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Over the last decade, graph neural networks (GNNs) have made significant progress in numerous graph machine learning tasks. In real-world applications, where domain shifts occur and labels are often unavailable for a new target domain, graph domain adaptation (GDA) approaches have been proposed to facilitate knowledge transfer from the source domain to the target domain. Previous efforts in tackling distribution shifts across domains have mainly focused on aligning the node embedding distributions generated by the GNNs in the source and target domains. However, as the core part of GDA approaches, the impact of the underlying GNN architecture has received limited attention. In this work, we explore this orthogonal direction, i.e., how to facilitate GDA with architectural enhancement. In particular, we consider a class of GNNs that are designed explicitly based on optimization problems, namely unfolded GNNs (UGNNs), whose training process can be represented as bi-level optimization. Empirical and theoretical analyses demonstrate that when transferring from the source domain to the target domain, the lower-level objective value generated by the UGNNs significantly increases, resulting in an increase in the upper-level objective as well. Motivated by this observation, we propose a simple yet effective strategy called cascaded propagation (CP), which is guaranteed to decrease the lower-level objective value. The CP strategy is widely applicable to general UGNNs, and we evaluate its efficacy with three representative UGNN architectures. Extensive experiments on five real-world datasets demonstrate that the UGNNs integrated with CP outperform state-of-the-art GDA baselines.

Open-set Domain Adaptation (OSDA) aims to adapt a model from a labeled source domain to an unlabeled target domain, where novel classes - also referred to as target-private unknown classes - are present. Source-free Open-set Domain Adaptation (SF-OSDA) methods address OSDA without accessing labeled source data, making them particularly relevant under privacy constraints. However, SF-OSDA presents significant challenges due to distribution shifts and the introduction of novel classes. Existing SF-OSDA methods typically rely on thresholding the prediction entropy of a sample to identify it as either a known or unknown class but fail to explicitly learn discriminative features for the target-private unknown classes. We propose Recall and Refine (RRDA), a novel SF-OSDA framework designed to address these limitations by explicitly learning features for target-private unknown classes. RRDA employs a two-step process. First, we enhance the model's capacity to recognize unknown classes by training a target classifier with an additional decision boundary, guided by synthetic samples generated from target domain features. This enables the classifier to effectively separate known and unknown classes. In the second step, we adapt the entire model to the target domain, addressing both domain shifts and improving generalization to unknown classes. Any off-the-shelf source-free domain adaptation method (e.g., SHOT, AaD) can be seamlessly integrated into our framework at this stage. Extensive experiments on three benchmark datasets demonstrate that RRDA significantly outperforms existing SF-OSDA and OSDA methods.

Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains., Comment: 17 pages, 9 figures

The deployment of affordable Internet of Things (IoT) sensors for air pollution monitoring has increased in recent years due to their scalability and cost-effectiveness. However, accurately calibrating these sensors in uncontrolled environments remains a significant challenge. While expensive reference sensors can provide accurate ground truth data, they are often deployed on a limited scale due to high costs, leading to a scarcity of labeled data. In diverse urban environments, data distributions constantly shift due to varying factors such as traffic patterns, industrial activities, and weather conditions, which impact sensor readings. Consequently, traditional machine learning models -- despite their increasing deployment for environmental sensor calibration -- often struggle to provide reliable pollutant measurements across different locations due to domain shifts. To address these challenges, we propose a novel unsupervised domain adaptation (UDA) method specifically tailored for regression tasks on graph-structured data. Our approach leverages Graph Neural Networks (GNNs) to model the relationships between sensors. To effectively capture critical spatial-temporal interactions, we incorporate spatial-temporal graph neural networks (STGNNs), which extend GNNs by incorporating temporal dynamics. To handle the resulting larger embeddings, we propose a domain adaptation method using a closed-form solution inspired by the Tikhonov-regularized least-squares problem. This method leverages Cholesky decomposition and power iteration to align the subspaces between source and target domains. By aligning these subspaces, our approach allows low-cost IoT sensors to learn calibration parameters from expensive reference sensors. This facilitates reliable pollutant measurements in new locations without the need for additional costly equipment.

Building energy modeling plays a vital role in optimizing the operation of building energy systems by providing accurate predictions of the building's real-world conditions. In this context, various techniques have been explored, ranging from traditional physics-based models to data-driven models. Recently, researchers are combining physics-based and data-driven models into hybrid approaches. This includes using the physics-based model output as additional data-driven input, learning the residual between physics-based model and real data, learning a surrogate of the physics-based model, or fine-tuning a surrogate model with real data. However, a comprehensive comparison of the inherent advantages of these hybrid approaches is still missing. The primary objective of this work is to evaluate four predominant hybrid approaches in building energy modeling through a real-world case study, with focus on indoor temperature dynamics. To achieve this, we devise three scenarios reflecting common levels of building documentation and sensor availability, assess their performance, and analyse their explainability using hierarchical Shapley values. The real-world study reveals three notable findings. First, greater building documentation and sensor availability lead to higher prediction accuracy for hybrid approaches. Second, the performance of hybrid approaches depend on the type of building room, but the residual approach using a Feedforward Neural Network as data-driven sub-model performs best on average across all rooms. This hybrid approach also demonstrates a superior ability to leverage the physics-based simulation from the physics-based sub-model. Third, hierarchical Shapley values prove to be an effective tool for explaining and improving hybrid models while accounting for input correlations.

Achieving the EU's climate neutrality goal requires retrofitting existing buildings to reduce energy use and emissions. A critical step in this process is the precise assessment of geometric building envelope characteristics to inform retrofitting decisions. Previous methods for estimating building characteristics, such as window-to-wall ratio, building footprint area, and the location of architectural elements, have primarily relied on applying deep-learning-based detection or segmentation techniques on 2D images. However, these approaches tend to focus on planar facade properties, limiting their accuracy and comprehensiveness when analyzing complete building envelopes in 3D. While neural scene representations have shown exceptional performance in indoor scene reconstruction, they remain under-explored for external building envelope analysis. This work addresses this gap by leveraging cutting-edge neural surface reconstruction techniques based on signed distance function (SDF) representations for 3D building analysis. We propose BuildNet3D, a novel framework to estimate geometric building characteristics from 2D image inputs. By integrating SDF-based representation with semantic modality, BuildNet3D recovers fine-grained 3D geometry and semantics of building envelopes, which are then used to automatically extract building characteristics. Our framework is evaluated on a range of complex building structures, demonstrating high accuracy and generalizability in estimating window-to-wall ratio and building footprint. The results underscore the effectiveness of BuildNet3D for practical applications in building analysis and retrofitting.

