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To avoid unexpected failures of engineering systems, sensors have been widely used to monitor the degradation process of the systems. A number of studies have been conducted to analyze the collected sensor signals and predict the failure time. However, the existing studies are usually restricted and cannot be adapted to different practical situations. In this paper, we propose a systematic method for degradation modeling and prognosis that can be widely applied in different scenarios. In particular, the proposed method is capable to handle one or multiple sensors, powerful to capture the nonlinear relations between sensor signals and the degradation process with few assumptions, generic to consider multiple failure modes, flexible to deal with unequally spaced sensor measurements or asynchronous signals, and easily understandable with little preprocessing required. The main idea is to predict the failure time of an in-service unit based on a subset of the nearest historical units, where features are extracted from each sensor to describe the progression of sensor signals and local linear regression models are constructed to establish the relation between failure time and the extracted features. The prediction variance is then used as the goodness-of-fit measure, based on which decision-level fusion and feature-level fusion are proposed to combine multiple sensors. A case study with two datasets on the degradation modeling of aircraft engines is conducted which shows satisfactory performance of the proposed method.

This article focuses on individualized degradation modeling and prognostics for a heterogeneous group, where each individual unit shows a distinct degradation process. Existing degradation models usually treat each unit separately and do not fully utilize the distinct characteristics of each individual. In this study, we propose a generic framework to handle the heterogeneity across units by effectively leveraging the intrinsic covariate information, which is closely related to the unit's degradation process. Specifically, we employ a multivariate Gaussian process (MGP) to nonparametrically establish the relation between the covariate information and degradation process. Through modeling the unit similarities based on the covariates, efficient information transfer among units is enabled for better degradation modeling and prognostics, as the collected degradation signals from one unit can be shared with the entire heterogeneous group. A theoretical justification for the proposed model is also investigated. Simulation studies are presented to evaluate the parameter estimation accuracy and the sensitivity of the proposed method. A case study on the Alzheimer's disease (AD) neuroimaging initiative data set is further conducted, which demonstrates the advantage of the proposed method over existing benchmark approaches.

To monitor the degradation status of units and prevent unexpected failures in engineering systems, health index (HI)-based data fusion technologies have been rapidly developed by combining multiple sensor signals, which are helpful to understand the degradation processes of units and predict their remaining useful lifetime (RUL). Although promising, existing HI-based data fusion models for degradation modeling are still limited due to the restrictive assumptions made during the fusion or the degradation modeling processes, e.g., assuming the fusion model as a linear or kernel-based function from multiple sensor signals, or modeling the degradation process by a preselected basis function. Such assumptions are often invalid in industrial practice and may fail to accurately characterize the complicated relationships between multiple sensor signals and the underlying degradation process. To address the issue, this article proposes a generic indirect deep learning method that constructs an HI by combining multiple sensor signals to better characterize the degradation process. In particular, our innovative idea is to seamlessly integrate a deep neural network (DNN) and a long short term memory (LSTM) model to construct the HI by fusing multiple sensor signals and characterize the degradation process, which can be applied to the degradation modeling of various engineering systems. Domain knowledge including the concept of failure threshold and monotonicity of the degradation process is also considered to enhance the interpretability of the proposed method. For parameter estimation, we develop an indirect gradient descent (IGD) algorithm to train the proposed method. Simulation studies and a case study on the degradation of aircraft gas turbine engines are presented to validate the performance of the proposed method.

