Industrial fault diagnosis increasingly benefits from Large Models (LMs), which can handle diverse data sources. Within this context, multimodal approaches, which integrate inputs like vibration, process, and video data, boost accuracy but often assume all modalities are available, which rarely holds in practice due to sensor failures, deployment limits, etc. While unimodal methods are more practical, they often lack sufficient information for complex scenarios. The key challenge is how to effectively fuse multimodal data and transfer that knowledge to enhance unimodal performance when some modalities are missing. This paper proposes an adaptive multimodal fault diagnosis framework that enables bidirectional enhancement between multimodal and unimodal representations. For model construction, a Cross-Fusion Channel Attention (CFCA) module is introduced to align features across modalities, and then a Shared Temporal Attention (STA) module captures sequential dependencies and facilitates representation sharing. A multi-head diagnosis structure is finally used to jointly supervise both multimodal and unimodal branches. For parameter estimation, we develop a similarity-aware and uncertainty-guided gradient modulation strategy to adaptively balance multimodal and unimodal learning, ensuring stable optimization and knowledge transfer. Experiments on the real-world industrial PRONTO dataset demonstrate that our method achieves superior performance and adaptability across various scenarios with varying modality availability.

With the rapid development of sensor and information technology, multi-sensor data related to system degradation processes are now readily available for condition monitoring and remaining useful life (RUL) prediction. However, this process is often complicated by the presence of censored sensor data. In this article, we propose a novel method called Bayesian LSTM-SURV, which integrates Survival Analysis (SA) with Neural Networks (NNs) to model the nonlinear relationship between degradation signals and RUL. This method addresses censored signals and the lack of RUL labels through a novel loss function. Additionally, we employ a Bayesian procedure to transfer information from the training data, enhancing the accuracy of predictions for the test data and maximizing the utilization of existing data. Instead of directly predicting RUL values, we assume that the lifetime follows a Weibull distribution. By modeling the lifetime distribution and survival function, we can calculate and predict RUL values while quantifying the uncertainty of these predictions. The advantageous features of the proposed method are demonstrated through simulation studies and its application to a high-fidelity gas turbine engine dataset.

Multiple sensors are widely used in the monitoring of the degradation process and prediction of the remaining useful lifetime (RUL) of units in complex engineering systems. However, ensuring the prognostic performance with only a few units available remains difficult. Under a few-shot scenario, the discordant observations that exist in sensor data introduce considerable uncertainty into the degradation model, which leads to an empirical loss far from the expected loss. On the other hand, the learned degradation model tends to be overfitted on the limited available units and results in a biased model parameter distribution, which limits the model generalization capability on unseen units. To address these issues, this paper proposes a restricted-learning network with observation credibility inference (OCI) for few-shot degradation modeling. We initially introduce the OCI to figure out discordant observations from sensor data. Then, OCI is incorporated into restrictive learning through the deletion of discordant observations from sensor data, which enforces a prior distribution constraint on degradation model parameters to prevent overfitting. Finally, a posterior augmented classifier is learned to estimate health status based on the posterior sensor paths, and the RUL can be predicted subsequently. A case study that uses the degradation dataset of aircraft engines demonstrates the superiority of the proposed method over benchmark methods under few-shot scenarios.Note to Practitioners—This paper aims to develop a few-shot degradation modeling method for conducting status monitoring and RUL prediction. Specifically, the developed method addresses two challenging issues in practice: 1) How to figure out discordant observations exist in sensor data; 2) How to prevent overfitting issues under few-shot scenarios. To implement this method, four steps are included as follows: First, collect multiple sensor data and failure time of historical units. Second, construct the degradation model network, and train the network with restricted parameter distribution after deleting discordant observations. Third, construct and learn the classifier for predicting the probability of failure. Fourth, estimate the degradation status of in-service units, and predict the RUL based on the classifier. The proposed method is expected to be able to characterize various degradation processes and be applied to the degradation modeling of engineering systems with limited data available.

