Online remaining useful life (RUL) prediction is a core function of prognostics and health management (PHM), which provides solutions for comprehensive and personalised system management. RUL is realised by extrapolating timely updated prognostic models to reach a user-defined failure threshold. As of today, there are mainly two kinds of Bayesian prognostic methods. The first kind of Bayesian prognostic methods are Bayesian regression prognostic methods that directly use Bayes’ theorem to update degradation model parameters. The second kind of Bayesian prognostic methods is Bayesian state-space prognostic methods that firstly reformulate a degradation model by using state-space representation and consequently update state-space model parameters with Bayes’ theorem. However, comparisons of these two kinds of Bayesian prognostic methods have not been actively explored and discussed in a unified paper. In this study, similarities and differences between Bayesian regression prognostic methods and Bayesian state-space prognostic methods under the assumptions of additive Gaussian and Brownian motion errors were explored to enrich the PHM domain. A significant difference was observed between Bayesian regression prognostic methods and Bayesian state-space prognostic methods under different error assumptions. Experimental results showed that Bayesian state-space prognostic methods have greater RUL prediction uncertainties in two run-to-failure cases with different fluctuation strengths. However, under the assumption of Gaussian errors, because of the good ability of degradation tracking, Bayesian state-space prognostic methods may predict worse than Bayesian regression prognostic methods in a strong fluctuation dataset, which is not evident in the situation of Brownian motion errors.Note to Practitioners—The Bayesian update of model parameters considering online condition monitoring data is of great practical significance for describing individual degradation and RUL prediction. Practitioners need to know the similarities and differences between different Bayesian prognostic methods, as well as how to choose an appropriate Bayesian prognostic method for a specific predicted objective that practitioners care about. This paper introduces the similarities and differences between several classic Bayesian prognostic methods, and provides their performance comparisons in different RUL prediction scenarios, providing a reference for practitioners to use Bayesian model parameters updating to predict individual RUL.

mmWave radar-based sound sensing have attracted extensive attention due to its advantages such as simultaneous measurement of multiple sound sources, and strong noise resistance. However, limited by the mmWave reflection properties of the target sound source, existing methods can only measure targets with strong mmWave reflection characteristics at relatively short distance. This paper proposes a long-distance, source-independent sound sensing (LISS) method with mmWave radar. By designing an mmWave-acoustic passive relay, the incoming sound wave excitation is converted into modulation of the mmWave signal, enabling long-distance sound sensing without being affected by the shape or material of the sound source. Additionally, the unique structure of the relay provides directionality for sound source while maintaining omnidirectionality for incident mmWave. The LISS sensing method, the design principles, and the working mechanism of the relay are detailed in this paper. Experimental validations demonstrate that the proposed method extends sound sensing range by more than 7.5 times compared to exising methods and is not affected by the intrinsic properties of the sound source, providing a promising approach for long-range, source-independent sound sensing.

Rolling element bearings are crucial key components in rotating machinery, and it is essential to monitor their condition to prevent unexpected breakdown or safety incidents. However, features that indicate the operating condition are often affected by strong background noise, leading to inaccurate detection. Additionally, classical monitoring methods often rely on a multivariate normal distributed (MND) assumption, which may not be suitable in real-world applications due to noise interference, outliers, and sampling errors. To address the aforementioned issues, this paper proposes a novel Hankel matrix-based multivariate homogeneously weighted moving average control chart with shrinkage estimator (HMHS chart). The first step involves segmenting the bearing vibration signal to create Hankel matrix sequences, and the singular features are obtained via singular value decomposition (SVD). To determine the optimal singular sequence, a criterion called mode entropy (ME) is proposed. Secondly, a shrinkage estimator is applied to establish a robust statistic with low covariance bias. Thirdly, a health index is constructed using the HMHS chart to track the bearing’s degradation process. Simulation studies and two real case studies are performed with comparison to classical charts to demonstrate the effectiveness and accuracy of the proposed method. The results demonstrate the effectiveness and accuracy of the proposed method in the condition monitoring of rolling bearings.Note to Practitioners—A novel condition monitoring method of rolling bearings is proposed in this work. Existing methods often rely on traditional statistics (such as kurtosis, root mean square), which can be easily disturbed by noise and outliers in training samples. Moreover, the MND assumption needed is not always tolerated in real applications, leading to poor performance in condition monitoring. To solve this problem, a Hankel matrix-based multivariate control chart is proposed in this paper, which includes several steps for implementation. These steps include: 1) collecting vibration signals of rolling bearings; 2) conducting Hankel matrix-based adaptive feature extraction; 3) constructing the monitoring statistic with robust estimators, and estimating the control limit; 4) conducting online health monitoring of rolling bearings. Extensive simulation studies and two real case studies are conducted to evaluate the accuracy and effectiveness of the proposed method in bearing condition monitoring.

