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.

The joint optimization of maintenance and spare parts inventory enables overall cost-effective decisions by integrating both system condition monitoring data and real-time inventory information. As sustainable manufacturing continues to evolve, remanufacturing is emerging as an essential strategy for extending component lifecycles and reducing environmental and economic costs. Nevertheless, recent studies have rarely integrated component remanufacturing into a dynamic decision framework for condition-based maintenance (CBM) and spare parts provisioning driven by system states, which will result in increased computational complexity. This paper investigates the joint optimization of CBM, spare parts inventory, and component remanufacturing for a multi unit system with degradation randomness. Firstly, we formulate this joint decision-making problem as a Markov Decision Process (MDP) that incorporates system states with degradation randomness and spare parts inventory accounting for multi-lifecycle remanufacturing. Building upon widely adopted threshold control methodologies, we design a heuristic Threshold-Based Policy to derive simple solutions to joint maintenance-inventory control with remanufacturing. However, the computational complexity induced by degradation randomness and remanufacturing severely limits the solution efficiency of the Threshold Based Policy. To further reduce computational time, we propose a Threshold-Optimized Deep Reinforcement Learning (TDRL) algorithm that integrates a threshold initialized policy, maintenance action filtering, and state standardization. A case study on a ball screw system demonstrates that the proposed TDRL algorithm outperforms the Threshold-Based Policy in terms of both cost and computational time. Sensitivity analyses are conducted to analyze the impact of key factors on the benefits of the remanufacturing policy within the joint optimization framework.

The increasing demand for integrated sensing and communication (ISAC) in sixth generation (6 G) mobile networks calls for advancements in sensing parameter estimation technologies. Orthogonal frequency division multiplexing (OFDM) is the core technology of the fifth generation (5G) system with excellent resilience to multi-path fading and is gaining popularity as an ISAC waveform. However, the performance of traditional range/velocity (r/v) estimation algorithms, e.g., multiple signal classification (MUSIC), is restricted by the resolution defined by the bandwidth and symbol duration of OFDM, especially in multi-target scenarios. To overcome this issue, we proposed a REsidual network based SPEctra Calibration (RESPEC) algorithm. It improved the multi-target sensing accuracy by residual network that resists gradient vanishment to calibrate the spectra generated with the two-dimensional MUSIC (2D-MUSIC). Simulation results demonstrated the superiority in r/v estimation accuracy of RESPEC in multi-target scenarios, compared to the traditional 2D-MUSIC algorithm and other benchmarks. The results also exposed a trade-off between neural network depth and communication bandwidth for range estimation.

Increasing market competition and growing mechanical structural complexity have urged the application of complex systems comprising multi-component machines. Ensuring the economical operation and maintenance (O&M) for such systems is paramount in industry. To achieve this, the component maintenance policy should cover both the machine-level disassembly sequence among critical components and the system-level configuration setting connecting individual machines. However, integrating such hierarchical structural dependencies into maintenance decision-making poses a formidable challenge and remains unexplored in existing literature. Facing this key issue, our study presents a component-targeting opportunistic maintenance policy considering hierarchical structural dependencies (COMP-HSD) to provide real-time cost-effective maintenance schemes. Aiming at deriving the optimal component maintenance group at each maintenance opportunity, this policy builds a decision-making process including triple-level analyzing framework to comprehensively involve the component degradation and the structural dependencies analyses of machine level and system level. Specifically, sequential component-level predictive maintenance (PdM) intervals are initially optimized according to individual health conditions. Then, a maintenance cost savings model is developed to assess the economy of adjusting PdM actions for each component at the current maintenance opportunity, accounting for the impacts of hierarchical structural dependencies. Furthermore, we incorporate maintenance resource limitation into the decision-making procedure to enhance the adaptability to industrial practice. Numerical examples extracted from a partner engine cylinder head manufacturing enterprise certify the significant cost reduction of this COMP-HSD methodology.Note to Practitioners—This work is motivated by the critical problem of calculating a cost-effective component-targeting maintenance policy for a complex production system with multi-component machines. According to the real O&M management of a manufacturing company, it is intractable to reasonably decide when to maintain each critical component in multiple CNC machine tools of a production system, which restricts the maintenance planning economy. This is due to the difficulty of evaluating the impacts brought by hierarchical structural dependencies (i.e., machine-level disassembly sequence and system-level series configuration). Existing approaches are limited to be directly applied to practice since they either focus solely on individual multi-component machine or assume that each machine in a multi-machine system only contains one component, neglecting the holistic evaluation. Besides, the maintenance resource restriction is rarely considered in the literature. To fill this gap, we present the COMP-HSD policy, which simultaneously considers the individual component degradations, systemic maintenance opportunities and complex structural dependencies analysis in the maintenance decision-making process. Referring to this policy, the manufacturers could determine the component maintenance timetable to conduct timely PdM actions with lower cost. Compared with the traditional maintenance policy, our study greatly reduces the total cost, and also offers extending applications such as maintenance tool preparation and spare part ordering according to the component maintenance scheme.

