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ABSTRACT In an effort to explore methods to improve overall system reliability, this systematic literature review (SLR) explores the current state of dynamic fault trees (DFTs) for complex, redundant systems that exhibit performance degradation over time. DFTs were first developed to manage and optimize redundant resources of computer system components, but have also been successfully used to manage redundant resources in aircraft and naval fuel distribution systems, transportation systems, industrial plants, computer networks, cardiac assist systems, and spacecraft systems. More recent DFT gates were added to identify, filter, and manage time‐dependent failures to minimize their impacts on the overall system performance and reliability, and have been applied to aircraft fault management systems, nuclear power plants, and alarm management systems. This SLR also explored the current state of technology for dynamically calculating not only the current capacity of system components, but also predicting their remaining useful life (RUL), remaining useful performance (RUP), and capacity degradation profiles. This is essential in understanding capacity degradation in the broader context of optimization of resources in complex, redundant systems. This SLR analysis revealed two gaps in the current technology and application of DFTs to complex systems. First, the usage of DFTs for failure management requires that the DFT is developed with a priori knowledge of specific failure modes, meaning that DFTs are inherently not scalable for new failures that are discovered. Second, although DFTs do address failure management, there are inherent limitations in the detection and application of partial failures or capacity degradation in the DFT infrastructure. [ABSTRACT FROM AUTHOR]

In conventional remaining useful life (RUL) prediction approaches grounded on maintenance, the maintenance threshold is typically established as a stationary value. However, the actual maintenance threshold may exceed its preset value due to the uncertainty of degradation and other factors. Therefore, it is necessary to consider the dynamic maintenance threshold to improve the precision of remaining useful life prediction. By considering the Wiener process, the maintenance threshold error is introduced to reflect the dynamic nature of the maintenance threshold. The influence of maintenance on degradation amount, degradation rate, and degradation path are comprehensively considered to establish a multi‐stage maintenance‐affected degradation process model. The RUL formula of the equipment is derived using the first hitting time (FHT). The maximum likelihood estimation (MLE) approach and Bayesian theory are employed to estimate the model's parameters. The proposed approach is validated using simulation data and gyroscope degradation data. The outcomes reveal that the proposed approach can significantly enhance the precision of life prediction for the equipment. [ABSTRACT FROM AUTHOR]

The prediction of remaining useful life (RUL) is a critical component of prognostic and health management for industrial systems. In recent decades, there has been a surge of interest in RUL prediction based on degradation data of a well‐defined degradation index (DI). However, in many real‐world applications, the DI may not be readily available and must be constructed from complex source data, rendering many existing methods inapplicable. Motivated by multivariate sensor data from industrial induction motors, this paper proposes a novel prognostic framework that develops a nonlinear DI, serving as an ensemble of representative features, and employs a similarity‐based method for RUL prediction. The proposed framework enables online prediction of RUL by dynamically updating information from the in‐service unit. Simulation studies and a case study on three‐phase industrial induction motors demonstrate that the proposed framework can effectively extract reliability information from various channels and predict RUL with high accuracy. [ABSTRACT FROM AUTHOR]

This document is a summary of a special issue of the journal Quality & Reliability Engineering International. The issue showcases original research presented at the 2023 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. The research papers cover a diverse range of topics related to reliability and safety in modern engineering systems. The papers address areas such as reliability modeling and analysis, reliability-based design and optimization, failure/safety analysis and prevention, and maintainability. The authors express their appreciation to the journal and the reviewers for their support and hope that the research presented will be valuable to researchers, engineers, scientists, and students in the field. [Extracted from the article]

Accurate prediction of remaining useful life (RUL) for in‐service systems plays an important role in ensuring efficient operation of industrial equipment and in preventing unexpected equipment failures. In this paper, we present a prognostic framework for real‐time RUL prediction based on joint modeling of both degradation signals and time‐to‐event data. The proposed model employs a change point‐based general path model to capture signal non‐linearity and Neural network (NN) based Cox model to link the time‐to‐event data with the estimated degradation trend. An empirical two‐step scheme for hyperparameter estimation is proposed to enhance prognostic accuracy. Furthermore, an efficient Bayesian model updating procedure, integrated with recursive particle filtering, is used to facilitate online prediction, achieving accurate RUL prediction in real‐time and accounting for uncertainties in RUL prediction. Simulation and real‐life case studies demonstrate the advantages of the proposed method over existing approaches. [ABSTRACT FROM AUTHOR]

Estimating the reliability and maintainability (R & M) parameters is crucial in various industrial applications. It serves purposes such as evaluating system performance and safety, minimising the risk and cost of potential failures, and designing efficient maintenance strategies. This task becomes challenging for complex repairable systems, where failures can occur due to different causes and performance may be affected by various covariates (such as material, environment, and labour). Another challenge in R & M studies arises from the presence of censorship in failure times. Existing methodologies often fail to account for all the aforementioned aspects of system‐related data in R & M analysis. By incorporating valuable information from covariates and utilising data from censored failure times alongside complete failure data, the accuracy of R & M parameter estimation can be significantly improved. This paper develops reliability models for repairable systems with multiple failure causes in the presence of covariates. The system can also be subject to imperfect maintenance. The R & M parameters are then estimated by applying the Kijima Type I and II model's virtual age concept. The proposed technique is illustrated using two case studies on gas pipelines and aero‐engine systems. Through these case studies, we show that the proposed method not only provides more efficient estimates of the R & M parameters compared to the alternative approach, but it is also easier to apply and yields more straightforward interpretations. [ABSTRACT FROM AUTHOR]

