMRaE effectively preserves transient impulsive features across multiple scales while suppressing stochastic fluctuations. Meanwhile, the AOO algorithm is employed to optimize the input weights and hidden biases of the ELM, alleviating performance instability caused by random initialization and improving generalization capability. Experimental validation on both laboratory-scale and real-world aviation bearing datasets demonstrates that the proposed RTSMRaE-AOO-ELM framework achieves a diagnostic accuracy of 99.47% with a standard deviation of ±0.48% using only five training samples per class. These results indicate that the proposed method offers superior diagnostic robustness and computational efficiency, providing a promising solution for intelligent condition monitoring in data-scarce industrial environments.

Precision rolling bearings serve as critical components in a range of diverse industrial applications, where their continuous health monitoring is essential for preventing costly downtime and catastrophic failures. Early-stage bearing defects present significant diagnostic challenges, as they manifest as weak, nonlinear, and non-stationary transient features embedded within high-amplitude random noise. While entropy-based methods have evolved substantially since Shannon’s pioneering work—from approximate entropy to multiscale variants—existing approaches continue to face limitations in their computational efficiency and information preservation. This paper introduces the Adaptive Composite Multiscale Slope Entropy (ACMSlE) framework, which overcomes these constraints through two innovative mechanisms: a time-window shifting strategy, generating overlapping coarse-grained sequences that preserve critical signal information traditionally lost in non-overlapping segmentation, and an adaptive scale optimization algorithm that dynamically selects discriminative scales through entropy variation coefficients. In a comparative analysis against recent innovations, our integrated fault diagnosis framework—combining Fast Ensemble Empirical Mode Decomposition (FEEMD) preprocessing with Particle Swarm Optimization-Extreme Learning Machine (PSO-ELM) classification—achieves 98.7% diagnostic accuracy across multiple bearing defect types and operating conditions. Comprehensive validation through a multidimensional stability analysis, complexity discrimination testing, and data sensitivity analysis confirms this framework’s robust fault separation capability.

Reliable fault diagnosis in aero-engine bearing systems is essential for maintaining process stability and safety. However, acquiring fault samples in aerospace applications is costly and difficult, resulting in severely limited data for model training. Traditional methods often perform poorly under such constraints, lacking the ability to extract discriminative features or effectively correlate observed signal changes with underlying process faults. To address this challenge, this study presents a process-oriented framework—WSET-CNN-OOA-LSSVM—designed for effective fault recognition in small-sample scenarios. The framework begins with Wavelet Synchroextracting Transform (WSET), enhancing time–frequency resolution and capturing energy-concentrated fault signatures that reflect degradation along the process timeline. A tailored CNN with asymmetric pooling and progressive dropout preserves temporal dynamics while preventing overfitting. To compensate for limited labels, confidence-based pseudo-labeling is employed, guided by Mahalanobis distance and adaptive thresholds to ensure reliability. Classification is finalized using an Osprey Optimization Algorithm (OOA)-enhanced Least Squares SVM, which adapts decision boundaries to reflect subtle process state transitions. Validated on both test bench and real aero-engine data, the framework achieves 93.4% accuracy with only five fault samples per class and 100% in full-scale scenarios, outperforming eight existing methods. Therefore, the experimental results confirm that the proposed framework can effectively overcome the data scarcity challenge in aerospace bearing fault diagnosis, demonstrating its practical viability for few-shot learning applications in industrial condition monitoring.