This paper considers a service-oriented manufacturer providing products and associated after-sales maintenance service with a warranty period to customers. The manufacturer gains revenue from both product sales and after-sales maintenance service which are affected by the warranty period length. The arrival tendency of customers for after-sales maintenance service is higher during the warranty period than that after the warranty expires. The manufacturer repairs stochastic failures of products with both spare parts of the right kind and employed service engineers. If the spare part is not available upon repair demand, the manufacturer can resort to the emergency suppliers (e.g., OEMs). We establish an original decision model for the service-oriented manufacturer and analytically derive the arrival rates of service demand under and out of warranty, and the repair call rates for requiring regular and emergency replenishment based on queuing theory. Then, a computationally efficient algorithm is designed to obtain the joint multiple spare parts inventory, service engineer employment and warranty period decisions. Numerical studies show that both the manufacturer and customers can benefit from the longer warranty period when customers are more inclined to require maintenance service out of warranty from the manufacturer. A higher service level target or quality levels of spare parts reduce the after-sales service dependence on emergency suppliers.Note to Practitioners—After-sales maintenance services often generate significant profit for many service-oriented manufacturers that sell products bundled with after-sales services. To offer efficient after-sales maintenance services, efficient joint management of spare part inventory, service engineers and warranty periods, which often interact with each other, is crucial for service-oriented manufacturers. However, in practice, facing the stochastic arrival of repair calls, it is challenging for manufacturers to jointly optimize the decisions of spare parts inventory, service engineers and warranty periods. Most existing studies optimized them separately. This research investigates the joint decision problem considering the three aspects based on queuing model. Based on the model analysis, an efficient and easy-to-implement heuristic algorithm is proposed to obtain reasonable joint decisions. Practitioners can implement the proposed approach to improve the integrated planning of spare parts inventory, warranty and service engineers and enhance profitability. Besides, sensitivity analysis is conducted to show how the changes of parameters such as payment to the supplier per emergency shipment and rate of the component lifespan will affect the joint decisions. Some managerial insights obtained can be useful to practitioners. First, if customers become more willing to require maintenance service from the manufacturer out of warranty, the manufacturer can benefit more from extending the warranty period length which is also beneficial to customers, leading to a win-win situation. Second, if the emergency replenishment cost becomes higher, the manufacturer should extend the warranty period length. Third, a higher service level target or quality levels of spare parts decline the dependence of the after-sales service on emergency suppliers.