Deriving health indicators of rotating machines is crucial for their maintenance. However, this process is challenging for the prevalent adopted intelligent methods since they may take the whole data distributions, not only introducing noise interference but also lacking the explainability. To address these issues, we propose a diffusion-based weakly-supervised approach for deriving health indicators of rotating machines, enabling early fault detection and continuous monitoring of condition evolution. This approach relies on a classifier-free diffusion model trained using healthy samples and a few anomalies. This model generates healthy samples. and by comparing the differences between the original samples and the generated ones in the envelope spectrum, we construct an anomaly map that clearly identifies faults. Health indicators are then derived, which can explain the fault types and mitigate noise interference. Comparative studies on two cases demonstrate that the proposed method offers superior health monitoring effectiveness and robustness compared to baseline models.

Power grid operators depend on accurate and reliable energy forecasts, aiming to minimize cases of extreme errors, as these outliers are particularly challenging to manage during operation. Incorporating planning information -- such as known data about users' future behavior or scheduled events -- has the potential to significantly enhance the accuracy and specificity of forecasts. Although there have been attempts to integrate such expected future behavior, these efforts consistently rely on conventional regression models to process this information. These models often lack the flexibility and capability to effectively incorporate both dynamic, forward-looking contextual inputs and historical data. To address this challenge, we conceptualize this combined forecasting and regression challenge as a sequence-to-sequence modeling problem and demonstrate, with three distinct models, that our contextually enhanced transformer models excel in this task. By leveraging schedule-based contextual information from the Swiss railway traction network, our proposed method significantly improved the average forecasting accuracy of nationwide railway energy consumption. Specifically, enhancing the transformer models with contextual information resulted in an average reduction of mean absolute error by 40.6\% , whereas other state-of-the-art methods did not demonstrate any significant improvement., Comment: 22 pages, 8 figures and tables, journal paper

Detecting and localizing leakages is a significant challenge for the efficient and sustainable management of water distribution networks (WDN). Leveraging the inherent graph structure of WDNs, recent approaches have used graph-based data-driven methods. However, these methods often learn shortcuts that work well with in-distribution data but fail to generalize to out-of-distribution data. To address this limitation and inspired by the perfect generalization ability of classical algorithms, we propose an algorithm-informed graph neural network (AIGNN). Recognizing that WDNs function as flow networks, incorporating max-flow information can be beneficial for inferring pressures. In the proposed framework, we first train AIGNN to emulate the Ford-Fulkerson algorithm for solving max-flow problems. This algorithmic knowledge is then transferred to address the pressure estimation problem in WDNs. Two AIGNNs are deployed, one to reconstruct pressure based on the current measurements, and another to predict pressure based on previous measurements. Leakages are detected and localized by comparing the outputs of the reconstructor and the predictor. By pretraining AIGNNs to reason like algorithms, they are expected to extract more task-relevant and generalizable features. Experimental results demonstrate that the proposed algorithm-informed approach achieves superior results with better generalization ability compared to GNNs that do not incorporate algorithmic knowledge.

Real-time condition monitoring is crucial for the reliable and efficient operation of complex systems. However, relying solely on physical sensors can be limited due to their cost, placement constraints, or inability to directly measure certain critical parameters. Virtual sensing addresses these limitations by leveraging readily available sensor data and system knowledge to estimate inaccessible parameters or infer system states. The increasing complexity of industrial systems necessitates deployments of sensors with diverse modalities to provide a comprehensive understanding of system states. These sensors capture data at varying frequencies to monitor both rapid and slowly varying system dynamics, as well as local and global state evolutions of the systems. This leads to heterogeneous temporal dynamics, which, particularly under varying operational end environmental conditions, pose a significant challenge for accurate virtual sensing. To address this, we propose a Heterogeneous Temporal Graph Neural Network (HTGNN) framework. HTGNN explicitly models signals from diverse sensors and integrates operating conditions into the model architecture. We evaluate HTGNN using two newly released datasets: a bearing dataset with diverse load conditions for bearing load prediction and a year-long simulated dataset for predicting bridge live loads. Our results demonstrate that HTGNN significantly outperforms established baseline methods in both tasks, particularly under highly varying operating conditions. These results highlight HTGNN's potential as a robust and accurate virtual sensing approach for complex systems, paving the way for improved monitoring, predictive maintenance, and enhanced system performance., Comment: This paper extends our previous conference paper (Best Paper at European Conference of the PHM Society 2024, https://doi.org/10.36001/phme.2024.v8i1.3998)

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation. Discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed. However, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on a predefined library of constitutive relations or manually crafted input features. These dependencies require significant expertise and specialized domain knowledge. Here, we introduce a machine learning approach called uLED, which overcomes the limitations by using the input convex neural network (ICNN) as the surrogate constitutive model. We improve the optimization strategy for training ICNN, allowing it to be trained end-to-end using direct strain invariants as input across various materials. Furthermore, we utilize the nodal force equilibrium at the internal domain as the training objective, which enables us to learn the constitutive relation solely from temporal displacement recordings. We validate the effectiveness of the proposed method on a diverse range of material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations.

This paper focuses on source-free domain adaptation for object detection in computer vision. This task is challenging and of great practical interest, due to the cost of obtaining annotated data sets for every new domain. Recent research has proposed various solutions for Source-Free Object Detection (SFOD), most being variations of teacher-student architectures with diverse feature alignment, regularization and pseudo-label selection strategies. Our work investigates simpler approaches and their performance compared to more complex SFOD methods in several adaptation scenarios. We highlight the importance of batch normalization layers in the detector backbone, and show that adapting only the batch statistics is a strong baseline for SFOD. We propose a simple extension of a Mean Teacher with strong-weak augmentation in the source-free setting, Source-Free Unbiased Teacher (SF-UT), and show that it actually outperforms most of the previous SFOD methods. Additionally, we showcase that an even simpler strategy consisting in training on a fixed set of pseudo-labels can achieve similar performance to the more complex teacher-student mutual learning, while being computationally efficient and mitigating the major issue of teacher-student collapse. We conduct experiments on several adaptation tasks using benchmark driving datasets including (Foggy)Cityscapes, Sim10k and KITTI, and achieve a notable improvement of 4.7\% AP50 on Cityscapes$\rightarrow$Foggy-Cityscapes compared with the latest state-of-the-art in SFOD. Source code is available at https://github.com/EPFL-IMOS/simple-SFOD., Comment: Accepted at ECCV 2024. 19 pages

