The present work proposes a multiresolution (MR) reduced order model (ROM) based on Krylov subspace techniques with a focus on parameter estimation and digital twin applications. The multiresolution finite wavelet domain (MR-FWD) method is utilised as the basis modelling method, and it is reduced by the second order Arnoldi iteration (SOAR) algorithm. The structure of the discretised algebraic system of the MR-FWD method is preserved, and thus, the coarse and fine solutions of the multiresolution wavelet Galerkin approximation are available after the reduction. Interestingly, the reduced fine solutions preserve the localisation and isolation capabilities of the full model’s fine solutions, showcasing their potential to be used in model update procedures. The proposed MR-ROM is evaluated in a wave-based structural identification case study, where full-field data from a guided wave experiment in a composite plate are acquired. The measurements are decomposed into detail and approximation datasets following the discrete wavelet transform. The detail dataset(s) can be correlated with the fine solution(s) of ROM results to estimate the involved design parameters through model updating. The measurement data can also be utilised through comparisons with the total solution of the MR-ROM. Through this multiresolution updating, the parameter estimation process can be more accurate due to the filtering capacity of the multiple components, and with the synergy of SOAR reduction, the physics-based numerical part of the envisioned digital twins can approximate real-time performance.

Unexpected failures and inefficient maintenance plans lead to costly downtime in many industrial fields, undermining operational sustainability and overall profitability, or, in the worst scenarios, creating unsafe situations for people. These issues justify a shift towards predictive maintenance, and structural health monitoring (SHM) has emerged as a viable option. By exploiting modern hardware and software technologies, the diagnosis and prognosis of monitored structures can be performed while accounting for estimation uncertainty. In addition, for complex structures, monitoring all components is not feasible for technical or economic reasons, and a mix of condition and schedule-based maintenance approaches is still required. To fully exploit the SHM benefits, an effective decision-making process is necessary, including Opportunistic Maintenance (OM) that accounts for both scheduled stops and the Residual Useful Life (RUL) predicted by prognostic models. In this context, decision-making becomes significantly more complex when managing an entire fleet rather than a single asset, reflecting the real-world challenges companies face.
This study explores the application of Reinforcement Learning (RL) to automated decision-making in aircraft fleet maintenance, aiming to minimise operational and maintenance (O&M) life-cycle costs. The RL agent is trained and deployed within a fleet life cycle simulator that replicates real-world conditions, including mission schedules, maintenance operations, repair bases with varying capabilities, and potential unforeseen events. Each aircraft is modelled as an ensemble of subcomponents, with only a portion equipped with an SHM system that provides Remaining Useful Life (RUL) predictions, expressed as probability distributions, and fault detection. The agent leverages this data to develop an optimal maintenance policy, aligning scheduled stops for non-monitored components with necessary interventions for monitored parts. Specifically, it determines maintenance schedules and selects which components to replace based on fleet-wide data, expected mission schedules, and aircraft availability.
While the study is demonstrated using a fleet life-cycle simulator, it serves as a preliminary step toward the real-world implementation of autonomous agents. The integration of the agent within the fleet simulator, potentially based on a real scenario, enhances its capabilities as a Digital Twin, supporting management decisions. Furthermore, it leverages the potential benefits of SHM technology, encouraging broader industry adoption.

Virtual sensing techniques, or soft sensing, aim at reconstructing physical quantities at locations where no direct measurements are available, enabling a complete representation of a system from sparse sensor information. These methods rely on the synergy between the measurement data, physics- or knowledge-based models, and statistical characterization of uncertainties. In recent years, virtual sensing has been consolidated into a broad set of approaches that include inverse finite-element formulations, data-driven methods, and control theory-based estimators. Among the latter, proportional observers (PO) and their multi-resolution extensions (MRPO) offer a practical alternative to Kalman-filters and “natural observers”. Their simple formulation, combined with frequency-band tuning, balances computational burden, noise robustness, and reconstruction accuracy.

This paper presents an observer-based virtual sensing (OB-VS) framework for reconstructing strain fields in ship structures using a limited number of physical sensors. The approach builds on PO and MRPO, exploiting linear relations between the measurement vector and the estimated state-space variables. The method leverages the mechanical transfer function of the structure and a statistical description of uncertainties in the frequency domain, including measurement noise, modelling inaccuracies, and unknown excitation. A key advantage of the PO formulation is that the prediction-error covariance matrix depends quadratically on the observer gain(s), ensuring the existence of a unique global minimum. The MRPO enhances this approach by defining multiple POs, each one tailored for a specific frequency band into which the signal is decomposed via wavelet multi-resolution analysis.

The methodology is applied to the experimental dataset relative to an elastic scaled ship-model campaign, performed within the “Digital Ship Structural Health Monitoring project” (dTHOR), granted by the European Defence Fund, aimed at developing a system based on innovative utilization of extensive on-board measurements, a comprehensive digital framework, and hybrid analysis and modelling. Measurements from 13 strain-gauges were utilized. Stepping forward with respect to previous 1D models, the present analysis employs a full 3D finite-element (FE) representation of the segmented hull. The observer is trained by extracting modal quantities from the FE solution (modal strains, modal mass, damping, and stiffness matrices) and constructing the corresponding transfer function. Because the FE model represents the dry hull, a correction is introduced to ensure consistency between numerical and experimental modal characteristics. The external (wave) excitation is estimated by combining acceleration, strain and rigid-body motion data.

