Reliable real-time analysis of sensor data is essential for structural health monitoring (SHM) of high-value assets, yet a major challenge is to obtain spatially resolved full-field aleatoric and epistemic uncertainties for trustworthy decision-making. We present an integrated SHM framework that combines principal component analysis (PCA), a Bayesian neural network (BNN), and Hamiltonian Monte Carlo (HMC) inference, mapping sparse strain gauge measurements onto leading PCA modes to reconstruct full-field strain distributions with uncertainty quantification. The framework was validated through cyclic four-point bending tests on carbon fiber reinforced polymer (CFRP) specimens with varying crack lengths, achieving accurate strain field reconstruction (R squared value > 0.9) while simultaneously producing real-time uncertainty fields. A key contribution is that the BNN yields robust full-field strain reconstructions from noisy experimental data with crack-induced strain singularities, while also providing explicit representations of two complementary uncertainty fields. Considered jointly in full-field form, the aleatoric and epistemic uncertainty fields make it possible to diagnose at a local level, whether low-confidence regions are driven by data-inherent issues or by model-related limitations, thereby supporting reliable decision-making. Collectively, the results demonstrate that the proposed framework advances SHM toward trustworthy digital twin deployment and risk-aware structural diagnostics.

Machine fault diagnosis (FD) is a critical task for predictive maintenance, enabling early fault detection and preventing unexpected failures. Despite its importance, existing FD models are operation-specific with limited generalization across diverse datasets. Foundation models (FM) have demonstrated remarkable potential in both visual and language domains, achieving impressive generalization capabilities even with minimal data through few-shot or zero-shot learning. However, translating these advances to FD presents unique hurdles. Unlike the large-scale, cohesive datasets available for images and text, FD datasets are typically smaller and more heterogeneous, with significant variations in sampling frequencies and the number of channels across different systems and applications. This heterogeneity complicates the design of a universal architecture capable of effectively processing such diverse data while maintaining robust feature extraction and learning capabilities. In this paper, we introduce UniFault, a foundation model for fault diagnosis that systematically addresses these issues. Specifically, the model incorporates a comprehensive data harmonization pipeline featuring two key innovations. First, a unification scheme transforms multivariate inputs into standardized univariate sequences. Second, a novel cross-domain temporal fusion strategy mitigates distribution shifts and enriches sample diversity and count, improving the model generalization across varying conditions. UniFault is pretrained on over 6.9 million samples spanning diverse FD datasets, enabling superior few-shot performance. Extensive experiments on real-world FD datasets demonstrate that UniFault achieves state-of-the-art performance, setting a new benchmark for fault diagnosis models and paving the way for more scalable and robust predictive maintenance solutions.

Energy estimation is critical to impact identification on aerospace composites, where low-velocity impacts can induce internal damage that is undetectable at the surface. Current methodologies for energy prediction are often constrained by data sparsity, signal noise, complex feature interdependencies, non-linear dynamics, massive design spaces, and the ill-posed nature of the inverse problem. This study introduces a physics-informed framework that embeds domain knowledge into machine learning through a dedicated input space. The approach combines observational biases, which guide the design of physics-motivated features, with targeted feature selection to retain only the most informative indicators. Features are extracted from time, frequency, and time-frequency domains to capture complementary aspects of the structural response. A structured feature selection process integrating statistical significance, correlation filtering, dimensionality reduction, and noise robustness ensures physical relevance and interpretability. Exploratory data analysis further reveals domain-specific trends, yielding a reduced feature set that captures essential dynamic phenomena such as amplitude scaling, spectral redistribution, and transient signal behaviour. Together, these steps produce a compact set of energy-sensitive indicators with both statistical robustness and physical significance, resulting in impact energy predictions that remain interpretable and traceable to measurable structural responses. Using this optimised input space, a fully-connected neural network is trained and validated with experimental data from multiple impact scenarios, including pristine and damaged states. The resulting model demonstrates significantly improved impact energy prediction accuracy, reducing errors by a factor of three compared to conventional time-series techniques and purely data-driven models.