Failure mode (FM) recognition and remaining useful lifetime (RUL) prediction play pivotal roles in the field of prognostics and health management (PHM), particularly in regard to monitoring machinery degradation. Advances in sensor technology have opened avenues for FM recognition and RUL prediction by leveraging data from multiple sensors. However, previous research has exhibited certain limitations. Some studies have taken all multisensor data as direct inputs, overlooking the potential heterogeneity in the relevance of individual sensor data to machinery degradation. Others have relied on visual inspection and subjective assessments for sensor selection. These approaches struggle to adaptively select sensors, especially in scenarios involving multiple FMs and operating conditions (OCs), and when only partial FM labels are available. To address these challenges, this paper proposes a novel deep-learning network that adaptively selects sensors to jointly recognize FMs and predict RUL under time-varying OCs. The core of this network incorporates an attention-based long short-term memory (LSTM) module. Within this module, adaptive sensor selection weights are generated, leading to the accurate recognition of FMs and the precise prediction of the RUL. In the context of model training, we construct loss functions utilizing semilabeled samples and extract OC-invariant features through domain adaptation, enhancing the accuracy of FM recognition and RUL prediction. To assess the effectiveness and the generalizability of the proposed method, numerical experiments and two case studies involving aircraft engines and bearings are conducted. Note to Practitioners—This paper proposes a deep-learning network designed for adaptive sensor selection in the context of semisupervised FM recognition and RUL prediction, particularly in scenarios involving multiple OCs. To operationalize this method, five key steps are outlined: First, Data Collection: data are gathered from multiple sensors, time-varying OCs, multiple FMs, and failure time of historical units. It is important to note that FM data are available for only a subset of historical units. Second, Data Preprocessing: The sensor data are tailored using the sliding time window technique, generating a substantial number of samples from historical units. Third, Network Construction: Subsequently, the adaptive sensor selection network is constructed. Fourth, Model Training: Loss functions are constructed, and model parameters are estimated through end-to-end training. Finally, Model Application: The method is utilized to recognize FMs and predict RUL for in-service units. This deep learning network can be applied effectively to various degraded machines experiencing multiple FMs and OCs. It is particularly suitable for machines with complex physical mechanisms or unknown failure thresholds.

In industrial scenarios with insufficient sensor data, intelligent few-shot failure mode recognition and remaining useful lifetime (RUL) prediction are critically essential for effective prognostics and health management. Existing few-shot learning (FSL) methods focus on either the failure mode recognition as a classification problem or the RUL prediction as a regression problem, failing to capture the dependence between failure modes and RUL given that units under different failure modes present distinct degradation characteristics. To address the issue, this paper proposes a distribution-agnostic probabilistic FSL method for multimodal recognition and prediction of operating units. The proposed model establishes a neural network with prototypes to solve a few-shot classification-and regression-integrated problem. To fully capture the uncertainty caused by limited sensor data, we develop multimodal Bayesian model-agnostic meta-learning (MBMAML) for the probabilistic modeling of failure modes and the RUL under multiple failure modes. We construct the loss function based on probabilistic modeling that captures the interaction between failure modes and RUL for model training. Finally, the proposed model adaptively learns the approximate distributions of failure modes and RUL for a new operating unit. We evaluate the proposed model performance through a case study on the degradation of aircraft gas turbine engines.Note to Practitioners—Failure mode recognition and RUL prediction are essential in prognostics health management (PHM) to avoid unexpected failures of units in industrial systems, such as aircraft gas turbine engines. However, insufficient sensor data are quite common issue in industrial scenarios due to expensive sensor deployment, the difficulty of installing sensors to certain special mechanical equipment, and so on. This paper aims to develop a FSL method to jointly recognize the failure mode and predict the RUL of a unit based on insufficient sensor data. The four steps to implement the proposed method in practice are as follows:First, collect sensor signal data, RUL data, and failure mode data of units.Second, construct the model framework via the proposed MBMAML.Third, formulate the loss function based on the probability distributions of failure modes and RUL, and train the model using collected data.Fourth, adaptively recognize the failure mode and predict the RUL of a new operating unit. The proposed method is expected to be applicable to many practical few-shot industrial scenarios due to its data-driven neural network with flexible model structure.

Efficient fault diagnosis in ship-to-shore cranes (STSC) is vital for reliable cargo transport. However, deep neural networks (DNNs) lack transparency, hindering their explainability and interaction with experts during diagnostic decision-making. Currently, neural-symbolic systems increasingly focus on knowledge translation and embedding to enhance DNNs applicability for real-world fault diagnosis. Hence, this article introduces a deep knowledge-augmented belief network (DKABN), where knowledge translation and embedding are conducted to visualize the behavior of deep belief networks and integrate domain knowledge. Specifically, for stacked restricted Boltzmann machines (RBMs) layers, a novel activation-weighted logic RBM (AWL-RBM) is designed to fairly consider the contribution of each literal and reduce the inconsistencies between symbolic logic and RBMs. In the AWL-RBM, we formally prove that multiple literal groups can still be mapped into a violation rank function be capable of equalizing RBM energy minimization. Besides, translation and embedding of symbolic literals are conducted to interpret how RBMs work and fuse domain knowledge. For fully connected layers, a rule format like IF-THENs is translated and embedded to provide a semantic representation for diagnosis decision-making, and integrate domain knowledge. Finally, verified using an STSC testbed, DKABN demonstrates exceptional diagnostic performance and significant application potential.