In this article, we focus on a joint scheduling problem that considers the corrective maintenance (CM) due to unexpected breakdowns and the scheduled preventive maintenance (PM) in a generic $M$ -machine flow shop. The objective is to find the optimal job sequence and PM schedule such that the total of the tardiness cost, PM cost, and CM cost is minimized. Currently, most existing studies on the PM schedules are based on a fixed PM interval, which is rigid and may lead to poor performance, as the fixed strategy fails to effectively balance the trade-offs between the production scheduling and maintenance. To address this critical research issue, our novel idea is to dynamically update the PM interval based on the real-time machine age, such that the maintenance activity coordinates with the job scheduling to the maximum extent, which results in an overall cost saving. Specifically, a correction factor is introduced to dynamically update the PM interval and to help evaluate whether it is worthwhile to process the job first at the risk of the CM before performing the PM action. To demonstrate the effectiveness of the adaptive strategy, simulations and a case study on mining operations are conducted to show that the adaptive strategy outperforms the existing methods with a less total cost. Note to Practitioners —This article is motivated by the critical problem of balancing the trade-offs between production scheduling and maintenance in a flow shop production line, where jobs are processed on the machines in the same route. On the one hand, production scheduling aims to meet the customer demands on time. On the other hand, the maintenance actions help restore the machines’ reliability by reducing the machine failure rate. Most existing approaches to scheduling the PM are based on the fixed PM interval, which is rigid and may lead to poor performance. Although the nonperiodic PM interval strategy has been proposed in the literature for production scheduling, it still does not consider the adaptive PM strategy in the context of flow shop scheduling with multiple machines. To fill this literature gap, in this article, we first model a generic $M$ -machine flow shop considering both the CM and PM. Then, we suggest a new adaptive and easy-to-implement approach to dynamically update the PM interval and improve the decision-making on the PM schedules. Compared with the conventional maintenance policy, the adaptive one greatly reduces the total cost in real-time scheduling.

Accurate modeling of a thermal field is one of the fundamental requirements in engineering thermal management in numerous industries. Existing studies have shown that using differential equations to model a thermal field delivers good performance when the parameters are predetermined through physical or experimental analysis. However, due to variations of the inner medium affected by certain latent factors, the parameters in differential equation models may not be treated as constants while the thermal field is estimated, and this fact poses a new challenge to field estimation by directly solving the differential equation models. In this study, a novel approach to thermal field modeling is developed by considering the parameters as functional variables that vary temporally in partial differential equations (PDEs). This approach provides a new perspective to model the dynamic thermal field by fully using the collected sensor data from the thermal system. Specifically, time-varying parameters can be constructed through a combination of basis functions whose coefficients can be efficiently estimated through the sensor data. A two-level iterative parameter estimation algorithm is also tailored to obtain the parameters in the PDE model. Both simulation and real case studies show that our proposed approach provides satisfactory estimation performance compared with the benchmark method that uses the constant parameter estimation. Note to Practitioners —The proposed method aims to model a thermal field using PDEs with time-varying parameters. To better implement this method in practice, three things are noteworthy: first, the proposed method models a thermal field by fully considering physics-specific engineering knowledge using PDEs and the collected sensor data from thermal systems. Second, because time-varying parameters in PDEs cannot be estimated directly, the proposed model represents the time-varying parameters by a combination of B-spline basis functions in terms of time. Estimating time-varying parameters is converted into estimating the constant coefficients of the basis functions. Because the derivatives of a thermal field might not have an analytical expression, the proposed model represents the thermal field by a combination of B-spline basis functions. Taking the derivatives of the thermal field is converted into taking the derivatives of the corresponding basis functions. Third, the proposed method can not only model a thermal field but can also be applied in other physics-specific engineering cases.