Data for training structural health monitoring (SHM) systems are often expensive and/or impractical to obtain, particularly for labelled data. Population-based SHM (PBSHM) aims to address this limitation by leveraging data from multiple structures. However, data from different structures will follow distinct distributions, potentially leading to large generalisation errors for models learnt via conventional machine learning methods. To address this issue, transfer learning -- in the form of domain adaptation (DA) -- can be used to align the data distributions. Most previous approaches have only considered \emph{unsupervised} DA, where no labelled target data are available; they do not consider how to incorporate these technologies in an online framework -- updating as labels are obtained throughout the monitoring campaign. This paper proposes a Bayesian framework for DA in PBSHM, that can improve unsupervised DA mappings using a limited quantity of labelled target data. In addition, this model is integrated into an active sampling strategy to guide inspections to select the most informative observations to label -- leading to further reductions in the required labelled data to learn a target classifier. The effectiveness of this methodology is evaluated on a population of experimental bridges. Specifically, this population includes data corresponding to several damage states, as well as, a comprehensive set of environmental conditions. It is found that combining transfer learning and active learning can improve data efficiency when learning classification models in label-scarce scenarios. This result has implications for data-informed operation and maintenance of structures, suggesting a reduction in inspections over the operational lifetime of a structure -- and therefore a reduction in operational costs -- can be achieved.

Abstract: Addressing the core problem of insufficient trustworthiness in industrial fault diagnosis, stemming from the limitations of existing methods -- both traditional and deep learning - based -- in terms of interpretability, generalization, and uncertainty quantification, this paper proposes a trustworthy industrial fault diagnosis architecture, the Hierarchical Cognitive Arbitration Architecture (HCAA), which integrates probabilistic models with Large Language Models (LLMs). The architecture conducts a preliminary analysis via a diagnostic engine based on a Bayesian network and features an LLM - driven cognitive arbitration module with multimodal input capabilities. This module performs expert - level arbitration on the initial diagnosis by analyzing structured features and diagnostic charts, holding the priority to make the final decision upon detecting conflicts. To ensure the reliability of the system's output, the architecture integrates a confidence calibration module based on Temperature Scaling and a risk assessment module, which objectively quantify system trustworthiness using metrics like Expected Calibration Error (ECE). Experimental results on a dataset containing multiple fault types demonstrate that the proposed framework improves diagnostic accuracy by over 28 percentage points compared to baseline models, while the post - calibration ECE is reduced by more than 75%. Case studies confirm that the HCAA effectively corrects misjudgments from traditional models caused by complex feature patterns or knowledge gaps, providing a novel and practical engineering solution for building high - trust, explainable AI diagnostic systems for industrial applications. Keywords: Industrial Fault Diagnosis; Large Language Model (LLM); Hierarchical Cognitive Arbitration; Probabilistic Model; Confidence Calibration; Trustworthy AI 1. Introduction With the deep development of Industry 4.0 and smart manufacturing concepts, modern industrial systems are evolving towards high levels of automation and intelligence. In this process, the reliability and safety of equipment have become key factors determining production efficiency and operational costs. Prognostics and Health Management (PHM), as a core technology, plays an indispensable role in improving equipment reliability, reducing unplanned downtime, and optimizing maintenance costs by monitoring equipment status in real - time, diagnosing potential faults, and predicting remaining useful life [1], [2].