The fault diagnosis of hoist mechanisms in ship-to-shore cranes (STSCs) is paramount for maintaining shipping schedules and ensuring personnel safety at ports. Although deep networks have achieved some success in diagnosing faults in hoist mechanisms, their opaque nature often precludes them from providing trustworthy explanations for their decisions. To address this problem, this article introduces a deep logic convolutional neural network (DLCNN), which incorporates two symbolic languages (confidence and classification rules) to visualize how convolutional neural networks (CNNs) work. Confidence rules are extracted from logic convolutions (LCs). In the LC, confidence rules are designed from three perspectives-information loss, the tradeoff between soundness and interpretability, and quantitative reasoning-to provide a comprehensive understanding of the feature learning and reasoning of stacked convolutions. Besides, classification rules are extracted from CNN's full-connected layers to elucidate implicit relationships between fault features and labels. Our experimental investigations on an STSC testbed demonstrate that DLCNNs have powerful performance in fault recognition, interpretability, and potential engineering value.

Data-driven feature extraction for machine health monitoring has garnered significant attention, yet two key limitations remain unaddressed: lack of interpretability and the need for extensive historical fault data. To overcome these problems, an online two-dimensional optimization framework is proposed that enables interpretable time-frequency feature extraction and health index (HI) construction without requiring faulty samples for model training. Our approach introduces a convex hull-based closest point optimization model for estimating time-frequency instances and learning interpretable time-frequency features. By leveraging a small set of baseline vibration samples and recent online data, rapid fault diagnosis can be achieved based on optimized interpretable time-frequency features. This method also facilitates long-term degradation tracking by constructing and updating an HI from collected time-frequency spectrograms. Once machine faults appear, updated time-frequency features can show apparent and interpretable fault signatures for prompt fault alarming. Moreover, the proposed framework allows continuous HI updates for incipient fault detection and degradation tracking. The proposed framework is validated by using two run-to-failure datasets and ablation experiments are conducted to demonstrate its superiority.

Future reconfigurable manufacturing systems (RMSs) can dynamically modify the system structures to achieve personalization, customization, and consumer-maker co-creation. The advanced Internet of Things (IoT) integrating deep learning and intelligent maintenance is critical for ensuring the operation and maintenance of RMS. On the one hand, a multi-head neural network is developed under the variability of individual machine degradations for deriving machine-level prognostics. It learns degradation features with superior generalization performance by simultaneously fitting multiple candidate distributions and updates remaining useful lifetime (RUL) distributions from diversified distribution ensembles. On the other hand, a flexible opportunistic maintenance policy is proposed to optimize the dynamic maintenance scheduling for the multi-phase RMS by utilizing real-time updated RUL distributions. Meanwhile, considering the unique attributes of RMSs, maintenance opportunities that arise from the in-situ machine PdM, system structure, and sequential reconstruction time are fully utilized. This IoT-enabled prognostics & opportunistic maintenance (POM) framework can achieve a bi-level interactive mechanism and inner/outer loops to reduce decision-making complexity and maintenance costs for future reconfigurable manufacturing. Numerical experiments demonstrate that this framework has superior predictive performance and significant cost savings to empower intelligent maintenance.