It is difficult to effectively predict remaining useful life (RUL) due to limited training samples and lack of life labels in some operating conditions of practical engineering. When existing deep learning methods predict the RUL of equipment in such operating conditions using a model trained on other operating conditions, the poor generalization of the model caused by large distribution differences cannot be ignored. In this study, an RUL prediction method based on integrated dilated convolution transfer is proposed. This method jointly adjusts the model parameters by inverting the loss function of the RUL prediction module and the domain adaptive module, and then realizes the extraction of domain‐invariant features between different operating condition data through the feature extraction module, which provides support for transfer RUL prediction between different operating conditions. In the feature extraction module, a one‐dimensional convolution network with a large‐size kernel reduces noise in the original data, which reduces the erroneous effect of noise on the trending expression of the original data, and a hybrid dilated convolution network extracts the features of the different sensory fields of the noise‐reduced data, which increases the richness of the extracted features and thus improves the accuracy of the modeling. Next, the extracted features are fed into the RUL prediction module to predict RUL; into the classification model in the domain adaptation module to divide the source and target domains; and into the distribution difference measurement model in the domain adaptation module to identify the feature distribution differences between the source and target domains, and inversely adjust the model parameters by reducing the distribution differences. Furthermore, domain invariant characteristics of the features in different receptive fields under multiple operating conditions are obtained to enhance the model's generalization ability and achieve RUL prediction across various operating conditions. Monte Carlo (MC) dropout simulation technology is used to quantify the uncertainty of prediction results. Finally, the effectiveness and superiority of the proposed method are verified using the prognostics and health management (PHM) 2012 bearing dataset. [ABSTRACT FROM AUTHOR]

In recent years, there has been growing interest in employing predictive methods to forecast the remaining useful life of industrial equipment. However, the challenge lies in how to take advantage of the dynamic predictive information to facilitate the maintenance of decision‐making. This problem becomes particularly challenging for complex industrial systems consisting of multiple components with economic dependencies. This paper aims at providing an effective maintenance strategy for multi‐component systems based on predictive information, while considering economic dependencies among different system components. To this end, a dynamic predictive maintenance (PdM) strategy that minimizes the mean maintenance cost over a decision period is proposed, where both long‐term and short‐term policies are integrated into the decision‐making framework. Specifically, the long‐term policy is formulated using predictions derived from historical degradation data through a Long Short‐Term Memory (LSTM) model. Concurrently, real‐time monitoring data is employed to forecast imminent degradation in components, serving as a basis for determining the necessity of short‐term adjustments. This paper embeds the consideration of economic dependencies among components within the maintenance strategy design and employs hierarchical clustering to establish an effective and efficient maintenance grouping policy. The experimental results demonstrate that our proposed strategy significantly outperforms conventional approaches, including block‐based and age‐based maintenance, resulting in substantial cost savings. The proposed strategy is also compared with a similar version without grouping, and the results verify the added value of the optimal maintenance grouping policy in cost reduction. Moreover, a comprehensive analysis of the proposed method is provided, including the impact of different inspection costs and inspection intervals on maintenance decision‐making, which can provide insightful guidance to various PdM scenarios in practice. [ABSTRACT FROM AUTHOR]

Accurate prediction of the engine's remaining useful life (RUL) is essential to ensure the safe operation of the aircraft because. However, traditional deep‐learning based methods for RUL prediction has been limited by interpretability and adjustment for hyperparameters in practical applications due to the intricate potential relations during the degradation process. To address these dilemmas, an improved multi‐strategy tuna swarm optimization‐assisted graph convolutional neural network (IMTSO‐GCN) is developed to achieve RUL prediction in this work. Specifically, mutual information is used to describe potential relationships among measured parameters so that they could be utilized in building edges for these parameters. Besides, considering that not all relational nodes will positively affect the RUL prediction and the inherent hyperparameters of the GCN are high‐dimensional. Inspired by “No Free Lunch (NFL)”, IMTSO is proposed to reduce the optimization cost of hyperparameters, in which cycle chaotic mapping is employed to achieve initialization of the population for improving the uniformity of the initial population distribution. Besides, a novel adaptive approach is proposed to enhance the exploration and exploitation of tuna swarm optimization (TSO). The CMAPSS dataset was used to validate the effectiveness and advancedness of IMTSO‐GCN, and the experimental results show that the R2 of the IMTSO‐GCN is greater than 0.99, RMSE is less than 3, the Score error is within 1. [ABSTRACT FROM AUTHOR]

Many deep learning methods typically assume that the marginal probability distribution between the training and testing bearing data is similar or the same. However, the probability distribution of rolling bearings may deviate significantly under diverse working conditions. To address the above limitations, a novel transferable remaining useful life (RUL) prediction method integrated with Bayesian deep learning and unsupervised domain adaptation (DA) is proposed. First, the signal alignment is executed on the data after the first prediction time to maintain the same granularity and scale across both source and target domains. Second, the multi‐domain features are extracted and sent into the dual‐channel Transformer network (DCTN) incorporating the convolutional block attention module (CBAM) to adequately exploit the abundant degradation information. Then, the DA module is incorporated into the model to mitigate the distribution discrepancies of the extracted high‐level merged features between the source and target domains. Finally, by applying the variational inference method, the DCTN‐CBAM is extended to the Bayesian deep neural network, and the RUL prediction and its corresponding confidence intervals can be conveniently derived. In addition, the generalization capability and effectiveness are validated through six bidirectional transfer RUL prediction tasks across two rolling bearing datasets. The experimental results demonstrate that it could provide a more reliable RUL prediction and efficiently account for the prediction uncertainty. [ABSTRACT FROM AUTHOR]

Modeling and evaluation of a system reliability is a key issue in shock model analysis. In cumulative shock model, a system fails when the total damages caused by shocks exceeds the system failure threshold level. The reliability of a system with random failure threshold level under cumulative shocks is investigated in this work, considering the general dependency between inter‐arrival times of shocks and their damages magnitudes. Clustering, as one of the unsupervised machine learning methods, is utilized here by applying a genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for its implementation. Phase‐type (PH) distributions and their properties are also applied for finding a system failure distribution functions, determining the convolutions, evaluating the integrals, and ultimately modeling the system reliability. An illustrative example is provided to demonstrate the implementation and effectiveness of the proposed modeling procedure and the suggested approach for computing the system reliability and remaining useful lifetime (RUL). Also, an example case study of X‐ray machine in healthcare industry is provided to demonstrate the application of the proposed model. Applying other machine learning methods for patterns recognition is an area for future research. [ABSTRACT FROM AUTHOR]

