Finite Element Model Updating Based on a Physics-Constrained Sparse Response Surface

Abstract

Accurate finite element models are essential for structural condition assessment, yet nominal material properties and idealized boundary conditions can produce systematic discrepancies between numerical and measured dynamics. This study proposes a physics-constrained sparse response-surface framework that combines Elastic Net basis selection, mechanically prescribed monotonicity, adaptive sample enrichment, and identifiability-aware uncertainty assessment within a transparent finite element model-updating procedure. A scaled steel truss was tested using millimeter-wave radar, and the first three vertical natural frequencies were identified by stochastic subspace identification. The resulting sparse polynomial surrogate was independently validated before bounded inversion and ANSYS back-substitution. The mean frequency error decreased from 5.55% to 0.82%. Jacobian and bootstrap analyses further showed that several combinations of material and boundary parameters can reproduce similar modal responses, so the updated parameters are best interpreted as a coupled equivalent calibration state rather than unique direct measurements. The proposed framework therefore improves physical consistency and computational efficiency while explicitly retaining the uncertainty associated with weakly identifiable parameter directions.