In addition to equipment maintenance decisions, spare parts ordering decisions from different suppliers play a key role in reducing related costs (e.g., maintenance, inventory and ordering costs). Since suppliers may use different production technologies and materials, spare parts (or products) from different suppliers can be different in quality. Nevertheless, in recent studies, the quality of spare parts is rarely considered to incorporate both equipment maintenance and spare parts ordering. In this paper, we investigate the joint optimization of condition-based maintenance and spare parts provisioning policy under two suppliers with different product quality. We formulate a sequential-decision problem with a Markov decision process and consequently obtain an optimal maintenance and ordering policy by an exact value iteration algorithm. To improve computation efficiency, based on the principle of sequential optimization, we develop heuristic methods. Extensive numerical experiments are conducted to assess the overall performance of the developed heuristic methods. Compared to the optimal method, results showed that the average cost gap is about 2% and computation time is reduced by 94% on average under the proposed heuristic method.Note to Practitioners—This paper is motivated by the observation that automobile industries tried to integrate emergency suppliers from which spare parts have different quality into maintenance schedules to avoid stockout and reduce equipment failure during the Covid-19 pandemic. Specifically, the article focuses on balancing the trade-offs between condition-based maintenance and inventory management from two suppliers with different lead times and spare parts quality for multi-unit systems. On the one hand, effective maintenance scheduling relies on spare parts for replacement to ensure the stability of production. On the other hand, inventory management needs to select the supplier with appropriate lead time and product quality to reduce the ordering cost and avoid stockout based on the degradation states of equipment. The joint optimization of these two aspects serves to reduce the total maintenance and ordering cost. Nevertheless, most existing research aims to optimize them separately. In this paper, we formulate the joint decision problem considering the two aspects based on a Markov decision process. We obtain an optimal maintenance and ordering policy by an exact value iteration algorithm and present heuristics to improve the computation efficiency when the system contains multiple machines. Practitioners can implement the proposed methodology to make condition-based maintenance and inventory management when spare parts with different qualities are ordered from two suppliers. To balance cost and computational efficiency, it is suggested to implement the optimal policy by an exact value iteration algorithm when the number of machines is small in the system and use the heuristic methods when the number of machines is large (i.e., usually larger than 3).

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.

Machine degradation modeling is an enabling methodology to use monitoring data to evaluate machine health conditions. Fault detection needs to confirm whether there exists an incipient fault in a machine while machine diagnostics require knowing where the fault occurs and checking a specific fault type. In this article, an anchor discrimination learning model (ADLM) for physics-informed machine degradation modeling is innovatively proposed to find a projection direction that minimizes a distance between an anchor and samples with a same label of the anchor, and simultaneously maximizes a distance between the anchor and samples with a different label of the anchor. Subsequently, the ADLM is mathematically derived and formulated as a generalized Rayleigh quotient. Instead of using hand-crafted features, this article directly inputs normal and abnormal raw square envelope spectra into the ADLM for machine degradation modeling and the responses of the ADLM, namely an optimal direction, can automatically localize informative frequency components for immediate machine fault detection and diagnostics. Unlike most data-driven methodologies, the proposed methodology is physics-informed and its outputs are capable of indicating physical fault frequencies and their relevant frequency bands for quick fault detection and diagnostics. Two experimental studies are conducted to verify the feasibility of the proposed ADLM for machine degradation modeling.

Nowadays, with the rapidly growing size of random orders and machine scales, cloud manufacturing (CMfg) is suffering from complex difficulties in scheduling enormous production services in real time. Especially when coupled with preventive maintenance (PM) scheduling for massive distributed machines, most current methods fail to promise agility and effectiveness simultaneously under this service-oriented paradigm. Therefore, this article aims to propose a collaborative scheduling algorithm to support real-time production and opportunistic maintenance (OM) in the highly dynamic CMfg environment. First, a novel collaborative scheduling model that combines real-time production and PM decision-making is formulated. Then, to address significant complexity in production scheduling, a dynamic suborder-oriented scheduling (DSS) strategy is designed to utilize frequent triggered events for allocating optimal manufacturing services in real time. Then, for improving computational capability in PM decision-making, a production-driven PM policy with two stage adjustment (TSA) is developed to adopt suborder changeovers as PM opportunities to formulate group PM decisions for massive machines. Finally, a collaborative DSS-TSA algorithm is designed to cyclically coordinate the real-time production scheduling with OM decision-making to avoid repetitively solving large-scale joint problems. Our collaborative scheduling algorithm is verified in a real CMfg scenario for gas turbine blades. The results prove the significant improvement in production timeliness, machine availability, and system profitability.