Accurately predicting the remaining useful life (RUL) is crucial for the safety and stability of battery systems. Considering the inherent challenges in directly measuring the capacity of lithium‐ion batteries during operation, this paper proposes an online hybrid cascaded data‐driven prediction algorithm for RUL. Health indicators (HIs) are extracted from the charge–discharge voltage and incremental capacity curves, following which gray correlation analysis is employed to quantitatively assess the relevance between the HIs and batteries' capacities. Redundancy of HIs is eliminated through kernel principal component analysis, which enhancing the efficiency of subsequent analysis. The proposed framework incorporates the sparrow search algorithm‐based kernel extreme learning machine (SSA‐KELM) as the first‐level prediction model, establishing the relationship between HIs and capacities. The bidirectional long short‐term memory (BiLSTM) is utilized as the secondary‐level model, which integrates the preliminary capacity predictions of SSA‐KELM. Finally, experimental validation using battery datasets from NASA and Oxford showed that the method has remarkable generalization ability and superior prediction accuracy. Quantitatively, the RMSE and MAPE of NASA batteries are within 0.03, while the errors of Oxford batteries are within 0.003. The RUL prediction errors of all lithium‐ion batteries are within two cycles. [ABSTRACT FROM AUTHOR]

In this paper, the problem of fault prognosis is investigated for linear stochastic systems with intermittent faults (IFs) and strong noise. Different from permanent faults, the degradation state of IFs are related to the fault duration time, leading to difficulties in the first step of fault prognosis, that is, the health indicator (HI) extraction. Generally, HI extraction of IFs is achieved by fault detection techniques. Therefore, the proposed fault prognosis approach mainly covers the following steps. First, the HI and degradation model are introduced for linear stochastic systems with IFs. Then, considering dynamic characteristic of systems and influence of strong noise, an IF detection algorithm under strong noise is proposed using weighted moving average methods to extract the HI. Moreover, an alternative HI extraction approach is given by an HI estimation way, which avoids using fault detection techniques. Subsequently, the degradation model is fitted by virtue of HIs and the least square method, and the remaining useful life is predicted with the aid of the obtained model. Finally, an experiment concerning the rotary steerable drilling tool system is provided to verify the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This study addresses the problem of performance reliability degradation and lifetime prediction in complex systems with high reliability but insufficient information. It comprehensively considers the effects of various uncertainties, such as measurement, cognitive, and stochastic uncertainties, and proposes a generalized normal grey cloud Bayesian Wiener process (GNGCBWP) stochastic degradation model. First, based on the historical degradation information of the system, the interval grey number sequence of the degradation increment is constructed, and the performance degradation path of the system is analyzed to determine the degradation model type. Then, combining the normal grey cloud and Bayesian estimation theory, the relevant definitions and theorems of generalized normal grey cloud Bayesian estimation (GNGCBE) are proposed. Finally, the parameter estimation results obtained using the GNGCBE method are substituted into the grey Wiener process degradation model to dynamically analyze performance reliability degradation and predict the remaining useful life (RUL) in real‐time. And the validity and scientificity of the proposed model is verified through a case study of laser equipment. Moreover, the comparison results of the models indicate that the proposed model has advantages in dynamic analysis of performance reliability degradation and real‐time RUL prediction for highly reliable complex systems with limited or poor degradation information. It can significantly reduce the impact of multiple uncertainties on the analysis results and improve the accuracy and reliability of the final prediction results. [ABSTRACT FROM AUTHOR]

As one of the key technologies in battery management system, accurate remaining useful life (RUL) prediction is critical to guarantee the reliability and safety for electrical equipment. However, the generalization and robustness of a single method are limited. A novel fusion data‐driven RUL prediction method CSSA‐ELM‐LSSVR based on charging‐discharging health features extraction is proposed in this paper, which fusions chaotic sparrow search algorithm (CSSA), extreme learning machine (ELM), and least squares support vector regression (LSSVR). First, four health indicators (HIs) are extracted from the charging‐discharging process, which can reflect the battery degradation phenomenon from multiple perspectives. Then, pearson correlation coefficient is used to numerically analyze the correlation between HIs and battery aging capacities. Second, the extracted HIs are used as the inputs for ELM and LSSVR to predict the degradation trend of battery, where CSSA is used for hyperparameters optimization in ELM. Finally, considering that CSSA‐ELM can capture the general trend of degradation curves, while LSSVR can trace the detail changes, a fusion framework based on CSSA‐ELM and LSSVR is proposed for RUL prediction. Two weighting schemes, namely precision‐based weighting (PW) and random forest regressor‐based weighting (RFRW) are put forward to fix the weights of CSSA‐ELM and LSSVR algorithms. Two publicly available datasets from National Aeronautics and Space Administration (NASA) and MIT are adopted to verify the feasibility and effectiveness of the proposed method. The results indicate that the proposed method with any weighting scheme has an overall superior prediction performance for different kinds of batteries compared with CSSA‐ELM, LSSVR, convolution neural network and long short term memory. Moreover, the RFRW scheme has better overall performance. Specifically, the maximum root mean square error of the predicted method is 2.5126%, the mean absolute percentage error is 12.9167%, the mean absolute error is 1.8376%, the predicted RUL errors are within one cycle, and the determination coefficient R2$R^2$ is above 0.97. [ABSTRACT FROM AUTHOR]