3-D dynamic field modeling using data acquired from sensor networks is typically complex due to the data sparsity and missing problem. In this article, we consider the ubiquitous missing data problem in current sensor networks and aim to take complete advantage of the existing sensor data for thermal field modeling. In the common scenario, data from the target network are not always obtainable, but data from other neighboring networks with homogeneous fields are accessible. Thus, a novel method that captures the information acquired from these neighboring networks is proposed. To achieve accurate thermal field estimation using limited sensor observations, we develop a mixed-effect model framework in which the dynamic field is decomposed into a mean profile and local variability. In particular, we establish a spatiotemporal field multitask learning (FML) approach to identify the spatiotemporal correlation by integrating a multitask Gaussian process (MGP) framework into an autoregressive (AR) model using neighboring data sources from homogeneous fields. Our proposed method is verified through a real case study of thermal field estimation during grain storage. Note to Practitioners —The proposed method aims to obtain an accurate estimation of a thermal field when certain sensor data are inaccessible. To better implement this method in practice, three things are noteworthy: First, the mean profile of the thermal field should be extracted using the thermodynamic model, so that the remaining data are able to follow a Gaussian process. Second, the FML approach considers neighboring data sources from homogeneous thermal fields to achieve an accurate estimation of the target thermal field. Thus, the target thermal field and other thermal fields should be under similar external conditions, e.g., environmental surroundings, geographical location, and field size. Third, the proposed method can not only process the data from grid-based sensor networks, but also can be extended to other topological structures of sensor networks for field estimation.

The state-space models (SSMs) are widely used in a variety of areas where a set of observable variables are used to track some latent variables. While most existing works focus on the statistical modeling of the relationship between the latent variables and observable variables or statistical inferences of the latent variables based on the observable variables, it comes to our awareness that an important problem has been largely neglected. In many applications, although the latent variables cannot be routinely acquired, they can be occasionally acquired to enhance the monitoring of the state-space system. Therefore, in this paper, novel dynamic inspection (DI) methods under a general framework of SSMs are developed to identify and inspect the latent variables that are most uncertain. Extensive numeric studies are conducted to demonstrate the effectiveness of the proposed methods. Note to Practitioners —The SSM aims to estimate crucial latent variables that characterize the states of a system but cannot be measured routinely or directly. The conventional way has been solely based on a measurement capacity dedicated to observed variables. However, we realize there are situations that, although latent variables cannot be measured routinely, it is possible to inspect a small portion of latent variables at a given frequency. Thus, the problem is how to allocate the inspection resources to help monitor the latent variables of the state-space system optimally, conditioning on the established statistical machinery of the SSM for model estimation and inference. We propose a DI method to select and partially measure the latent variables and improve the estimation accuracy by combining the measured latent variables and observations.

With recent development in sensor technology, multiple sensors have been widely adopted to monitor the degradation of a single unit simultaneously. The challenge of multisensor degradation modeling lies in that the sensor signals are often correlated and may contain only partial or even no information on the degradation status of a unit. To address these issues, this paper proposes a novel data fusion method that constructs a 1-D health index (HI) via automatically selecting and combining multiple sensor signals to better characterize the degradation process. In particular, this paper develops a new latent linear model that constructs the HI and selects informative sensors in a unified manner. Compared to the existing literature, the proposed method enjoys several unique advantages: 1) being able to derive the best linear unbiased estimator of the fusion coefficients; 2) offering high computational efficiency; 3) not requiring to know the exact value of the failure threshold; and 4) exhibiting general applicability in practice by not imposing restrictive assumptions on the degradation process. Simulation studies are presented to illustrate the effectiveness and evaluate the sensitivity of the proposed method. A case study on the degradation of aircraft gas turbine engines is also performed which shows a better prognostic performance of the proposed method compared with existing approaches. Note to Practitioners —This paper is motivated by the practical issue of degradation modeling and prognostics when multiple sensors simultaneously monitor the degradation status of a unit. Specifically, there are two fundamental questions involved, including: 1) how to screen out noninformative sensors and 2) how to properly combine the information from the selected sensor signals to accurately estimate the underlying degradation status of the unit. The novelty of this paper lies in developing an innovative latent model that tackles these two challenging questions in an integrated manner. There are four main steps involved when implementing the proposed method: 1) collecting multiple sensor signals and failure time of historical units; 2) selecting the informative sensors and deriving the optimal weight for each selected sensor; 3) constructing the health indices (HIs) of in-service units; and 4) predicting the remaining useful life of the in-service units using the constructed HIs. The proposed method is very useful when the degradation is under a single failure mode in a single environmental condition. In the future research, we will study the extension of the proposed model when sensor signals have a nonlinear relationship, as well as when the degradation process is under more complex scenarios such as multiple failure modes and multiple operation conditions.