Infrared thermography is increasingly exploited to track mechanical degradation in a noncontact manner, readily available for further prognostics. Recently, wavelet networks have coalesced deep learning and wavelet transform (WT), expected to achieve data-driven and interpretable prognostics. However, traditional wavelet networks neither possess enough adaptability to extract degradation-related features nor sufficiently fuse learned wavelet coefficients. Thus, this article presents a spatiotemporal dynamic convolution-based wavelet network to handle the above difficulties in industry. First, a spatiotemporal dynamic convolution layer is presented to flexibly modulate kernels according to input samples and the multidimensional kernel space. Second, a learnable lifting scheme structure is constructed to perform signal-adapted WT while incorporating crucial properties to link the optimization of lifting filters and degradation-related feature learning. Finally, a bilinear feature fusion is implemented to jointly represent extracted wavelet energy across decomposition levels, facilitating synergistic optimization. The superiority of the proposed method is illustrated through infrared degradation image datasets.

Infrared thermography captures real-time degradation temperature information, facilitating noncontact machine health monitoring. However, the inherent multiscale characteristics and spatiotemporal degradation discrepancy in infrared images pose a challenge in learning discriminative degradation features and adaptive prognostic analytics. This article presents a sparse hierarchical parallel residual networks ensemble (SHPRNE) method to tackle this challenge. First, the hierarchical parallel residual network (HPRN) leverages parallel multiscale kernels to capture complementary degradation patterns separately and embeds a hierarchical residual connection procedure to facilitate the interactivity between coarse-to-fine level features. Moreover, SHPRNE develops a sparse ensemble algorithm integrated with a synergy of network pruning and local minima perpetuation to derive diverse HPRNs while alleviating the parameter storage budget. Pruned HPRNs with varying sparsity and local minima are further integrated into an ensemble learner with higher generalization. Case studies on two infrared image datasets are conducted to demonstrate the effectiveness and superiority of the proposed method.

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.

Convex hulls based maximum margin classification has been widely studied for machine fault diagnosis, while its exploration for machine degradation modeling is seldom reported. In this study, a sparse and flexible convex-hull representation for machine degradation modeling is proposed to realize degradation trajectory tracking and fault diagnosis at a same time. First, considering using vibration data as health monitoring signals, globally normal and abnormal spectral lines can be obtained based on the fast Fourier transform and they are, respectively, characterized as individually flexible convex hulls. Subsequently, a sparse and flexible convex-hull representation degradation model is constructed by simultaneously finding the closest pair of samples and its sparse regularization between normal and abnormal convex hulls. Finally, a health indicator can be developed for early fault detection and degradation trajectory tracking during a machine life cycle. Meanwhile, quick fault diagnosis can be realized by finding a difference between the optimal closest samples in a normal convex hull and an abnormal convex hull. Two experimental cases are used to show the effectiveness and superiority of the proposed model to recent existing works.

With the popularization of service-oriented manufacturing, the current operation & maintenance (O&M) has shifted from traditional in-house maintenance to proactive outsourcing maintenance. It is paramount for an original equipment manufacturer (OEM) to provide timely and cost-effective maintenance schemes to geographically distributed customer enterprises. Interestingly, transportation theories could be combined to facilitate multi-location O&M management. In this paper, a transportation-oriented cross-regional opportunistic maintenance (TCOM) policy is developed for solving O&M optimizations and planning real-time schemes for the multi-center service network. The optimization model of this TCOM policy addresses several inter-related decisions: (1) most suitable maintenance times for each leased machine, (2) cost-effective arrangements of technician teams to perform maintenance tasks, and (3) optimal service routes for required teams. We not only integrate maintenance grouping and technician routing, but also investigate the new issues arising from the collaborative sharing of technician teams belonging to different maintenance centers. Numerical examples show that this TCOM policy can achieve significant cost-saving in cross-regional maintenance grouping and multi-location routing optimization for OEMs.Note to Practitioners—This paper is motivated by the critical problem of computing an optimal maintenance policy for the multi-center service network of geographically distributed production systems to achieve a timely and cost-effective O&M management. We consider individual machine degradations, complex maintenance opportunities and network logistics optimization to establish a global maintenance scheme for the multi-center service network. The existing approaches are to schedule the preventive maintenance (PM) for a single machine or multi-unit leased system, which is unilateral and cannot be applied to multi-location production systems. Although the network opportunistic maintenance policy has been proposed in the literature for maintenance grouping and technician routing problem, it still does not consider the limited workforce resource and the collaborative sharing of technician teams from different maintenance centers. To fill this literature gap, in this paper, we develop the TCOM policy to determine the optimal maintenance timetable for leased machines, as well as the cost-effective service route of technician teams belonging to multiple maintenance centers, so as to conduct timely and cost-effective PM on multi-location production systems. Compared with the conventional maintenance policy, our adaptive policy greatly reduces the total outsourcing maintenance cost in long-term O&M services.