Failure Mode (FM) diagnosis and Remaining Useful Life (RUL) prediction are two major tasks in prognostics health management. Numerous data fusion-based methods have been employed to construct the Health Index (HI) derived from multiple sensors that provide a holistic view of system degradation status to make prognosis, allowing for early detection of anomalies and predictive maintenance actions. However, few studies have focused on constructing the HI to capture diverse degradation characteristics in the context of multiple FMs. To address this issue, this paper proposes an adversarial branched model to achieve FM diagnosis and RUL prediction. We first establish an unsupervised branched Deep Neural Network (DNN) to construct the HIs of units under multiple FMs by fully considering degradation properties. Then, an adversarial training strategy is developed based on data of historical units to capture diverse degradation properties of different FMs. Finally, we diagnose the FM of an in-service unit via a similarity measurement method based on the constructed HIs. Given the diagnosed FM and corresponding HI, the RUL of the in-service unit is predicted. A simulation study and a case study on the degradation of aircraft gas turbine engines are presented to evaluate the performance of the proposed method. Note to Practitioners—The paper aims to develop an adversarial branched model to construct the HI under multiple FMs for failure diagnosis and RUL prediction of operating units. Specifically, the developed method addresses a challenging issue in practice, i.e., how to construct an HI from multiple sensor signals that can effectively extract distinguishable degradation features under multiple FMs. To implement this method in practice, four steps are included as follows: First, collect multiple run-to-failure sensor signals and FMs of historical units. Second, establish the branched DNN to construct the HI for multiple FMs. Third, train the branched DNN via the adversarial algorithm using data of historical units. Fourth, diagnose the FM and predict the RUL based on the HI for in-service units. As a deep learning model, the branched DNN is expected to be applicable to a large number of scenarios and practical cases, especially for manufacturing systems with complex structures and multiple FMs.

Failure mode (FM) recognition and remaining useful lifetime (RUL) prediction play pivotal roles in the field of prognostics and health management (PHM), particularly in regard to monitoring machinery degradation. Advances in sensor technology have opened avenues for FM recognition and RUL prediction by leveraging data from multiple sensors. However, previous research has exhibited certain limitations. Some studies have taken all multisensor data as direct inputs, overlooking the potential heterogeneity in the relevance of individual sensor data to machinery degradation. Others have relied on visual inspection and subjective assessments for sensor selection. These approaches struggle to adaptively select sensors, especially in scenarios involving multiple FMs and operating conditions (OCs), and when only partial FM labels are available. To address these challenges, this paper proposes a novel deep-learning network that adaptively selects sensors to jointly recognize FMs and predict RUL under time-varying OCs. The core of this network incorporates an attention-based long short-term memory (LSTM) module. Within this module, adaptive sensor selection weights are generated, leading to the accurate recognition of FMs and the precise prediction of the RUL. In the context of model training, we construct loss functions utilizing semilabeled samples and extract OC-invariant features through domain adaptation, enhancing the accuracy of FM recognition and RUL prediction. To assess the effectiveness and the generalizability of the proposed method, numerical experiments and two case studies involving aircraft engines and bearings are conducted. Note to Practitioners—This paper proposes a deep-learning network designed for adaptive sensor selection in the context of semisupervised FM recognition and RUL prediction, particularly in scenarios involving multiple OCs. To operationalize this method, five key steps are outlined: First, Data Collection: data are gathered from multiple sensors, time-varying OCs, multiple FMs, and failure time of historical units. It is important to note that FM data are available for only a subset of historical units. Second, Data Preprocessing: The sensor data are tailored using the sliding time window technique, generating a substantial number of samples from historical units. Third, Network Construction: Subsequently, the adaptive sensor selection network is constructed. Fourth, Model Training: Loss functions are constructed, and model parameters are estimated through end-to-end training. Finally, Model Application: The method is utilized to recognize FMs and predict RUL for in-service units. This deep learning network can be applied effectively to various degraded machines experiencing multiple FMs and OCs. It is particularly suitable for machines with complex physical mechanisms or unknown failure thresholds.