Domain adaptation is a transfer learning method that is widely applied for remaining useful life (RUL) prediction under different operating conditions. However, current RUL prediction methods based on domain adaptation only consider minimizing degradation feature differences, while ignoring the correlation between features and labels, which may result in significant errors in the mapping relationship between the two learned by the model, and thus reduce the accuracy of prediction. To address this issue, this paper proposes an unsupervised subdomain adversarial network (USDAN) for RUL estimation under various conditions. On the basis of traditional domain adversarial adaptation networks, the network uses temporal convolutional networks to construct the feature extractor to learn the long‐term dependencies between degradation data, and a multilinear conditioning scheme is designed to combine the features and subdomain labels as input features to the domain discriminator. Finally, with backpropagation and gradient reversal, the feature extractor is prompted to generate cross‐domain invariant features that are correlated with the labels, improving the prediction accuracy and enhancing the transferability of the network. In the experimental section, the public turbofan engine degradation dataset is used to validate the effectiveness of the network, and the comparison with other approaches demonstrates its advantages. [ABSTRACT FROM AUTHOR]

Predicting the remaining useful life (RUL) of an engine is one of the key tasks of Prognostics and health management (PHM). Modern mechanical equipment typically operates in complex operating conditions and fault modes, leading to dispersed distribution of sensor data and challenges for feature extraction. To improve the accuracy of predicting the RUL under the complex scenarios, this paper proposes a multi‐scale convolutional network (CNN) and bidirectional gated recurrent unit (MSC‐BiGRU) mode under a dual path framework with temporal attention. Specifically, the multi‐scale CNN in the first path is to learn complex features, and Swish Activation function is used to improve the prediction ability of the network; the bidirectional gated recurrent unit (BiGRU) in the second path can handle both forward and backward time series, and adaptively capture the importance of outputs at different times using temporal attention, enhancing the model's feature extraction ability in the temporal dimension. A feature fusion mechanism is developed to connect two paths in parallel, overcoming the overfitting and high computational complexity in deep complex models. We verify the effectiveness of the proposed method using a simulated turbofan engine dataset, especially on datasets FD002 and FD004 under complex operating conditions and fault modes, the RMSE values were reduced by 17.37% and 9.97%, respectively, compared to the BiGRU‐TSAM. [ABSTRACT FROM AUTHOR]

Remaining useful life prediction (RUL) is a critical procedure in the application of prognostics and health management for devices or systems. It is difficult to predict the RUL in a time‐varying external environment. Specifically, many mechanical systems typically experience various operating conditions, which have impacts on the degradation process and degradation rate. In particular, the linear degradation modeling of the Wiener process‐based RUL prediction method has attracted considerable attention recently. However, the dependency of degradation rate and operating conditions is generally ignored in the current degradation modeling, which leads to inaccurate issues in the RUL prediction. Therefore, to solve the above issues, a novel RUL prediction method based on the Wiener process considering parameter dependence is proposed in this paper. At first, a linear Wiener process degradation model considering parameter dependence is constructed to describe the dependency of the drift coefficient and operating conditions. Secondly, the probability density function of RUL is derived under the concept of first hit time. After that, the collaboration between the Bayesian update and expectation maximization algorithm is introduced to update and estimate the model parameters. Finally, the validity and applicability of the proposed method are verified by a numerical simulation and three case studies of bearings. [ABSTRACT FROM AUTHOR]

Accurate prediction of the Remaining Useful Life (RUL) of components and systems is crucial for avoiding an unscheduled shutdown of production by planning maintenance interventions effectively in advance. For high‐reliability equipment, few complete‐run‐to‐failure trajectories may be available in practice. This constitutes a technical challenge for data‐driven techniques for estimating the RUL. This paper proposes a novel data‐driven approach for fault prognostics using the Long‐Short Term Memory (LSTM) model combined with the Multi‐Head Self‐Attention (MHSA) mechanism. The former is applied to the input signals, whereas the latter is used to extract features from the LSTM hidden states, benefiting from the information from all hidden states rather than utilizing that of the final hidden state only. The proposed approach is characterized by its capability to recognize long‐term dependencies while extracting features in both global and local contexts. This enables the approach to provide accurate RUL estimates in various stages of the equipment's life. The proposed approach is applied to an artificial case study simulated to mimic the realistic degradation behaviour of a heterogeneous fleet of aluminium electrolytic capacitors used in the automotive industry (under variable operating and environmental conditions). Results indicate that the proposed approach can provide accurate RUL estimates for high‐reliability equipment compared to four benchmark models from the literature. [ABSTRACT FROM AUTHOR]

For degraded products with multiple performance characteristics (PCs), one way to model their degradation process is by using a multivariate independent Wiener process model with random drift. However, it fails to capture the latent correlation in degradation paths for multiple PCs caused by the common environmental condition. In this paper, we model the degradation processes of multiple PCs using multiple correlated Wiener processes. The commonly shared environmental condition function incorporates the degradation correlation and random effect. Thus, it directly catches the strong correlation of degradation rates and volatilities to all dimensions of multiple PCs. Our model is more economical in the number of parameters than the multivariate independent Wiener process. The correlation coefficients and RUL distribution approximation are provided in closed forms. We extend the proposed model to a two‐stage degradation process to correlate multiple PCs in each stage. An adaptive drift is adopted in the Wiener process model for the real‐time degradation states updating with the help of the Bayesian and the expectation‐maximization (EM) algorithm. The proposed model's effectiveness is illustrated by numerical studies and a real‐world application to the wheel treads on high‐speed trains. [ABSTRACT FROM AUTHOR]

Successful modeling of degradation data is of great importance for both accurate reliability assessment and effective maintenance decision‐making. Many of existing degradation performance modeling approaches either assume a homogeneous population of units or characterize a heterogeneous population with some restrictive assumptions, such as pre‐specifying the number of sub‐populations. This paper proposes a Bayesian heterogeneous degradation performance modeling framework to relax the conventional modeling assumptions. Specifically, a Bayesian non‐parametric model formulation and learning algorithm are proposed to characterize the historical degradation data of a heterogeneous population of units with an unknown number of homogeneous sub‐populations and allowing the joint model estimation and sub‐population number identification. Based on the off‐line population‐level model, an on‐line individual‐level degradation model with sequential model updating is further developed to improve remaining useful life prediction of individual units with sparse data. A real case study using the heterogeneous degradation data of deteriorating roads is provided to illustrate the proposed approach and demonstrate its validity. [ABSTRACT FROM AUTHOR]

