Accurate modeling of temporal point processes is critical for reliable event forecasting and informed decision-making. While historical event sequences provide a foundation for intensity estimation, existing approaches often neglect external covariates whose lagged effects impact future intensities across multiple temporal granularities. To address this gap, we propose Multi-Granularity Integration of External Covariates for Temporal Point Processes (METP), a framework for incorporating lagged external influences into intensity modeling. METP extracts periodic structures and decomposes external covariate series into multiple temporal granularities. At each granularity, a lag-aware calibration module is introduced to align covariates with event dynamics. Finally, a hierarchical mixture-of-experts strategy is employed to integrate the multi-granular external covariates with historical event embeddings, enabling a representation of the conditional intensity function with enhanced information. Extensive experiments on public and proprietary datasets demonstrate that METP consistently outperforms existing methods in predictive accuracy.

This paper presents a structured and comprehensive review of joint maintenance scheduling operation in production systems, with a focus on identifying future directions that align with Industry 4.0 and emerging Industry 5.0 paradigms. A total of 130 peer-reviewed articles were systematically selected to examine current modeling practices, solution algorithms, and research trends. The review classifies problem settings based on production system structures, maintenance policies, and joint influencing factors, and summarizes core problem formulation and advanced algorithms deployment. This review also discusses how to represent the technique transition from Industry 4.0 to 5.0, particularly concerning adaptive, human-aware, and sustainable scheduling systems. It aims to guide both researchers and practitioners in aligning academic developments with the evolving requirements of intelligent manufacturing.

Event prediction plays a pivotal role in analyzing consumer behavior for inventory and pricing optimization. In dynamic financial markets, customer behavior is often influenced by price commitment policies, where the historical and pre-announced future transaction price dynamics can lead to complex behavior patterns, such as advance consumption or delayed purchasing. Therefore, these phenomena pose significant challenges to traditional event modeling approaches that rely solely on consumer behaviors. To address this problem, we propose SCAlign, a cross-domain and multi-scale framework for market dynamics alignment, designed for event prediction. Our model integrates both heterogeneous historical and limited observable future commitment prices at different scales, aligning customer behavior with market fluctuations across multiple time scales. Finally, through a Mixture-of-Experts (MoE) framework, the model dynamically fuses these aligned features, enabling adaptive selection of the relevant and appropriate representations for prediction tasks. Empirical evaluations across diverse transaction environments demonstrate that our model outperforms state-of-the-art prediction baselines. Furthermore, it achieves optimal performance across varying data scales, showcasing its robustness and generalizability.

Automatic sleep staging is critical for understanding sleep patterns and diagnosing sleep-related disorders, yet traditional manual scoring methods remain time-consuming, laborintensive, and subjective. Existing research often fails to fully exploit both cross-spatial and local-global temporal information in polysomnography (PSG) data. To address these challenges, we propose GateSleepNet, a novel dual-level spatiotemporal framework designed to handle the unique properties of PSG data, which comprises multi-channel physiological signals such as EEG, EOG, and EMG that capture temporal and cross-spatial interactions. GateSleepNet combines a Global Spatial Encoder and a Temporal Vision Transformer (ViT) Encoder to effectively capture both local and global temporal features. To enhance cross-spatial understanding, the framework incorporates a Global Spatial Encoder that models inter-channel cross-spatial relationships using sparsely connected graphs. A key innovation of GateSleepNet is the dual-level surrogate loss, which combines global epoch-level accuracy with local temporal consistency, ensuring alignment between predictions and actual sleep patterns. Experimental results on PSG datasets demonstrate the effectiveness of GateSleepNet, achieving high performance in classifying sleep stages and outperforming existing methods. The proposed framework provides a powerful solution for clinical and research applications in sleep medicine, with potential for broader adoption in automated health diagnostics.