In industrial scenarios with insufficient sensor data, intelligent few-shot failure mode recognition and remaining useful lifetime (RUL) prediction are critically essential for effective prognostics and health management. Existing few-shot learning (FSL) methods focus on either the failure mode recognition as a classification problem or the RUL prediction as a regression problem, failing to capture the dependence between failure modes and RUL given that units under different failure modes present distinct degradation characteristics. To address the issue, this paper proposes a distribution-agnostic probabilistic FSL method for multimodal recognition and prediction of operating units. The proposed model establishes a neural network with prototypes to solve a few-shot classification-and regression-integrated problem. To fully capture the uncertainty caused by limited sensor data, we develop multimodal Bayesian model-agnostic meta-learning (MBMAML) for the probabilistic modeling of failure modes and the RUL under multiple failure modes. We construct the loss function based on probabilistic modeling that captures the interaction between failure modes and RUL for model training. Finally, the proposed model adaptively learns the approximate distributions of failure modes and RUL for a new operating unit. We evaluate the proposed model performance through a case study on the degradation of aircraft gas turbine engines.Note to Practitioners—Failure mode recognition and RUL prediction are essential in prognostics health management (PHM) to avoid unexpected failures of units in industrial systems, such as aircraft gas turbine engines. However, insufficient sensor data are quite common issue in industrial scenarios due to expensive sensor deployment, the difficulty of installing sensors to certain special mechanical equipment, and so on. This paper aims to develop a FSL method to jointly recognize the failure mode and predict the RUL of a unit based on insufficient sensor data. The four steps to implement the proposed method in practice are as follows:First, collect sensor signal data, RUL data, and failure mode data of units.Second, construct the model framework via the proposed MBMAML.Third, formulate the loss function based on the probability distributions of failure modes and RUL, and train the model using collected data.Fourth, adaptively recognize the failure mode and predict the RUL of a new operating unit. The proposed method is expected to be applicable to many practical few-shot industrial scenarios due to its data-driven neural network with flexible model structure.

Sleep apnea, a prevalent sleep-related breathing disorder, often remains undiagnosed and untreated in a large patient population due to the need of extensive manual annotations on various physiological signals for clinical diagnosis. Despite the surge of interest in applying machine learning to automate apnea detection, the effectiveness of existing techniques highly relies on strongly supervised learning that requires massive finely labeled training data for sufficiently short time intervals - a requirement often unmet due to the prohibitively high cost of manual labeling in clinical practice. In this article, we incorporate clinical knowledge to establish a weakly supervised deep learning framework for automatically estimating the latent fine-grained apnea severity when only coarse-grained labels indicating apnea presence are available in the training data. Specifically, a novel knowledge-enhanced dual-granularity consistency loss, which simultaneously considers the consistency between coarse- and fine-granularity and the integration of clinical knowledge on apnea diagnosis, is designed to boost the model's learning of apnea severity at the fine granularity. A mathematical encoding of clinical knowledge is proposed to calibrate fine-grained estimation accuracy through ordinal alignment functions, which quantitatively relates the severity of apnea to the prominence of key diagnosis-informed physiological symptoms. The proposed method is able to accurately estimate fine-grained apnea severity in real time with significantly reduced labeling costs, extending the reach of sleep apnea diagnostics to larger population both in lab and at home. An experiment is conducted to demonstrate the superior estimation performance of the proposed method for monitoring apnea severity at high temporal resolution.

Existing periodic Gaussian process (PGP) modeling methods rely on the regularly-spaced-signal assumption (i.e., signals are evenly spaced) and the integer-period assumption for the sake of computational feasibility. However, such an assumption prevents conventional efficient modeling approaches from working properly on irregularly (unevenly) spaced signals, such as evenly spaced signals with missing data. Moreover, without the integer-period assumption, it is computationally prohibitive to accurately search the decimal period of PGP due to the severe non-convexity of its likelihood function. To address these issues, this study proposes a PGP-controlled B-spline for scalable modeling of irregularly spaced signals with a decimal period. The proposed model integrates PGP with B-spline basis functions, allowing for nonlinear and nonparametric modeling of periodic signals. An explore-exploit optimization is developed to overcome the non-convexity of the likelihood, enabling effective and efficient decimal period estimation. The proposed PGP modeling approach has a linear time complexity. Asymptotic properties of the proposed method are studied, which shed light on the period estimation of other PGP models. Simulation and real case studies are conducted to demonstrate the superiority of the proposed method.

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.

