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<article article-type="research-article" dtd-version="1.3" 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" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">zhps</journal-id><journal-title-group><journal-title xml:lang="ru">Журнал прикладной спектроскопии</journal-title><trans-title-group xml:lang="en"><trans-title>Zhurnal Prikladnoii Spektroskopii</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0514-7506</issn><publisher><publisher-name>B. I. Stepanov Institute of Physics of the National Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">zhps-1985</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>АННОТАЦИИ АНГЛОЯЗЫЧНЫХ СТАТЕЙ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>ABSTRACTS ENGLISH-LANGUAGE ARTICLES</subject></subj-group></article-categories><title-group><article-title>Оптимизированное генетическим алгоритмом B-сплайн извлечение признаков для точного прогнозирования концентрации в онлайн спектроскопии комбинационного рассеяния света: сравнительный анализ эффективности разреженных обучающих данных</article-title><trans-title-group xml:lang="en"><trans-title>Genetic Algorithm-Optimized B-Spline Feature Extraction for Accurate Concentration Prediction by Online Raman Spectroscopy: a Comparative Analysis of the Efficacy of Sparse Training Data</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Wang</surname><given-names>S.</given-names></name><name name-style="western" xml:lang="en"><surname>Wang</surname><given-names>Shu</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><email xlink:type="simple">b24020804018@cjlu.edu.cn</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Xiong</surname><given-names>P.-F.</given-names></name><name name-style="western" xml:lang="en"><surname>Xiong</surname><given-names>Peng-Fan</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Xu</surname><given-names>B.</given-names></name><name name-style="western" xml:lang="en"><surname>Xu</surname><given-names>Bo</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Meng</surname><given-names>Y.-L.</given-names></name><name name-style="western" xml:lang="en"><surname>Meng</surname><given-names>Yan-Long</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Zhan</surname><given-names>C.-L.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhan</surname><given-names>Chun-Lian</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Zhou</surname><given-names>Z.-Y.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhou</surname><given-names>Zheng-Ye</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чжэцзян</p></bio><bio xml:lang="en"><p>Zhejiang</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Китайский университет Илян</institution></aff><aff xml:lang="en"><institution>China Jiliang University</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>China Nuclear Power Operation Management Co., Ltd.</institution></aff><aff xml:lang="en"><institution>China Nuclear Power Operation Management Co., Ltd.</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>26</day><month>09</month><year>2025</year></pub-date><volume>92</volume><issue>5</issue><fpage>708</fpage><lpage>708</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Wang S., Xiong P., Xu B., Meng Y., Zhan C., Zhou Z., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Wang S., Xiong P., Xu B., Meng Y., Zhan C., Zhou Z.</copyright-holder><copyright-holder xml:lang="en">Wang S., Xiong P., Xu B., Meng Y., Zhan C., Zhou Z.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://zhps.ejournal.by/jour/article/view/1985">https://zhps.ejournal.by/jour/article/view/1985</self-uri><abstract><p>Представлена структура, которая интегрирует аппроксимацию B-сплайном для извлечения признаков в модели наименьших квадратов для преодоления ограничений точности спектрометров комбинационного рассеяния света (КР) при количественном исследовании аналитов с низкой концентрацией, которая улучшена за счет оптимизации гиперпараметров с помощью генетического алгоритма (ГА). Производительность структуры оценена по сравнению с четырьмя альтернативными моделями прогнозирования, оптимизированными ГА: извлечение признаков с помощью вейвлет-преобразования с гребневой регрессией, линейные регрессионные нейронные сети, автономная гребневая регрессия и полиномиальная аппроксимация методом наименьших квадратов. Для экспериментальной проверки использованы наборы спектральных данных КР растворов борной и азотной кислот в 11 концентрациях (0–500 мг/л). Использован подход стратифицированного разбиения данных, при котором в тестовую выборку включены шесть уровней концентрации, а пять использованы для создания трех отдельных обучающих выборок (3, 4 и 5 уровней концентрации). Модель B-сплайн наименьших квадратов достигла оптимальной точности прогнозирования при обучении на четырех уровнях концентрации и среднеквадратичного отклонения (СКО) 5.83 мг/л для обоих аналитов. Модель вейвлет-гребневой регрессии (5-уровневая обучающая выборка, СКО = 6.02 мг/л) оказалась вторым по эффективности методом. Линейные регрессионные нейронные сети, гребневая регрессия и полиномиальные модели наименьших квадратов достигли оптимальной производительности при пяти обучающих концентрациях с СКО = 7.35, 9.17 и 12.21 мг/л соответственно. </p></abstract><trans-abstract xml:lang="en"><p>Raman spectroscopy combined with machine learning techniques is a promising approach for quantitative substance analysis. Online Raman spectrometers have intrinsic limits in sampling circumstances, preventing the utilization of surface-enhanced Raman scattering (SERS) approaches and therefore hindering highprecision predictions for low-concentration analytes. This paper introduces an innovative framework that integrates B-spline fitting for feature extraction with a least squares concentration prediction model, which is improved by hyperparameter optimization using a genetic algorithm (GA). The performance of this framework was carefully evaluated against four alternative GA-optimized prediction models: wavelet transform feature extraction with ridge regression, linear regression neural networks, standalone ridge regression, and polynomial fitting using least squares. Experimental validation included Raman spectral datasets obtained from boric acid and nitric acid solutions throughout 11 concentration gradients (0–500 mg/L) that were evenly dispersed within the designated range. A stratified data partitioning approach, which assigned six concentration levels to the test set, while leveraging the remaining five to create three separate training subsets (3, 4, and  5 concentration levels), was employed. A comparative investigation revealed that the B-spline-least-squares model achieved optimal prediction accuracy when it was trained on four concentration levels, resulting  in a mean root-mean-square error (RMSE) of 5.83 mg/L for both analytes. The performance hierarchy revealed that the wavelet-ridge regression model (5-level training subset, RMSE = 6.02 mg/L) was the secondbest method. Linear regression neural networks, ridge regression, and polynomial least squares models achieved optimal performance with five training concentrations, yielding mean RMSE values of 7.35, 9.17, and 12.21 mg/L, respectively.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>спектроскопия комбинационного рассеяния света</kwd><kwd>количественный анализ</kwd><kwd>генетический алгоритм</kwd><kwd>извлечение признаков</kwd><kwd>регрессионный анализ</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Raman spectroscopy</kwd><kwd>quantitative analysis</kwd><kwd>genetic algorithm</kwd><kwd>feature extraction</kwd><kwd>regression analysis</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This study was funded by the National Natural Science Foundation of China under the Youth Science Foundation Program (No. 62405301).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Muhammad Shahbaz, Ayesha Tariq, Muhammad I. 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