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DOI: https://doi.org/10.25296/2221-5514-2025-17-2-44-64

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“Геотехника”, Том XVII, № 2/2025

ПРИМЕНЕНИЕ АВТОЭНКОДЕРОВ И АЛГОРИТМОВ МНОГОМЕРНОЙ КЛАСТЕРИЗАЦИИ ПРИ ПРОВЕДЕНИИ ГЕОТЕХНИЧЕСКОЙ СХЕМАТИЗАЦИИ

Озмидов О.Р., Тишин Н.Р., Селиванова О.С., Гаврилович А.С.

Озмидов О.Р., Тишин Н.Р., Селиванова О.С., Гаврилович А.С., 2025. Применение автоэнкодеров и алгоритмов многомерной кластеризации при проведении геотехнической схематизации. Геотехника, Том ХVII, № 2, с. 44–64, https://doi.org/10.25296/2221-5514-2025-17-2-44-64.

В статье предлагается современный подход к анализу пространственных моделей, основанный на объединении современных алгоритмов машинного обучения и геостатистических методов. Основное внимание уделяется применению автоэнкодеров для снижения размерности данных, алгоритмов кластеризации (k-means, fuzzy c-means, density-based spatial clustering of applications with noise (DBSCAN), Gaussian mixture models (GMM) и self-organizing map (SOM)) для выделения доменов однородности (кластеров сходных свойств грунтов), сопоставляемых с экспертно выделенными инженерно-геологическими элементами, а также индикаторного кригинга для пространственного моделирования. Автоэнкодеры, обученные на лабораторных данных 90 образцов грунта, обеспечили высокую точность восстановления данных (R2 = 0,72; MSE = 0,02), что позволило эффективно проводить кластеризацию в скрытом пространстве. Несмотря на более низкие метрики кластеризации (коэффициент силуэта — 0,513), SOM продемонстрировала высокую скорость и эффективность при предварительном анализе массивов данных, а также более точное совпадение с классическим методом выделения инженерно-геологических элементов (скорректированный индекс Рэнда = 0,9). Алгоритмы k-means и GMM показали наилучшие результаты по метрикам коэффициента силуэта (0,635) и коэффициента Дэвиса — Болдина (0,454), что делает их предпочтительными для анализа переходных слоев грунта. Для построения пространственной модели авторы использовали индикаторный кригинг с введением дополнительной анизотропии в вариограмму, что отражает зависимость пространственной изменчивости свойств грунта от направления и учитывает различия в степени корреляции между точками в разных направлениях. В статье подчеркивается перспективность применения методов машинного обучения для повышения точности классификации, интерполяции и пространственного анализа инженерно-геологических моделей.

