<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="brief-report" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences</journal-id><journal-title-group><journal-title xml:lang="en">Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences</journal-title><trans-title-group xml:lang="ru"><trans-title>Вестник Самарского государственного технического университета. Серия «Физико-математические науки»</trans-title></trans-title-group></journal-title-group><issn publication-format="print">1991-8615</issn><issn publication-format="electronic">2310-7081</issn><publisher><publisher-name xml:lang="en">Samara State Technical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">636857</article-id><article-id pub-id-type="doi">10.14498/vsgtu2120</article-id><article-id pub-id-type="edn">ZDTCBW</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Short Communications</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Краткие сообщения</subject></subj-group><subj-group subj-group-type="article-type"><subject>Short Communication</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Development of a predictive model for two- and three-component inorganic systems in aqueous solutions using spectral analysis</article-title><trans-title-group xml:lang="ru"><trans-title>Построение модели для прогнозирования двух- и трехкомпонентных неорганических систем в водных растворах спектральным анализом</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0003-6214-7470</contrib-id><name-alternatives><name xml:lang="en"><surname>Massalov</surname><given-names>Kirill Y.</given-names></name><name xml:lang="ru"><surname>Массалов</surname><given-names>Кирилл Юрьевич</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Master’s Student; Senior Researcher; Dept. of Elementary Particle Physics; Institute of Nuclear Physics and Engineering</p></bio><bio xml:lang="ru"><p>магистрант; каф. физика элементарных частиц; институт ядерной физики и технологий</p></bio><email>kirill.massalov@yandex.ru</email><uri>https://www.mathnet.ru/person228575</uri><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1070-3151</contrib-id><name-alternatives><name xml:lang="en"><surname>Moshchenskaya</surname><given-names>Elena Y.</given-names></name><name xml:lang="ru"><surname>Мощенская</surname><given-names>Елена Юрьевна</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Cand. Chem. Sci., Associate Professor; Associate Professor; Dept. of Analytical and Physical Chemistry</p></bio><bio xml:lang="ru"><p>кандидат химических наук, доцент; доцент; каф. аналитической и физической химии</p></bio><email>lmos@rambler.ru</email><uri>https://www.mathnet.ru/person39351</uri><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">National Engineering Physics Institute “MEPhI”</institution></aff><aff><institution xml:lang="ru">Национальный исследовательский ядерный университет «МИФИ»</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Samara State Technical University</institution></aff><aff><institution xml:lang="ru">Самарский государственный технический университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-05-20" publication-format="electronic"><day>20</day><month>05</month><year>2025</year></pub-date><volume>29</volume><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>174</fpage><lpage>186</lpage><history><date date-type="received" iso-8601-date="2024-10-09"><day>09</day><month>10</month><year>2024</year></date><date date-type="accepted" iso-8601-date="2025-03-21"><day>21</day><month>03</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Authors; Samara State Technical University (Compilation, Design, and Layout)</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Авторский коллектив; Самарский государственный технический университет (составление, дизайн, макет)</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Authors; Samara State Technical University (Compilation, Design, and Layout)</copyright-holder><copyright-holder xml:lang="ru">Авторский коллектив; Самарский государственный технический университет (составление, дизайн, макет)</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.eco-vector.com/1991-8615/article/view/636857">https://journals.eco-vector.com/1991-8615/article/view/636857</self-uri><abstract xml:lang="en"><p>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.The developed model enables accurate prediction of two- and threecomponent 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.