Fault identification plays a pivotal role in condition-based maintenance of rotating machinery, with identification accuracy highly dependent on the quality of extracted features. Multiscale permutation entropy (PE) methods have emerged as promising feature extraction tools due to the fast computation of PE and informative scalability of multiscale procedures. However, PE is unresponsive to amplitude variation due to the binary orbit similarity state, and the multiscale procedure suffers from scale information loss or even scale absence, all of which decrease the identification accuracy. To address these issues, this article proposes a novel approach termed the scale-compensation community distance entropy (SCDE) method for fault identification. On one hand, the community distance-based orbit similarity value is put forward to diversify orbit similarity states, achieving a dual-characteristic perception of both frequency and amplitude changes. On the other hand, the scale-compensation procedure is proposed to enrich overall and detailed information on continuous scales. The efficiency and superiority of SCDE are rigorously demonstrated using simulation data and experimental datasets.

Wheeled robot fault diagnosis is indispensable for ensuring its reliable and safe operations. However, two challenges impede the application of prevalent intelligent diagnosis methods. 1) Multisensor fusion: The complexity of robot movements necessitates multisensor for comprehensive monitoring, generating strong-coupled, and high-dimensional data that complicate both intrinsic relationship mining and effective fusion; 2) Heterogeneous data silos: Dispersibility, heterogeneity and privacy constraints across different robots lead to non-independent and identically distributed (Non-IID) data silos, severely limiting the development of universal diagnostic models. To overcome these two problems, this article proposes a tailored federated physics-informed graph framework (FedMA-PIG). On the client side, the kinematics mathematical model is constructed for each robot, which explores the inter-sensor correlations and forms a physics-informed graph. It enables multisensor data fusion and assists the client in training a local graph neural network. On the federated framework side, a Non-IID federated framework based on a multianchor contrastive mechanism is devised. It employs multiple anchors to capture common knowledge from heterogeneous robot data, guiding feature representations toward corresponding anchors and away from others, thereby promoting consistency and mitigating inter-client data heterogeneity. Comprehensive experiments were conducted on three representative wheeled robots- Mecanum-wheeled, 4WD-wheeled, and Omni-wheeled- distributed across four federated clients. The results demonstrate that FedMA-PIG achieves generalized and superior diagnostic performance compared to state-of-the-art methods.

Remaining useful life (RUL) prediction is fundamental to prognostics and health management (PHM) in industrial systems. In practical deployment, rotating machinery operates over long service lifecycles under continuously evolving loads and rotational speeds. Such variability, combined with long-term acquisition of monitoring data, gives rise to non-stationary degradation patterns and distributional shifts. These characteristics challenge conventional deep learning-based RUL models, which are typically trained on static datasets and lack adaptability to sequentially arriving operating conditions. Moreover, most existing approaches lack explicit mechanisms for predictive uncertainty quantification in dynamic task environments, restricting their reliability in risk-aware maintenance decision-making. To address these challenges, this paper proposes a hybrid Bayesian learning framework for uncertainty-aware continual RUL prediction in non-stationary industrial settings. The framework employs Bayesian neural networks (BNNs) to jointly model aleatoric and epistemic uncertainties and integrates prior-guided Bayesian knowledge transfer with likelihood-guided generative replay for continual learning. A conditional diffusion-based replay mechanism is introduced to synthesize representative pseudo-samples, together with a dual-uncertainty-driven sample selection strategy that retains informative historical knowledge without storing raw data. Extensive experiments on multiple run-to-failure bearing and gear datasets under diverse operating conditions demonstrate that the proposed method achieves superior RUL prediction accuracy, enhanced robustness to distributional shifts, and more reliable uncertainty quantification in continual learning scenarios, underscoring its suitability for long-term industrial monitoring and predictive maintenance.

Bearing health monitoring (BHM) is vital in preventing unforeseen machinery shutdowns caused by frequent bearing failures. Within the BHM process, constructing health indicators takes center stage, serving the dual purpose of detecting incipient faults and assessing the monotonous degradation trend for predicting residual useful life. In terms of detecting incipient faults, permutation entropy (PE) serves as a promising tool due to its simplicity and rapid computation. However, when it comes to assessing irreversible degradation, PE often exhibits notable fluctuations and nonmonotonicity even after signal denoising processes. This issue arises from PE's vulnerability to impulsive noise and its invariance to monotonic signal transformations. To tackle this challenge, the article introduces a novel approach termed condition-adaptive permutation entropy (CAPE) for BHM. CAPE begins with a condition-based signal processing method to mitigate the influence of impulsive noise, followed by an amplitude-aware algorithm to break PE's invariance to monotonic signal processing. Moreover, CAPE adaptively selects fault-relevant permutation patterns to enhance its monotonicity. The effectiveness, superiority, and applicability of CAPE are rigorously demonstrated using simulation data and two experimental datasets.