The task of open-set domain generalization (OSDG) involves recognizing novel classes within unseen domains, which becomes more challenging with multiple modalities as input. Existing works have only addressed unimodal OSDG within the meta-learning framework, without considering multimodal scenarios. In this work, we introduce a novel approach to address Multimodal Open-Set Domain Generalization (MM-OSDG) for the first time, utilizing self-supervision. To this end, we introduce two innovative multimodal self-supervised pretext tasks: Masked Cross-modal Translation and Multimodal Jigsaw Puzzles. These tasks facilitate the learning of multimodal representative features, thereby enhancing generalization and open-class detection capabilities. Additionally, we propose a novel entropy weighting mechanism to balance the loss across different modalities. Furthermore, we extend our approach to tackle also the Multimodal Open-Set Domain Adaptation (MM-OSDA) problem, especially in scenarios where unlabeled data from the target domain is available. Extensive experiments conducted under MM-OSDG, MM-OSDA, and Multimodal Closed-Set DG settings on the EPIC-Kitchens and HAC datasets demonstrate the efficacy and versatility of the proposed approach. Our source code is available at https://github.com/donghao51/MOOSA., Comment: Accepted by ECCV 2024, code: https://github.com/donghao51/MOOSA

Damage to road pavement can develop into cracks, potholes, spallings, and other issues posing significant challenges to the integrity, safety, and durability of the road structure. Detecting and monitoring the evolution of these damages is crucial for maintaining the condition and structural health of road infrastructure. In recent years, researchers have explored various data-driven methods for image-based damage detection in road monitoring applications. The field gained attention with the introduction of the Road Damage Detection Challenge (RDDC2018), encouraging competition in developing object detectors on street-view images from various countries. Leading teams have demonstrated the effectiveness of ensemble models, mostly based on the YOLO and Faster R-CNN series. Data augmentations have also shown benefits in object detection within the computer vision field, including transformations such as random flipping, cropping, cutting out patches, as well as cut-and-pasting object instances. Applying cut-and-paste augmentation to road damages appears to be a promising approach to increase data diversity. However, the standard cut-and-paste technique, which involves sampling an object instance from a random image and pasting it at a random location onto the target image, has demonstrated limited effectiveness for road damage detection. This method overlooks the location of the road and disregards the difference in perspective between the sampled damage and the target image, resulting in unrealistic augmented images. In this work, we propose an improved Cut-and-Paste augmentation technique that is both content-aware (i.e. considers the true location of the road in the image) and perspective-aware (i.e. takes into account the difference in perspective between the injected damage and the target image)., Comment: Extended abstract accepted at ESREL 2024. 2 pages

Fault detection is crucial in industrial systems to prevent failures and optimize performance by distinguishing abnormal from normal operating conditions. Data-driven methods have been gaining popularity for fault detection tasks as the amount of condition monitoring data from complex industrial systems increases. Despite these advances, early fault detection remains a challenge under real-world scenarios. The high variability of operating conditions and environments makes it difficult to collect comprehensive training datasets that can represent all possible operating conditions, especially in the early stages of system operation. Furthermore, these variations often evolve over time, potentially leading to entirely new data distributions in the future that were previously unseen. These challenges prevent direct knowledge transfer across different units and over time, leading to the distribution gap between training and testing data and inducing performance degradation of those methods in real-world scenarios. To overcome this, our work introduces a novel approach for continuous test-time domain adaptation. This enables early-stage robust anomaly detection by addressing domain shifts and limited data representativeness issues. We propose a Test-time domain Adaptation Anomaly Detection (TAAD) framework that separates input variables into system parameters and measurements, employing two domain adaptation modules to independently adapt to each input category. This method allows for effective adaptation to evolving operating conditions and is particularly beneficial in systems with scarce data. Our approach, tested on a real-world pump monitoring dataset, shows significant improvements over existing domain adaptation methods in fault detection, demonstrating enhanced accuracy and reliability., Comment: 11 pages including references

Graph signal processing represents an important advancement in the field of data analysis, extending conventional signal processing methodologies to complex networks and thereby facilitating the exploration of informative patterns and structures across various domains. However, acquiring the underlying graphs for specific applications remains a challenging task. While graph inference based on smooth graph signal representation has become one of the state-of-the-art methods, these approaches usually overlook the unique properties of networks, which are generally derived from domain-specific knowledge. Overlooking this information could make the approaches less interpretable and less effective overall. In this study, we propose a new graph inference method that leverages available domain knowledge. The proposed methodology is evaluated on the task of denoising and imputing missing sensor data, utilizing graph signal reconstruction techniques. The results demonstrate that incorporating domain knowledge into the graph inference process can improve graph signal reconstruction in district heating networks. Our code is available at \href{https://github.com/Keiv4n/IGL}{github.com/Keiv4n/IGL}., Comment: Accepted to EUSIPCO 2024

Visual anomaly detection (AD) inherently faces significant challenges due to the scarcity of anomalous data. Although numerous works have been proposed to synthesize anomalous samples, the generated samples often lack authenticity or can only reflect the distribution of the available training data samples. In this work, we propose CUT: a Controllable, Universal and Training-free visual anomaly generation framework, which leverages the capability of Stable Diffusion (SD) in image generation to generate diverse and realistic anomalies. With CUT, we achieve controllable and realistic anomaly generation universally across both unseen data and novel anomaly types, using a single model without acquiring additional training effort. To demonstrate the effectiveness of our approach, we propose a Vision-Language-based Anomaly Detection framework (VLAD). By training the VLAD model with our generated anomalous samples, we achieve state-of-the-art performance on several benchmark anomaly detection tasks, highlighting the significant improvements enabled by our synthetic data., Comment: 9 pages excluding appendix

Regression models often fail to generalize effectively in regions characterized by highly imbalanced label distributions. Previous methods for deep imbalanced regression rely on gradient-based weight updates, which tend to overfit in underrepresented regions. This paper proposes a paradigm shift towards in-context learning as an effective alternative to conventional in-weight learning methods, particularly for addressing imbalanced regression. In-context learning refers to the ability of a model to condition itself, given a prompt sequence composed of in-context samples (input-label pairs) alongside a new query input to generate predictions, without requiring any parameter updates. In this paper, we study the impact of the prompt sequence on the model performance from both theoretical and empirical perspectives. We emphasize the importance of localized context in reducing bias within regions of high imbalance. Empirical evaluations across a variety of real-world datasets demonstrate that in-context learning substantially outperforms existing in-weight learning methods in scenarios with high levels of imbalance.

