Abstract
The reconstruction of structural deformation fields from sparse or indirect measurements represents a key challenge in structural health monitoring, particularly for real-time applications involving lightweight mechanical components. In linear elastic systems, any deformation state can be represented as a linear combination of structural mode shapes through modal superposition. Exploiting this property, the present work proposes a machine learning-based framework for the real-time reconstruction of the deflection field of an aluminium plate subjected to the impingement of a non-stationary water flow. The methodology combines modal superposition with a supervised Random Forest classifier trained on a database of known deformation states generated from a finite element model. For each deformation state, the retained modes are selected through a novel linear-regression-based criterion, in which the optimal modal subset is identified by simultaneously promoting a unit regression slope, a vanishing intercept, and a Pearson correlation coefficient close to unity between the reconstructed and reference deflection fields. The proposed strategy is compared with the previously developed Internal Strain Potential Energy Criterion (ISPEC), providing a direct comparison between an energy-based and a reconstruction-oriented mode selection approach. Experimental deflections are acquired through a vision-based displacement tracking system. Seven measurement points, located close to the clamped boundary and therefore far from the fluid excitation, are used as input to the reconstruction algorithm, whereas additional markers positioned closer to the fluid-loaded region are retained exclusively for validation, providing a more demanding assessment of the methodology. The classifier identifies the active modes from the measured deflection pattern, while the full-field structural response is recovered through modal superposition. Experimental validation demonstrates that the proposed regression-based approach consistently improves the reconstruction accuracy with respect to ISPEC. At the most demanding validation point, located closest to the fluid excitation, the mean reconstruction error is approximately 1.65mm for deflection amplitudes reaching 25mm, corresponding to an NRMSE of 10.60%, compared with 14.74% obtained using ISPEC, representing a reduction of 28.1%. Despite this improvement, the average computation time remains below 0.3ms, confirming the suitability of the proposed framework for real-time applications. These results demonstrate that the proposed methodology provides an accurate, computationally efficient, and robust solution for real-time full-field deformation estimation from sparse non-contact optical measurements.