</p></abstract><trans-abstract xml:lang="ru"><p>Представлен алгоритм и разработанная на его основе программа, реализующая методы математического моделирования для анализа спектральных данных, построения прогностической модели и выбора оптимальных спектральных интервалов при проектировании мультисенсорных систем на основе светодиодов. Алгоритм прошел апробацию на реальных смесях водных растворов неорганических солей.Для обработки экспериментальных данных применялись методы многомерной калибровки, включая PLS-регрессию и множественную линейную регрессию. Информативные длины волн определялись с использованием значений вектора Шепли, после чего методом перебора была найдена оптимальная комбинация спектральных интервалов.Разработанная модель позволяет прогнозировать состав двух- и трехкомпонентных систем в водных растворах солей металлов с использованием ограниченного спектрального диапазона вместо полного видимого спектра. Проведенная кроссвалидация продемонстрировала сопоставимое качество новой модели по сравнению с полноспектральными аналогами, подтвердив ее адекватность и практическую применимость.</p></trans-abstract><kwd-group xml:lang="en"><kwd>multivariate calibration</kwd><kwd>PLS regression</kwd><kwd>spectral interval selection</kwd><kwd>metal ion quantification</kwd><kwd>Shapley values</kwd><kwd>chemometrics</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>многомерная калибровка</kwd><kwd>PLS-регрессия</kwd><kwd>выбор спектральных интервалов</kwd><kwd>количественное определение ионов металлов</kwd><kwd>значения Шепли</kwd><kwd>хемометрика</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Dubrovkin J. Data Compression in Spectroscopy. Cambridge Scholars Publ., 2022, 355 pp.</mixed-citation><mixed-citation xml:lang="ru">Dubrovkin J. Data Compression in Spectroscopy. Cambridge Scholars Publ., 2022. 355 pp.</mixed-citation></citation-alternatives></ref><ref id="B2"><label>2.</label><citation-alternatives><mixed-citation xml:lang="en">Rodionova O. E. Chemometric approaches for analysis of large chemical data arrays, Ros. Khim. Zh., 2006, vol. 50, no. 2, pp. 128–144 (In Russian). EDN: HTUUSZ.</mixed-citation><mixed-citation xml:lang="ru">Родионова О.Е. Хемометрический подход к исследованию больших массивов химических данных // Рос. хим. ж., 2006. Т. 50, №2. С. 128–144. EDN: HTUUSZ.</mixed-citation></citation-alternatives></ref><ref id="B3"><label>3.</label><citation-alternatives><mixed-citation xml:lang="en">Smilde A., Bro R., Geladi P. Multi-Way Analysis: Applications in the Chemical Sciences. Chichester, John Wiley &amp; Sons, 2004, xiv+381 pp. DOI: https://doi.org/10.1002/0470012110.</mixed-citation><mixed-citation xml:lang="ru">Smilde A., Bro R., Geladi P. Multi-Way Analysis: Applications in the Chemical Sciences. Chichester: John Wiley &amp; Sons, 2004. xiv+381 pp. DOI: https://doi.org/10.1002/0470012110.</mixed-citation></citation-alternatives></ref><ref id="B4"><label>4.</label><citation-alternatives><mixed-citation xml:lang="en">Bogomolov A. Yu. Optical multisensor systems in analytical spectroscopy, J. Anal. Chem., 2022, vol. 77, no. 3, pp. 277–294. EDN: YORSQC. DOI: https://doi.org/10.1134/S1061934822030030.</mixed-citation><mixed-citation xml:lang="ru">Богомолов А. Ю. Оптические мультисенсорные системы в аналитической спектроскопии // Рос. хим. ж., 2022. Т. 77, №3. С. 227-247. EDN: MFSPES. DOI: https://doi.org/10.31857/S0044450222030033.</mixed-citation></citation-alternatives></ref><ref id="B5"><label>5.</label><citation-alternatives><mixed-citation xml:lang="en">Bogomolov A. Multivariate process trajectories: capture, resolution and analysis, Chemom. Intel. Lab. Syst., 2011, vol. 108, no. 1, pp. 49–63. DOI: https://doi.org/10.1016/j.chemolab.2011.02.005.</mixed-citation><mixed-citation xml:lang="ru">Bogomolov A. Multivariate process trajectories: capture, resolution and analysis // Chemom. Intel. Lab. Syst., 2011. vol. 108, no. 1. pp. 49–63. DOI: https://doi.org/10.1016/j.chemolab.2011.02.005.</mixed-citation></citation-alternatives></ref><ref id="B6"><label>6.</label><citation-alternatives><mixed-citation xml:lang="en">Galyanin V., Melenteva A., Bogomolov A. Selecting optimal wavelength intervals for an optical sensor: A case study of milk fat and total protein analysis in the region 400–1100 nm, Sens. Actuat. B: Chem., 2015, vol. 218, pp. 97-104. EDN: UFYADR. DOI: https://doi.org/10.1016/j.snb.2015.03.101.</mixed-citation><mixed-citation xml:lang="ru">Galyanin V., Melenteva A., Bogomolov A. Selecting optimal wavelength intervals for an optical sensor: A case study of milk fat and total protein analysis in the region 400–1100 nm// Sens. Actuat. B: Chem., 2015. vol. 218. pp. 97-104. EDN: UFYADR. DOI: https://doi.org/10.1016/j.snb.2015.03.101.