vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2018-54-1-77-83vestifm-301Research ArticleФИЗИКАPHYSICSМЕТОДЫ ПОСТРОЕНИЯ ОБУЧАЮЩЕГО НАБОРА ДЛЯ КАЛИБРОВКИ С ПОМОЩЬЮ ФЛУОРЕСЦЕНТНОЙ СПЕКТРОСКОПИИ НЕБОЛЬШИХ ВЫБОРОК ОБРАЗЦОВTRAINING SUBSET SELECTION METHODS FOR CALIBRATION WITH FLUORESCENCE SPECTROSCOPY IN SMALL DATA SETS OF SAMPLESХодасевичМ. А.KhodasevichM. A.

кандидат физико-математических наук, заместитель заведующего лабораторией

Ph. D. (Physics and Mathematics), Deputy Head of the Laboratory

m.khodasevich@ifanbel.bas-net.byСаскевичН. А.SaskevichN. A.

кандидат физико- математических наук, старший научный сотрудник

Ph. D. (Physics and Mathematics), Senior Researcher

n.saskevich@ifanbel.bas-net.byИнститут физики им. Б. И. Степанова Национальной академии наук Беларуси, МинскB. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus, Minsk2018050420185417783Copyright © Ходасевич М.А., Саскевич Н.А., 20182018Ходасевич М.А., Саскевич Н.А.Khodasevich M.A., Saskevich N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/301

При проведении калибровки с помощью многопараметрического спектрального анализа ограниченность количества образцов и невозможность априорного контроля величины искомого параметра обусловливают важность решения задачи построения обучающего набора с целью уменьшения ошибки калибровки. На примере калибровки температуры с помощью проекции на латентные структуры в диапазоне от 66 до 150 °C по спектрам флуоресценции Yb3+:CaF2 , зарегистрированным в диапазоне 880–1120 нм с разрешением около 0,2 нм и шагом по температуре 2 °C, продемонстрированы возможные варианты построения обучающего набора из небольших по количеству образцов выборок с применением равномерного распределения, алгоритма Кеннарда – Стоуна и методов кластерного анализа в пространстве главных компонент, показано их влияние на точность калибровки. Применение метода главных компонент позволяет проводить отбор спектров без привлечения априорных знаний о температуре, которой соответствуют спектры флуоресценции. Показано, что среднеквадратичная ошибка предсказанной величины температуры при равномерном распределении образцов обучающего набора по пространству первой главной компоненты составляет 3,98 °C, при использовании алгоритма Кеннарда – Стоуна – 1,07 °C. Минимальная среднеквадратичная ошибка 0,98 °C может быть достигнута с помощью иерархического кластерного анализа пространства главных компонент исследуемых спектров.

 

A limited number of samples and an impossible a priori control of a desired parameter value stipulate how it is important to solve the problem of selecting a training set for calibration by the multivariate spectral analysis in order to reduce a calibration error. Possible variants of a training subset selection from small data sets are shown for temperature calibration with fluorescence spectra of Yb3+:CaF2 recorded in the range of 880–1120 nm with a resolution of about 0.2 nm for the temperature range from 66 to 150 °C and at a step of 2 °C. The methods applied are the uniform distribution, the Kennard and Stone algorithm and the cluster analysis in principal component space. The effect of the method choice on the calibration accuracy has been evaluated. The application of the principal component analysis gives the possibility to select spectra without a priori knowledge of a temperature, to which the fluorescence spectra correspond. The root-mean-square error of the predicted temperature value is shown to be 3.98 ° C for the uniform distribution of the training subset samples over the space of the first principal component and 1.07 ° C for the Kennard and Stone algorithm. The minimum root-mean-square prediction error of 0.98 °C is shown to be achieved with the training subset selection by the hierarchical cluster analysis in the space of the principal components of the spectra studied.

