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JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences // Archive

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2025 Volume 29, Number 1, Pages 174–186 (Mi vsgtu2120)

Short Communication
Mathematical Modeling, Numerical Methods and Software Complexes

Development of a predictive model for two- and three-component inorganic systems in aqueous solutions using spectral analysis

K. Y. Massalova, E. Yu. Moshchenskayab

a National Engineering Physics Institute "MEPhI", Moscow, 115409, Russian Federation
b Samara State Technical University, Samara, 443100, Russian Federation

Abstract: This study presents an algorithm for analyzing spectral data through mathematical modeling, constructing prognostic models, and selecting optimal wavelength intervals for designing LED-based multisensor systems. The algorithm is implemented in Python and validated using experimental data from aqueous solutions of inorganic salts.
Key methodological aspects include:
– Application of multivariate calibration methods (PLS regression and multiple linear regression);
– Utilization of Shapley values to identify informative spectral wavelengths;
– Systematic enumeration to determine optimal wavelength intervals.
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The developed model enables accurate prediction of two- and three-component systems in metal salt solutions using partial spectral data rather than full-spectrum analysis. Cross-validation demonstrates that:
– The model achieves comparable accuracy to full-spectrum approaches;
– The solution remains computationally efficient while maintaining predictive reliability.
The results confirm the model's adequacy for quantitative spectral analysis, particularly in resource-constrained environments where partial spectral data acquisition is advantageous.

Keywords: multivariate calibration, PLS regression, spectral interval selection, metal ion quantification, Shapley values, chemometrics

UDC: 519.24:543.5:544.3

MSC: 65C20, 62P99, 92E20

Received: October 9, 2024
Revised: February 11, 2025
Accepted: February 21, 2025
First online: April 11, 2025

DOI: 10.14498/vsgtu2120



© Steklov Math. Inst. of RAS, 2025