Comparison and Internal Cross-Validation of Segmented and Conventional Calibration Models for a Near-Infrared Nephelometric Turbidity Sensor

Calibration of nephelometric turbidity sensors is often performed with a single linear regression, which is inadequate when sensor sensitivity changes across the measurement range, particularly in the metrologically critical region below 1 FNU. This work compares eight calibration models, namely linear, quadratic, power, saturating exponential, hyperbolic, continuous segmented, cubic spline and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), applied to the raw response of a near-infrared probe operated in the ISO 7027 configuration (860 nm, detector at 90°) over 22 turbidity levels between 0 and 20 FNU. Predictive capability was assessed using leave-one-concentration-level-out cross-validation on the 20 internal levels; this constitutes internal cross-validation of the calibration models on the acquired dataset. Breakpoint selection was based on the Davies test, the Bayesian information criterion and a grid of candidate midpoints, with the same monotone inversion applied to all models. Linear regression yielded the largest error under all conditions (RMSE 1.45–3.21 FNU); no single model performed best in every case, but segmented regression reduced the error by 66–70% relative to linear regression and remained among the best-performing models in the ≤1 FNU region, providing slopes and breakpoints that can be interpreted in terms of sensitivity regimes. The number of regimes was stable across folds, whereas the locations of some individual breakpoints showed substantial fold-to-fold variability. Model choice depends on the shape of the response, the variance structure and the density of levels; segmented regression offers a favourable trade-off between accuracy, interpretability and ease of implementation in embedded systems.