Detecting out-of-distribution (OOD) samples is important for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. Existing research has mainly focused on unimodal scenarios on image data. However, real-world applications are inherently multimodal, which makes it essential to leverage information from multiple modalities to enhance the efficacy of OOD detection. To establish a foundation for more realistic Multimodal OOD Detection, we introduce the first-of-its-kind benchmark, MultiOOD, characterized by diverse dataset sizes and varying modality combinations. We first evaluate existing unimodal OOD detection algorithms on MultiOOD, observing that the mere inclusion of additional modalities yields substantial improvements. This underscores the importance of utilizing multiple modalities for OOD detection. Based on the observation of Modality Prediction Discrepancy between in-distribution (ID) and OOD data, and its strong correlation with OOD performance, we propose the Agree-to-Disagree (A2D) algorithm to encourage such discrepancy during training. Moreover, we introduce a novel outlier synthesis method, NP-Mix, which explores broader feature spaces by leveraging the information from nearest neighbor classes and complements A2D to strengthen OOD detection performance. Extensive experiments on MultiOOD demonstrate that training with A2D and NP-Mix improves existing OOD detection algorithms by a large margin. Our source code and MultiOOD benchmark are available at https://github.com/donghao51/MultiOOD., Comment: NeurIPS 2024 spotlight. Code and MultiOOD benchmark: https://github.com/donghao51/MultiOOD

Deep learning approaches have recently been extensively explored for the prognostics of industrial assets. However, they still suffer from a lack of interpretability, which hinders their adoption in safety-critical applications. To improve their trustworthiness, explainable AI (XAI) techniques have been applied in prognostics, primarily to quantify the importance of input variables for predicting the remaining useful life (RUL) using post-hoc attribution methods. In this work, we propose the application of Concept Bottleneck Models (CBMs), a family of inherently interpretable neural network architectures based on concept explanations, to the task of RUL prediction. Unlike attribution methods, which explain decisions in terms of low-level input features, concepts represent high-level information that is easily understandable by users. Moreover, once verified in actual applications, CBMs enable domain experts to intervene on the concept activations at test-time. We propose using the different degradation modes of an asset as intermediate concepts. Our case studies on the New Commercial Modular AeroPropulsion System Simulation (N-CMAPSS) aircraft engine dataset for RUL prediction demonstrate that the performance of CBMs can be on par or superior to black-box models, while being more interpretable, even when the available labeled concepts are limited. Code available at \href{https://github.com/EPFL-IMOS/concept-prognostics/}{\url{github.com/EPFL-IMOS/concept-prognostics/}}., Comment: Under review

Urban Air Mobility (UAM) aims to expand existing transportation networks in metropolitan areas by offering short flights either to transport passengers or cargo. Electric vertical takeoff and landing aircraft powered by lithium-ion battery packs are considered promising for such applications. Efficient mission planning is cru-cial, maximizing the number of flights per battery charge while ensuring completion even under unforeseen events. As batteries degrade, precise mission planning becomes challenging due to uncertainties in the end-of-discharge prediction. This often leads to adding safety margins, reducing the number or duration of po-tential flights on one battery charge. While predicting the end of discharge can support decision-making, it remains insufficient in case of unforeseen events, such as adverse weather conditions. This necessitates health-aware real-time control to address any unexpected events and extend the time until the end of charge while taking the current degradation state into account. This paper addresses the joint problem of mission planning and health-aware real-time control of opera-tional parameters to prescriptively control the duration of one discharge cycle of the battery pack. We pro-pose an algorithm that proactively prescribes operational parameters to extend the discharge cycle based on the battery's current health status while optimizing the mission. The proposed deep reinforcement learn-ing algorithm facilitates operational parameter optimization and path planning while accounting for the degradation state, even in the presence of uncertainties. Evaluation of simulated flights of a NASA concep-tual multirotor aircraft model, collected from Hardware-in-the-loop experiments, demonstrates the algo-rithm's near-optimal performance across various operational scenarios, allowing adaptation to changed en-vironmental conditions.

The Industrial Internet of Things (IIoT) is reshaping manufacturing, industrial processes, and infrastructure management. By fostering new levels of automation, efficiency, and predictive maintenance, IIoT is transforming traditional industries into intelligent, seamlessly interconnected ecosystems. However, achieving highly reliable IIoT can be hindered by factors such as the cost of installing large numbers of sensors, limitations in retrofitting existing systems with sensors, or harsh environmental conditions that may make sensor installation impractical. Soft (virtual) sensing leverages mathematical models to estimate variables from physical sensor data, offering a solution to these challenges. Data-driven and physics-based modeling are the two main methodologies widely used for soft sensing. The choice between these strategies depends on the complexity of the underlying system, with the data-driven approach often being preferred when the physics-based inference models are intricate and present challenges for state estimation. However, conventional deep learning models are typically hindered by their inability to explicitly represent the complex interactions among various sensors. To address this limitation, we adopt Graph Neural Networks (GNNs), renowned for their ability to effectively capture the complex relationships between sensor measurements. In this research, we propose physics-enhanced GNNs, which integrate principles of physics into graph-based methodologies. This is achieved by augmenting additional nodes in the input graph derived from the underlying characteristics of the physical processes. Our evaluation of the proposed methodology on the case study of district heating networks reveals significant improvements over purely data-driven GNNs, even in the presence of noise and parameter inaccuracies., Comment: 14 pages, 10 figures. Accepted to IEEE Internet of Things Journal

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency., Comment: Revised: References, Figures 3&4, Equation 19&31, and discussions