The input of low-quality feedstocks triggers the interdependence between workpiece quality and machine reliability, which will further adversely impact the performance of manufacturing systems. Considering the interconnected manufacturing system structures, our primary goal is to provide an effective method to compute the performance of networked manufacturing systems suffering from machine and low-quality feedstock interdependence. The strength of our work first lies in the model for the compound degradation process of machines and dissemination of low-quality feedstocks, which enables us to construct a response chain to model the interdependence between machines and feedstocks in the manufacturing network. Then, the second strength is the effective algorithm for the computation of route connectivity and quality loss of a manufacturing network based on the interdependence model. A computational experiment shows our models and algorithm can work well for evaluating the operational performance of manufacturing networks.

Bayesian importance measures (BIMs) are useful tools for quantifying the contribution of an edge to the up or down state of the network. This article investigates BIMs for the K-terminal networks under the assumption that the failures of edges occur according to a branching process in which the total number of the failed edges follows a saturated Lagrangian Poisson distribution (SLPD). First, we derive two types of BIM equations when the total number of the failed edges follows a certain probability distribution. Both BIMs are represented in terms of network spectra that depend only on the network structure. It is also found that both BIMs are equivalent as they lead to the identical ranking order of network edges. Next, when the total number of the failed edges has an SLPD, several unique properties of BIMs rankings are explicitly derived. We further prove that under certain conditions, the rankings based on the BIMs belong to the structural ranking, namely, the spectra-based rankings solely depend on the network structure. Finally, the numerical analyses of a transportation network show that the BIMs can effectively measure the edge importance for the medium and relatively large networks.

Fierce global competition drives automated manufacturing systems (AMSs) to be increasingly complex, which poses significant challenges on performance analysis and production control. The multistage production via serial stations will lead to the propagation of failures in AMSs, which will affect system performance by triggering complex competitions among multiple failure modes. Although machine performance and product quality have been considered, very little has been done to investigate the effect of imperfect quality inspection on competing failures. Focusing on a time balance serial AMS, this article presents a new competing failure model to investigate the complex interactions among machine failures, product quality, and inspection process, which enables the characterizations of time-delayed propagation of failure, accumulation of degradation, and dynamics of states in serial AMSs. In order to further analyze the impact of competing behaviors on system performance, we have also developed decision diagram models and algorithms, which are evaluated and validated on serial AMSs with imperfect inspection, revealing the characteristic of multistate interactions. Experimental results show that the proposed methods have strong potentials for performance modeling and analysis of serial AMSs and also demonstrate general applicability for manufacturing decision making.

Importance measure can be used to identify the most vulnerable components with respect to system functionality or failure. Traditional importance measures may not be effective to evaluate the contribution of an individual component if its reliability value does not fall in the full range between 0 and 1. Based on the cost-reliability relation, this paper proposes a generalized Birnbaum importance measure (GBIM) to quantify the contribution of individual components to system reliability improvement by considering reliability range, manufacturing complexity, and technology feasibility. Since GBIM possesses several unique features in terms of guiding system reliability optimization, in this paper, we further develop a GBIM-based genetic algorithm to solve a type of optimal reliability allocation problem. The numerical studies show that both the computational efficiency and the near global optimality based on GBIM outperforms the methods using the traditional importance measures.

The continuous state system is a special kind of a system in which the states of the system and its components have continuous values, ranging from perfect functioning to complete failure. This paper introduces the performance improvement for a continuous state system, which can be used to measure the improvement of systems performance comparing pre- and postmaintenance time. The probabilistic characteristics of performance improvement are discussed in detail. Then, the performance improvement for multicomponent maintenance and corresponding calculation method are also put forward to establish the objective function for maintenance optimization. Third, a maintenance optimization model for such a system is studied, and corresponding performance improvement based genetic algorithm is provided to search a near global optimal solution. Finally, two numerical examples and an oil transportation system application case study are implemented to verify the effectiveness of the proposed method.

Importance measures are widely used to characterize the roles of components in systems. The system lifetime can be divided into different life stages. Traditionally, importance measures do not consider the possible effect of the expected number of component failures over a system's lifetime and over different life stages, which, however, has a great effect on the system performance changes, and should therefore be taken into consideration. This paper extends the integrated importance measure (IIM) from unit time to system lifetime, and to different life stages. Based on the renewal functions of components, this measure can evaluate the changes of the system performance due to component failures. This generalization of the IIM describes which component is the most important to improve the performance of the system during the system lifetime and at different life stages. An example of the application of an oil transportation system is presented to illustrate the use of the generalized IIM.

This paper mainly focuses on the integrated importance measure (IIM) of component states for maintenance processes. To describe the impact of each component state in maintenance processes, a maintenance cost function of multi-state systems is defined at first. Second, considering the probability distributions, transition rates of the component states, and system maintenance costs, the IIM of component states is described. The corresponding characteristics of the IIM of the component states are discussed in both series systems and parallel systems. Then the relationships between IIM and Griffith importance, Wu importance, mean absolute deviation, and multi-state redundancy importance measures are also discussed. At last, a numerical example is given to demonstrate the IIM of component states. The results show that IIM can be used to identify the most important component state for the maintenance decision.