Rolling bearings, an essential fundamental component in machinery and equipment, have been widely used. Predicting the remaining useful life (RUL) of rolling bearings helps maintain the reliability of mechanical systems. Accurate prediction of RUL requires extracting deep features in complex non‐linear vibration signals, the prediction results often vary widely. This paper proposes a RUL prediction method based on convolutional neural network (CNN), bi‐directional long‐short term memory (BiLSTM), and bootstrap method (CNN‐BiLSTM‐Bootstrap) to model the forecasting uncertainty. The first step is to extract the first prediction time (FPT) of the degradation phase of rolling bearings using an adaptive method for the 3σ intervals of rolling bearing vibration signal kurtosis. The model extracts the spatio‐temporal features through CNN and BiLSTM, and combines the bootstrap method to quantify the RUL prediction interval (PI) of rolling bearings. The comparison with existing models verified the effectiveness and generalization of the proposed model. [ABSTRACT FROM AUTHOR]

This paper constructs a remaining useful life (RUL) prediction model combining a convolutional neural network and a long short‐term memory network (CNNLSTM) to support decision‐making, especially the safety of rotational equipment. It avoids the influence of personnel and realizes the complementary advantages of the network. With the assistance of Bayesian short‐term and long‐term memory neural networks, the remaining life prediction method is able to provide the confidence interval of the remaining life prediction of rolling bearings. The compression between the proposed method and existing state‐of‐the‐art methods validated the good performance of the proposed method. Overall, the proposed method contributes to life prediction and condition‐based maintenance of bearings and complex rotational systems. [ABSTRACT FROM AUTHOR]

The data measured by the pitot tube (PT) is related to airspeed indication and flight safety. However, there are few methods to solve the problem of failure prediction and predictive maintenance of PT. This study proposes a method for predicting the remaining useful life (RUL) of the PT based on dynamic operating data. First, an exposure index (EI) characterizing the severity level of operating conditions is proposed based on multiple dynamic operating and environmental parameters, then a cumulative exposure model (CEM) is developed to calculate the cumulative exposure. Dynamic covariate information is incorporated into the time‐to‐failure distribution of PT through the CEM, the RUL distribution of the individual PT is then obtained by Monte Carlo simulation. A case study is carried out based on actual data of a commercial aircraft fleet and shows that the proposed CEM can effectively use historical aircraft environmental information and truncated failure data of the components. The relative error of the remaining life prediction is substantially improved compared to the traditional reliability analysis methods, which means that the proposed model can provide more reliable RUL results based on historical operating conditions, providing better support for PT risk assessment and condition‐based maintenance decisions. [ABSTRACT FROM AUTHOR]

This paper evaluates the remaining useful life (RUL) for the accelerated Wiener process with mixed random effects and measurement errors. In the discussed model, the random effects are included in both the drift and diffusion parameters of the Wiener process to model the heterogeneity among different degradation paths of products. The measurement errors are introduced to describe the inaccuracy during the measurement process. The effect of the accelerated stress level is included in the drift parameter. The expectation‐maximization (EM) algorithm is applied to obtain the estimation of the model parameters. The expressions of the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the lifetime and RUL distributions of products under the normal usage stress level are derived theoretically. Finally, an example of stress relaxation data is used to illustrate the effectiveness of the developed model and method. [ABSTRACT FROM AUTHOR]

The remaining useful life (RUL) prediction plays an increasingly important role in predictive maintenance. With the development of big data and the Internet‐of‐Things (IoT), deep learning (DL) techniques have been widely adopted for RUL prediction. Addressing the limitation of the current methods for data under multiple operating conditions, this paper proposes a three‐stage feature selection approach for DL‐based RUL prediction models. The k‐medoids cluster is initially used to sort raw data based on different operating conditions. In the first stage of feature selection, an operational‐based normalisation approach is applied to reconstruct the data. Afterwards, Spearman's rank and pair‐wise Pearson correlation coefficients are used to eliminate irrelevant and redundant features in the second and third stages, respectively. A case study using NASA's Commercial Modular Aero‐Propulsion System Simulation (C‐MAPSS) dataset is presented to quantitatively evaluate the influence of the proposed feature selection method using the Recurrent Neural Network (RNN) and its' variants, enhanced by an optimised activation function and optimiser. The results confirm that the proposed method can improve the stability of DL models and achieve about a 7.3% average improvement in the RUL prediction for popular and state‐of‐the‐art DL models. [ABSTRACT FROM AUTHOR]

The remaining useful life (RUL) of the machine is one of the key information for predictive maintenance. If there is a lack of predictive maintenance strategy, it will increase the maintenance and breakdown costs of the machine. We apply transfer learning techniques to develop a new method that predicts the RUL of target data using degradation trends learned from complete bearing test data called source data. The training length of the model plays a crucial role in RUL prediction. First, the exponentially weighted moving average (EWMA) chart is used to identify the abnormal points of the bearing to determine the starting point of the model's training. Secondly, we propose transfer learning based on a bidirectional long and short‐term memory with attention mechanism (BiLSTMAM) model to estimate the RUL of the ball bearing. At the same time, the public data set is used to compare the estimation effect of the BiLSTMAM model with some published models. The BiLSTMAM model with the EWMA chart can achieve a score of 0.6702 for 11 target bearings. The accuracy of the RUL estimation ensures a reliable maintenance strategy to reduce unpredictable failures. [ABSTRACT FROM AUTHOR]