Pumped-storage hydropower plants (PSH) actively participate in grid power-frequency control and therefore often operate under dynamic conditions, which results in rapidly varying system states. Predicting these dynamically changing states is essential for comprehending the underlying sensor and machine conditions. This understanding aids in detecting anomalies and faults, ensuring the reliable operation of the connected power grid, and in identifying faulty and miscalibrated sensors. PSH are complex, highly interconnected systems encompassing electrical and hydraulic subsystems, each characterized by their respective underlying networks that can individually be represented as graphs. To take advantage of this relational inductive bias, graph neural networks (GNNs) have been separately applied to state forecasting tasks in the individual subsystems, but without considering their interdependencies. In PSH, however, these subsystems depend on the same control input, making their operations highly interdependent and interconnected. Consequently, hydraulic and electrical sensor data should be fused across PSH subsystems to improve state forecasting accuracy. This approach has not been explored in GNN literature yet because many available PSH graphs are limited to their respective subsystem boundaries, which makes the method unsuitable to be applied directly. In this work, we introduce the application of spectral-temporal graph neural networks, which leverage self-attention mechanisms to concurrently capture and learn meaningful subsystem interdependencies and the dynamic patterns observed in electric and hydraulic sensors. Our method effectively fuses data from the PSH's subsystems by operating on a unified, system-wide graph, learned directly from the data, This approach leads to demonstrably improved state forecasting performance and enhanced generalizability., Comment: 11 pages, 8 figures, conference

Accurate bearing load monitoring is essential for their Prognostics and Health Management (PHM), enabling damage assessment, wear prediction, and proactive maintenance. While bearing sensors are typically placed on the bearing housing, direct load monitoring requires sensors inside the bearing itself. Recently introduced sensor rollers enable direct bearing load monitoring but are constrained by their battery life. Data-driven virtual sensors can learn from sensor roller data collected during a batterys lifetime to map operating conditions to bearing loads. Although spatially distributed bearing sensors offer insights into load distribution (e.g., correlating temperature with load), traditional machine learning algorithms struggle to fully exploit these spatial-temporal dependencies. To address this gap, we introduce a graph-based virtual sensor that leverages Graph Neural Networks (GNNs) to analyze spatial-temporal dependencies among sensor signals, mapping existing measurements (temperature, vibration) to bearing loads. Since temperature and vibration signals exhibit vastly different dynamics, we propose Heterogeneous Temporal Graph Neural Networks (HTGNN), which explicitly models these signal types and their interactions for effective load prediction. Our results demonstrate that HTGNN outperforms Convolutional Neural Networks (CNNs), which struggle to capture both spatial and heterogeneous signal characteristics. These findings highlight the importance of capturing the complex spatial interactions between temperature, vibration, and load., Comment: 8 pages, 6 figures

Thermal scene reconstruction holds great potential for various applications, such as analyzing building energy consumption and performing non-destructive infrastructure testing. However, existing methods typically require dense scene measurements and often rely on RGB images for 3D geometry reconstruction, projecting thermal information post-reconstruction. This can lead to inconsistencies between the reconstructed geometry and temperature data and their actual values. To address this challenge, we propose ThermoNeRF, a novel multimodal approach based on Neural Radiance Fields that jointly renders new RGB and thermal views of a scene, and ThermoScenes, a dataset of paired RGB+thermal images comprising 8 scenes of building facades and 8 scenes of everyday objects. To address the lack of texture in thermal images, ThermoNeRF uses paired RGB and thermal images to learn scene density, while separate networks estimate color and temperature data. Unlike comparable studies, our focus is on temperature reconstruction and experimental results demonstrate that ThermoNeRF achieves an average mean absolute error of 1.13C and 0.41C for temperature estimation in buildings and other scenes, respectively, representing an improvement of over 50% compared to using concatenated RGB+thermal data as input to a standard NeRF. Code and dataset are available online.

Symbolic regression holds great potential for uncovering underlying mathematical and physical relationships from empirical data. While existing transformer-based models have recently achieved significant success in this domain, they face challenges in terms of generalizability and adaptability. Typically, in cases where the output expressions do not adequately fit experimental data, the models lack efficient mechanisms to adapt or modify the expression. This inflexibility hinders their application in real-world scenarios, particularly in discovering unknown physical or biological relationships. Inspired by how human experts refine and adapt expressions, we introduce Symbolic Q-network (Sym-Q), a novel reinforcement learning-based model that redefines symbolic regression as a sequential decision-making task. Sym-Q leverages supervised demonstrations and refines expressions based on reward signals indicating the quality of fitting precision. Its distinctive ability to manage the complexity of expression trees and perform precise step-wise updates significantly enhances flexibility and efficiency. Our results demonstrate that Sym-Q excels not only in recovering underlying mathematical structures but also uniquely learns to efficiently refine the output expression based on reward signals, thereby discovering underlying expressions. Sym-Q paves the way for more intuitive and impactful discoveries in physical science, marking a substantial advancement in the field of symbolic regression.

Unsupervised Domain Adaptation for Regression (UDAR) aims to adapt models from a labeled source domain to an unlabeled target domain for regression tasks. Traditional feature alignment methods, successful in classification, often prove ineffective for regression due to the correlated nature of regression features. To address this challenge, we propose Uncertainty-Guided Alignment (UGA), a novel method that integrates predictive uncertainty into the feature alignment process. UGA employs Evidential Deep Learning to predict both target values and their associated uncertainties. This uncertainty information guides the alignment process and fuses information within the embedding space, effectively mitigating issues such as feature collapse in out-of-distribution scenarios. We evaluate UGA on two computer vision benchmarks and a real-world battery state-of-charge prediction across different manufacturers and operating temperatures. Across 52 transfer tasks, UGA on average outperforms existing state-of-the-art methods. Our approach not only improves adaptation performance but also provides well-calibrated uncertainty estimates.

The Health Index (HI) is crucial for evaluating system health and is important for tasks like anomaly detection and Remaining Useful Life (RUL) prediction of safety-critical systems. Real-time, meticulous monitoring of system conditions is essential, especially in manufacturing high-quality and safety-critical components such as spray coatings. However, acquiring accurate health status information (HI labels) in real scenarios can be difficult or costly because it requires continuous, precise measurements that fully capture the system's health. As a result, using datasets from systems run-to-failure, which provide limited HI labels only at the healthy and end-of-life phases, becomes a practical approach. We employ Deep Semi-supervised Anomaly Detection (DeepSAD) embeddings to tackle the challenge of extracting features associated with the system's health state. Additionally, we introduce a diversity loss to further enrich the DeepSAD embeddings. We also propose applying an alternating projection algorithm with isotonic constraints to transform the embedding into a normalized HI with an increasing trend. Validation on the PHME2010 milling dataset, a recognized benchmark with ground truth HIs, confirms the efficacy of our proposed HI estimations. Our methodology is further applied to monitor the wear states of thermal spray coatings using high-frequency voltage. These contributions facilitate more accessible and reliable HI estimation, particularly in scenarios where obtaining ground truth HI labels is impossible., Comment: 13 pages, 8 figures

