Non-Destructive Structural Deformation Reconstruction via Data-Driven Modal Superposition

Modal superposition enables efficient estimation of full-field structural displacements from sparse measurements, forming a keystone of structural health monitoring (SHM) in linear elastic systems. Accurate reconstruction critically depends on selection of the most relevant vibration modes, traditionally guided by the Internal Strain Potential Energy Criterion (ISPEC), which identifies modes contributing most to internal strain energy. However, the purely analytical formulation of ISPEC requires full knowledge of the deformation field, limiting its applicability in real-time monitoring. This study extends ISPEC using supervised machine learning to enable adaptive mode selection for previously unseen deformation states. A Random Forest classifier is trained on synthetic deformation data generated from a finite element model of a square steel plate. Measurement signals are obtained from a transient analysis in which harmonic displacements are applied to four nodes at the plate plane. Reconstruction performance is evaluated numerically by comparing predicted displacements against reference finite element solutions, using instantaneous residuals, normalised root-mean-square error (NRMSE) and normalised cross-correlation. Results demonstrate that the hybrid ISPEC–machine learning approach accurately reconstructs full-field deflections from eight measurement nodes, with NRMSE typically below 5% and cross-correlation above 0.75. Minor overestimation at peak deflections indicates conservative predictions, while computational efficiency allows real-time implementation.