Accurate prediction of remaining useful life (RUL) plays an important role in the formulation of maintenance strategies. However, due to the diversity of the failure mode of equipment, there are significant differences between the degradation data, which greatly affects the accuracy of RUL prediction. In this case, an ensemble prediction model considering health index‐based (HI‐based) classification is proposed in this paper. Firstly, the stacked autoencoder (SAE) is employed to construct the HI. Then, the time window is used to sequentially process the HI sequence, so that many data segments with the same length can be achieved. To differentiate the data with the similar degradation process, K‐means and Xgboost are selected to construct offline and online data classification models respectively. Finally, according to the results of the data classification, the ensemble model that integrates multiple machine learning methods are separately trained and then adaptively used for RUL prediction. In addition, integrating multiple methods helps to improve the generalization ability of the model. The NASA C‐MAPSS dataset is applied to verify the effectiveness of the proposed method, and the results show that the proposed method achieves a higher prediction accuracy and shorter computational time than other existing prediction models. [ABSTRACT FROM AUTHOR]

Most of the stochastic models adopted to describe the evolution over time of degradation phenomena of technological units assume that their degradation level can increase indeterminately. However, these degradation phenomena are typically subjected to obvious bounds, if only because technological units have finite size. In fact, very often, this inconsistency does not significantly affect the effectiveness of unbounded degradation models, since degrading units are usually assumed to fail when their degradation level exceeds a failure threshold that is much smaller than the obvious bounds. Nevertheless, in some cases, due to the very nature of the underlying degradation mechanism, less obvious bounds could exist, which are not necessarily far from the failure thresholds. The question that arises is whether the use of a bounded degradation model, in this latter type of experimental situations, could be beneficial. For this purpose, since a bounded degradation process should necessarily have dependent increments, in this paper we investigate the potential of a new bounded transformed gamma (TG) process to adequately describe bounded degradation phenomena and predict their future evolution. Differently from other existing gamma process based bounded degradation models, here the upper bound is treated as an unknown parameter that has to be estimated from the available degradation data. A numerical example is presented where the parameters of the proposed model are estimated from simulated data. Then the model is applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion, which have also stimulated this study. Model parameters are estimated by using the maximum likelihood (ML) method. The fitting ability of the proposed new bounded process is compared to that of an unbounded gamma process, which was previously adopted to analyze the same liner wear data. Obtained results are critically discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider small sample statistical inference methods for the constant stress accelerated life test (CSALT) under the proportional reverse hazards family (PRHF). The model parameters are assumed to be the exponential functions of the stress. The generalized confidence intervals (GCIs) are derived for the model parameters and some commonly used reliability metrics such as the quantile and the reliability function of the lifetime at the designed stress level. The generalized prediction interval (GPI) is also proposed for the future failure time (FFT) and the remaining useful life (RUL) at the designed stress level. The Monte Carlo simulation study for the generalized Lindley distribution (GLD) and the inverse Weibull distribution are used to illustrate the performance of the proposed GCIs and GPI. The simulation results indicate that the performance of the proposed GCIs and GPI is better than the Wald confidence intervals (CIs) and bootstrap‐p CIs in terms of the coverage probability (CP). Finally, a real example is used to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]

The degradation model and the remaining useful life (RUL) prediction are two key metrics for machine health prognostics. However, the precision of RUL prediction highly depends on the validity of the degradation model. Consequently, the uncertainty of RUL prediction based on the two‐phase degradation process may cause the estimated product reliability to differ from its actual value and lead to a faulty predictive maintenance strategy. However, recent studies have rarely compared the RUL predictions based on two‐phase and single‐phase degradation models. In this study, a real‐time RUL prediction approach was developed for a two‐phase linear Wiener degradation process. A two‐phase Wiener degradation model was proposed along with an estimation method for the change point and model parameters. Based on a state‐space model and Markov chain Monte Carlo, the drift coefficient of the degradation model was updated, and a real‐time RUL prediction model was developed. To examine whether the two‐phase Wiener degradation model was incorrectly assumed to be single‐phase, a case study was conducted to analyze RUL prediction based on the original and incorrect models. The results demonstrated that to obtain a more accurate RUL prediction, a sufficient number of samples should be used in addition to updating the drift coefficient of the degradation model when new measurement data are available. [ABSTRACT FROM AUTHOR]

Remaining useful life (RUL) plays an important role in prognostic and health management to reduce maintenance costs and avoid possible accidents. Massive multi‐sensor data makes it challenging to extract degradation features and predict RUL. This paper develops a novel RUL prediction framework consisted of a multi‐sensor fusion model and a hybrid prediction model. HI curves are constructed by synthesizing multiple metrics including time correlation, monotonicity, robustness, and consistency, making our data fusion method different from existing methods considering only one metric. In many practical situations, the initial degradation levels of obtained HI curves are different, and treating all curves without classification will result in errors in RUL prediction. The K‐means method is used to partition degradation paths into discrete states and the obtained HI curves are grouped by their initial states and then trained separately. A hybrid prediction model combining Long Short‐Term Memory (LSTM) network and Support Vector Regression (SVR) is developed to predict the RUL. The dataset of turbofan engines is used to verify the proposed method. The results show that the proposed method performs better than many existing methods. [ABSTRACT FROM AUTHOR]

Remaining useful life prediction (RUL) is a key component in the application of prognostics and health management associated with devices or systems. But such RUL predictions are cumbersome owing to complexities from external effects and internal degradation mechanisms within systems. Specifically, it is common for degradation processes to comprise distinct multiple stages rather than just one uniform stage in many mechanical systems. In particular, the two‐stage degradation modeling for RUL prediction based on the Wiener process with linear drift has received significant attention in recent years. However, negative effects of measurement errors and stochasticity of the degradation states are generally excluded from current degradation modeling, which causes inaccuracy problems that can impact system maintenance schedules and operational efficiency. Therefore, to solve such problems, measurement errors are considered in this paper and a two‐stage degradation model is proposed, in which an adaptive term is also characterized by the Wiener process. The transition probability density function (TPDF) of the degradation state at the two‐stage changing point is derived and an analytical solution for the RUL is obtained under the concept of the first hit time (FHT). A Kalman filter and smoothing algorithm are introduced to estimate variables, and the expectation maximization (EM) algorithm is applied to update and estimate model parameters. Finally, the effectiveness and applicability of the proposed model in RUL predictions are verified through numerical simulation and a case study of bearings. [ABSTRACT FROM AUTHOR]