Intelligent Fault Diagnosis (IFD) based on deep learning has proven to be an effective and flexible solution, attracting extensive research. Deep neural networks can learn rich representations from vast amounts of representative labeled data for various applications. In IFD, they achieve high classification performance from signals in an end-to-end manner, without requiring extensive domain knowledge. However, deep learning models usually only perform well on the data distribution they have been trained on. When applied to a different distribution, they may experience performance drops. This is also observed in IFD, where assets are often operated in working conditions different from those in which labeled data have been collected. Unsupervised domain adaptation (UDA) deals with the scenario where labeled data are available in a source domain, and only unlabeled data are available in a target domain, where domains may correspond to operating conditions. Recent methods rely on training with confident pseudo-labels for target samples. However, the confidence-based selection of pseudo-labels is hindered by poorly calibrated confidence estimates in the target domain, primarily due to over-confident predictions, which limits the quality of pseudo-labels and leads to error accumulation. In this paper, we propose a novel UDA method called Calibrated Adaptive Teacher (CAT), where we propose to calibrate the predictions of the teacher network throughout the self-training process, leveraging post-hoc calibration techniques. We evaluate CAT on domain-adaptive IFD and perform extensive experiments on the Paderborn benchmark for bearing fault diagnosis under varying operating conditions. Our proposed method achieves state-of-the-art performance on most transfer tasks., Comment: Accepted for publication in Sensors. 24 pages

Anomaly detection (AD) is essential in identifying rare and often critical events in complex systems, finding applications in fields such as network intrusion detection, financial fraud detection, and fault detection in infrastructure and industrial systems. While AD is typically treated as an unsupervised learning task due to the high cost of label annotation, it is more practical to assume access to a small set of labeled anomaly samples from domain experts, as is the case for semi-supervised anomaly detection. Semi-supervised and supervised approaches can leverage such labeled data, resulting in improved performance. In this paper, rather than proposing a new semi-supervised or supervised approach for AD, we introduce a novel algorithm for generating additional pseudo-anomalies on the basis of the limited labeled anomalies and a large volume of unlabeled data. This serves as an augmentation to facilitate the detection of new anomalies. Our proposed algorithm, named Nearest Neighbor Gaussian Mixup (NNG-Mix), efficiently integrates information from both labeled and unlabeled data to generate pseudo-anomalies. We compare the performance of this novel algorithm with commonly applied augmentation techniques, such as Mixup and Cutout. We evaluate NNG-Mix by training various existing semi-supervised and supervised anomaly detection algorithms on the original training data along with the generated pseudo-anomalies. Through extensive experiments on 57 benchmark datasets in ADBench, reflecting different data types, we demonstrate that NNG-Mix outperforms other data augmentation methods. It yields significant performance improvements compared to the baselines trained exclusively on the original training data. Notably, NNG-Mix yields up to 16.4%, 8.8%, and 8.0% improvements on Classical, CV, and NLP datasets in ADBench. Our source code is available at https://github.com/donghao51/NNG-Mix.

In real-world scenarios, achieving domain generalization (DG) presents significant challenges as models are required to generalize to unknown target distributions. Generalizing to unseen multi-modal distributions poses even greater difficulties due to the distinct properties exhibited by different modalities. To overcome the challenges of achieving domain generalization in multi-modal scenarios, we propose SimMMDG, a simple yet effective multi-modal DG framework. We argue that mapping features from different modalities into the same embedding space impedes model generalization. To address this, we propose splitting the features within each modality into modality-specific and modality-shared components. We employ supervised contrastive learning on the modality-shared features to ensure they possess joint properties and impose distance constraints on modality-specific features to promote diversity. In addition, we introduce a cross-modal translation module to regularize the learned features, which can also be used for missing-modality generalization. We demonstrate that our framework is theoretically well-supported and achieves strong performance in multi-modal DG on the EPIC-Kitchens dataset and the novel Human-Animal-Cartoon (HAC) dataset introduced in this paper. Our source code and HAC dataset are available at https://github.com/donghao51/SimMMDG., Comment: NeurIPS 2023

Monitoring surface cracks in infrastructure is crucial for structural health monitoring. Automatic visual inspection offers an effective solution, especially in hard-to-reach areas. Machine learning approaches have proven their effectiveness but typically require large annotated datasets for supervised training. Once a crack is detected, monitoring its severity often demands precise segmentation of the damage. However, pixel-level annotation of images for segmentation is labor-intensive. To mitigate this cost, one can leverage explainable artificial intelligence (XAI) to derive segmentations from the explanations of a classifier, requiring only weak image-level supervision. This paper proposes applying this methodology to segment and monitor surface cracks. We evaluate the performance of various XAI methods and examine how this approach facilitates severity quantification and growth monitoring. Results reveal that while the resulting segmentation masks may exhibit lower quality than those produced by supervised methods, they remain meaningful and enable severity monitoring, thus reducing substantial labeling costs., Comment: 49 pages. Accepted for publication in Automation in Construction

In the presented work, we propose to apply the framework of graph neural networks (GNNs) to predict the dynamics of a rolling element bearing. This approach offers generalizability and interpretability, having the potential for scalable use in real-time operational digital twin systems for monitoring the health state of rotating machines. By representing the bearing's components as nodes in a graph, the GNN can effectively model the complex relationships and interactions among them. We utilize a dynamic spring-mass-damper model of a bearing to generate the training data for the GNN. In this model, discrete masses represent bearing components such as rolling elements, inner raceways, and outer raceways, while a Hertzian contact model is employed to calculate the forces between these components. We evaluate the learning and generalization capabilities of the proposed GNN framework by testing different bearing configurations that deviate from the training configurations. Through this approach, we demonstrate the effectiveness of the GNN-based method in accurately predicting the dynamics of rolling element bearings, highlighting its potential for real-time health monitoring of rotating machinery.

The use of Internet of Things (IoT) sensors for air pollution monitoring has significantly increased, resulting in the deployment of low-cost sensors. Despite this advancement, accurately calibrating these sensors in uncontrolled environmental conditions remains a challenge. To address this, we propose a novel approach that leverages graph neural networks, specifically the graph attention network module, to enhance the calibration process by fusing data from sensor arrays. Through our experiments, we demonstrate the effectiveness of our approach in significantly improving the calibration accuracy of sensors in IoT air pollution monitoring platforms.