Prognostics and health management aims to use on-line sensor data to monitor and predict current and future health conditions of degraded systems and components. Nowadays, constructing composite health indices for characterizing current health conditions of a system from multiple degradation-based sensor data has attracted much attention. These kinds of “data-level” models show strong ability to provide a better degradation characterization of a degraded system than a model solely depending on data from an individual sensor. Although numerous efforts have been made to propose “data-level” fusion methodologies for process data, such as temperature, pressure, speeds, etc., little research has targeted “data-level” fusion models for nonprocess data, such as vibration and acoustic signals. In this article, a methodology for constructing a composite health index from fusion of spectrum amplitudes is proposed. Here, each spectrum amplitude can be regarded as “an individual sensor.” The goal of this article is that a composite health index generated from fusion of spectrum amplitudes can simultaneously detect incipient faults and provide a monotonically increasing trend for degradation assessment. Our proposed methodology was verified by two illustrative examples including gearbox run-to-failure vibration data and bearing run-to-failure vibration data. Results showed that our proposed methodology is better than popular sparse measures for gear and bearing health monitoring and degradation assessment.Note to Practitioners—Process data, such as temperature, pressure, speed, etc., are capable of directly showing degradation trends of degraded systems and components. “Data-level” fusion models can be directly used to fuse process data from multiple sensors to show a better-fused degradation trend than a sole trend obtained from an individual process data sensor. Being different from process data, nonprocess data, such as vibration and acoustic data, cannot be used to directly show degradation trends unless they are transformed into a health index. One of the benefits of nonprocess data is that they have been proved to be sensitive to incipient machine faults. Nevertheless, due to complicated transmission paths and multiple responses, transforming nonprocess data into a health index is still a challenging task. This article presents a methodology to fuse spectrum amplitudes to form a health index that can simultaneously detect incipient machine faults and assess monotonic machine degradation. The main idea of this article is to regard each spectrum amplitude as “an individual sensor” and the sum of weighted spectrum amplitudes as a health index. To implement the proposed methodology, it is necessary: 1) to transform temporal nonprocess data into frequency spectra by using the well-known Fourier transform; 2) to know two essential properties about detecting incipient machine faults and assessing machine degradation; and 3) to train weights based on the essential properties by any convex optimization algorithms. Once optimal weights are obtained, the health index has ability to simultaneously detect incipient machine faults and monotonically assess machine degradation.

Recently, various fault diagnosis methods based on domain adaptation (DA) have been explored to solve the problem of discrepancy between the source and target domains. However, given complex industrial scenarios, DA-based methods usually fail when the working conditions of machines are unseen, i.e., target data are unavailable during model training. In this article, a generic domain-regressive framework for fault diagnosis, namely, adversarial domain-invariant generalization (ADIG), is proposed. ADIG leverages multiple available domain data to exploit domain-invariant knowledge through adversarial learning between the feature extractor and the domain classifier. Simultaneously, the fault classifier generalizes the knowledge from the source-related domain to diagnose the unseen but related target domain signals. Moreover, customized strategies of feature normalization and adaptive weight are proposed to promote diagnosis performance. Comprehensive case studies show that ADIG achieves satisfactory diagnosis accuracy and robustness under unseen conditions, indicating that ADIG is a remarkably potential diagnosis tool for real-case industrial machines.