The existing studies on degradation modeling and remaining useful life (RUL) prediction have typically been conducted on the basis of the following two assumptions: one is the single degradation indicator, and the other is the neglect of the influence of dynamic operating conditions. However, they are oversimplified for the real‐world situations. In this paper, a bivariate degradation modeling method based on the Bayesian dynamic model (BDM) and a joint RUL distribution prediction method is proposed. The covariate model is adopted to illustrate the influence of the dynamic operating conditions on the degradation process. A time‐varying copula method is used to describe the joint RUL distributions of the bivariate system. A real case study on the microwave device is conducted to demonstrate the effectiveness and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Remaining useful life (RUL) prediction technology is important for optimizing maintenance schedules. With the advancement of sensing technology, several deep learning approaches have been proposed to predict RUL without relying on prior knowledge about systems. However, previous deep learning‐based approaches rarely consider the future operational conditions, which can be known according to the future work plan and is an important influential factor for RUL prediction. This paper proposes a multi‐input neural network based on long short‐term memory for RUL prediction considering the temporal dependencies among the measurements when the future operational conditions are known. The sliding window approach is employed for determining the input time sequences of previous monitoring data (including operational condition and sensor measurements), and the length of input time sequences of the future operational conditions are determined based on the prior estimated RUL. Fine‐tuning strategy is proposed to make the training of the multi‐input network more effective. To illustrate the effectiveness of the proposed methods, a case study referring to the C‐MAPSS dataset is used and a sensitivity analysis is also conducted on the future operational conditions. [ABSTRACT FROM AUTHOR]

Diagnostics and prognostics have a significant role in the reliability enhancement of systems and are focused topics of active research. Engineered systems are becoming more complex and are subjected to miscellaneous failure modes that impact adversely their performability. This ever-increasing complexity makes fault diagnostics and prognostics challenging for the system-level functions. A significant number of successes have been achieved and acknowledged in some review papers; however, these reviews rarely focused on application to complex engineered systems nor provided a systematic review of diverse techniques and approaches to address the related challenges. To bridge the gap, this paper first presents a review to systematically cover the general concepts and recent development of various diagnostics and prognostics approaches, along with their strengths and shortcomings for the application of diverse engineered systems. Afterwards, given the characteristics of complex systems, the applicability of different techniques and methods that are capable to address the features of complex systems are reviewed and discussed, and some of the recent achievements in the literature are introduced. Finally, the unaddressed challenges are discussed by taking into account the characteristics of automotive systems as an example of complex systems. In addition, future development and potential research trends are offered to address those challenges. Consequently, this review provides a systematic view of the state-of-the-art and case studies with a reference value for scholars and practitioners. [ABSTRACT FROM AUTHOR]

Advancements in information technology have made various industrial equipment increasingly sophisticated in recent years. The remaining useful life (RUL) of equipment plays a crucial important role in the industrial process. It is difficult to establish a functional RUL model as it requires the fusion of time‐series data across different scales. This paper proposes a long‐short term memory neural network, which integrates a novel partial least square based on a genetic algorithm (GAPLS‐LSTM). The parameters are first analyzed by PLS to obtain the parameter fusion function of the health index (HI). The GA then searches the optimal coefficients of the function; the expected HI values can be calculated with the fusion function. Finally, the RUL of the equipment is predicted with the LSTM method. The proposed GAPLS‐LSTM was applied to RUL prediction of a marine auxiliary engine to validate it by comparison against GAPLS‐BP and GAPLS‐RNN methods. The results show that the proposed method is capable of effective RUL prediction. [ABSTRACT FROM AUTHOR]

In this study, a three‐step remaining service life (RSL) prediction method, which involves feature extraction, feature selection, and fusion and prognostics, is proposed for large‐scale rotating machinery in the presence of scarce failure data. In the feature extraction step, eight time‐domain degradation features are extracted from the faulty variables. A fitness function as a weighted linear combination of the monotonicity, robustness, correlation, and trendability metrics is defined and used to evaluate the suitability of the features for RSL prediction. The selected features are merged using a canonical variate residuals‐based method. In the prognostic step, gray model is used in combination with empirical Bayesian algorithm for RSL prediction in the presence of scarce failure data. The proposed approach is validated on failure data collected from an operational industrial centrifugal pump and a compressor. [ABSTRACT FROM AUTHOR]

In this paper, we propose new fusion and selection approaches to accurately predict the remaining useful life. The fusion scheme is built upon the combination of outcomes delivered by an ensemble of Gaussian process regression models. Each regressor is characterized by its own covariance function and initial hyperparameters. In this context, we adopt the induced ordered weighted averaging as a fusion tool to achieve such combination. Two additional fusion techniques based on the simple averaging and the ordered weighted averaging operators besides a selection approach are implemented. The differences between adjacent elements of the raw data are used for training instead of the original values. Experimental results conducted on lithium‐ion battery data report a significant improvement in the obtained results. This work may provide some insights regarding the development of efficient intelligent fusion alternatives for further prognostic advances. [ABSTRACT FROM AUTHOR]

Multivariable stochastic degradation system (MSDS) is quite common in industries such as blast furnace ironmaking, vehicle transportation, and aerospace manufacturing. Large‐scale complex equipments may be affected by multiple factors, resulting in not just a single deteriorating performance characteristic. It is difficult to handle unknown failure structures of practical systems by using traditional univariate degradation modeling methods. A novel health index (HI) is constructed to quantitatively analyze the health state for the overall system. Considering the interaction between internal reactions and external environments, the fractional Brownian motion (FBM), a typical non‐Markovian diffusion process, is added for the purpose of reflecting stochastic uncertainties and memory effects. Based on the wavelet estimators and the maximum likelihood estimation (MLE) algorithm, multi‐sensor observations of degradation variables are analyzed simultaneously to identify model parameters. A closed‐form distribution of system‐level remaining useful life (RUL) is obtained with a mild two‐layer approximation. Relevant case studies are then handled that adequately demonstrate the effectiveness and the practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