An important initial step in fault detection for complex industrial systems is gaining an understanding of their health condition. Subsequently, continuous monitoring of this health condition becomes crucial to observe its evolution, track changes over time, and isolate faults. As faults are typically rare occurrences, it is essential to perform this monitoring in an unsupervised manner. Various approaches have been proposed not only to detect faults in an unsupervised manner but also to distinguish between different potential fault types. In this study, we perform a comprehensive comparison between two residual-based approaches: autoencoders, and the input-output models that establish a mapping between operating conditions and sensor readings. We explore the sensor-wise residuals and aggregated residuals for the entire system in both methods. The performance evaluation focuses on three tasks: health indicator construction, fault detection, and health indicator interpretation. To perform the comparison, we utilize the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dynamical model, specifically a subset of the turbofan engine dataset containing three different fault types. All models are trained exclusively on healthy data. Fault detection is achieved by applying a threshold that is determined based on the healthy condition. The detection results reveal that both models are capable of detecting faults with an average delay of around 20 cycles and maintain a low false positive rate. While the fault detection performance is similar for both models, the input-output model provides better interpretability regarding potential fault types and the possible faulty components., Comment: 10 pages, submitted to the 15th Annual Conference of the Prognostics and Health Management Society

With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion for reliable health indicators is their capability to discern a degradation trend. However, trending can pose challenges due to the variability of operating conditions. An optimal transformation of health indicators would therefore be one that converts degradation dynamics into a coordinate system where degradation trends exhibit linearity. Koopman theory framework is well-suited to address these challenges. In this work, we demonstrate the successful extension of the previously proposed Deep Koopman Operator approach to learn the dynamics of industrial systems by transforming them into linearized coordinate systems, resulting in a latent representation that provides sufficient information for estimating the system's remaining useful life. Additionally, we propose a novel Koopman-Inspired Degradation Model for degradation modelling of dynamical systems with control. The proposed approach effectively disentangles the impact of degradation and imposed control on the latent dynamics. The algorithm consistently outperforms in predicting the remaining useful life of CNC milling machine cutters and Li-ion batteries, whether operated under constant and varying current loads. Furthermore, we highlight the utility of learned Koopman-inspired degradation operators analyzing the influence of imposed control on the system's health state.

In the Industrial Internet of Things (IIoT), condition monitoring sensor signals from complex systems often exhibit nonlinear and stochastic spatial-temporal dynamics under varying conditions. These complex dynamics make fault detection particularly challenging. While previous methods effectively model these dynamics, they often neglect the evolution of relationships between sensor signals. Undetected shifts in these relationships can lead to significant system failures. Furthermore, these methods frequently misidentify novel operating conditions as faults. Addressing these limitations, we propose DyEdgeGAT (Dynamic Edge via Graph Attention), a novel approach for early-stage fault detection in IIoT systems. DyEdgeGAT's primary innovation lies in a novel graph inference scheme for multivariate time series that tracks the evolution of relationships between time series, enabled by dynamic edge construction. Another key innovation of DyEdgeGAT is its ability to incorporate operating condition contexts into node dynamics modeling, enhancing its accuracy and robustness. We rigorously evaluated DyEdgeGAT using both a synthetic dataset, simulating varying levels of fault severity, and a real-world industrial-scale multiphase flow facility benchmark with diverse fault types under varying operating conditions and detection complexities. The results show that DyEdgeGAT significantly outperforms other baseline methods in fault detection, particularly in the early stages with low severity, and exhibits robust performance under novel operating conditions., Comment: 16 pages, 8 figures

The application of unsupervised domain adaptation (UDA)-based fault diagnosis methods has shown significant efficacy in industrial settings, facilitating the transfer of operational experience and fault signatures between different operating conditions, different units of a fleet or between simulated and real data. However, in real industrial scenarios, unknown levels and types of noise can amplify the difficulty of domain alignment, thus severely affecting the diagnostic performance of deep learning models. To address this issue, we propose an UDA method called Smart Filter-Aided Domain Adversarial Neural Network (SFDANN) for fault diagnosis in noisy industrial scenarios. The proposed methodology comprises two steps. In the first step, we develop a smart filter that dynamically enforces similarity between the source and target domain data in the time-frequency domain. This is achieved by combining a learnable wavelet packet transform network (LWPT) and a traditional wavelet packet transform module. In the second step, we input the data reconstructed by the smart filter into a domain adversarial neural network (DANN). To learn domain-invariant and discriminative features, the learnable modules of SFDANN are trained in a unified manner with three objectives: time-frequency feature proximity, domain alignment, and fault classification. We validate the effectiveness of the proposed SFDANN method based on two fault diagnosis cases: one involving fault diagnosis of bearings in noisy environments and another involving fault diagnosis of slab tracks in a train-track-bridge coupling vibration system, where the transfer task involves transferring from numerical simulations to field measurements. Results show that compared to other representative state of the art UDA methods, SFDANN exhibits superior performance and remarkable stability.

The occurrence of manufacturing defects in wind turbine blade (WTB) production can result in significant increases in operation and maintenance costs and lead to severe and disastrous consequences. Therefore, inspection during the manufacturing process is crucial to ensure consistent fabrication of composite materials. Non-contact sensing techniques, such as Frequency Modulated Continuous Wave (FMCW) radar, are becoming increasingly popular as they offer a full view of these complex structures during curing. In this paper, we enhance the quality assurance of manufacturing utilizing FMCW radar as a non-destructive sensing modality. Additionally, a novel anomaly detection pipeline is developed that offers the following advantages: (1) We use the analytic representation of the Intermediate Frequency signal of the FMCW radar as a feature to disentangle material-specific and round-trip delay information from the received wave. (2) We propose a novel anomaly detection methodology called focus Support Vector Data Description (focus-SVDD). This methodology involves defining the limit boundaries of the dataset after removing healthy data features, thereby focusing on the attributes of anomalies. (3) The proposed method employs a complex-valued autoencoder to remove healthy features and we introduces a new activation function called Exponential Amplitude Decay (EAD). EAD takes advantage of the Rayleigh distribution, which characterizes an instantaneous amplitude signal. The effectiveness of the proposed method is demonstrated through its application to collected data, where it shows superior performance compared to other state-of-the-art unsupervised anomaly detection methods. This method is expected to make a significant contribution not only to structural health monitoring but also to the field of deep complex-valued data processing and SVDD application., Comment: 17 pages, 5 figures, 3 Tables