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7. Begum M., Shuvo M.H., Mostofa M.G., Riad A.B.M.K.I., Talukder M.A.I., Akter M.S., Shahriar H., 2024. M-DBSCAN: modified DBSCAN clustering algorithm for detecting and controlling outliers. Proceedings of the 39th ACM/SIGAPP Symposium on applied computing, Avila, Spain, 2024, pp. 1034–1035, https://doi.org/10.1145/3605098.3636188.
8. Bilski P., 2014. Conceptual clustering for the geotechnical data analysis. Proceedings of the 20th World Congress of soil science, Jeju, Korea, 2014, pp. 223–224.
9. Catuneanu O., 2019. Model-independent sequence stratigraphy. Earth-Science Reviews, Vol. 188, рр. 312–388, https://doi.org/10.1016/j.earscirev.2018.09.017.
10. Choudhury S., Pal N., 2021. Deep and structure-preserving autoencoders for clustering data with missing information. IEEE Transactions on Emerging Topics in Computational Intelligence, Vol. 5, pp. 639–650, https://doi.org/10.1109/TETCI.2019.2949264.
11.Dal Forno G., Gasperini L., 2008. ChirCor: a new tool for generating synthetic chirp-sonar seismograms. Computers and Geosciences, Vol. 34, No. 2, pp. 103–114, https://doi.org/10.1016/j.cageo.2007.01.004.
12. Gogebakan M., 2021. Gaussian mixture model-based clustering of multivariate data using soft computing hybrid algorithm. Trends in data engineering methods for intelligent systems, Proceedings of the International Conference on artificial intelligence and applied mathematics in engineering, Vol. 76, Antalya, Turkey, 2020, pp. 502–513, https://doi.org/10.1007/978-3-030-79357-9_49.
13. Goovaerts P., 2009. AUTO-IK: a 2D indicator kriging program for the automated non-parametric modeling of local uncertainty in earth sciences. Computers and Geosciences, Vol. 35, No. 6, pp. 1255–1270, https://doi.org/10.1016/j.cageo.2008.08.014.
14. Guo X., Liu X., Zhu E., Yin J., 2017. Deep clustering with convolutional autoencoders. Neural Information Processing, Proceedings of the 24th International Conference, Vol. 10635, Guangzhou, China, 2017, pp. 373–382, https://doi.org/10.1007/978-3-319-70096-0_39.
15. Harefa E., Zhou W., 2021. Performing sequential forward selection and variational autoencoder techniques in soil classification based on laser-induced breakdown spectroscopy. Analytical Methods, Vol. 13, Issue 41, рр. 4926–4933, https://doi.org/10.1039/D1AY01257F.
16. He Y., Chen D., Li B.G., Huang Y.F., Hu K.L., Li Y., Willett I.R., 2009. Sequential indicator simulation and indicator kriging estimation of 3-dimensional soil textures. Soil Research, Vol. 47, No. 6, pp. 622–631, https://doi.org/10.1071/SR08218.
17. Hinton G.E., Salakhutdinov R.R., 2006. Reducing the dimensionality of data with neural networks. Science, Vol. 313(5786), pp. 504–507, https://doi.org/10.1126/science.1127647.
18. Hohn M.E., McDowell R.R., 1994. Geostatistical analysis of oil production and potential using indicator kriging. In J.M. Yarus, R.L. Chambers (eds), Stochastic modeling and geostatistics: principles, methods, and case studies (computer applications in geology), Vol. 3. Publishing house of the American Association of Petroleum Geologists, Morgantown, WV, USA, pp. 121–130.
19. Juang K., Chen Y., Lee D., 2004. Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils. Environmental Pollution, Vol. 127, No. 2, pp. 229–238, https://doi.org/10.1016/j.envpol.2003.07.001.
20. Khanchouch I., Charrad M., Limam M., 2016. An improved multi-SOM algorithm for determining the optimal number of clusters. Computer and Information Science 2015. Studies in Computational Intelligence, Vol. 614, Las Vegas, NV, USA, 2015, pp. 189–201, https://doi.org/10.1007/978-3-319-23467-0_13.
21. Lee S., 2008. Development of subsurface spatial information model system using clustering and geostatistics approach. Journal of the Korean Association of Geographic Information Studies, Vol. 11, No. 4, pp. 64–75.
22. Lim K., Jiang X., Yi C., 2020. Deep clustering with variational autoencoder. IEEE Signal Processing Letters, Vol. 27, pp. 231–235, https://doi.org/10.1109/LSP.2020.2965328.
23. Marinoni O., 2003. Improving geological models using a combined ordinary-indicator kriging approach. Engineering Geology, Vol. 69, Issues 1–2, pp. 37–45, https://doi.org/10.1016/S0013-7952(02)00246-6.
24. Merembayev T., Yunussov R., Amirgaliyev Y., 2018. Machine learning algorithms for classification geology data from well logging. Proceedings of the 14th International Conference on electronics computer and computation, Kaskelen, Kazakhstan, 2018, pp. 206–212, https://doi.org/10.1109/ICECCO.2018.8634775.
25. Romero-Ruiz A., Gallardo L., 2015. Borehole constrained inversion of geophysical data based on fuzzy clustering. Abstracts of the 21st European Meeting of environmental and engineering geophysics, Vol. 34, Turin, Italy, 2015, pp. 1792–1796, https://doi.org/10.1190/SEGAM2015-5931667.1.
26. Shafizadeh-Moghadam H., 2021. Fully component selection: an efficient combination of feature selection and principal component analysis to increase model performance. Expert Systems with Applications, Vol. 186, ID 115678, https://doi.org/10.1016/j.eswa.2021.115678.
27. Shahapure K.R., Nicholas C., 2020. Cluster quality analysis using silhouette score. Proceedings of the 2020 IEEE 7th International Conference on data science and advanced analytics, Sydney, Australia, 2020, pp. 747–748, https://doi.org/10.1109/DSAA49011.2020.00096.
28. Sitharam T., Samui P., 2007. Geostatistical modelling of spatial and depth variability of SPT data for Bangalore. Geomechanics and Geoengineering, Vol. 2, Issue 4, pp. 307–316, https://doi.org/10.1080/17486020701678851.
29. Wang C., Illman W.A., 2023. Hydraulic tomography estimates improved by zonal information from the clustering of geophysical survey data. Water Resources Research, Vol. 59, Issue 9, ID e2023WR035191, https://doi.org/10.1029/2023WR035191.
30. Xia S., 2013. Problem analysis of geological properties evaluation using indicator kriging. URL: https://scispace.com/papers/problem-analysis-ofgeological-properties-evaluation-using-3eg5qzsyq6 (дата обращения: 11.05.2025).
31. Zaeri K., Hazbavi S., Toomanian N., 2013. Creating surface soil texture map with indicator kriging technique: a case study of central Iran soils. International Journal of Agriculture and Crop Sciences, Vol. 6, No. 9, pp. 518–521.
32. Zhang S., Xiao K., Carranza E., Yang F., Zhao Z., 2019. Integration of auto-encoder network with density-based spatial clustering for geochemical anomaly detection for mineral exploration. Computers and Geosciences, Vol. 130, pp. 43–56, https://doi.org/10.1016/j.cageo.2019.05.011.

