A novel 1D iFEM framework for structural health monitoring under degrading boundary conditions

The inverse finite element method (iFEM) reconstructs full-field displacements from strain data without prior knowledge of loads or material properties. However, unknown or time-varying boundary conditions can degrade shape-sensing accuracy. This work advances smart sensing and structural health monitoring for beam-like structures by coupling iFEM with an online identification of boundary-condition degradation. An aluminum beam instrumented with an fiber Bragg grating sensor network is tested under controlled degradations—rotational stiffness reduction and vertical support settlement—each modeled as a virtual spring with unknown stiffness. A nonlinear optimization routine estimates the spring parameters while iFEM performs real-time shape reconstruction. Results show high-accuracy displacement fields and reliable quantification of support degradation, with a maximum deviation of about 10% from ground truth for both rotational and vertical cases. The framework demonstrates practical feasibility for simultaneous shape sensing and boundary-condition assessment in operational environments.