With the advancements in sensor technology, it is now possible to measure and record a multitude of features that reflect the health condition of complex systems. These measurements are stored in a sizable data matrix, enabling the detection of anomalies. Nevertheless, the presence of this large data matrix poses a significant computational burden. The dimension-reduction methods, such as non-negative matrix factorization (NMF), can efficiently reduce computational burden. However, their pure data-driven nature can lead to overfitting and biases in anomaly detection results. To address this shortcoming, we propose a physics-enhanced NMF (PNMF) method by incorporating physical knowledge into NMF with the help of graph technique. The graph technique organizes measurements and features into two graph objects, respectively, and the physical knowledge guides the formation of edges between nodes in the graph. This allows the PNMF to capture not only the data-driven patterns but also the physical structure inherent in the system. The closed-form update algorithm is developed for the PNMF model, which can guarantee the convergence of parameters estimation. The superior performance of the PNMF model in detecting anomalies is demonstrated by comparing prevailing methods in both public datasets and real-world applications.

Supervisory control and data acquisition (SCADA) data from a complex mechanical system, such as a high-speed train power bogie, nonpower bogie, and wind turbine, are widely used for anomaly detection and fault isolation. The SCADA data include measurements of process variables and exogenous covariates for key components in the system. The process variables refer to the performance characteristics of the key component while the exogenous covariates are working loads or working conditions of the complex mechanical system. Dominated by such physical mechanisms as dynamic motion laws of the system, there are complex relationships between the process variables and covariates, that complicate anomaly detection and fault isolation. To solve this problem, we propose a framework that integrates physical knowledge and statistical learning. We first build a spline model to capture the relationship between process variables and exogenous covariates. To make the model interpretable, we use physical knowledge to impose constraints on the model parameters. We then conduct anomaly detection at a system level based on the physical-statistical regression model. Once an anomaly is detected, we propose a Lasso-based method to isolate the faulty components. Our fault isolation method does not require historical failure data or knowing the true number of faulty components. Real-world case studies on power bogies from high-speed trains illustrate the advantages of our framework: the best benchmark achieves at least 2.50% lower F1-score in anomaly detection and 6.01% lower F1-score in fault isolation compared to our method.

A main challenge in reliability analysis of repairable systems is to model the heterogeneity in their failure behavior, which can be reflected by the corresponding recurrent failure-time data. To capture the system heterogeneity for data analysis, a system-specific random effect is typically introduced in most existing statistical models. In practice, the random effect of repairable systems tends to be time varying; for example, each repair action could change system's physical properties. Prior studies, however, generally do not take account of this time-varying nature and few of them circumvent the risk of model misspecification on the parametric distribution of frailty. In this article, we propose a semiparametric model that uses multivariate Gaussian convolution processes (MGCPs) to meet the above challenges. First, we use the trend RP to model the baseline intensity function of each repairable system. Based on the baseline intensity function, we then introduce MGCPs to simultaneously factor in heterogeneity and infer commonalities across multiple systems. A Bayesian framework is used for parameter estimation and time-to-failure prediction. Simulation studies show the advantages of our model in terms of robustness and estimation accuracy. A group of oil and gas well systems are used to illustrate the application of the proposed model.

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

This study considers a repairable production system operated under an age-based preventive replacement policy that is subject to independent random production waits and failures. In addition to the age-based replacement policy, we propose a maintenance model that uses production waits to schedule preventive replacement. That is, a decision maker can preventively replace the system either during a production wait or at the age threshold, whereas if a failure occurs during production, the decision maker must decide whether to perform a minimal repair or a corrective replacement to restore the system. Under the above setting, we develop a semi-Markov decision process (SMDP) to obtain the optimal maintenance policy that minimizes the long-run average maintenance cost rate. We establish the existence of the optimal maintenance policy and provide an algorithm to numerically obtain the optimal action for each state. We further generalize the model to incorporate imperfect maintenance and the nonhomogeneous arrival of production waits. In the latter case, it is computationally intractable to optimize the SMDP using a value iteration algorithm due to the curse of dimensionality. To address this challenge, we further develop an approximate dynamic programming framework to generate high-quality solutions. An attractive feature of our model is its generality, such that the model includes many existing maintenance models as special cases. A real-world example from a steel factory is used to demonstrate the proposed model.

Degradation is one of the major root causes of system failure. In some applications, the degradation levels are different upon failure, in which the fixed failure threshold assumption commonly adopted in the degradation literature may not hold. This article tackles the difficulty by jointly analyzing the system degradation and the lifetime data, which enables the corresponding remaining useful life (RUL) prediction. We treat the degradation level as a multiplicative time-varying covariate of the system hazard rate, where a random-effects Wiener process is adopted to model the degradation process. The model parameters are estimated under a Bayesian framework, and we also develop a particle filter method to update the estimates when new data are available. This makes the proposed model be able to realize online RUL prediction based on the in-situ system health state signals. Through case studies on lead-acid batteries and digital communication systems, the proposed model is shown to outperform existing methods in terms of the RUL prediction accuracy.