Analysis of complex data structures in the form of matrix or tensor format data has gained immense popularity in diverse fields. However, forecasting time series based on high-order historical tensor data presents significant challenges due to the huge number of parameters derived by the high-dimensional nature of these data. Traditional time series models, designed for scalar or vector data, are insufficient for handling such data, necessitating the development of novel techniques to tackle these challenges. To address this issue, we propose a Tensor-variate method with Compressed Parameters in Auto-Regressive Moving Average (TCP-ARMA) model for time series forecasting, which integrates a smoothed mean and a tensor-variate autoregressive moving average (ARMA) model with a parameter reduction technique. The proposed method captures the global trend within each dimension of tensors as well as the time-dimension by a tensor-based smoothed mean. The high-order parameters, commonly with tremendous elements, are compressed into a series of factor matrices, significantly reducing computational difficulty and complexity. To solve the optimization problem efficiently and avoid the computational challenge of inverting large matrices, we have designed an algorithm named BCD-PALM that combines block coordinate descent (BCD) with proximal alternating linearized minimization (PALM). We have employed a real-world case study to validate our proposed approach, and the results demonstrate its effectiveness in addressing the challenges associated with high-dimensional tensor data.Note to Practitioners—In response to the challenges associated with capturing the evolution within high-order tensor time series data, we develop a tensor-variate time series forecasting method that incorporates a smoothed mean and a tensor-variate autoregressive moving average (ARMA) model with parameter reduction. To effectively implement this method, there are three key considerations to bear in mind. Firstly, it is crucial to ensure that sufficient historical data is available for the model training process to be completed successfully. Secondly, while we have chosen the B-spline as the smoothing method for capturing the smoothed mean, it is only one among various smoothing methods available. Depending on the specific context or scenario, alternative smoothing techniques may be more suitable. Lastly, it is essential to carefully determine the CP rank in the decomposition process, taking into account the actual compression requirements of the data being analyzed. By considering these factors, our proposed method can be tailored and optimized to address the unique challenges posed by high-order tensor time series data.

Production scheduling and machine maintenance are two inseparable operational issues in multistage production systems. Previous studies attempted to deal with this issue by simplifying this problem due to the degradation uncertainties of the machines, ignoring the substantial interactions between these two tasks and leading to less efficiency of the entire production system. In this study, we fill the gap and formulate the joint optimization problem with more emphasis on the interaction between job scheduling and maintenance for a series-parallel multistage production system. Specifically, a mixed-effect degradation model is proposed to leverage the underlying interaction between job scheduling and machine maintenance. To efficiently solve this joint problem, several properties from this formulation have been derived. A two-phase method considering condition-based information, with a proactive algorithm for local intensification and a condition-based workload reallocation strategy & maintenance strategy, is then developed to address the uncertainties from the machine degradation status. A numerical study is finally borrowed to demonstrate the higher production efficiency achieved by applying the proposed method, compared with other benchmarks.Note to Practitioners—This study is motivated by a practical scenario where both job allocation and maintenance need to be determined simultaneously in the multistage production system by the operators to achieve time and cost efficiency. We focus on developing a new scheme that job scheduling and machine maintenance are able to be conducted simultaneously. Two issues are noteworthy to better implement this scheme. First, for characterizing the interaction between scheduling and maintenance, the data collected in real-time can provide a sufficient basis for the degradation path, and the production parameters can be acquired from real practice. Second, this scheme can be offered to help decision-making by a two-phase solution framework given the condition-based information during the production process. Specifically, an appropriate job allocation planning can be obtained offline in the first phase of the proposed two-phase solution framework under a limited computing resource. Meanwhile, a condition-based adjustment strategy in the second phase can update the solution based on the in-situ condition information collected from the data platform to achieve higher production efficiency.

Cyber-Physical Systems (CPS) has emerged as a paradigm that connects cyber and physical worlds, which provides unprecedented opportunities to realize intelligent applications such as smart home, smart cities, and smart manufacturing. However, CPS faces a great number of information security challenges (e.g., attacks) due to the integration of CPS as well as the human behaviors and interactions. Therefore, accurate and real-time attack detection and identification are essential to ensure information security and reliability of CPS. In this paper, we propose a novel integrated learning method that accurately detects an attack of a CPS system and then identifies the attack type in real time. Specifically, we consider a One-Class Support Vector Machine (OCSVM) model that only relies on the data from the normal state for training to achieve a real-time and effective detection of a CPS system state (i.e., normal or under-attack). If the system is detected to be under-attack, we then develop a Pairwise Self-supervised Long Short-Term Memory (PSLSTM) approach to identify the attack type, which aims to accurately distinguish the known attack types and discover unknown new attacks. Lastly, experimental results show the proposed method achieves promising performances compared with conventional and state-of-the-art learning-based benchmarks.

The individual physiological difference has been recognized as one of the major problems while assessing subjects using multiple physiological data modeling and fusion techniques. To address this issue, we propose a one-step tensor-based modeling procedure to fuse the subject-variant information and multi-channel physiological data. Specifically, we consider the information similarity of the information matrixes from the tensor decomposition while introducing the subject-variant information, and form a tensor-based optimization problem to achieve the goal of physiological status assessment. To well solve this problem, a tailored alternating direction method of multipliers (ADMM) embedded block coordinate descent (BCD) algorithm has been proposed. Four real-case datasets from different scenarios have been employed to validate our proposed approach, and the performance indicates the superiority compared to several existing methods.Note to Practitioners—The proposed method aims to assess the physiological status by fusing multi-channel physiological data and subject-variant information. To better implement this method, three things are noteworthy. First, the dataset used in the proposed method should contain aligned multi-channel physiological data and subject-variant data, that is, the multi-channel physiological data and the subject-variant data should be correspondingly related. Second, the size of physiological data segments should be moderate due to the limited number of physiological data channels. Third, the initial value of the rank of CANDECOMP/PARAFAC (CP) tensor decomposition,${k}$, should be carefully chosen with the contextual knowledge. The value of${k}$is suggested not higher than the number of channels.

