A Statistical Framework for Nonlinear Calibration of a Single FBG Sensor Under Coupled Pressure–Temperature Loading

Fiber Bragg Grating (FBG) sensors are widely used to measure pressure and temperature. However, when both are subjected to a coupled environment, the Bragg wavelengths influence each other, causing biased measurements if not properly calibrated. Most calibration models assume linear sensitivity, which may not hold across the entire operating range. This study proposes a five-step statistical calibration framework for a single FBG sensor under coupled pressure–temperature conditions: data preparation; fitting linear, quadratic, and cubic models; model selection using AIC/BIC; local sensitivity calculation; and contribution decomposition via Response Surface Methodology (RSM). The framework was tested on experimental data from an FBG sensor mounted on a metal membrane, at pressures of 0 MPa–2.0 MPa and temperatures of 5 °C–45 °C. Nonlinear models outperformed linear ones, with R¯2 values of 0.9725–0.9992. The model was validated using Leave-One-Out Cross-Validation (LOOCV), yielding an out-of-sample RMSE (Root Mean Square Error) of 0.0452 nm. Pressure sensitivity remained constant at 0.2250 nm/MPa, while temperature sensitivity decreased from 0.0224 nm/°C at 5 °C to 0.0069 nm/°C at 45 °C. RSM showed that pressure influences the slope and temperature influences the offset, with no significant interaction. Residual analysis satisfied the regression assumptions, and the combined uncertainty (0.008 nm/MPa; 0.0003 nm/°C) was much smaller than the observed sensitivity range, confirming that the variations are physical, not instrument noise. This framework is practical and statistically sound for single FBG sensor calibration.