Remaining useful life (RUL) prediction plays an important role in predictive maintenance systems to support decision‐makers for arranging maintenance tasks and related resources. We propose a hybrid approach that is combined an exponential weighted moving average (EWMA) control chart for anomaly detection and machine learning models such as support vector regression (SVR) and random forest regression (RFR) with differential evolution (DE) algorithm to predict the RULs of ball bearings. Here, DE algorithm is used to find the optimal hyperparameters of SVR model. The datasets of ball bearings from the Prognostics Data Repository of NASA are used to compare the prediction performance of different methods. The degradation behavior of training data from the anomaly time to the end of life is used to transfer learning for the testing data in the SVR and RFR models. The results indicate that the proposed methods outperform the other four existing methods in terms of score. Therefore, the proposed hybrid approach is a reliable tool for the RUL prediction of ball bearings. [ABSTRACT FROM AUTHOR]

Prognostics, in other words, remaining useful life (RUL) estimation is a core task of prognostics and health management (PHM). Reliable RUL predictions can reduce maintenance costs, improve production efficiency, and avoid unexpected downtime. Lots of models for RUL predictions have been proposed; however, noise and the nonlinear nature of degradation phenomena often leads to poor prognostics results, and the acquired engineered system data are usually subject to a high level of uncertainty. This makes the RUL estimation models less than satisfactory. Accurate RUL estimation and prediction not only rely on an accurate model but also depend on the adjustments of model parameters to track the variation. In this paper, an ensemble model combining the health index synthesis (HIS) approach and improved particle filtering (PF) is introduced. HIS approach was used to obtain the synthesized health index (SHI) for an engineered system with multiple sensors, which indicated the system's degradation model, while the improved PF approach was used to adjust the parameters of the degradation model obtained from the HIS approach and optimized the RUL estimation results. The performance of the prognostics approach introduced in this paper was demonstrated by using turbofan engine degradation data sets, which was supplied by NASA Ames, and results were compared with several usually used methods. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive maintenance model for equipment that can be adjusted (minor preventive maintenance, imperfect state) or replaced (major preventive maintenance, as good as new) at specific scheduled times based on degradation measurements. An initial reliability law that uses a degradation-based model is built from the collection of hitting times of a failure threshold. Inspections are performed to update the reliability, the remaining useful life, and the optimum time for preventive maintenance. The case of both as good as new replacements and imperfect adjustments is considered. The proposed maintenance model is based on the optimization of the long-term expected cost per unit of time. The model is then tested on a numerical case study to assess its effectiveness. This results in an improvement for the occurrences of maintenance tasks that minimizes the mean cost per unit of time as well as an optimized number of adjustments that can be considered before replacing an item. The practical application is a decision aid support to answer the 2 following questions: Should we intervene now or wait for the next inspection? For each intervention, should we adjust or replace the item of equipment? The originality is the presence of 2 criteria that help the maintainer to decide to postpone or not the preventive replacement time depending on the measured degradation and to decide whether the item should be adjusted or replaced. [ABSTRACT FROM AUTHOR]

Rolling element bearings are among the most widely used and also vulnerable components in rotating machinery equipment. Recently, prognostics and health management of rolling element bearings is more and more attractive both in academics and industry. However, many studies have been focusing on the prognostic aspect of bearing prognostics and health management and few efforts have been performed in relation to the optimal degradation feature selection issue. For more effective and efficient remaining useful life predictions, three goodness metrics of correlation, monotonicity and robustness are defined and combined for automatically more relevant degradation feature selection in this paper. Effectiveness of the proposed method is verified by rolling element bearing degradation experiments. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of how to estimate remaining useful life (RUL) for a class of systems with high fluctuating dagradation caused by time-varying mean and variance. In engineering practice, the fluctuation of the degradation data can reflect the system stability, and hence it can serve as an additional indicator for the system's health state in addition to the degradation observations. To estimate the RUL for this class of systems, three issues should be considered jointly: (i) how to model the degradation data with high fluctuation, (ii) how to define an indicator denoting the fluctuation's level, and (iii) how to combine the degradation path and the fluctuation for the RUL estimating task. In responses to the above issues, this paper characterizes the degree of the fluctuation by the standard deviation of the stochastic degradation process and defines the standard deviation as an additional performance variable. Moreover, a stochastic degradation model is proposed to reflect the high fluctuating degradation data, in which the standard deviation is time dependent. To obtain the marginal distribution of the RUL derived by the standard deviation, the failure threshold of the standard deviation is given according to its influence on the degradation process. Another marginal distribution derived by the degradation data is also obtained by the time distribution of the degradation process crossing the degradation threshold. Then, through deriving the correlation between the two marginal distributions based on the probability theory, the joint distribution of the RUL is obtained. Finally, a practical case study for gyro is conducted. The results demonstrate the feasibility and applicability of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

With the increase of product reliability, collecting time-to-failure data is becoming difficult, and degradation-based method has gained popularity. In this paper, a novel multi-hidden semi-Markov model is proposed to identify degradation and estimate remaining useful life of a system. Multiple fused features are used to describe the degradation process so as to improve the effectiveness and accuracy. The similarities of the features are depicted by a new variable combined with forward and backward variables to reduce computational effort. The degradation state is identified using modified Viterbi algorithm, in which linear function is adopted to describe the contribution of each feature to the state recognition. Subsequently, the remaining useful life can be forecasted by backward recursive equations. A case study is presented, and the results demonstrate the validity and effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper aims at developing a model for the monitoring of a rotating machine. The contribution in this model is the development of the last stage of monitoring which is the prognostic; indeed, the method used takes into account the required quality criteria of the product on one hand and the state of the current system of one somewhere else on the other. The objective of this contribution is to estimate the reliability of the system in time and to plan the time of total system dysfunction. The interval constrained Petri nets are used for the modeling of an industrial example which is the centrifuge pump. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]