Equation discovery provides a grey-box approach to system identification by uncovering governing dynamics directly from observed data. However, a persistent challenge lies in ensuring that identified models generalise across operating conditions rather than over-fitting to specific datasets. This work investigates this issue by applying a Bayesian relevance vector machine (RVM) within a multi-task learning (MTL) framework for simultaneous parameter identification across multiple datasets. In this formulation, responses from the same structure under different excitation levels are treated as related tasks that share model parameters but retain task-specific noise characteristics. A simulated single degree-of-freedom oscillator with linear and cubic stiffness provided the case study, with datasets generated under three excitation regimes. Standard single-task RVM models were able to reproduce system responses but often failed to recover the true governing terms when excitations insufficiently stimulated non-linear dynamics. By contrast, the MTL-RVM combined information across tasks, improving parameter recovery for weakly and moderately excited datasets, while maintaining strong performance under high excitation. These findings demonstrate that multi-task Bayesian inference can mitigate over-fitting and promote generalisation in equation discovery. The approach is particularly relevant to structural health monitoring, where varying load conditions reveal complementary aspects of system physics.

The diagnosis of induction machines has traditionally relied on model-based methods that require the development of complex dynamic models, making them difficult to implement and computationally expensive. To overcome these limitations, this paper proposes a model-free approach using Graph Neural Networks (GNNs) for fault diagnosis in induction machines. The focus is on detecting multiple fault types -- including eccentricity, bearing defects, and broken rotor bars -- under varying severity levels and load conditions. Unlike traditional approaches, raw current and vibration signals are used as direct inputs, eliminating the need for signal preprocessing or manual feature extraction. The proposed GNN-ASE model automatically learns and extracts relevant features from raw inputs, leveraging the graph structure to capture complex relationships between signal types and fault patterns. It is evaluated for both individual fault detection and multi-class classification of combined fault conditions. Experimental results demonstrate the effectiveness of the proposed model, achieving 92.5\% accuracy for eccentricity defects, 91.2\% for bearing faults, and 93.1\% for broken rotor bar detection. These findings highlight the model's robustness and generalization capability across different operational scenarios. The proposed GNN-based framework offers a lightweight yet powerful solution that simplifies implementation while maintaining high diagnostic performance. It stands as a promising alternative to conventional model-based diagnostic techniques for real-world induction machine monitoring and predictive maintenance.

Accurate estimation of Remaining Useful Life (RUL) and State of Health (SOH) is essential for Prognostics and Health Management (PHM) across a wide range of industrial applications. We propose a novel framework -- Reinforced Graph-Based Physics-Informed Neural Networks Enhanced with Dynamic Weights (RGPD) -- that combines physics-based supervision with advanced spatio-temporal learning. Graph Convolutional Recurrent Networks (GCRNs) embed graph-convolutional filters within recurrent units to capture how node representations evolve over time. Graph Attention Convolution (GATConv) leverages a self-attention mechanism to compute learnable, edge-wise attention coefficients, dynamically weighting neighbor contributions for adaptive spatial aggregation. A Soft Actor-Critic (SAC) module is positioned between the Temporal Attention Unit (TAU) and GCRN to further improve the spatio-temporal learning. This module improves attention and prediction accuracy by dynamically scaling hidden representations to minimize noise and highlight informative features. To identify the most relevant physical constraints in each area, Q-learning agents dynamically assign weights to physics-informed loss terms, improving generalization across real-time industrial systems and reducing the need for manual tuning. In both RUL and SOH estimation tasks, the proposed method consistently outperforms state-of-the-art models, demonstrating strong robustness and predictive accuracy across varied degradation patterns across three diverse industrial benchmark datasets.

Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the Lilleb{\ae}lt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.

A Nonlinear Auto-Regressive with eXogenous inputs (NARX) model can be used to describe time-varying processes; where the output depends on both previous outputs and current/previous external input variables. One limitation of NARX models is their propensity to overfit and result in poor generalisation for future predictions. The proposed method to help to overcome the issue of overfitting is a NARX model which predicts outputs at both the current time and several lead times into the future. This is a form of multi-task learner (MTL); whereby the lead time outputs will regularise the current time output. This work shows that for high noise level, MTL can be used to regularise NARX with a lower Normalised Mean Square Error (NMSE) compared to the NMSE of the independent learner counterpart.