Machine life cycle performance assessment is of great significance to use a health index to inform the time of incipient fault initiation in a normal stage and realize fault identification and fault trending in a performance degradation stage. However, most existing works consider using unexplainable model parameters and historical data to build models and infer their off-line parameters for machine life cycle performance assessment. To overcome these limitations, an online piecewise convex-optimization interpretable weight learning framework without needing any historical abnormal and faulty data is proposed in this article to generate a piecewise health index to practically implement machine life cycle performance assessment. Firstly, based on a separation criterion, the first submodel in the proposed framework is built to detect the time of incipient fault initiation. Here, the piecewise health index generated by the first submodel is continuously updated by on-line monitoring data to timely detect the occurrence of any abnormal health conditions. Secondly, once the time of incipient fault initiation is informed, online updated model weights are highly correlated with fault characteristic frequencies and informative frequency bands for immediate fault identification. Simultaneously, the second submodel integrated with monotonicity and fitness properties in the proposed framework is triggered to generate the piecewise health index to realize overall monotonic fault trending. The significance of this article is that only online monitoring data are used to continuously update interpretable model weights as fault frequencies and informative frequency bands to generate the proposed piecewise health index so as to practically realize machine life cycle performance assessment. Two run-to-failure cases are studied to show the effectiveness and superiority of the proposed framework.

Stemming from complex mechanisms and working conditions of bearings, single degradation models often fail to adequately describe complex degradation process and provide reliable prediction of remaining useful life (RUL). To address this challenge, an adaptive two-stage degradation framework based on Gaussian process regression (GPR) is proposed. This framework dynamically selects the appropriate degradation model based on the observed characteristics of the actual degradation data, resulting in improved prediction accuracy and adaptability. In the process of constructing the degradation model, the suitable detection method is adaptively determined based on change point locations, facilitating real-time monitoring of degradation pattern shifts. Within the two-stage GPR model, matched kernel functions are chosen based on degradation rate and trend changes, and a degradation indicator is constructed using the genetic programming algorithm. This indicator serves as target set for the GPR model to accurately estimate RUL. The reliability of the proposed method is validated through comparison with other alternative models on prognostics and health management (PHM) challenge bearing datasets, confirming its effectiveness, robustness, and superiority.

Intelligent machine fault diagnosis technique has recently exploded interest in digital health, energy power, and industrial maintenance. Collecting machine fault data in engineering practice is usually costly, causing big challenges in the intelligent diagnosis of most fresh-from-the-factory machines that are missing fault data. Inspired by the main idea of the digital twin, in this article, we propose a dynamic model-embedded intelligent machine fault diagnosis framework. Specifically, a machine dynamic modeling and parameter identification approach is introduced for building the machine digital model. The digital model is used to predict machine fault data from the measured healthy vibration signals. Furthermore, a parameterized convolutional neural network structure is designed for learning optimization features and recognizing the machine's healthy state. Experimental investigation demonstrates the effectiveness of the framework. The results show that the proposed framework enables intelligent machine fault diagnosis without fault data. The diagnosis effect outperforms supervised, unsupervised, and small-sample learning approaches and can be generalized to another load and speed with acceptable accuracy.

