Hierarchical Error Suppression for High-Precision Displacement Reconstruction in OFDR-Based Distributed Inclinometers

Abstract

Distributed optical fiber sensing (DOFS) based on optical frequency domain reflectometry (OFDR) provides millimeter-scale spatial resolution for distributed deformation monitoring in geotechnical infrastructure. However, the enhanced sensitivity of OFDR also makes measured strain fields vulnerable to localized nonphysical anomalies, which can propagate through strain-to-displacement conversion and induce cumulative reconstruction errors over long sensing distances. To address this challenge, a hierarchical error suppression framework integrating isolation forest (IF)-based anomaly detection and piecewise cubic Hermite interpolating polynomial (PCHIP) reconstruction is proposed to identify localized strain anomalies and restore the continuity and mechanical admissibility of distributed strain fields. The error propagation characteristics of four representative displacement reconstruction algorithms, including the trapezoidal integration method (TIM), difference element method (DEM), conjugate beam method (CBM), and beam element method (BEM), are systematically investigated. Experimental validation using a 72-m laboratory cantilever demonstrates that the proposed framework effectively reduces cumulative reconstruction errors, with BEM achieving the largest improvement and reducing the root mean square error (RMSE) from 1.03 to 0.24 cm. A field deployment in a 12-m-deep foundation pit in Nanjing further verifies the engineering applicability of the proposed approach, achieving an RMSE of 0.28 mm relative to reference MEMS inclinometer measurements. The results demonstrate that physically consistent strain-field reconstruction is essential for improving the accuracy and reliability of long-distance distributed deformation monitoring based on OFDR.