Inference of pile capacity from distributed strain sensing via PDE-constrained optimization

Distributed fiber-optic sensing (DFOS) provides high-resolution, continuous strain measurements along piles, offering new opportunities for detailed assessment of pile quality and soil–structure interaction. However, field DFOS data often exhibit oscillatory patterns traditionally treated as noise, obscuring actual physical insights into variations in pile radius and shaft friction for example. To address this challenge, we propose a numerical framework that formulates the strain-matching problem as a partial differential equation constrained optimization (PDECO) problem. This approach not only infers pile quality and soil response profiles from noisy DFOS data, but also rigorously enforces mechanical equilibrium at each loading step, yielding a physically consistent interpretation of high-resolution distributed measurements.Numerical benchmarks and application to a DFOS-monitored pile load test demonstrate that the PDECO scheme is robust to measurement noise and capable of reconstructing spatially continuous profiles of pile rigidity, soil stiffness, and shaft friction. Comparisons with independent Thermal Integrity Profiling results further validate the inferred pile radius variations, confirming the method’s effectiveness for detailed pile integrity assessment. Overall, the proposed framework advances pile evaluation by moving beyond traditional layered models and black-box optimization, enabling a more accurate and physically grounded interpretation of DFOS data. Overall, this study establishes a mathematically rigorous approach for high-resolution pile monitoring using distributed sensing technologies.