In practical applications, intelligent diagnostic methods for actuator-integrated gearboxes in industrial driving systems encounter challenges such as the scarcity of fault samples and variable operating conditions, which undermine diagnostic accuracy. This paper introduces a multi-layer feature fusion meta-learning (MLFFML) approach to address fault diagnosis problems in cross-condition scenarios with class imbalance. First, meta-training is performed to develop a mature fault diagnosis model on the source domain, obtaining cross-domain meta-knowledge; subsequently, meta-testing is conducted on the target domain, extracting meta-features from limited fault samples and abundant healthy samples to rapidly adjust model parameters. For data augmentation, this paper proposes a frequency-domain weighted mixing (FWM) method that preserves the physical plausibility of signals while enhancing sample diversity. Regarding the feature extractor, this paper integrates shallow and deep features by replacing the first layer of the feature extraction module with a dual-stream wavelet convolution block (DWCB), which transforms actuator vibration or acoustic signals into the time-frequency space to flexibly capture fault characteristics and fuses information from both amplitude and phase aspects; following the convolutional network, an encoder layer of the Transformer network is incorporated, containing multi-head self-attention mechanisms and feedforward neural networks to comprehensively consider dependencies among different channel features, thereby achieving a larger receptive field compared to other methods for actuation system monitoring. Furthermore, this paper experimentally investigates cross-modal scenarios where vibration signals exist in the source domain while only acoustic signals are available in the target domain, specifically validating the approach on industrial actuator assemblies.

Planetary gearbox serves as a key transmission component in planetary ball screw actuator systems. Under the action of alternating loads, the stress concentration locations of the planet carrier in actuators with planetary gear trains are prone to fatigue cracks, which can lead to catastrophic system breakdowns. However, due to the complex vibration transmission path and the interference of uninterested vibration components, the characteristic modulation signal is ambiguous, so it is challenging to diagnose this fault. Therefore, this paper proposes a new fault diagnosis method. Firstly, a vibration signal model is established to accurately characterize the amplitude and phase modulation effects caused by cracked carriers, providing theoretical guidance for fault feature identification. Subsequently, three novel sideband evaluators of the modulation signal bispectrum (MSB) and their parameter selection ranges are proposed to efficiently locate the optimal fault-related bifrequency signatures and reduce computational cost, leveraging the effects identified by the model. Finally, a novel health indicator, the mean absolute root value (MARV), is used to monitor the state of the planet carrier. The effectiveness of this method is verified by experiments on the planetary gearbox test rig. The results show that the robustness of the amplitude and phase modulation effect of the cracked carrier in the low-frequency band is significantly higher than that in the high-frequency band, and the initial carrier crack can be accurately identified using this phenomenon under different operating conditions. This study provides a reliable solution for the condition monitoring and health management of the actuation system, which is helpful to improve the safety and reliability of operation.

Accurate lithium-ion battery capacity prediction is critical for reliable battery management. However, measured capacity sequences contain slowly varying evolution, local oscillations, and short-term fluctuations, which makes direct raw-sequence prediction difficult. This study proposes an ICEEMDAN-guided fine-grained VMD and frequency-specific TCN–LR framework, named IFVMD-FSTLR. ICEEMDAN first performs coarse separation, retaining the residual as a slowly varying low-frequency component and aggregating the remaining oscillatory components. VMD then refines the aggregated component into compact higher-frequency modes. These components are treated as signal-scale representations rather than direct indicators of specific electrochemical mechanisms. Guided by the reconstruction-error analysis, TCN is used to model the refined higher-frequency components, while linear regression is used for the smoother low-frequency component. The final prediction is obtained by summing the component-wise forecasts. Experiments on the NASA and CALCE datasets are independently repeated five times, with mean ± standard deviation used to characterize result variability. The RMSE, MAE, and MRE are below 0.0033 Ah, 0.0026 Ah, and 0.18% on NASA, and below 0.0044 Ah, 0.0033 Ah, and 0.62% on CALCE, respectively. Overall, IFVMD-FSTLR achieves lower average errors in most evaluated cases.