In complex real-world industrial systems, few-shot fault diagnosis greatly challenges model-free methods. Interest in domain adaptation methods, which enriches the diversity of accessible samples by narrowing the distance between the source and target domain distributions, has grown. However, these approaches generally rely on specific domain pairs and numerous labeled source data, which are difficult conditions to satisfy in industrial scenarios with complex/changeable working conditions and limited fault samples. Herein, we creatively propose a distribution-agnostic few-shot framework by imitating brain awareness process in unseen tasks. Our framework can generate a learnable and interpretable paradigm to learn common similarities in task embedding space, alleviating the dependence on deep supervised training and reducing the time required for conducting credible exploration from scratch. In particular, we design an adaptation-aware nonconvex matrix optimization procedure for optimal deep adaptation features transport process updating. Experimental results validate the superiority of our framework in two industrial applications, magnetic flux leakage, and bearing datasets, showing it is feasible and promising.

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.Note to Practitioners—The article aims to develop a generic health index (HI)-based data fusion method for degradation modeling when multiple sensors are available to monitor the degradation status of a unit. Specifically, the developed method addresses two challenging questions in practice: 1) how to effectively combine multiple sensor signals to construct an HI that accurately characterizes the underlying degradation status and 2) how to flexibly model the degradation evolution based on the constructed HI. To implement this method in practice, four steps are included as follows:First, collecting multiple sensor signals and failure time of historical units.Second, constructing the HI and describing the underlying degradation process by training a deep neural network (DNN) model and a long short term memory (LSTM) model, respectively.Third, estimating model parameters using the proposed IGD algorithm.Fourth, constructing the HI of in-service units and predicting their remaining useful lifetime (RUL) using the constructed HI. The proposed method is expected to be able to characterize various degradation processes and be applied to the degradation modeling of different engineering systems.

Crowdsourcing has been a prompt and cost-effective way of obtaining labels in many machine learning applications. In the literature, a number of algorithms have been developed to infer the ground truth based on the collected labels. However, most existing studies assume workers to be independent and are vulnerable to worker collusion. This paper aims at detecting the collusive behaviors of workers in labeling tasks. Specifically, we consider collusion in a pairwise manner and propose a penalized pairwise profile likelihood method based on the adaptive LASSO penalty for collusion detection. Many models that describe the behavior of independent workers can be incorporated into our proposed framework as the baseline model. We further investigate the theoretical properties of the proposed method that guarantee the asymptotic performance. An algorithm based on expectation-maximization algorithm and coordinate descent is proposed to numerically maximize the penalized pairwise profile likelihood function for parameter estimation. To the best of our knowledge, this is the first statistical model that simultaneously detects collusion, learns workers’ capabilities, and infers the ground true labels. Numerical studies using synthetic and real data sets are also conducted to verify the performance of the method.

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.

Influenza rapidly spreads in seasonal epidemics and imposes a considerable economic burden on hospitals and other healthcare costs. Thus, predicting the propagation of influenza accurately is crucial in preventing influenza outbreaks and protecting public health. Most current studies focus on the spread simulation of influenza. However, few studies have investigated the dependencies between meteorological variables and influenza activity. This study develops a non-parametric model based on Gaussian process regression for influenza prediction considering meteorological effect to capture temporal dependencies hidden in influenza time series. To identify the most explanatory external variables, L1-regularization is applied to identify meteorology factor subsets, and three types of covariance functions are designed to characterize non-stationary and periodic behavior in influenza activity. The dependencies of diseases and meteorology are modeled through the designed cross-covariance function. A real case in Shenzhen, China was studied to validate our proposed model along with comparisons to recently developed multivariate statistical models for influenza prediction. Results show that our proposed influenza prediction approach achieves superior performance in terms of one-week-ahead prediction of influenza-like illness.

