To address the demand for real-time deformation monitoring of offshore fixed jacket structures, this paper presents an experimental study on displacement reconstruction based on the Static Condensation Inverse Finite Element Method (iFEM-S). A scaled jacket model was constructed and subjected to dynamic loading. An inverse finite element model, incorporating both the main structure and substructures, was established using inverse beam elements. Experimental validation confirms the effectiveness of iFEM-S under realistic operational conditions. The study also analyzes the impact of model fabrication errors, sensor installation deviations, and environmental noise on reconstruction accuracy. The results demonstrate that iFEM-S can effectively monitor the global and substructural responses of jacket platforms. Although local deformations near tubular joints lead to a slight overestimation of reconstructed values, the algorithm exhibits robust performance overall. This research provides experimental support and a theoretical reference for digital health monitoring and high-fidelity state assessment of offshore engineering structures.

Real-time deformation reconstruction and load identification are critical for developing high-fidelity digital twins of engineering structures, enabling early detection of structural anomalies and facilitating performance optimization under varying environmental and operational conditions. This study presents a unified inverse finite element method (iFEM) framework for reconstructing full-field deformation and identifying structural loads in real time based on strain measurements. The proposed approach was experimentally validated across different scenarios, including a metallic wing shaped plate, a composite shell, and a composite panel, under both quasi static and dynamic conditions using strain gauges and distributed fiber optic sensors (FOS). The results demonstrate that the iFEM successfully identified stress concentration regions in the metallic structure, confirming its capability for damage localization. For the composite shell, the method accurately captured high-fidelity displacement fields across both smooth and discontinuous strain regions. The method was further validated on a composite plate under dynamic sinusoidal excitations at 5, 8, 10, and 15 Hz, with displacement errors below 0.3 mm. These findings validate the proposed iFEM based framework as an effective tool for precise full-field deformation and load reconstruction, providing a robust foundation for physics based digital twins and real-time structural integrity assessment in aerospace and other engineering applications.

The inverse finite-element method (iFEM) is a promising approach to estimate wind and hydrodynamic loads on floating offshore wind turbines (FOWT). Accurate load estimation on such structures requires combining iFEM with a multi-body dynamical representation of the FOWT, due to the strong coupling between rigid-body motions, flexible structural dynamics, and external forces. This work presents the Muscade iFEM framework and its extension to multi-body systems. Muscade leverages automatic differentiation to compute mass and stiffness matrices, eigenmodes, and sensitivities of system responses, enabling efficient estimation of external loads from limited measurements. The framework is validated on three rotating systems: single- and double-arm flexible pendulums, and a simplified 2D rotor. Eigenmodes from automatic differentiation are compared with dynamic time-domain responses computed using Kane-method-derived finite elements, demonstrating the framework’s ability to capture coupled dynamics with minimal model complexity.

The inverse finite element method (iFEM) is formulated based on the strain-based weighted least-squares variational principle. Its primary advantage lies in utilizing measured strain data rather than predefined natural boundary conditions, thereby enabling structural health monitoring under complex environmental loadings. In this study, a Timoshenko beam-based iFEM model is presented for shape sensing of steel structures under seismic loading. A three-story steel frame structure with dimensions of 9 m × 6 m × 6 m subjected to seismic excitation from the 1995 Kobe earthquake is considered as a numerical example. The displacement responses reconstructed by the proposed iFEM model are compared with reference solutions obtained from LS-DYNA simulations. The results show good agreement in both time-history responses and spatial displacement distributions, with the majority of relative errors remaining within 5%. Meanwhile, the proposed iFEM model requires only 0.005 s of computational time per sampling step, demonstrating its capability for real-time shape sensing under seismic loading.

One of the critical challenges to the scalability, cost-effectiveness, and sustainability of floating offshore wind systems is the fatigue life of mooring lines, which are subjected to loads covering a wide range of amplitudes and frequencies.

Structural health monitoring of mooring lines requires accurate tension load history, which is obtained from strain gauges mounted at the fairlead level. However these measurements drift significantly over time and are affected by noise.
The present study aims at adressing this issue and performing real-time tension estimation of the mooring lines on a large 22MW floating wind turbine, subjected to wave and wind loads.
It is a purely numerical exercise: reference data is obtained from SIMA, a non-linear dynamic fluid-structure coupled solver. The resulting tension signals are artificially polluted with noise and bias, and serve as a starting point to the estimation problem.

The reconstruction of the tension is based on an inverse Finite Element method (iFEM). This method formulates an optimization problem with quadratic costs on deviation from measurements and on unknown parameters estimation, while equality constraints enforce the dynamic equilibrium.

Results shows fairly good tension estimation and good reconstruction of the model parameters with scarce measurements.

Ensuring the structural integrity of rotors is crucial in Structural Health Monitoring (SHM). Structural damage occurring in rotating shafts can alter both the mechanical properties and the load distribution, resulting in changes to the system’s dynamic behaviour. This work presents a numerical investigation into the implementation of the Inverse Finite Element Method (iFEM) for rotor condition monitoring. Within the framework of Euler–Bernoulli beam theory, the iFEM approach enables the reconstruction of the full three-dimensional displacement field through a 0^th-order inverse finite element beam formulation. Dynamic Finite Element (FE) analyses are employed to validate the performance of the proposed approach under varying boundary and loading conditions. To emulate realistic sensing conditions and determine the minimum detectable shaft unbalance, Gaussian noise is added to the strain data, replicating the measurement variability of Fiber Bragg Grating (FBG) sensors. Furthermore, a systematic approach is developed to identify the optimal trade-off between iFEM reconstruction accuracy and sensor network density for a given rotor configuration. The analyses confirm the robustness of the iFEM methodology in accurately reproducing the displacement field, highlighting its potential for online shaft monitoring. In addition, iFEM demonstrates high sensitivity to variations in structural properties. The results obtained establish a strong foundation for the advancement of iFEM-based SHM frameworks, extending the method’s applicability to new industrial applications.