An Advanced Stochastic 1D Inverse Finite Element Method for Strain Extrapolation with Experimental Validation

The Inverse Finite Element Method (iFEM) is a valuable tool for reconstructing displacement fields from strain measurements, making it ideal for structural health monitoring. Traditional iFEM approaches are deterministic and typically require dense sensor networks for accurate results. However, practical constraints—such as limited sensor placement and cost—call for robust extrapolation techniques to estimate strain in non-instrumented regions. This paper proposes a stochastic 1D iFEM framework that integrates uncertainty quantification into the strain extrapolation process. By assigning confidence weights to extrapolated values, the method enhances the reliability of displacement reconstruction in sparsely instrumented structures. The approach is validated through numerical and experimental studies, demonstrating improved accuracy and robustness compared to traditional interpolation methods, even under varying loading conditions. The results confirm the method’s suitability for real-world applications in aerospace, civil, and naval engineering, particularly when direct strain measurements are limited.