</mixed-citation></citation-alternatives></ref><ref id="B7"><label>7.</label><citation-alternatives><mixed-citation xml:lang="en">Moshchenskaya E. Yu., Stifatov B. M. Modeling "composition-property" diagrams for the "aluminum-silicon" system, J. Sib. Fed. Univ. Chem., 2023, vol. 16, no. 1, pp. 107–115 (In Russian). EDN: JWRAGD.</mixed-citation><mixed-citation xml:lang="ru">Мощенская Е. Ю., Стифатов Б. М. Моделирование диаграмм "состав-свойство" для системы "алюминий-кремний" // Журн. Сиб. федер. ун-та. Химия, 2023. Т. 16, №1. С. 107–115. EDN: JWRAGD.</mixed-citation></citation-alternatives></ref><ref id="B8"><label>8.</label><citation-alternatives><mixed-citation xml:lang="en">Moshchenskaya E. Yu., Stifatov B. M. Investigation of the possibility of using theoretical modeling methods to determine the eutectic composition of binary alloys, Vestn. Tversk. Gos. Univ., Ser. Khimiia, 2021, no. 3, pp. 105–122 (In Russian). EDN: JDZAEI. DOI: https://doi.org/10.26456/vtchem2021.3.12.</mixed-citation><mixed-citation xml:lang="ru">Мощенская Е. Ю., Стифатов Б. М. Исследование возможности применения методов теоретического моделирования для определения эвтектического состава бинарных сплавов // Вестн. Тверск. гос. ун-та. Сер. Химия, 2021. №3. С. 105–122. EDN: JDZAEI. DOI: https://doi.org/10.26456/vtchem2021.3.12.</mixed-citation></citation-alternatives></ref><ref id="B9"><label>9.</label><citation-alternatives><mixed-citation xml:lang="en">Holland P. W., Welsch R. E. Robust regression using iteratively reweighted least-squares, Commun. Stat–Theor. M., 1977, vol. 6, no. 9, pp. 813–827. DOI: https://doi.org/10.1080/03610927708827533.</mixed-citation><mixed-citation xml:lang="ru">Holland P. W., Welsch R. E. Robust regression using iteratively reweighted least-squares // Commun. Stat–Theor. M., 1977. vol. 6, no. 9. pp. 813–827. DOI: https://doi.org/10.1080/03610927708827533.</mixed-citation></citation-alternatives></ref><ref id="B10"><label>10.</label><citation-alternatives><mixed-citation xml:lang="en">Wegelin J. A. A Survey of Partial Least Squares (PLS) Methods, with Emphasis on the Two-Block Case, Technical Report 371. Washington, Univ. of Washington, 2000, 44 pp. https://stat.uw.edu/research/tech-reports/survey-partial-least-squares-plsmethods-emphasis-two-block-case.</mixed-citation><mixed-citation xml:lang="ru">Wegelin J. A. A Survey of Partial Least Squares (PLS) Methods, with Emphasis on the Two-Block Case: Technical Report 371. Washington: Univ. of Washington, 2000. 44 pp. https://stat.uw.edu/research/tech-reports/survey-partial-least-squares-plsmethods-emphasis-two-block-case.</mixed-citation></citation-alternatives></ref><ref id="B11"><label>11.</label><citation-alternatives><mixed-citation xml:lang="en">Pedregosa F., Varoquaux G., Gramfort A., et. al. Scikit-learn: Machine learning in Python, J. Mach. Learn. Res., 2011, vol. 12, pp. 2825–2830.</mixed-citation><mixed-citation xml:lang="ru">Pedregosa F., Varoquaux G., Gramfort A., et. al. Scikit-learn: Machine learning in Python // J. Mach. Learn. Res., 2011. vol. 12. pp. 2825–2830.</mixed-citation></citation-alternatives></ref><ref id="B12"><label>12.</label><citation-alternatives><mixed-citation xml:lang="en">Lundberg S. M., Lee S.-I. A unified approach to interpreting model predictions, In: Proc. Intern. Conf. Neural Inform. Proces. Systems, 2017, pp. 4768–4777, arXiv: 1705.07874 [cs.AI]. DOI: https://doi.org/10.48550/arXiv.1705.07874.</mixed-citation><mixed-citation xml:lang="ru">Lundberg S. M., Lee S.-I. A unified approach to interpreting model predictions / Proc. Intern. Conf. Neural Inform. Proces. Systems, 2017. pp. 4768–4777, arXiv: 1705.07874 [cs.AI]. DOI: https://doi.org/10.48550/arXiv.1705.07874.</mixed-citation></citation-alternatives></ref><ref id="B13"><label>13.</label><citation-alternatives><mixed-citation xml:lang="en">de Myttenaere A., Golden B., Le Grand B., Rossi F. Mean Absolute Percentage Error for regression models, Neurocomputing, 2016, vol. 192, pp. 38-48. DOI: https://doi.org/10.1016/j.neucom.2015.12.114.</mixed-citation><mixed-citation xml:lang="ru">de Myttenaere A., Golden B., Le Grand B., Rossi F. Mean Absolute Percentage Error for regression models // Neurocomputing, 2016. vol. 192. pp. 38-48. DOI: https://doi.org/10.1016/j.neucom.2015.12.114.</mixed-citation></citation-alternatives></ref></ref-list></back></article>
