Abstract
Accurate calibration of spectroscopic measurements is essential for reliable real-time monitoring and control of crystallization processes. In this work, calibration strategies for Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) spectroscopy were systematically evaluated for concentration monitoring in batch cooling crystallization of paracetamol in ethanol. Linear regression (LR), Partial Least Squares Regression (PLSR), Principal Component Regression (PCR), and symbolic regression (SR) were compared using both peak-based features and full spectral representations. Peak-based models provided a transparent baseline, with peak-area-based models consistently outperforming peak-height-based models. For LR, incorporating multiple absorption bands reduced the mean squared error (MSE) by nearly one order of magnitude compared to single-peak models. Using the same peak-based inputs, SR further improved performance, reducing prediction bias at high concentrations and yielding higher coefficients of determination (R² > 0.99) compared to LR. A substantial improvement was achieved when full spectral information was used. Among all evaluated approaches, SR with unprocessed spectra yielded the best overall performance, achieving an R² of 0.996 and an MSE of 1.4 × 10?6 on the validation dataset. This model also demonstrated strong generalization on an independent solubility test dataset, closely reproducing the reference solubility curve over the full temperature range with minimal deviation. In contrast, PCR and PLSR models showed increased sensitivity to preprocessing choices and exhibited larger errors on the test dataset. SR provided an accurate, robust, and interpretable calibration framework for ATR-FTIR, with reduced reliance on spectral preprocessing and potential for real-time process analytical technology and control applications.