флуоресцентная спектроскопиякалибровкакластерный анализпроекция на латентные структурыfluorescence spectroscopycalibrationcluster analysisprojection to latent structuresReferencesKalivas, J. H. Calibration Methodologies / J. H. Kalivas // Comprehensive Chemometrics: Chemical and Biochemical Data Analysis / editors-in-chief: R. Tauler, B. Walczak, S. D. Brown. – Elsevier, 2009. – P. 1–32.Kalivas, J. H. Calibration Methodologies. Tauler R., Walczak B., Brown S. D. (eds.). Comprehensive Chemometrics: Chemical and Biochemical Data Analysis. Elsevier, 2009, pp. 1–32. Doi: 10.1016/b978-044452701-1.00072-7Rapid identification of soil cadmium pollution risk at regional scale based on visible and near-infrared spectroscopy / Tao Chen [et al.] // Environ. Pollut. – 2015. – Vol. 206. – P. 217–226.Tao Chen, Qingrui Chang, Clevers J.G.P.W., Kooistra L. Rapid identification of soil cadmium pollution risk at regional scale based on visible and near-infrared spectroscopy. Environmental Pollution, 2015, vol. 206, pp. 217–226. Doi: 10.1016/j. envpol.2015.07.009Noninvasive and fast measurement of blood glucose in vivo by near infrared (NIR) spectroscopy / Xue Jintao [et al.] // Spectrochim. Acta Part A: Molecular and Biomolecular Spectroscopy. – 2017. – Vol. 179. – P. 250–254.Xue Jintao, Ye Liming, Liu Yufei, Li Chunyan, Chen Han. Noninvasive and fast measurement of blood glucose in vivo by near infrared (NIR) spectroscopy. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 2017, vol. 179, pp. 250–254. Doi: 10.1016/j.saa.2017.02.032Joint analyses model for total cholesterol and triglyceride in human serum with near-infrared spectroscopy / Lijun Yao [et al.] // Spectrochim. Acta Part A: Molecular and Biomolecular Spectroscopy. – 2016. – Vol. 159. – P. 53–59.Lijun Yao, Ning Lyu, Jiemei Chen, Tao Pan, Jing Yu. Joint analyses model for total cholesterol and triglyceride in human serum with near-infrared spectroscopy. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 2016, vol. 159, pp. 53–59. Doi: 10.1016/j.saa.2016.01.022Da Silva, V. H. Portable near-infrared instruments: Application for quality control of polymorphs in pharmaceutical raw materials and calibration transfer / V. H. da Silva, J. J. da Silva, C. F. Pereira // J. Pharm. Biomed. Anal. – 2017. – Vol. 134. – P. 287–294.Da Silva V. H., da Silva J. J., Pereira C. F. Portable near-infrared instruments: Application for quality control of poly-morphs in pharmaceutical raw materials and calibration transfer. Journal of Pharmaceutical and Biomedical Analysis, 2017, vol. 134, pp. 287–294. Doi: 10.1016/j.jpba.2016.11.036Identification of anisodamine tablets by Raman and near-infrared spectroscopy with chemometrics / Lian Li [et al.] // Spectrochim. Acta Part A: Molecular and Biomolecular Spectroscopy. – 2014. – Vol. 127. – P. 91–97.Lian Li, Hengchang Zang, Jun Li, Dejun Chen, Tao Li, Fengshan Wang. Identification of anisodamine tablets by Raman and near-infrared spectroscopy with chemometrics. Spectrochimica Acta Part A: Molecular and Biomolecular Spec-tro scopy, 2014, vol. 127, pp. 91–97. Doi: 10.1016/j.saa.2014.02.022Sulub, Y. Determination of polymer blends composed of polycarbonate and rubber entities using near-infrared (NIR) spectroscopy and multivariate calibration / Y. Sulub, J. DeRudder // Polym. Test. – 2013. – Vol. 32, № 4. – P. 802–809.Sulub Y., DeRudder J. Determination of polymer blends composed of polycarbonate and rubber entities using near- infrared (NIR) spectroscopy and multivariate calibration. Polymer Testing, 2013, vol. 32, no. 4, pp. 802–809. Doi: 10.1016/j. polymertesting.2013.03.008Application of benchtop and portable near-infrared spectrometers for predicting the optimum harvest time of Verbena officinalis / C. K. Pezzei [et al.] // Talanta. – 2017. – Vol. 169. – P. 70–76.Pezzei C. K., Schonbichler S. A., Kirchler C. G., Schmelzer J., Hussain S., Huck-Pezzei V. A., Popp M., Krolitzek J., Bonn G. K. Application of benchtop and portable near-infrared spectrometers for predicting the optimum harvest time of Verbena officinalis. Talanta, 2017, vol. 169, pp. 70–76. Doi: 10.1016/j.talanta.2017.03.067Comparing predictive ability of laser-induced breakdown spectroscopy to visible near-infrared spectroscopy for soil property determination / M. Knadel [et al.] // Biosystems Engineering. – 2017. – Vol. 156. – P. 157–172.Knadel M., Gislum R., Hermansen C., Peng Y., Moldrup P., de Jonge L. W., Greve M. H. Comparing predictive ability of laser-induced breakdown spectroscopy to visible near-infrared spectroscopy for soil property determination. Biosystems Engineering, 2017, vol. 156, pp. 157–172. Doi: 10.1016/j.biosystemseng.2017.01.007Eating quality evaluation of Khao Dawk Mali 105 rice using near-infrared spectroscopy / P. Siriphollakul [et al.] // LWT – Food Science and Technology. – 2017. – Vol. 79. – P. 70–77.Siriphollakul P., Nakano K., Kanlayanarat S., Ohashi S., Sakai R., Rittiron R., Maniwara P. Eating quality evaluation of Khao Dawk Mali 105 rice using near-infrared spectroscopy. LWT – Food Science and Technology, 2017, vol. 79, pp. 70–77. Doi: 10.1016/j.lwt.2017.01.014Monitoring of alcohol strength and titratable acidity of apple wine during fermentation using near-infrared spectroscopy / B. Peng [et al.] // LWT – Food Science and Technology. – 2016. – Vol. 66. – P. 86–92.Peng B., Ge N., Cui L., Zhao H. Monitoring of alcohol strength and titratable acidity of apple wine during fermentation using near-infrared spectroscopy. LWT – Food Science and Technology, 2016, vol. 66, pp. 86–92. Doi: 10.1016/j. lwt.2015.10.018Определение химических характеристик и производителя дивинов по их широкополосным спектрам пропускания / М. А. Ходасевич [и др.] // Оптика и спектроскопия. – 2016. – Т. 120, № 6. – С. 1046–1051.Khodasevich M. A., Sinitsyn G. V., Skorbanova E. A., Rogovaya M. V., Kambur E. I., and Aseev V. A. Determination of the Chemical Parameters and Manufacturer of Divins from Their Broadband Transmission Spectra. Optics and Spectroscopy, 2016, vol. 120, pp. 978–982. Doi: 10.1134/s0030400x16050155Применение многопараметрического анализа широкополосных спектров пропускания для идентификации вин с географическим наименованием происхождения / М. А. Ходасевич [и др.] // Приборы и методы измерений. – 2016. – Т. 7, № 1. – С. 104–113.Khodasevich M. A., Skorbanova E. A., Obade L. I., Degtyar N. F., Kambur E. I., Rogovaya M. V. Application of multivariate analysis of transmission spectra to identify wines with protected geographical indication (IGP). Pribory i metody izmerenii = Devices and Methods of Measurements, 2016, vol. 7, no. 1, pp. 104–113 (in Russian). Doi: 10.21122/2220-9506-2016-7-1-104-113Alves, J. C. L. Quantification of conventional and advanced biofuels contents in diesel fuel blends using near-infrared spectroscopy and multivariate calibration / J. C. L. Alves, R. J. Poppi // Fuel. – 2016. – Vol. 165. – P. 379–388.Alves J. C. L., Poppi