Most systems can fail in multiple ways, and the failure modes are usually positively correlated. This phenomenon complicates the reliability analysis and makes the corresponding maintenance planning challenging. This article proposes a condition-based maintenance policy for systems that are subject to both degradation-induced soft failure and sudden hard failure, where a higher degradation level leads to a higher hazard rate of the hard failure. The Wiener process is adopted for the degradation process, and the Weibull model is used to describe the baseline hazard rate of the hard failure. The degradation level is then treated as a time-varying covariate that affects the hazard rate of the hard failure, and the closed-form of the reliability function is derived by using the Brownian bridge theory. An inspection/replacement maintenance policy is employed, and the long-run cost rate is formulated based on the semiregenerative property of the system state. The optimal inspection interval and the preventive replacement threshold are then jointly determined by minimizing the long-run cost rate. A numerical study on a hydraulic sliding spool system is conducted to validate the derived reliability function and the maintenance policy.

The mission abort is an effective action to reduce the risk of casualties and enhance the survivability of mission-based systems such as aircrafts, submarines, and unmanned aerial vehicles (UAVs). A main task in real operations is to strive for balance between the mission reliability and the system survivability via elaborate mission abort plans. In this paper, we design the optimal mission abort policies based on the information of early-warning signals, which indicates the possible forthcoming fatal malfunction. Depending on the acquisition time of such information, the operator may immediately abort the mission, or ignore the information and continue the task. Within the framework of a constant mission duration, we carry out an economic analysis for the above problem. The optimal abort decision that minimizes the expected total economic loss is investigated. We further extend the proposed model to the scenario of a random mission duration and derive the corresponding optimal abort decisions. A case study on a UAV executing power-grid inspection missions is used to illustrate the applicability of the abort policies.

During the useful life period of a costly system, it has been a common practice to perform imperfect preventive maintenances (PMs) with the purpose of failure prevention and useful life extension. Nevertheless, a system cannot be restored to an as-good-as-new state even though the imperfect PM actions are performed with a high frequency. This is known as the saturation effect and it is commonly overlooked in the existing literature. Motivated by a PM problem in a manufacturing company, this study proposes two PM models to capture the dynamics of the saturation effect. The first model divides the system deterioration into recoverable damage and irreversible intrinsic fatigue. The PMs are assumed to be effective only in healing the first type of damage. When the intrinsic fatigue for some complex systems cannot be well defined, we propose another model that generalizes the existing virtual age models by allowing the proportion of virtual age reduction to depend on the PM frequency. The long-run average costs of the two models are derived, and optimization of the cost models is investigated. The proposed PM models are then applied to two types of mechanical systems in the manufacturing company. The case study shows that ignorance of the saturation effect will make inferior maintenance policy that incurs substantial losses. The proposed models are also shown to be robust in the sense that the parameter estimation errors cannot significantly increase the system operational cost rate.

Motivated by the need to support effective asset management of infrastructure systems, this paper presents a novel reliability model for a load-sharing system where the operator can adjust component work load to balance system degradation. The operator-intervention effect, combined with other system complexities, makes modeling reliability interesting and challenging. We first develop cost modeling for a load-sharing system that has experienced operational service at the time of analysis. The system replacement process is modeled as a delayed renewal process for which the expected operational cost of the system is derived. A numerical algorithm is proposed to compute the cost, and the error bound is shown to be of order O(n-1). Next, we extend modeling to consider multiple heterogeneous systems located at different sites within the infrastructure network. Heterogeneities here refer to possible cross-site differences in the operating environments and the operators' actions. When the heterogeneities are observable, we model as covariates; otherwise, we model as random effects. Statistical inference methods are developed for the proposed models. An example using real data from a water utility illustrates the logical model behavior given parameter choices as well as showing how analysis might inform asset management.

Condition-based maintenance (CBM) is proved to be effective in reducing the long-run operational cost for a system subject to degradation failure. Most existing research on CBM focuses on single-unit systems where the whole system is treated as a black box. However, a system usually consists of a number of components and each component has its failure behavior. When degradation of the components is observable, CBM can be applied to the component level to improve the maintenance efficiency. This paper aims to study the optimal inspection/replacement CBM strategy for a multi-unit system. Degradation of each component is assumed to follow a Wiener process and periodic inspection is considered. We cast the problem into a Markov decision framework and derive the optimal maintenance decisions that minimize the maintenance cost. To better illustrate the optimal maintenance strategy, we start from a 1-out-of-2: G system and show that the optimal maintenance policy is a two-dimensional control limit policy. The argument used in the 1-out-of-2: G system can be readily extended to general cases in a similar way. The value iteration algorithm is used to find the optimal control limits, and the optimal inspection interval is subsequently determined through a one-dimensional search. A numerical study and a comprehensive sensitivity analysis are provided to illustrate the optimal maintenance strategy.