Dielectric spectroscopy technology combined with machine learning methods for nondestructive detection of protein content in fresh milk

To quickly achieve nondestructive detection of protein content in fresh milk, this study utilized a network analyzer and an open coaxial probe to analyze the dielectric spectra of milk samples at 100 frequency points within the 2–20 GHz range, focusing on the dielectric constant ε' and the dielectric loss factor ε''. Feature variables were extracted from the full dielectric spectra using the successive projections algorithm (SPA), uninformative variables elimination (UVE), and the combined UVE-SPA method. These variables were then used to develop partial least squares regression (PLSR), support vector machine (SVM), decision tree (DT), random forest (RF), and least squares boosting (LSBOOST) models for predicting protein content. The results showed that ε' decreased monotonically with increasing frequency, while ε'' increased monotonically. The UVE-SPA method for feature extraction demonstrated superior performance, with the UVE-SPA-PLSR model being the best for predicting milk protein content, achieving the highest R_C² = 0.998 and R_P² = 0.989 and the lowest RMSEC = 0.019% and RMSEP = 0.032%. This study provides a theoretical reference for evaluating milk quality and developing intelligent detection equipment for natural milk.