A high-precision tensile and compressive strain calibration method based on Lagrange polynomial interpolation for FBG strain sensors

FBG strain sensor calibration need to move beyond linear tensile models to address practical compression and nonlinearities from shear lag and material behavior. In this paper, a high-precision tensile and compressive strain calibration method based on Lagrange polynomial interpolation for FBG strain sensors is proposed. A surface-mounted FBG strain sensor and an FBG temperature sensor were designed. A specialized thin-walled cylindrical calibration device was developed, capable of withstanding large tensile and compressive strains. A tensile and compressive strain calibration experimental system was constructed, applying 11 strains covering over ± 5000με for strain calibration model fitting or interpolation, followed by 10 additional strains for error evaluation. The experimental results show that the strain sensitivity coefficient is 1.21pm/με, and the maximum strain measurement error is 1.9% when using the traditional strain calibration method. In the proposed method, 11 strains are divided into two parts for segmented Lagrange polynomial interpolation. More accurate strain of the FBG strain sensor can be obtained by using the proposed method. The maximum strain measurement error is 0.9% by compare with the strain measured by the resistance strain gauge. The proposed method effectively reduces the strain measurement error of the FBG strain sensor by introducing a nonlinear strain calibration model.