ОЗМИДОВ О.Р.
АО «МОСТДОРГЕОТРЕСТ», г. Москва, Россия, ozmidov@mail.ru
Адрес: ул. Искры, д. 31, корп. 1, г. Москва, 129344, Россия
ТИШИН Н.Р.*
АО «МОСТДОРГЕОТРЕСТ», г. Москва, Россия, tnick1502@mail.ru
СЕЛИВАНОВА О.С.
АО «МОСТДОРГЕОТРЕСТ», г. Москва, Россия, support@mdgt.ru
ГАВРИЛОВИЧ А.С.
АО «МОСТДОРГЕОТРЕСТ», г. Москва, Россия, support@mdgt.ru

Geotechnics, Vol. XVII, No. 2/2025

APPLICATION OF AUTO ENCODERS AND ALGORITHMS OF MULTIDIMENSIONAL CLUSTERING DURING GEOTECHNICAL SCHEMATIZATION

Ozmidov O.R., Tishin N.R., Selivanova O.S., Gavrilovich A.S.

Ozmidov O.R., Tishin N.R., Selivanova O.S., Gavrilovich A.S., 2025. Application of auto encoders and algorithms of multidimensional clustering during geotechnical schematization. Geotechnics, Vol. XVII, No. 2, pp. 44–64, https://doi.org/10.25296/2221-5514-2025-17-2-44-64.

The paper presents a modern approach to the analysis of spatial models based on uniting contemporary algorithms of machine learning and geostatistical methods. Basic attention is paid to application of auto encoders to reduce data dimension, clustering algorithms (k-means, fuzzy c-means, density-based spatial clustering of applications with noise (DBSCAN), Gaussian mixture models (GMM) и self-organizing map (SOM)) to sort out homogeneity domains (clusters of similar soil properties) cross-referenced with engineering-geological elements selected by experts, as well as to make indicator kriging for spatial modeling. Auto encoders learned on the basis of laboratory data on 90 soil samples provided high accuracy of data recovery (R2 = 0.72; MSE = 0.02) that ensured efficient clustering in a hidden space. Despite lower clustering metric (outline index — 0.513), SOM demonstrated a high speed and efficiency during preliminary analysis of datasets and more accurate coincidence with the traditional method of sorting out engineering-geological elements (adjusted Rand index = 0.9). Algorithms k-means and GMM showed the best results as per metric of outline index (0.635) and Davies — Bouldin index (0.454) that makes them preferable for analyzing transitional soil layers. In order to build a spatial model, the authors used indicator kriging with introduction of additional anisotropy into a variogram that reflects a dependency of spatial variability of soil properties on a direction and considers differences in a degree of correlation between points in different directions. The work emphasizes good prospects of using methods of machine learning to increase accuracy of classification, interpolation and spatial analysis of engineeringgeological models.

