Sustainable Dyeing Process Modeling for Recycled PET/PCT Microfibers via Gaussian Process Regression

As the textile industry moves toward more sustainable and resource-efficient manufacturing, minimizing the experimental burden in dyeing processes has become increasingly critical. This study presents a Gaussian process regression (GPR)-based framework for predicting the colorimetric outcomes of dyeing processes involving ecofriendly fiber blends composed of recycled polyethylene terephthalate and polycyclohexylene dimethylene terephthalate. Using only 52 experimental data points, the model was trained to predict CIELAB color coordinates (L*, a*, b*) as well as the K/S value based on dyeing variables such as temperature, time, and dye concentration. The GPR model achieved high prediction accuracy with coefficients of determination (R ²) of 0.96, 0.96, 0.73, and 0.95 for L*, a*, b*, and K/S, respectively. Moreover, the probabilistic nature of GPR enables uncertainty quantification through posterior predictive distributions, offering both mean estimates and 95% confidence intervals. This capability supports robust decision-making in dyeing process design and quality control, especially in low-data regimes. The proposed approach demonstrates significant potential for reducing resource consumption and experimental iterations in fiber coloration, contributing to the development of data-efficient and environmentally sustainable dyeing systems.