The rapid development of information technologies provided unprecedented big data environments for condition monitoring and degradation analyses. However, the available big data sets are often sparse with a limited number of observations per recorded unit. For example, in many healthcare systems, data are collected from a large number of patients, but the available observations from each patient are quite limited. Unfortunately, most of the existing approaches for data-driven degradation modeling may not work well in this scenario as they either pool the information from the population or require rich historical observations in each unit. To address the challenges in “sparse data environments,” this paper proposes a structural degradation modeling framework (SDM). The SDM is inspired by the recommender system, which provides recommendations about specific items for the user. In addition, it is also tailored to the needs of degradation modeling. In particular, the framework takes into consideration: 1) the available data from the unit of interest; 2) the population characteristics; 3) the relationship between the available units; and 4) the precision of the available units. Simulation studies and a case study that involves the Alzheimer’s disease (AD) neuroimaging initiative data set are conducted, which shows satisfactory performance of the proposed method. Note to Practitioners —This paper proposes a framework for modeling and predicting the degradation level and/or condition of units with time. Our framework is particularly useful where many units have missing and/or limited degradation observations. Essentially, our proposed method integrates two important ideas: 1) leveraging the available data from the unit of interest to improve the modeling fitting of the individual unit over the observed time domain and 2) considering the relationship between the available units to extract proper and accurate population characteristics to address the challenge of limited observations. The proposed approach is validated via simulation studies as well as a healthcare case study based on AD. In the future research, we will further explore the extension of the proposed method such as considering more generic degradation models and optimal parameter tunings.

Due to the rapid development of sensing and computing technologies, multiple sensors have been widely used in a system to simultaneously monitor the health status of an operating unit. Such a data-rich environment creates an unprecedented opportunity to better understand the degradation behavior of the system and make accurate inferences about the remaining lifetime. Since data collected from multiple sensors are often correlated and each sensor data contains only partial information about the degraded unit, data fusion methodologies that integrate the data from multiple sensors provide an essential tool for degradation modeling and prognostics. To achieve this goal, a fundamental question needs to be answered first is how to measure the signal quality of a degradation signal. If such a question can be addressed, then the data fusion approach can be simplified as a mission-specific task: to construct a composite health index with the goal of optimizing its signal quality. In this paper, a new signal-to-noise ratio (SNR) metric that is tailored to the needs of degradation signals is proposed. Then, based on the new quality metric, we develop a data-level fusion model to construct a health index via fusion of multiple degradation-based sensor data. Our goal is that the developed health index provides a much better characterization of the health condition of the unit and thus leads to a better prediction of the remaining lifetime. A case study that involves the degradation dataset of aircraft gas turbine engines is conducted to numerically evaluate the performance of the developed health index regarding prognostics and further compare the result with existing literature.

Complex systems often consist of multiple units that are required to work together in parallel to satisfy a specific engineering objective. As an example, in manufacturing processes, several identical machines may need to operate together to simultaneously fabricate the same products in order to meet the high production demand. This parallel configuration is often designed with some level of redundancy to compensate for unexpected events. In this way, when only a small portion of units fail to operate due to either unexpected machine downtime or scheduled maintenance, the remaining units can still achieve the engineering objective by increasing their workloads up to the designed capacities. However, the workload of a unit apparently impacts the unit's degradation rate as well as its failure time. Specifically, this paper considers the case that a higher workload assignment accelerates the unit's degradation and vice versa. Based on this assumption, we develop a method to actively control the degradation as well as the predicted failure time of each unit by dynamically adjusting its workloads. Our goal is to prevent the overlap of unit failures within a certain time period through taking advantage of the natural redundancy of the parallel structure, which may potentially lead to a better utilization of maintenance resources as well as a consistently ensured system throughput. A numerical study is used to evaluate the performance of the proposed method under different scenarios.