Auto encoder multidimensional clustering geostatistics indicator kriging probabilistic modeling of categorical data spatial modeling of a profile

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6. Bastante F.G., Ordóñez C., Taboada J., Matías J.M., 2008. Comparison of indicator kriging, conditional indicator simulation and multiple-point statistics used to model slate deposits. Engineering Geology, Vol. 98, No. 1–2, pp. 50–59, https://doi.org/10.1016/j.enggeo.2008.01.006.
7. Begum M., Shuvo M.H., Mostofa M.G., Riad A.B.M.K.I., Talukder M.A.I., Akter M.S., Shahriar H., 2024. M-DBSCAN: modified DBSCAN clustering algorithm for detecting and controlling outliers. Proceedings of the 39th ACM/SIGAPP Symposium on applied computing, Avila, Spain, 2024, pp. 1034–1035, https://doi.org/10.1145/3605098.3636188.
8. Bilski P., 2014. Conceptual clustering for the geotechnical data analysis. Proceedings of the 20th World Congress of soil science, Jeju, Korea, 2014, pp. 223–224.
9. Catuneanu O., 2019. Model-independent sequence stratigraphy. Earth-Science Reviews, Vol. 188, рр. 312–388, https://doi.org/10.1016/j.earscirev.2018.09.017.
10. Choudhury S., Pal N., 2021. Deep and structure-preserving autoencoders for clustering data with missing information. IEEE Transactions on Emerging Topics in Computational Intelligence, Vol. 5, pp. 639–650, https://doi.org/10.1109/TETCI.2019.2949264.
11. Dal Forno G., Gasperini L., 2008. ChirCor: a new tool for generating synthetic chirp-sonar seismograms. Computers and Geosciences, Vol. 34, No. 2, pp. 103–114, https://doi.org/10.1016/j.cageo.2007.01.004.
12. Gogebakan M., 2021. Gaussian mixture model-based clustering of multivariate data using soft computing hybrid algorithm. Trends in data engineering methods for intelligent systems, Proceedings of the International Conference on artificial intelligence and applied mathematics in engineering, Vol. 76, Antalya, Turkey, 2020, pp. 502–513, https://doi.org/10.1007/978-3-030-79357-9_49.
13. Goovaerts P., 2009. AUTO-IK: a 2D indicator kriging program for the automated non-parametric modeling of local uncertainty in earth sciences. Computers and Geosciences, Vol. 35, No. 6, pp. 1255–1270, https://doi.org/10.1016/j.cageo.2008.08.014.
14. Guo X., Liu X., Zhu E., Yin J., 2017. Deep clustering with convolutional autoencoders. Neural Information Processing, Proceedings of the 24th International Conference, Vol. 10635, Guangzhou, China, 2017, pp. 373–382, https://doi.org/10.1007/978-3-319-70096-0_39.
15. Harefa E., Zhou W., 2021. Performing sequential forward selection and variational autoencoder techniques in soil classification based on laser-induced breakdown spectroscopy. Analytical Methods, Vol. 13, Issue 41, рр. 4926–4933, https://doi.org/10.1039/D1AY01257F.
16. He Y., Chen D., Li B.G., Huang Y.F., Hu K.L., Li Y., Willett I.R., 2009. Sequential indicator simulation and indicator kriging estimation of 3-dimensional soil textures. Soil Research, Vol. 47, No. 6, pp. 622–631, https://doi.org/10.1071/SR08218.
17. Hinton G.E., Salakhutdinov R.R., 2006. Reducing the dimensionality of data with neural networks. Science, Vol. 313(5786), pp. 504–507, https://doi.org/10.1126/science.1127647.
18. Hohn M.E., McDowell R.R., 1994. Geostatistical analysis of oil production and potential using indicator kriging. In J.M. Yarus, R.L. Chambers (eds), Stochastic modeling and geostatistics: principles, methods, and case studies (computer applications in geology), Vol. 3. Publishing house of the American Association of Petroleum Geologists, Morgantown, WV, USA, pp. 121–130.
19. Juang K., Chen Y., Lee D., 2004. Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils. Environmental Pollution, Vol. 127, No. 2, pp. 229–238, https://doi.org/10.1016/j.envpol.2003.07.001.
