Remaining useful life (RUL) prediction is a reliable tool for the health management of components. The main concern of RUL prediction is how to accurately predict the RUL under uncertainties. In order to enhance the prediction accuracy under uncertain conditions, the relevance vector machine (RVM) is extended into the probability manifold to compensate for the weakness caused by evidence approximation of the RVM. First, tendency features are selected based on the batch samples. Then, a dynamic multistep regression model is built for well describing the influence of uncertainties. Furthermore, the degradation tendency is estimated to monitor degradation status continuously. As poorly estimated hyperparameters of RVM may result in low prediction accuracy, the established RVM model is extended to the probabilistic manifold for estimating the degradation tendency exactly. The RUL is then prognosticated by the first hitting time (FHT) method based on the estimated degradation tendency. The proposed schemes are illustrated by a case study, which investigated the capacitors' performance degradation in traction systems of high-speed trains.

Relevance vector regression (RVR) is a useful tool for degradation modeling and remaining useful life (RUL) prediction. However, most RVR models are for 1-D degradation processes and can only handle univariate observations. This article proposes a degradation path-based RUL prediction framework using a dynamic multivariate relevance vector regression model. Specifically, a multistep regression model is established for describing the degradation dynamics and extending the classical RVR into a multivariate one with consideration of the multivariate environment. The article introduces a matrix Gaussian distribution-based RVR approach and then estimates the hyperparameters with Nesterov’s accelerated gradient method to avoid the exhausting re-estimation phenomenon in seeking analytical solutions. It further forecasts the degradation path for monitoring the degradation status. Based on the forecasted path, the RUL is predicted by the first hitting time method. Finally, the proposed methods are illustrated by two case studies, one is presented in this article and the other in the supplement, which investigate the capacitors’ and bearings’ performance degradations.

Data-driven fault detection and isolation (FDI) depends on complete, comprehensive, and accurate fault information. Optimal test selection can substantially improve information achievement for FDI and reduce the detecting cost and the maintenance cost of the engineering systems. Considerable efforts have been worked to model the test selection problem (TSP), but few of them considered the impact of the measurement uncertainty and the fault occurrence. In this article, a conditional joint distribution (CJD)-based test selection method is proposed to construct an accurate TSP model. In addition, we propose a deep copula function which can describe the dependency among the tests. Afterward, an improved discrete binary particle swarm optimization (IBPSO) algorithm is proposed to deal with TSP. Then, application to an electrical circuit is used to illustrate the efficiency of the proposed method over two available methods: 1) joint distribution-based IBPSO and 2) Bernoulli distribution-based IBPSO.

With the development of monitoring technology, increasing attention has been paid to condition-based maintenance (CBM). Also, if condition information for maintenance can be obtained with fewer inspections, the cost of the entire maintenance process could be reduced. However, in application, the monitoring equipment cannot maintain always a reliable operating state, for example, due to various uncertain factors, such as sensor errors, component tolerances, and environment disturbances, the inspections from the sensors are often unreliable. Motivated by these simple observations, we propose a non-periodic condition-based maintenance policy under unreliable inspections. The time interval of the non-periodic inspections is obtained via an inspection scheduling function. The unknown parameters of the component degradation process are updated by gradient descent, while simultaneously the maintenance decision variables are adjusted. A catastrophe strategy-based particle swarm optimization is used to set the optimal decision variables by minimizing the long-run cost rate. Application to laser degradation data illustrates the effectiveness of the proposed method.

Effective and comprehensive fault information can reduce the maintenance cost of a system. Selection of proper test is important to obtain accurate information for fault detection and isolation (FDI), once a fault occurs. In real systems, the FDI task is made difficult by the correlations in the physical behaviors of the components and the possible co-existence of multiple faults. In this paper, a new type of test selection model based on deep joint distribution is proposed, which takes into account the dependency and ambiguity groups. The optimal test can, then, be selected by an improved discrete binary particle swarm optimization (IBPSO) algorithm. The strengths of the proposed optimal test selection strategy are: 1) it can greatly improve the accuracy of test selection; 2) it considers the influence of multiple faults; 3) the dependency problem of the test outcomes can be addressed; 4) it is computationally efficient and capable of selecting optimal test points meeting the requirements of realtime FDI. Application to a negative feedback circuit demonstrates the performance of the proposed method.