On top of the condition-based maintenance (CBM) practice for rotating machinery, the robust estimation of remaining useful life (RUL) for rolling-element bearings (REB) is of particular interest. The failure of a single bearing often results in secondary defects in the connected structure and catastrophic system failures. The prediction of RUL facilitates proactive maintenance planning to ensure system reliability and minimize financial loss due to unscheduled downtime. In this paper, to acquire early and reliable estimations of useful life, the RUL prediction of REBs is formulated into nonlinear degradation state estimation tackled by the combination of the envelope spectral indicator (ESI) and extended Kalman filter (EKF). By fusing the spectral energy of the bearing fault characteristic frequencies (FCFs) in the averaged envelope spectrum, the ESI is crafted to remove the interference from rotor-dynamics and reveal the bearing deterioration process. Once the fault is identified, the recursive Bayesian method based on EKF is utilized for estimating the bearing end-of-life time via the exponential state-space model. The distinctive advantage of the proposed approach lies in its ability to make an early prediction of RUL using a small number of ESI observations, offering an efficient practice for predictive health management at the early stage of bearing fault. The performance of the proposed method is validated using publicly available experimental bearing vibration data across three different operating conditions.

The incipient damages of mechanical equipment excite weak impulse vibration, which is hidden, almost unobservable, in the collected signal, making fault detection and failure prevention at the inchoate stage rather challenging. Traditional feature extraction techniques, such as bandpass filtering and time-frequency analysis, are suitable for matrix processing but challenged by the higher-order data. To tackle these problems, a novel method of impulse feature extraction for vibration signals, based on sparse non-negative tensor factorization is presented in this paper. Primarily, the phase space reconstruction and the short time Fourier transform are successively employed to convert the original signal into time-frequency distributions, which are further arranged into a three-way tensor to obtain a time-frequency multi-aspect array. The tensor is decomposed by sparse non-negative tensor factorization via hierarchical alternating least squares algorithm, after which the latent components are reconstructed from the factors by the inverse short time Fourier transform and eventually help extract the impulse feature through envelope analysis. For performance verification, the experimental analysis on the bearing datasets and the swashplate piston pump has confirmed the effectiveness of the proposed method. Comparisons to the traditional methods, including maximum correlated kurtosis deconvolution, singular value decomposition, and maximum spectrum kurtosis, also suggest its better performance of feature extraction.

This study presents an efficient vibration-based fault detection method for rotating machines utilising the poly-coherent composite spectrum (pCCS) and machine learning techniques. pCCS combines vibration measurements from multiple bearing locations into a single spectrum, retaining amplitude and phase information while reducing background noise. The use of pCCS significantly reduces the number of extracted parameters in the frequency domain compared to using individual spectra at each measurement location. This reduction in parameters is crucial, especially for large industrial rotating machines, as processing and analysing extensive datasets demand significant computational resources, increasing the time and cost of fault detection. An artificial neural network (ANN)-based machine learning model is then employed for fault detection using these reduced extracted parameters. The methodology is developed and validated on an experimental rotating machine at three different speeds: below the first critical speed, between the first and second critical speeds, and above the second critical speed. This range of speeds represents the diverse dynamic conditions commonly encountered in industrial settings. This study examines both healthy machine conditions and various simulated fault conditions, including misalignment, rotor-to-stator rub, shaft cracks, and bearing faults. By combining the pCCS technique with machine learning, this study enhances the reliability, efficiency, and practical applicability of fault detection in rotating machines under varying dynamic conditions and different machine conditions.

Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. Once faults are detected, accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their robustness and practicability need further improvement regarding physical interpretation and uncertainty quantification. This work leverages variational neural networks to model bearing degradation behind envelope spectra. A convolutional variational autoencoder for regression (CVAER) is developed to probabilistically predict RUL distributions with confidence measures. Enhanced average envelope spectra (AES) are used as network input for its physical robustness in bearing condition assessment and fault detection. The use of the envelope spectrum ensures that it contains only bearing-related information by removing other rotor-related frequencies, hence it improves the RUL prediction. Unlike traditional variational autoencoders, the probabilistic regressor and latent generator are formulated to quantify uncertainty in RUL estimates and learn meaningful latent representations conditioned on specific RUL. Experimental validations are conducted on vibration data collected using multiple accelerometers whose natural frequencies cover bearing resonance ranges to ensure fault detection reliability. Beyond conventional bearing diagnosis, envelope spectra are extended for statistical RUL prediction integrating physical knowledge of actual defect conditions. Comparative and ablation studies are conducted against benchmark models to demonstrate their effectiveness.

For early fault detection of a bearing, the localized defect generally brings a complex vibration signal, so it is difficult to detect the periodic transient characteristics from the signal spectrum using conventional bearing fault diagnosis methods. Therefore, many matrix analysis technologies, such as singular value decomposition (SVD) and reweighted SVD (RSVD), were proposed recently to solve this problem. However, such technologies also face failure in bearing fault detection due to the poor interpretability of the obtained eigenvector. Non-negative Matrix Factorization (NMF), as a part-based representation algorithm, can extract low-rank basis spaces with natural sparsity from the time–frequency representation. It performs excellent interpretability of the factor matrices due to its non-negative constraints. By this virtue, NMF can extract the fault feature by separating the frequency bands of resonance regions from the amplitude spectrogram automatically. In this paper, a new feature extraction method based on sparse kernel NMF (KNMF) was proposed to extract the fault features from the amplitude spectrogram in greater depth. By decomposing the amplitude spectrogram using the kernel-based NMF model with L1 regularization, sparser spectral bases can be obtained. Using KNMF with the linear kernel function, the time–frequency distribution of the vibration signal can be decomposed into a subspace with different frequency bands. Thus, we can extract the fault features, a series of periodic impulses, from the decomposed subspace according to the sparse frequency bands in the spectral bases. As a result, the proposed method shows a very high performance in extracting fault features, which is verified by experimental investigations and benchmarked by the Fast Kurtogram, SVD and NMF-based methods.