The Inverse Finite Element Method (iFEM) is a valuable tool for reconstructing displacement fields from strain measurements, making it well suited for structural health monitoring. Traditional iFEM formulations are deterministic and typically rely on dense sensor layouts to achieve accurate reconstructions. However, practical constraints—such as limited accessibility, sensor-placement restrictions, and cost—often lead to sparse instrumentation, motivating the need for robust extrapolation strategies to estimate strain in non-instrumented regions. This paper proposes a stochastic one-dimensional iFEM framework that extends the capabilities of classical deterministic iFEM by embedding uncertainty quantification into the strain extrapolation stage through a Gaussian process regression (GPR)-based regression model. The predictive confidence provided by GPR is used to assign spatially varying weights to the iFEM inputs, thereby down-weighting highly uncertain extrapolated values and improving the overall robustness of the displacement reconstruction. The proposed framework is demonstrated exclusively through experimental measurements on a simple yet representative aluminum-beam case study, considering several healthy and damaged scenarios. A fiber Bragg grating-based layout is installed and subsequently optimized in terms of the number and location of measurement points. The resulting reduced-sensing configurations are handled via GPR-based strain reconstruction and confidence-weighted iFEM, and the same setup is further used to showcase damage identification capabilities through a load-independent anomaly-index strategy. The experimental results indicate improved accuracy and stability compared to conventional interpolation-based approaches, even under different loading and boundary-condition scenarios, supporting the applicability of the method to real-world aerospace, civil, and naval structures where direct strain measurements are limited.
Bardiani et al. (Mon,) studied this question.