Developing numerically accurate and practically scalable models is essential for effective Structural Health Monitoring (SHM) of railway infrastructure. Since finite element models inherently represent finite domains, absorbing boundary conditions such as Perfectly Matched Layers (PMLs) are commonly used to mitigate artificial wave reflections. However, the accuracy of the resulting receptance depends on both the PML thickness and the modelled track length, and their combined influence is rarely quantified. This study presents a systematic parametric investigation of 32 configurations covering four PML thicknesses and eight track lengths (6 to 48 sleepers) on a UIC60 ballasted track, analysed between 300 and 1500 Hz. Convergence is assessed using peak frequency shifts and a band-limited Frequency Response Assurance Criterion (FRAC), targeting a coupled rail-sleeper bending resonance near 400 Hz and the pinned-pinned resonance near 1040 Hz. Within the investigated range, PML thickness has only a marginal effect; track length is the dominant parameter. The minimum configuration satisfying the convergence thresholds consists of 30 sleepers and a PML thickness parameter η = 0.25 ( L_track = 18.0 m, L_PML = 0.3 m). Expressed in terms of the rail bending wavelength at the highest frequency of interest, this corresponds to a minimum track length of approximately 15 wavelengths, providing a wavelength-based convergence guideline that can support the design of similar track models.

The statistical finite element method (statFEM) has emerged has a new approach to performing uncertainty quantification over a domain. Assuming parameters of the system can be modelled as random fields, a probability density over the set of possible solutions can be obtained. In the context of static elasticity (structural) problems, one may intend to model the uncertainty over the deflection of a system, given some prior uncertainty over the Young's modulus. In standard finite element (FE) methods, it is common to use the solution to compute the stress and strain fields over the domain. In the context of statistical approaches, the uncertainty over the stress and strain fields would also be of particular interest. Nevertheless, computing this uncertainty can be challenging, with the computation of the stress field also being inherently dependent on the Young's modulus. In this work, the authors derive how to appropriately propagate the uncertainty from the solution to the stress and strain fields for statFEM and demonstrate its application on a simulated case study.

The interconnection between advanced instrumentation SHM and mechanical computations represents a major lever for the reliability and performance of industrial structures in operation.

It is also a key lever for opening up prospects for extending the service life of components.

In this context, the JUNAP project – Jumeau Numérique des Appareils à Pression - led by CETIM between 2021 and 2024, focused on digital twins (DT), is part of an innovative approach aimed at coupling predictive numerical mechanical simulations with real-time monitoring. The goal is to go beyond traditional methods by integrating data from Structural Health Monitoring (SHM) sensors — such as traditional strain gauges and two types of optical fibers gauges: Fiber Bragg grating (FBG) and distributed fiber — into adaptive numerical models.

This interconnection relies on a bidirectional loop, at different levels of the digital twin’s construction and development:

• on one hand, mechanical simulations identify critical areas to be instrumented, based on stress analyses and damage criteria;
• on the other hand, experimental measurements feed and adjust the models, thereby improving prediction accuracy.

This synergy paves the way for predictive maintenance strategies, where early detection of degradation and continuous updating of digital twins help optimize component lifespan.

Applied to pressure vessels, the digital twin appears as a reliable way to monitor operation, evaluate resistance and safety in real service conditions, and finally to capitalize on data to optimize the design of new products.

The presented work concerns an application of the digital twin concept to evaluate fatigue behaviour and optimize predictive maintenance of an industrial polymerization reactor. The steps involved in this work are:

• Design, manufacturing of the physical twin
• Optimize the deployment of SHM sensors for a smart, connected device
• Construction of the digital twin by hybridization of physical / data models, by conducting fatigue tests under representative loads

Modern Structural Health Monitoring (SHM) systems, combined with digital twins based on building information modelling and finite element analysis of civil, industrial, and military structures, are designed to enable early diagnosis and identification of damage. The complex highly inhomogeneous design of the structures and materials used, result in that neither unattenuated wave propagation can be assumed for a vibration-based monitoring, nor can every individual wave-reflecting or dissipating micro-defect be tracked separately within the global SHM framework. A structural intensity redistribution approach is proposed to determine the interconnected conductive and dissipative local structural properties as a measure of its current damage-related state. With this aim, a constitutive relation for structural intensity is proposed, that incorporates both the wave-propagation and dissipative characteristics of energy transport. A model for time-averaged structural intensity under dynamic steady-state conditions is formulated, which introduces energy resistivity as a measure of the damage-related structural properties. Energy resistivity experimental identification is realized using SHM data from a bridge equipped with accelerometers in three spans and subjected to shaker excitation and finite element modal analysis of its high-fidelity digital twin. The experimentally identified energy resistivity parameter has elevated values in bridge segments where damage is anticipated. Furthermore, it is shown to be sensitive to the current structural state, specifically regarding the stress levels within the pre-stressed tendon ducts.

Vibration-based techniques are widely used for structural parameter estimation and finite-element model updating. In large-scale structures, however, practical limitations on sensor deployment result in incomplete modal data, which severely restricts the applicability of conventional sensitivity-based updating methods. Existing sensitivity formulations often rely on mass-normalized mode shapes. In full-scale applications, mass normalization of incomplete measured modes is inherently unreliable because accurate mass matrices of undamaged or damaged structures are typically unavailable. Moreover, mass-normalized approaches require complete response measurements, including translational and rotational degrees of freedom, which are rarely attainable in practice. Although various data expansion and model-reduction techniques have been proposed to address data incompleteness, their effectiveness for accurate and robust model calibration remains limited. Hence, structural model updating based on the unnormalized mode shapes is of great interest.

This research introduces a novel sensitivity formulation that completely avoids the use of mass-normalized mode shapes. The proposed approach is based on arbitrary scaling of unnormalized incomplete mode shapes. It establishes a direct sensitivity relationship between measured modal data and structural parameter variations by selecting a single measured degree of freedom in each mode shape as a reference. This formulation enables finite-element model updating using incomplete modal data without requiring mass-normalized mode shapes, rotational measurements, modal expansion, or model reduction procedures. Additional data relationships are created by varying the selected degree of freedom for mode shape scaling. It increases the number of equations and mitigates the adverse effects of an ill-conditioned system, an issue in inverse methods. The method is validated through model updating of a frame structure. It demonstrates high accuracy and robustness even under substantial measurement and modeling errors, highlighting its suitability for real-world structural health monitoring and large-scale engineering applications. An example of the proposed model calibration, using incomplete and unnormalized mode shape data, produced accurate estimates of stiffness parameters, even in the presence of measurement and mass modeling errors, for structural model updating and damage assessment.

Keywords: Vibration measurements, modal data, unnormalized incomplete mode shapes, structural parameter estimation, finite element, model updating, innovative sensitivity equation