Performance degradation modeling is promising to construct an advanced health index (HI). Currently, domain knowledge including monotonicity, trendabilty, and identifiability has been widely recognized as desirable properties to evaluate the suitability of an HI. Nevertheless, a quantitative criterion to evaluate the suitability of the curvature of an HI is still lacked, which can be used to describe different machine degradation rates. In this article, a new property of an HI named “shapeness” is proposed and it expects that an HI would have a monotonic degradation rate when the HI has a monotonic curve. Subsequently, a mathematical quantitative formulation and optimization model of the shapeness is put forward to be integrated with other desirable properties, which can formulate a composite optimization degradation model. Here, the main variables of the proposed optimization degradation model are weights that are used to fuse spectra lines of vibration signals so that the sum of weighted spectra lines can be used to form a generalized HI. Besides, it is proved that the proposed optimization model is a convex optimization problem so that a global optimal solution is uniquely guaranteed. Two run-to-failure case studies are conducted and some comparisons with state-of-the-art models show that the proposed HI has better performance.

Fault detection and degradation modeling are two main concerns in condition-based maintenance (CBM). The initial machine degradation is called first predicting time (FPT) or incipient failure time. FPT is typically assumed prior information. FPT detection aims to provide such prior information for subsequent degradation modeling in CBM. Moreover, the majority of existing methodologies regard FPT detection and degradation modeling as two separate tasks. A generic framework for integration of the FPT detection with degradation modeling is proposed in this article via fusion of spectrum amplitudes in the frequency domain to realise FPT detection and degradation modeling in a unified manner. First, a generalised health index is constructed using the sum of weighted spectrum amplitudes. Second, two properties are proposed to describe FPT detection and degradation modeling. Third, these two properties and their constraints are mathematically formulated as a quadratic programming model to find optimal weights for the fusion of spectrum amplitudes automatically. Finally, three illustrative examples are used to demonstrate the superiority of the proposed methodology over some existing commonly used sparse measures and a machine learning method in the FPT detection and degradation modeling.

Prognostics and health management of the rotating machine aim to use monitoring data to infer the health conditions of the rotating machine in order to avoid unexpected accidents and minimize economic losses. Since health indices can detect an abnormality and provide observations for prognostic modeling, they are the basis of prognostics and health management. The spectralLp/Lqnorm ratio and the spectral Gini index have been recognized as popular health indices to characterize the impulsiveness of repetitive transients caused by machine faults for rotating machine health monitoring. Here, some special forms of the spectralLp/Lqnorm ratio include spectral kurtosis, the spectralL2/L1norm ratio, the reciprocal of the spectral smoothness index, and so on. In this article, theoretical and experimental investigations on the spectralLp/Lqnorm ratio and the spectral Gini index for machine health monitoring are conducted to prove how they characterize the impulsiveness of repetitive transients. Results showed that an increase in the total length of the nonimpulsive regions of repetitive transients makes the spectralLp/Lqnorm ratio and the spectral Gini index become large, which, in turn, can be used to explain changes of health indices during machine degradation at varying operating conditions and in the case of impulsive noises. To solve the problem of the sensitiveness of popular health indices to impulsive noises, a fused health index for characterizing cyclostationarity of repetitive transients is proposed. Analyses of bearing run-to-failure showed that the proposed fused index has better monitoring performance than the aforementioned popular health indices.Note to Practitioners—This article was motivated by the problem of characterizing nonprocessed signals for automatic machine health monitoring. Practically, nonprocessed signals, such as vibration signals, acoustic signals, and so on, cannot directly be applied to reflect machine health conditions. The transformation of nonprocessed signals by using health indices into process signals is great of a concern. Most existing methods directly use intuition and experience to choose health indices in order to realize machine health monitoring. Thus, these methods do not provide theoretical investigations and support to illustrate how health indices characterize nonprocessed signals generated from a faulty machine. This article uses mathematical models and inferences to explain how popular health indices characterize impulsive signals generated from a faulty machine. Then, it is shown that direct applications of popular health indices in a time domain are sensitive to impulsive noises, which causes failures of health indices for machine health monitoring in the occurrence of impulsive noises. To solve this problem, it is suggested to use indices to characterize frequency information of faulty signals. Finally, an efficient and reliable fusion of health indices in a frequency domain is proposed for machine health monitoring.

In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.