Change point detection in torque signals has widely been adopted for quality inspection during pipe tightening processes. Previous studies on the change point detection in this process generally focus on directly detecting the change points throughout torques without considering the underlying mechanism that generates various quasi-periodic nonlinear profiles, thereby introducing a series of false change points and increasing the risk of releasing defective pipes. To overcome this problem, we propose a novel change-point detection approach by fully considering the profile generating mechanism, and introduce a similarity-weighted matrix with an integration of dynamic time warping and tightening physics. Thus, the probability of false detection of change points is reduced. A weighted regression model is developed to determine the authentic change points by introducing the tightening process constraints. The performance of the proposed approach is demonstrated by both numerical and real case studies, and results show that the proposed method achieves a more effective detection power than the other existing methods in the pipe tightening processes.

To prevent unexpected failures of complex engineering systems, multiple sensors have been widely used to simultaneously monitor the degradation process and make inference about the remaining useful life in real time. As each of the sensor signals often contains partial and dependent information, data-level fusion techniques have been developed that aim to construct a health index via the combination of multiple sensor signals. While the existing data-level fusion approaches have shown a promise for degradation modeling and prognostics, they are limited by only considering a linear fusion function. Such a linear assumption is usually insufficient to accurately characterize the complicated relations between multiple sensor signals and the underlying degradation process in practice, especially for complex engineering systems considered in this study. To address this issue, this study fills the literature gap by integrating kernel methods into the data-level fusion approaches to construct a health index for better characterizing the degradation process of the system. Through selecting a proper kernel function, the nonlinear relation between multiple sensor signals and the underlying degradation process can be captured. As a result, the constructed health index is expected to perform better in prognosis than existing data-level fusion methods that are based on the linear assumption. In fact, the existing data-level fusion models turn out to be only a special case of the proposed method. A case study based on the degradation signals of aircraft gas turbine engines is conducted and finally shows the developed health index by using the proposed method is insensitive for missing data and leads to an improved prognostic performance.

Traditional approaches based on short-term heart rate variability for cardiovascular disease diagnosis fail to capture the long-term dynamic information and individual effect from electrocardiography signals among subjects when examining the physiological condition. These shortages may lead to incorrect disease detection and weaken diagnosis performance. To address these problems, this paper proposes a new disease detection approach by considering the long-term dynamics and meanwhile the individual effect existing among subjects. Specifically, a multistate general Gamma cumulative sum (GGCUSUM) scheme is developed for signal state detection. Further, a backward elimination algorithm based on the exponential likelihood ratio test (ELRT) is proposed to reduce the risk of incorrect detection of change points. A general disease severity index is then designed based on our approach to satisfy the clinical requirement for disease diagnosis. A real clinical case from one of cardiovascular diseases, is given to validate the proposed approach, of which the result demonstrates the effectiveness with a satisfactory detection performance.

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.

Due to the rapid advances in sensing and computing technology, multiple sensors have been widely used to simultaneously monitor the health status of an operation unit. This creates a data-rich environment, enabling an unprecedented opportunity to make better understanding and inference about the current and future behavior of the unit in real time. Depending on specific task requirements, a unit is often required to run under multiple operational conditions, each of which may affect the degradation path of the unit differently. Thus, two fundamental challenges remain to be solved for effective degradation modeling and prognostic analysis: 1) how to leverage the dependent information among multiple sensor signals to better understand the health condition of the unit; and 2) how to model the effects of multiple conditions on the degradation characteristics of the unit. To address these two issues, this paper develops a data fusion methodology that integrates the information from multiple sensors to construct a health index when the monitored unit runs under multiple operational conditions. Our goal is that the developed health index provides a much better characterization of the health condition of the degraded unit, and, thus, leads to a better prediction of the remaining lifetime. Unlike other existing approaches, the developed data fusion model combines the fusion procedure and the degradation modeling under different operational conditions in a unified manner. The effectiveness of the proposed method is demonstrated in a case study, which involves a degradation dataset of aircraft gas turbine engines collected from 21 sensors under six different operational conditions.

Traditional approaches for obstructive sleep apnea (OSA) diagnosis are apt to using multiple channels of physiological signals to detect apnea events by dividing the signals into equal-length segments, which may lead to incorrect apnea event detection and weaken the performance of OSA diagnosis. This paper proposes an automatic-segmentation-based screening approach with the single channel of Electrocardiogram (ECG) signal for OSA subject diagnosis, and the main work of the proposed approach lies in three aspects: (i) an automatic signal segmentation algorithm is adopted for signal segmentation instead of the equal-length segmentation rule; (ii) a local median filter is improved for reduction of the unexpected RR intervals before signal segmentation; (iii) the designed OSA severity index and additional admission information of OSA suspects are plugged into support vector machine (SVM) for OSA subject diagnosis. A real clinical example from PhysioNet database is provided to validate the proposed approach and an average accuracy of 97.41% for subject diagnosis is obtained which demonstrates the effectiveness for OSA diagnosis.

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.