Performance is evaluated by computing the errors in signal reconstruction both in time (Time Response Assurance Criterion) and frequency (Frequency Response Assurance Criterion). Both PO and MRPO achieve a high fidelity in predicting the strains measured by sensors not involved in the virtual sensing process. An a-posteriori comparison of several sensor layouts highlights the possibility of achieving an optimal trade-off between instrumentation effort and reconstruction accuracy based on end-user needs. The OB-VS approach keeps accurate in signal tracking even under incorrect assumptions on the external excitation, thus demonstrating its robustness.

Overall, this study highlights the potential of multi-resolution analysis for improving robustness to noise and spectral representation for real-time observer-based virtual sensing, enabling predictive digital-twin capabilities not only limited to on-board monitoring of ship structures.

Wind turbine blades are critical structural components of the machine, responsible for capturing the kinetic energy of the wind and transferring it to the rotor shaft for conversion into electrical power. Throughout their operational life, they are subjected to complex combinations of static and dynamic loads. Self-weight, rotational forces, aerodynamic interaction, and transient wind effects generate continuously varying stress states. In addition to mechanical loading, blades are exposed to environmental degradation mechanisms such as ice formation, surface contamination, lightning strikes, manufacturing defects, and erosion due to harsh weather conditions. These factors progressively alter the aerodynamic behaviour of the blade, increase internal stresses, and raise the probability of severe structural damage or system-level failure.

The financial impact of such failures is significant. Downtime, repair operations, logistics for offshore interventions, and potential turbine replacement represent major economic risks for operators and investors. The increasing scale of turbines and the expansion of offshore wind farms further amplify these risks, as both structural complexity and intervention costs grow substantially. Although conventional Structural Health Monitoring (SHM) systems provide useful local measurements, they often deliver fragmented information that does not fully capture the global structural response. As a result, accurately estimating fatigue accumulation, structural degradation, and Remaining Useful Life (RUL) remains a challenge.

To address this limitation, an integrated digital twin framework is proposed, combining multiple data sources to provide a comprehensive representation of the blade’s structural behaviour. Among these data sources, advanced laser-based geometric measurements are incorporated as a key input for capturing high-resolution information on blade deflection and global dynamic response under real operating conditions.

These laser-derived measurements, together with other operational and structural inputs, feed a physics-informed digital twin of the blade. The digital model integrates real-time and historical data, enabling calibration of structural parameters and continuous updating of boundary conditions. Machine Learning techniques are applied to enhance predictive capability, allowing accurate modelling of fatigue evolution, detection of anomalous behaviour, and estimation of Remaining Useful Life.

By integrating high-fidelity geometric measurements into the digital twin environment, the system enables condition-based maintenance strategies, early anomaly detection, and optimization of turbine operation. This approach reduces operational risk, minimizes downtime, and improves long-term asset performance without relying on invasive inspection techniques. The following sections describe the methodological framework for data integration, digital twin calibration strategies, and the performance improvements achievable through advanced data-driven structural modelling.

Circular hollow sections (CHS) are ubiquitous within civil infrastructure, serving as common structural members within bridges, floating platforms and wind turbine supporting structures. Throughout their service lives, these structures withstand cyclical loading arising from a combination of environmental and live loads, increasing their susceptibility to fatigue cracks especially at welded joints. Hence, accurate crack sizing is essential for structural health monitoring and fatigue reliability assessment. Monitoring variations in the local strain compliance neighbouring the weldments serve as reliable indicators of crack size. The relationship between strain compliance and crack size may be elucidated from numerical solutions and modelled with machine learning algorithms. As a result, data-driven models, trained on synthetic data generated from numerical simulations, have emerged as popular engines to create digital twins for structural health monitoring.

These models, however, often suffer from domain shift, where the statistical properties of the target domain (e.g., real-world structures) diverge from those of the source domain (e.g., finite element simulations). This discrepancy undermines model generalization, where models perform well within the source domain but yield low accuracy in the target domain. In welded CHS joints, domain shift becomes particularly critical as strain responses captured in simulations do not always reflect those of experimental or field conditions due to uncertainties in the loading environment, material properties and construction quality. To address this challenge, this paper proposes a novel extrapolative crack sizing framework that enables fatigue crack monitoring in CHS X-joints under domain-shifted conditions. This framework first employs the Siamese neural network, which learns to embed both source and target strain field inputs into a shared low-dimensional latent space. The source and target embeddings are aligned at minimal known states, i.e., ground truths of cracked and uncracked conditions, by minimizing the contrastive loss function. Once aligned, crack size estimation in the target domain proceeds via a k-nearest neighbor search in the latent space, leveraging similarities with source domain embeddings. To ensure reliable extrapolation, the framework includes a latent space distance metric that quantifies confidence in the predictions and guides decisions on further ground truth data collection to refine domain alignments.

The framework is validated using two fatigue test cases, one each under high- and low-cycle fatigue loading, featuring geometrically similar and dissimilar domain pairings. The results demonstrate the framework’s capability to accurately track crack growth with minimal target domain supervision, even under significant geometric variation. The success of this study highlights the proposed framework’s potential for population-based structural health monitoring across diverse welded joint configurations.