Infrared thermography provides abundant spatiotemporal degradation information, facilitating non-contact condition monitoring. Reducing domain shift between simulated and industrial infrared images is significantly desired for leveraging labeled simulated data to tackle practical insufficiency of run-to-failure samples. Recently, adversarial-based domain adaptation (DA) techniques have aroused broad concern in solving domain shifts. However, simultaneously aligning marginal and conditional distributions in cross-domain remaining useful life (RUL) prediction is rarely researched in adversarial-based DA. In this article, an adversarial regressive domain adaptation (ARDA) approach is, thus, put forward to address this challenge. First, a regressive disparity discrepancy is designed to describe the dissimilarity between distributions and derive the generalization bound for cross-domain prognostics. Guided by this bound, the ARDA effectively aligns marginal and conditional distributions by learning indistinguishable features and considering the relationship between samples and prediction tasks. Simulated and experimental infrared degradation image datasets are used to demonstrate the effectiveness and superiority of the proposed approach over existing methods for cross-domain RUL prediction.

Increasing machine investments and expensive operations and maintenance (O&M) costs have made manufacturing system leasing and maintenance service outsourcing gaining a momentum. Leading original equipment manufacturers, as lessors, have focused on providing cost-effective maintenance schemes to serve their client-enterprises (lessees) all over the world. However, individual equipment degradations, complex system structures, and global network layout bring challenges for the real-time decision-making. This article comprehensively develops a service-outsourcing progressive opportunistic maintenance methodology for a global service-outsourcing network with prognostic updating and dynamical optimization. At the equipment layer, an automated prognostic model is utilized to characterize and update the individual path of each leased equipment's degradation signals. At the local layer, an opportunistic maintenance policy is developed for balancing production capacity and optimizing maintenance decisions of each system with even series-parallel structure. At the global layer, a routing optimization policy is proposed for the service-outsourcing network by integrating service time windows and multiple geographical locations to optimize the service route of required maintenance teams and the service start time of each group set. Finally, this hierarchical methodology has been verified in a multilocation service-outsourcing network. Its mechanism with real-time prognostic updating and dynamical O&M optimization can significantly ensure cost reduction, service timeliness and network robustness.

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.

Owing to distribution discrepancy between source training and target testing data, the performance of fault diagnosis by traditional supervised learning models will degenerate. Though domain adaptation methods for diagnosis have been actively investigated recently, most of them are devoted to learning from a single source. However, in reality, the supervised samples can be collected from different sources such as various working conditions. These sources are not only different from target but also from each other. The way of effectively fusing these sources to contribute the prediction of target remains a challenge. In this work, a new framework of multi-source domain adaptation is proposed for cross-domain fault diagnosis under different working conditions. Specially, this framework is realized by two alignment stages. At the first stage, multiple specific feature spaces are obtained, then the distributions of each pair of source and target domain are aligned since it is difficult to extract the common domain-invariant features for all domains. At the second stage, by considering the domain specific decision boundaries, the probabilistic outputs of classifiers are also aligned. Various experimental analysis on four different bearing working conditions is conducted to show the effectiveness of the proposed method. The performance of the proposed method is superior to state-the-art cross-domain fault diagnosis methods.

Bearings are the most common mechanical components used in machinery to support rotating shafts. Due to harsh working conditions, bearing performance deteriorates over time. To prevent any unexpected machinery breakdowns caused by bearing failures, statistical modeling of bearing degradation signals should be immediately conducted. In this paper, given observations of a health indicator, a statistical model of bearing degradation signals is proposed to describe two distinct stages existing in bearing degradation. More specifically, statistical modeling of Stage I aims to detect the first change point caused by an early bearing defect, and then statistical modeling of Stage II aims to predict bearing remaining useful life. More importantly, an underlying assumption used in the early work of Gebraeel et al. is discovered and reported in this paper. The work of Gebraeel et al. is extended to a more general prognostic method. Simulation and experimental case studies are investigated to illustrate how the proposed model works. Comparisons with the statistical model proposed by Gebraeel et al. for bearing remaining useful life prediction are conducted to highlight the superiority of the proposed statistical model.