Abstract：In this paper, a new method for stable weighted mixture contraction of variables is proposed to address the problems of low prediction accuracy and poor interpretability of calibration models due to high spectral line dimensionality and many irrelevant variables when using attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectrometers for measuring solution concentrations in crystallization processes. The method first proposes a stable weighted variable population analysis (SWVCPA) with a random binary sampling of the spectral variables and a weighted evaluation of the selected frequencies of the variables in the established superior sub-models and the stability indicators of the regression coefficients of the variables in all sub-models. By ranking the importance of variables and using an exponentially decreasing function to gradually force the filtering out of variables of low importance during the iterative process, an initial contraction of the spectral variable space is achieved, and the stability of the contraction is substantially improved. Then a new Dynamic Sparrow Search Algorithm (DSSA) is continued on the shrunken subspace to optimize the combination of variables further using the minimization of the root mean square error of training prediction (RMSEC) as the fitness function. This hybrid optimization approach combines the advantages of both types of variable selection algorithms, ensuring the stability of the prior variable contraction through a sub-model competition approach, preventing the algorithm from falling into a local optimum, and avoiding the traversal search for the remaining variable combinations through an intelligent optimization algorithm, allowing more variables to be retained for accurate selection. ATR-FTIR spectral data collected at six different concentrations during the cooling and crystallization of L-glutamic acid solutions were tested. The results showed that the new method reduced the number of spectral variables from 613 to 46 and that the root mean square error of prediction (RMSEP) was reduced from 1.727 9 to 0.165 4, and the coefficient of determination of prediction (R2) improved from 0.973 7 to 0.999 7 for the partial least squares (PLSR) model built using the selected variables compared to the original spectra. Genetic algorithm (GA) and variable population combination analysis (VCPA) for selecting variables, the solution concentration prediction model developed using the new method has higher accuracy and stability, indicating the practical application of the method to improve the accuracy and reliability of measuring solution concentration in cooling crystallization processes using ATR-FTIR spectroscopy.
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