Accurate prognostics are crucially important to prevent unexpected failures in industrial and service systems. This process aims to monitor the degradation status of units and predict their remaining useful lifetime (RUL) by analyzing the data collected from multiple sensors. Existing studies for prognostics either focus on health index (HI)-based statistical fusion methods that are limited by restrictive assumptions or machine learning methods that model the HI and degradation status in two separate steps. However, the restrictive assumptions are often invalid in practice, and the intrinsic connection between the HI and degradation status is missing if the two parts are modeled separately, leading to poor prognostic results. This paper proposes an integrated deep learning-based data fusion and degradation modeling method by integrating a deep neural network (DNN) and a long short-term memory (LSTM) to characterize the nonlinear relationship between the HI and multiple sensor signals and to describe the underlying degradation status of units. In particular, our innovative idea is to develop an integrated backpropagation parameter estimation algorithm to solve the fusion procedure and the degradation modeling in an integrated manner by considering the properties of HI construction in the loss functions. Thus, the constructed HI is expected to better characterize the underlying degradation process and lead to a superior prognostic result. In the case study on the degradation of aircraft gas turbine engines, the proposed method achieves promising performance compared with the existing benchmarks of statistical models and other deep learning models. Note to Practitioners—This paper develops an integrated deep learning-based data fusion and degradation modeling method for improving prognostics when multiple sensors are available to monitor the degradation status of a unit. There are four steps for implementing this method in practice: 1) collecting multiple sensor signals of historical units; 2) constructing the HI and modeling the degradation status of units by combining a DNN model and an LSTM model; 3) solving the fusion procedure and the degradation modeling in an integrated manner by developing an integrated backpropagation parameter estimation algorithm; and 4) making prognostics for in-service units. The novelty of the proposed method is that it conducts prognostics by combining a DNN fusion model and an LSTM degradation model, and seamlessly integrates the fusion procedure with the degradation modeling to construct the HI for better characterizing the status of a unit. As a result, the proposed method has two main advantages: (i) capable of characterizing various degradation processes of different engineering systems; and (ii) superior prognostic results by constructing more suitable HI for the degradation process.

To avoid unexpected failures of units in manufacturing systems, failure mode recognition and prognostics are critically important in prognostics health management (PHM). Most existing methods either ignored the effects of various failure modes on remaining useful lifetime (RUL) prediction or implemented failure mode recognition and RUL prediction as two independent tasks, which failed to exploit failure mode information to obtain accurate RUL prediction. In fact, RUL highly depends on failure modes because sensor signals under different failure modes usually present different degradation patterns. To address the issue, this paper proposes a joint learning model of failure mode recognition and RUL prediction for degradation processes based on multiple sensor signals. The proposed joint learning model first extracts features by considering the degradation mechanism to ensure good interpretability for degradation modeling, and then takes the extracted features as inputs to a deep neural network. By conducting failure mode recognition and RUL prediction as a collaborative task, the proposed model can fully characterize the complex relationship among the extracted features, RUL and failure modes, and outputs the recognized failure modes and the predicted RUL of units simultaneously. A case study on the degradation of aircraft gas turbine engines is presented to evaluate the proposed model performance.Note to Practitioners—The paper aims to develop a joint learning method for failure mode recognition and RUL prediction of operating units. Specifically, the developed method addresses a challenging issue in practice, i.e., how to effectively conduct failure mode recognition and RUL prediction as a joint task based on interpretable extracted degradation features from multiple sensor signals. To implement this method in practice, four steps are included as follows: First, collect multiple sensor signals, failure time, and failure modes of historical units. Second, construct the joint learning model based on features extracted from sensor signals by considering the degradation mechanism. Third, estimate model parameters using the data of historical units. Fourth, recognize the failure mode and predict the RUL of an in-service unit. Since the proposed method is a data-driven neural network with flexible model structure that considers complex data relationships, it is expected to be applicable to many practical situations and use cases, especially for manufacturing systems with complex structures and unknown failure thresholds.

Although degradation modeling has been widely applied to use multiple sensor signals to monitor the degradation process and predict the remaining useful lifetime (RUL) of operating machinery units, three challenging issues remain. One challenge is that units in engineering cases usually work under multiple operational conditions, causing the distribution of sensor signals to vary over conditions. It remains unexplored to characterize time-varying conditions as a distribution shift problem. The second challenge is that sensor signal fusion and degradation status modeling are separated into two independent steps in most of the existing methods, which ignores the intrinsic correlation between the two parts. The last challenge is how to find an accurate health index (HI) of units using previous knowledge of degradation. To tackle these issues, this article proposes an adaptation-aware interactive learning (AAIL) approach for degradation modeling. First, a condition-invariant HI is developed to handle time-varying operation conditions. Second, an interactive framework based on the fusion and degradation model is constructed, which naturally integrates a supervised learner and an unsupervised learner. To estimate the model parameters of AAIL, we propose an interactive training algorithm that shares learned degradation and fusion information during the model training process. A case study that uses the degradation data set of aircraft engines demonstrates that the proposed AAIL outperforms related benchmark methods.

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.

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.

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.