Imbalanced data classification remains a fundamental challenge in machine learning, especially in multi-class scenarios where feature noise, class overlap, and small disjunct sub-concepts are prevalent. While various oversampling techniques have been proposed, most existing methods are primarily designed for binary classification and often struggle with noise sensitivity and structural preservation in complex multi-class settings. To address these gaps, this paper proposes a Newton’s Cooling Law-Based Weighted Oversampling strategy (MC-NCLWO) specifically tailored for imbalanced multi-class datasets. First, a dynamic noise-cleaning mechanism inspired by Newton’s Cooling Law is introduced to adaptively identify and eliminate noisy majority class samples based on the classification difficulty of each instance. Second, a difficulty-weighted sample generation strategy is employed to maintain local class balance and preserve the intrinsic structure of minority class sub-concepts. Furthermore, a sampling-priority strategy is designed to coordinate the oversampling process among multiple classes, thereby reducing mutual interference and ensuring the structural integrity of each minority class. Comprehensive experiments on 23 benchmark datasets demonstrate that MC-NCLWO consistently outperforms 10 state-of-the-art methods across multiple performance metrics, including F_βM, AvAcc, CBA, and CEN. Additionally, the proposed method exhibits strong robustness in high-noise environments, significantly mitigating performance degradation caused by feature-level noise.

Strong noise can obscure the transient and modulation signatures used for bearing fault diagnosis, while envelope-based methods remain sensitive to the frequency band selected before demodulation. This study proposes a learnable band-selective envelope fusion WDCNN (LBEF-WDCNN). A raw-waveform branch extracts temporal features, whereas an auxiliary branch applies four differentiable Gaussian masks, reconstructs the corresponding spectrally selected waveforms, and encodes their Hilbert envelope spectra. Both branches are trained jointly and combined using a fixed, sample-independent residual coefficient of $0.1$. The method was evaluated on HUST using a matched-noise protocol comprising additive white Gaussian noise (AWGN), colored noise, and impulse noise at 0, $-6$, and $-10$ dB, with additional dataset-specific evaluations on CWRU and PU. Across the nine HUST conditions, LBEF-WDCNN achieved the highest average Macro-F1 of $98.53\%$ using 74,065 trainable parameters. At $-10$ dB AWGN, it reached $95.30\%$ Macro-F1, exceeding DRSN-CW by 7.68 percentage points. Ablation results showed that learnable band selection improved the three-noise average at $-10$ dB from $94.79\%$ for fixed bands to $96.73\%$. DRSN-CW remained stronger under severe impulse noise. These results indicate that the proposed representation is particularly effective under severe broadband contamination while retaining a compact model size.

Reliable fault diagnosis of rotating machinery is critical for averting serious failures in modern industrial systems. While data-driven deep learning has advanced condition monitoring, its success is fundamentally predicated on the availability of independent and identically distributed (I.I.D.) datasets. In realistic operational environments, machinery frequently experiences massive domain shifts induced by varying rotational speeds. Concurrently, acquiring high-fidelity fault instances is limited compared to abundant healthy baseline data, often resulting in a long-tailed distribution. Under such data-starved conditions, conventional few-shot domain adaptation (FSDA) methodologies often may be affected by distributional erasure; global alignment objectives are mainly driven by the healthy majority, causing sparse fault signatures to be erroneously absorbed as noise and leading to severe diagnostic performance degradation. To address this setting, this study develops a physics-guided dual-stream fusion framework for extreme few-shot cross-domain fault diagnosis. The method does not treat the Laplace wavelet, STFT, CNNs, or AdaBN as newly introduced techniques. Instead, it integrates these components into a unified diagnostic pipeline designed for long-tailed target support sets under large speed shifts. A learnable Laplace wavelet convolution is used in the temporal branch to emphasize transient impact responses, while STFT spectrograms provide a complementary time-frequency representation for the two-dimensional branch. The two feature streams are then fused for target fault classification. For domain adaptation, a Strict AdaBN strategy is applied using only the target support set, rather than the target test data or a large unlabeled target pool. Under the evaluated 50 healthy + 12 fault support condition, the healthy samples provide target-domain operating-background statistics for BN recalibration, while the limited fault samples are used for supervised classifier adjustment. Experiments on the HUSTbearing and Torino DIRG datasets show that the proposed integrated framework achieves stable performance under the evaluated few-shot cross-speed settings. These results suggest that combining physics-guided Laplace convolution, time-frequency representations, and support-set-restricted BN recalibration can be useful for bearing fault diagnosis when target fault samples are limited.