R. J. Quantification of conventional and advanced biofuels contents in diesel fuel blends using near-infrared spectroscopy and multivariate calibration. Fuel, 2016, vol. 165, pp. 379–388. Doi: 10.1016/j.fuel.2015.10.079Clustering and training set selection methods for improving the accuracy of quantitative laser induced breakdown spectroscopy / R. B. Anderson [et al.] // Spectrochim. Acta Part B. – 2012. – Vol. 70. – P. 24–32.Anderson R. B., Bell J. F., Wiens R. C., Morris R. V., Clegg S. M. Clustering and training set selection methods for improving the accuracy of quantitative laser induced breakdown spectroscopy. Spectrochimica Acta Part B, 2012, vol. 70, pp. 24–32. Doi: 10.1016/j.sab.2012.04.004Abdi, H. Partial least squares regression and projection on latent structure regression / H. Abdi // Wiley Interdisciplinary Reviews: Computational Statistics. – 2010. – Vol. 2, № 1. – P. 97–106.Abdi H. Partial least squares regression and projection on latent structure regression. Wiley Interdisciplinary Reviews: Computational Statistics, 2010, vol. 2, pp. 97–106. Doi: 10.1002/wics.51Determining the Stark structure of Yb3+ energy levels in Y3Al5O12 and CaF2 using principal component analysis of tem perature dependences of fluorescence spectra / M. Khodasevich [et al.] // J. Lmin. – 2017. – Vol. 187. – P. 295–297.Khodasevich M., Varaksa Y., Sinitsyn G., Aseev V., Demesh M., Yasukevich A. Determining the Stark structure of Yb3+ energy levels in Y3Al5O12 and CaF2 using principal component analysis of temperature dependences of fluorescence spectra. Journal of Luminescence, 2017, vol. 187, pp. 295–297. Doi: 10.1016/j.jlumin.2017.03.014Esbensen, K. H. Principal Component Analysis: Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice / K. H. Esbensen, P. Geladi // Comprehensive Chemometrics. – 2009. – Vol. 2. – P. 211–226.Esbensen K. H., Geladi P. Principal Component Analysis: Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice. Comprehensive Chemometrics, 2009, vol. 2, pp. 211–226. Doi: 10.1016/b978-044452701-1.00043-0Применение регрессии на латентные структуры для определения температуры активированной ионами эрбия свинцово-фторидной наностеклокерамики по спектрам апконверсионной флуоресценции / В. А. Асеев [и др.] // Оптика и спектроскопия. – 2015. – Т. 118, № 2. – С. 47–49.Aseev V. A., Varaksa Yu. A., Kolobkova E. V., Sinitsyn G. V., Khodasevich M. A. Application of Projection on Latent Structures for Determining Temperature of Erbium-Doped Lead Fluoride Nano-Glass-Ceramics from Upconversion Fluorescence Spectra. Optics and Spectroscopy, 2015, vol. 118, pp. 727–728. Doi: 10.1134/s0030400x15050033Kennard, R. W. Computer aided design of experiments / R. W. Kennard, L. A. Stone // Technometrics. – 1969. – Vol. 11, № 1. – P. 137–148.Kennard R. W., Stone L. A. Computer aided design of experiments. Technometrics, 1969, vol. 11, no. 1, pp. 137–148. Doi: 10.2307/1266770Daszykowski, M. Representative subset selection / M. Daszykowski, B. Walczak, D. L. Massart // Anal. Chim. Acta. – 2002. – Vol. 468. – P. 91–103.Daszykowski M., Walczak B., Massart D. L. Representative subset selection. Analytica Chimica Acta, 2002, vol. 468, pp. 91–103. Doi: 10.1016/s0003-2670(02)00651-7Мандель, И. Д. Кластерный анализ / И. Д. Мандель. – М.: Финансы и статистика, 1988. – 176 с.Mandel I. D. Cluster analysis. Moscow, Finansy i statistika Publ., 1988, 176 p. (in Russian).

The authors declare that there are no conflicts of interest present.