20. Khanchouch I., Charrad M., Limam M., 2016. An improved multi-SOM algorithm for determining the optimal number of clusters. Computer and Information Science 2015. Studies in Computational Intelligence, Vol. 614, Las Vegas, NV, USA, 2015, pp. 189–201, https://doi.org/10.1007/978-3-319-23467-0_13.
21. Lee S., 2008. Development of subsurface spatial information model system using clustering and geostatistics approach. Journal of the Korean Association of Geographic Information Studies, Vol. 11, No. 4, pp. 64–75.
22. Lim K., Jiang X., Yi C., 2020. Deep clustering with variational autoencoder. IEEE Signal Processing Letters, Vol. 27, pp. 231–235, https://doi.org/10.1109/LSP.2020.2965328.
23. Marinoni O., 2003. Improving geological models using a combined ordinary-indicator kriging approach. Engineering Geology, Vol. 69, Issues 1–2, pp. 37–45, https://doi.org/10.1016/S0013-7952(02)00246-6.
24. Merembayev T., Yunussov R., Amirgaliyev Y., 2018. Machine learning algorithms for classification geology data from well logging. Proceedings of the 14th International Conference on electronics computer and computation, Kaskelen, Kazakhstan, 2018, pp. 206–212, https://doi.org/10.1109/ICECCO.2018.8634775.
25. Romero-Ruiz A., Gallardo L., 2015. Borehole constrained inversion of geophysical data based on fuzzy clustering. Abstracts of the 21st European Meeting of environmental and engineering geophysics, Vol. 34, Turin, Italy, 2015, pp. 1792–1796, https://doi.org/10.1190/SEGAM2015-5931667.1.
26. Shafizadeh-Moghadam H., 2021. Fully component selection: an efficient combination of feature selection and principal component analysis to increase model performance. Expert Systems with Applications, Vol. 186, ID 115678, https://doi.org/10.1016/j.eswa.2021.115678.
27. Shahapure K.R., Nicholas C., 2020. Cluster quality analysis using silhouette score. Proceedings of the 2020 IEEE 7th International Conference on data science and advanced analytics, Sydney, Australia, 2020, pp. 747–748, https://doi.org/10.1109/DSAA49011.2020.00096.
28. Sitharam T., Samui P., 2007. Geostatistical modelling of spatial and depth variability of SPT data for Bangalore. Geomechanics and Geoengineering, Vol. 2, Issue 4, pp. 307–316, https://doi.org/10.1080/17486020701678851.
29. Wang C., Illman W.A., 2023. Hydraulic tomography estimates improved by zonal information from the clustering of geophysical survey data. Water Resources Research, Vol. 59, Issue 9, ID e2023WR035191, https://doi.org/10.1029/2023WR035191.
30. Xia S., 2013. Problem analysis of geological properties evaluation using indicator kriging. URL: https://scispace.com/papers/problem-analysis-ofgeological-properties-evaluation-using-3eg5qzsyq6 (accessed: 11 May 2025).
31. Zaeri K., Hazbavi S., Toomanian N., 2013. Creating surface soil texture map with indicator kriging technique: a case study of central Iran soils. International Journal of Agriculture and Crop Sciences, Vol. 6, No. 9, pp. 518–521.
32. Zhang S., Xiao K., Carranza E., Yang F., Zhao Z., 2019. Integration of auto-encoder network with density-based spatial clustering for geochemical anomaly detection for mineral exploration. Computers and Geosciences, Vol. 130, pp. 43–56, https://doi.org/10.1016/j.cageo.2019.05.011.

OLEG R. OZMIDOV
MOSTDORGEOTREST JSC; Moscow, Russia; ozmidov@mail.ru
Address: Bld. 31, Pde 1, Iskry St., 129344, Moscow, Russia
NIKITA R. TISHIN*
MOSTDORGEOTREST JSC; Moscow, Russia; tnick1502@mail.ru
OLESYA S. SELIVANOVA
MOSTDORGEOTREST JSC; Moscow, Russia; support@mdgt.ru
ARINA S. GAVRILOVICH
MOSTDORGEOTREST JSC; Moscow, Russia; support@mdgt.ru

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