The value of luxury goods, particularly investment-grade gemstones, is greatly influenced by their origin and authenticity, sometimes resulting in differences worth millions of dollars. Traditionally, human experts have determined the origin and detected treatments on gemstones through visual inspections and a range of analytical methods. However, the interpretation of the data can be subjective and time-consuming, resulting in inconsistencies. In this study, we propose Gemtelligence, a novel approach based on deep learning that enables accurate and consistent origin determination and treatment detection. Gemtelligence comprises convolutional and attention-based neural networks that process heterogeneous data types collected by multiple instruments. Notably, the algorithm demonstrated comparable predictive performance to expensive laser-ablation inductively-coupled-plasma mass-spectrometry (ICP-MS) analysis and visual examination by human experts, despite using input data from relatively inexpensive analytical methods. Our innovative methodology represents a major breakthrough in the field of gemstone analysis by significantly improving the automation and robustness of the entire analytical process pipeline.

Extensive research has been conducted on fault diagnosis of planetary gearboxes using vibration signals and deep learning (DL) approaches. However, DL-based methods are susceptible to the domain shift problem caused by varying operating conditions of the gearbox. Although domain adaptation and data synthesis methods have been proposed to overcome such domain shifts, they are often not directly applicable in real-world situations where only healthy data is available in the target domain. To tackle the challenge of extreme domain shift scenarios where only healthy data is available in the target domain, this paper proposes two novel domain knowledge-informed data synthesis methods utilizing the health data map (HDMap). The two proposed approaches are referred to as scaled CutPaste and FaultPaste. The HDMap is used to physically represent the vibration signal of the planetary gearbox as an image-like matrix, allowing for visualization of fault-related features. CutPaste and FaultPaste are then applied to generate faulty samples based on the healthy data in the target domain, using domain knowledge and fault signatures extracted from the source domain, respectively. In addition to generating realistic faults, the proposed methods introduce scaling of fault signatures for controlled synthesis of faults with various severity levels. A case study is conducted on a planetary gearbox testbed to evaluate the proposed approaches. The results show that the proposed methods are capable of accurately diagnosing faults, even in cases of extreme domain shift, and can estimate the severity of faults that have not been previously observed in the target domain., Comment: Under review / added arXiv identifier / Updated to revised version

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines.

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions between interactive entities. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. The associated challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively by explicitly encoding the correlation among incoming interactions with a joint distribution, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. We further show that when combined with known constraints, it allows us, for example, to discover physics-consistent interaction laws of particle systems. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning., Comment: Under review. Links to the supporting code can be found at the end of the main content

Operators from various industries have been pushing the adoption of wireless sensing nodes for industrial monitoring, and such efforts have produced sizeable condition monitoring datasets that can be used to build diagnosis algorithms capable of warning maintenance engineers of impending failure or identifying current system health conditions. However, single operators may not have sufficiently large fleets of systems or component units to collect sufficient data to develop data-driven algorithms. Collecting a satisfactory quantity of fault patterns for safety-critical systems is particularly difficult due to the rarity of faults. Federated learning (FL) has emerged as a promising solution to leverage datasets from multiple operators to train a decentralized asset fault diagnosis model while maintaining data confidentiality. However, there are still considerable obstacles to overcome when it comes to optimizing the federation strategy without leaking sensitive data and addressing the issue of client dataset heterogeneity. This is particularly prevalent in fault diagnosis applications due to the high diversity of operating conditions and system configurations. To address these two challenges, we propose a novel clustering-based FL algorithm where clients are clustered for federating based on dataset similarity. To quantify dataset similarity between clients without explicitly sharing data, each client sets aside a local test dataset and evaluates the other clients' model prediction accuracy and uncertainty on this test dataset. Clients are then clustered for FL based on relative prediction accuracy and uncertainty.

Limited availability of representative time-to-failure (TTF) trajectories either limits the performance of deep learning (DL)-based approaches on remaining useful life (RUL) prediction in practice or even precludes their application. Generating synthetic data that is physically plausible is a promising way to tackle this challenge. In this study, a novel hybrid framework combining the controlled physics-informed data generation approach with a deep learning-based prediction model for prognostics is proposed. In the proposed framework, a new controlled physics-informed generative adversarial network (CPI-GAN) is developed to generate synthetic degradation trajectories that are physically interpretable and diverse. Five basic physics constraints are proposed as the controllable settings in the generator. A physics-informed loss function with penalty is designed as the regularization term, which ensures that the changing trend of system health state recorded in the synthetic data is consistent with the underlying physical laws. Then, the generated synthetic data is used as input of the DL-based prediction model to obtain the RUL estimations. The proposed framework is evaluated based on new Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS), a turbofan engine prognostics dataset where a limited avail-ability of TTF trajectories is assumed. The experimental results demonstrate that the proposed framework is able to generate synthetic TTF trajectories that are consistent with underlying degradation trends. The generated trajectories enable to significantly improve the accuracy of RUL predictions., Comment: 22 pages,12 figures

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use of the inductive bias of the interdependencies between the different sensor measurements. However, there are some limitations with these GNN-based fault diagnosis methods. First, they lack the ability to realize multiscale feature extraction due to the fixed receptive field of GNNs. Secondly, they eventually encounter the over-smoothing problem with increase of model depth. Lastly, the extracted features of these GNNs are hard to understand owing to the black-box nature of GNNs. To address these issues, a filter-informed spectral graph wavelet network (SGWN) is proposed in this paper. In SGWN, the spectral graph wavelet convolutional (SGWConv) layer is established upon the spectral graph wavelet transform, which can decompose a graph signal into scaling function coefficients and spectral graph wavelet coefficients. With the help of SGWConv, SGWN is able to prevent the over-smoothing problem caused by long-range low-pass filtering, by simultaneously extracting low-pass and band-pass features. Furthermore, to speed up the computation of SGWN, the scaling kernel function and graph wavelet kernel function in SGWConv are approximated by the Chebyshev polynomials. The effectiveness of the proposed SGWN is evaluated on the collected solenoid valve dataset and aero-engine intershaft bearing dataset. The experimental results show that SGWN can outperform the comparative methods in both diagnostic accuracy and the ability to prevent over-smoothing. Moreover, its extracted features are also interpretable with domain knowledge.