This study provides a comprehensive overview of challenges and advancements in vibration analysis for machinery operations under non-stationary and non-linear conditions. Non-stationary operation in machinery occurs when operating conditions such as speed, load, and environmental factors change over time. This results in dynamic behaviours that cause fluctuating vibration signals, making fault detection challenging with traditional methods that assume stationary conditions. The paper provides foundational insights and clear concepts on essential topics, including non-stationary operations in rotary machinery , vibration signals in non-stationary operations, cycle-stationary analysis, and the quantification of non-stationary operations. Further advancing, this paper explores the challenges and methodologies in condition-based monitoring for non-stationary machinery operations, focusing on the analysis of vibrational signals. It examines the complexities of working with non-stationary and cyclo -stationary signals and the limitations of traditional signal processing techniques . The study reviews classical time–frequency and advanced signal-processing methods, highlighting their advantages, drawbacks, and applicability in real-world scenarios. Additionally, it addresses the identification of defects across varying operational speeds, identifying gaps in current methodologies and suggesting potential avenues for future research. The paper also emphasizes the importance of transfer learning in non-stationary environments, analyzing various approaches and their effectiveness in improving monitoring performance. Lastly, it discusses the development of expertise and adoption pathways for AI-based predictive maintenance , offering insights into the practical integration of advanced technologies in industrial settings.

The statistical characterization of heavy-tailed data with hidden irregular periodicities is introduced. Specifically, processes generated by the interaction of random phenomena with heavy-tailed distribution and almost-periodic phenomena with possibly irregular or disturbed peridicities are characterized in terms of fractional lower-order moments. For this wide class of processes, fractional lower-order moments are expressed as the superposition of amplitude- and angle-modulated sine waves. The model introduced in the paper extends the previously introduced one for heavy-tailed almost cyclostationary (ACS) processes to the case of irregular periodicities. Moreover, it introduces for the class of the oscillatory ACS processes a characterization in terms of fractional lower-order moments. For the new class, the problem of statistical function estimation is addressed. The effectiveness of the proposed methodology is corroborated by the analysis of simulated alpha-stable time-warped ACS processes and of real acoustic helicopter data. • The statistical characterization of heavy-tailed data with hidden irregular periodicities is introduced. • Fractional lower-order moments are expressed as the superposition of amplitude- and angle- modulated sine waves. • The problem of statistical function estimation is addressed. • Simulated alpha-stable time-warped almost-cyclostationary processes and real acoustic helicopter data are analyzed.

Local damage of bearings can be detected as a weak cyclic and impulsive component in a highly noisy measured signal. A key problem is how to extract the signal of interest (SOI) from the raw signal, i.e., how to identify and design an optimal filter. To tackle this problem, in this article, we propose to use stochastic sampled orthogonal nonnegative matrix factorization for extracting frequency-based features from a spectrogram of the measured signal. The proposed algorithm finds a selective filter that is tailored to the frequency band of the SOI. We show that our approach outperforms the other state-of-the-art selectors that were previously used in condition monitoring. The efficiency of the proposed method is illustrated using both a simulation study and the following real signals: vibration signal from a test rig in the laboratory and acoustic signal from a belt conveyor.

Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied to local damage detection in rolling elements of bearings via spectrogram factorization. NMF applied to the spectrogram allows one to find an informative frequency band, which could be further used as a filter characteristic. However, the obtained filter characteristics mostly detect the informative frequency band, which also encompasses a lot of noise. In the case where noise is more problematic, as is the case for acoustic signals from industrial machines, the NMF hardly detects the damage. To solve this problem and obtain more selective filters, which are more robust to noise, we propose the non-negative matrix under-approximation (NMU) as an informative frequency band selector. Due to the more sparse parts-based representation of the NMU compared to NMF, NMU provides more selective filter characteristics, which neglect the non-informative frequency bands related to the noise. In practice, it means that NMU gives a better signal-to-noise ratio for the filtered signal. The efficiency of the proposed approach has been validated on the vibration signal from the test rig and the acoustic signal from an idler.

The prognosis of a machine condition becomes a hot topic nowadays, as the condition monitoring installations provide a massive amount of Health Index (HI) data that could be used for machine remaining lifetime prognosis. However, existing methodologies might not be effective since in many cases the real HI datasets exhibit non-Gaussian characteristics. Thus, to improve efficiency, there is a need to introduce novel approaches which take into account the possible non-Gaussian distribution of HI data. In the proposed methodology, several innovative components are considered to form an efficient solution for the HI time series prediction. As HI is a mixture of trend and random non-Gaussian, non-homogeneous noise, we propose to forecast the HI distribution rather than the direct HI value. The Skewed Generalized t (SGT) distribution is considered as the general non-Gaussian model. Moreover, the combination of convolutional neural network (CNN) and long short-term memory (LSTM) are used to predict SGT distribution parameters. By incorporating the standardization module and the modified activation function alongside a custom time series standardization method, the architecture of the ConvLSTM neural network is created to be appropriate for non-stationary time series data with non-Gaussian behavior. Finally, a pre-training of the model has been proposed, which improves the efficiency of the designed procedure, as usually the amount of HI data is limited and insufficient to reliably train an artificial intelligence (AI) system. The proposed solution is shown to be robust and more resilient to outliers than the classical Gaussian-based approach. Using simulated and real HI data (known as a benchmark), we may conclude that the superiority of our method increases with the increasing non-Gaussianity level of the analyzed time series.