In progressive stamping processes, condition monitoring based on tonnage signals is of great practical significance. One typical fault in progressive stamping processes is a missing part in one of the die stations due to malfunction of part transfer in the press. One challenging question is how to detect the fault due to the missing part in certain die stations as such a fault often results in die or press damage, but only provides a small change in the tonnage signals. To address this issue, this article proposes a novel automatic process monitoring method using the recurrence plot (RP) method. Along with the developed method, we also provide a detailed interpretation of the representative patterns in the recurrence plot. Then, the corresponding relationship between the RPs and the tonnage signals under different process conditions is fully investigated. To differentiate the tonnage signals under normal and faulty conditions, we adopt the recurrence quantification analysis (RQA) to characterize the critical patterns in the RPs. A parameter learning algorithm is developed to set up the appropriate parameter of the RP method for progressive stamping processes. A real case study is provided to validate our approach, and the results are compared with the existing literature to demonstrate the outperformance of this proposed monitoring method.

The rapid development of sensing and computing technologies has enabled multiple sensors embedded in a system to simultaneously monitor the degradation status of an operation unit. This creates a data-rich environment for degradation modeling and prognostics that could potentially lead to an accurate inference about the remaining lifetime of the degraded unit. However, as data collected from multiple sensors are often correlated and each sensor data contains only partial information about the same degradation process, there is a pressing need to develop data fusion methodologies that can integrate the data from multiple sensors for better characterizing the stochastic nature of the degradation process. Unlike other existing data fusion methodologies that treat the fusion procedure and the degradation modeling as two separate tasks, this paper aims at solving these two challenging problems in a unified manner. Specifically, we develop a methodology to construct a health index via fusion of multiple degradation-based sensor data. Our goal is that the developed health index provides a much better characterization of the condition of the unit and thus leads to a better prediction of the remaining lifetime. A case study that involves a degradation dataset of an aircraft gas turbine engine is implemented to numerically evaluate and compare the prognostic performance of the developed health index with existing literature.

Multivariate process control in Distributed Sensor Networks (DSNs) is an important and challenging topic. Although a fully deployed sensor network will minimize information loss, the associated sensing cost can be overwhelming. Many efforts have been made to investigate the optimal sensor allocation strategy for different process control applications; however, most of them assume that the sensor layout is fixed once sensors are deployed in the system. This paper proposes a novel approach to adaptively reallocate sensor resources based on online observations, which can enhance both monitoring and diagnosis capabilities. The proposed adaptive sensor allocation strategy addresses two fundamental issues: when to reallocate sensors and how to update sensor layout. A max-min criterion is developed to manage sensor reallocation and process change detection in an integrated manner. To investigate the adaptive strategy, a Bayesian Network (BN) model is assumed available to represent the causal relationships among a set of variables. Case studies are performed on a hot forming process and a cap alignment process to illustrate the procedure and evaluate the performance of the proposed method under different fault scenarios.

Prognostics involves the effective utilization of condition or performance-based sensor signals to accurately estimate the remaining lifetime of partially degraded systems and components. The rapid development of sensor technology, has led to the use of multiple sensors to monitor the condition of an engineering system. It is therefore important to develop methodologies capable of integrating data from multiple sensors with the goal of improving the accuracy of predicting remaining lifetime. Although numerous efforts have focused on developing feature-level and decision-level fusion methodologies for prognostics, little research has targeted the development of “data-level” fusion models. In this paper, we present a methodology for constructing a composite health index for characterizing the performance of a system through the fusion of multiple degradation-based sensor data. This methodology includes data selection, data processing, and data fusion steps that lead to an improved degradation-based prognostic model. Our goal is that the composite health index provides a much better characterization of the condition of a system compared to relying solely on data from an individual sensor. Our methodology was evaluated through a case study involving a degradation dataset of an aircraft gas turbine engine that was generated by the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS).