{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T10:34:07Z","timestamp":1775126047262,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T00:00:00Z","timestamp":1638921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The grant was provided for state support for the establishing and development of a world-class Scientific Center \u201cAgrotechnologies for the Future\u201d.","award":["075-15-2020-905"],"award-info":[{"award-number":["075-15-2020-905"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>Currently, the load on railway tracks is increasing due to the increase in freight traffic. Accordingly, more and more serious requirements are being imposed on the reliability of the roadbed, which means that studies of methods for monitoring the integrity of the railway roadbed are relevant. The article provides a mathematical substantiation of the possibility of using seismoelectric and phasemetric methods of geoelectric control of the roadbed of railway tracks in order to identify defects and deformations at an early stage of their occurrence. The methods of laboratory modeling of the natural\u2013technical system \u201crailway track\u201d are considered in order to assess the prospects of using the presented methods. The results of laboratory studies are presented, which have shown their high efficiency in registering a weak useful electrical signal caused by seismoacoustic effects against the background of high-level external industrial and natural interference. In the course of laboratory modeling, it was found that on the amplitude spectra of the output electrical signals of the investigated geological medium in the presence of an elastic harmonic action with a frequency of 70 Hz, the frequency of a harmonic electrical signal with a frequency of 40 Hz is observed. In laboratory modeling, phase images were obtained for the receiving line when simulating the process of sinking the soil base of the railway bed, confirming the presence of a transient process that causes a shift in the initial phase of the signal \u0394\u03c6 = 40\u00b0 by ~45\u00b0 (\u0394\u03c6\u2019 = 85\u00b0), which allows detection of the initial stage of failure formation.<\/jats:p>","DOI":"10.3390\/math9243164","type":"journal-article","created":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T23:30:00Z","timestamp":1639006200000},"page":"3164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Mathematical Description and Laboratory Study of Electrophysical Methods of Localization of Geodeformational Changes during the Control of the Railway Roadbed"],"prefix":"10.3390","volume":"9","author":[{"given":"Artem","family":"Bykov","sequence":"first","affiliation":[{"name":"Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Leningrad Avenue 49, 125993 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anastasia","family":"Grecheneva","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Russian State Agrarian University\u2014Moscow Timiryazev Agricultural Academy, Timiryazevskaya Street 49, 127550 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oleg","family":"Kuzichkin","sequence":"additional","affiliation":[{"name":"Department of Informational and Robototechnical Systems, Belgorod National Research University, Pobedy Street 85, 308015 Belgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Surzhik","sequence":"additional","affiliation":[{"name":"Department of Informational and Robototechnical Systems, Belgorod National Research University, Pobedy Street 85, 308015 Belgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gleb","family":"Vasilyev","sequence":"additional","affiliation":[{"name":"Department of Informational and Robototechnical Systems, Belgorod National Research University, Pobedy Street 85, 308015 Belgorod, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yerbol","family":"Yerbayev","sequence":"additional","affiliation":[{"name":"Higher School of Mechanical Engineering, Zhangir Khan West Kazakhstan Agrarian-Technical University, Zhangir Khan Street 51, Uralsk 090009, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1080\/00423110802621561","article-title":"Fundamentals of vehicle-track coupled dynamics","volume":"47","author":"Zhai","year":"2009","journal-title":"Veh. Syst. Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107336","DOI":"10.1016\/j.ymssp.2020.107336","article-title":"A spatial coupling model to study dynamic performance of pantograph-catenary with vehicle-track excitation","volume":"151","author":"Song","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.ssci.2019.05.042","article-title":"Risk assessment for construction of urban rail transit projects","volume":"118","author":"Yan","year":"2019","journal-title":"Saf. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106888","DOI":"10.1016\/j.soildyn.2021.106888","article-title":"An experimental\/numerical hybrid methodology for the prediction of railway-induced ground-borne vibration on buildings to be constructed close to existing railway infrastructures: Numerical validation and parametric study","volume":"150","author":"Arcos","year":"2021","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_5","unstructured":"(2012, November 15). Draft Environmental Impact Report, Preston Property Residential Project State Clearinghouse No: 2012022075; City of Milpitas, CA, USA, 15 November 2012, Available online: http:\/\/www.ci.milpitas.ca.gov\/_pdfs\/plan_eir_PrestonPropertyAppendices-Part1.pdf."},{"key":"ref_6","first-page":"122","article-title":"Modern methods of monitoring geodynamic processes in oil and gas production areas, XXI century","volume":"13","author":"Cheverikin","year":"2019","journal-title":"Technosphere Secur."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0963-8695(02)00053-1","article-title":"Evaluation of railway trackbed and formation: A case study","volume":"36","author":"Brough","year":"2003","journal-title":"NDT E Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e07680","DOI":"10.1016\/j.heliyon.2021.e07680","article-title":"Refraction seismic complementing electrical method in subsurface characterization for tunneling in soft pyroclastic, (a case study)","volume":"7","author":"Fisseha","year":"2021","journal-title":"Heliyon"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103839","DOI":"10.1016\/j.jappgeo.2019.103839","article-title":"Joint probabilistic inversion of DC resistivity and seismic refraction data applied to bedrock\/regolith interface delineation","volume":"170","author":"Linde","year":"2019","journal-title":"J. Appl. Geophys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104880","DOI":"10.1016\/j.jseaes.2021.104880","article-title":"High-resolution electrical resistivity tomography and seismic refraction for groundwater exploration in fracture hard rocks: A case study in Kanthan, Perak, Malaysia","volume":"218","author":"Lee","year":"2021","journal-title":"J. Asian Earth Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"125320","DOI":"10.1016\/j.jhydrol.2020.125320","article-title":"Simulation of karst spring discharge using a combination of time\u2013frequency analysis methods and long short-term memory neural networks","volume":"589","author":"An","year":"2020","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103988","DOI":"10.1016\/j.tust.2021.103988","article-title":"Characteristics, challenges and countermeasures of giant karst cave: A case study of Yujingshan tunnel in high-speed railway","volume":"114","author":"Zheng","year":"2021","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105529","DOI":"10.1016\/j.enggeo.2020.105529","article-title":"A comprehensive approach to karst identification and groutability evaluation\u2014A case study of the Dehou reservoir, SW China","volume":"269","author":"Shangxin","year":"2020","journal-title":"Eng. Geol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.enggeo.2019.02.019","article-title":"Identification of gypsum karstification using an electrical resistivity tomography technique: The case-study of the Sivas gypsum karst area (Turkey)","volume":"252","author":"Drahor","year":"2019","journal-title":"Eng. Geol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"124282","DOI":"10.1016\/j.jhydrol.2019.124282","article-title":"Modelling long-term and short-term evolution of karst in vicinity of tunnels","volume":"581","author":"Kaufmann","year":"2020","journal-title":"J. Hydrol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2983087","DOI":"10.1155\/2019\/2983087","article-title":"A review of the advantages and limitations of geophysical investigations in Landslide studies","volume":"2019","author":"Pazzi","year":"2019","journal-title":"Int. J. Geophys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"100497","DOI":"10.1016\/j.trgeo.2020.100497","article-title":"Dynamic prediction models of rock quality designation in tunneling projects","volume":"27","author":"Mahmoodzadeh","year":"2021","journal-title":"Transp. Geotech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.eng.2019.04.009","article-title":"Challenges and Development Prospects of Ultra-Long and Ultra-Deep Mountain Tunnels","volume":"5","author":"Zhu","year":"2019","journal-title":"Engineering"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"100535","DOI":"10.1016\/j.trgeo.2021.100535","article-title":"Analysis of cyclic deformation and post-cyclic strength of reinforced railway tracks on soft subgrade","volume":"28","author":"Chawla","year":"2021","journal-title":"Transp. Geotech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"042085","DOI":"10.1088\/1755-1315\/459\/4\/042085","article-title":"The modeling of the Phase-Metric Method of the Geoelectrical Control of Oil Sludge Straits","volume":"459","author":"Baknin","year":"2020","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_21","unstructured":"Yun, B. (2019). Underground Engineering, Academic Press."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Patel, A. (2019). Geotechnical Investigations and Improvement of Ground Conditions, Woodhead Publishing.","DOI":"10.1016\/B978-0-12-817048-9.00009-3"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Maxim, B., Artem, B., Dmitry, S., and Oleg, K. (2020, January 16\u201325). Geotechnical monitoring of the foundations of structures based on integrated seismoelectric measurements in conditions of karst hazard. Proceedings of the 20th International Multidisciplinary Scientific GeoConference Proceedings SGEM 2020, Albena, Bulgaria.","DOI":"10.5593\/sgem2020\/1.2\/s05.071"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kuzichkin, O., Grecheneva, A., Bykov, A., Dorofeev, N., and Surzhik, D. (2018, January 2\u20138). Methods and algorithms of joint processing of geoelectric and seismoacoustic signals in real time. Proceedings of the SGEM2018 Conference, Albena, Bulgaria.","DOI":"10.5593\/sgem2018\/1.1\/S05.109"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"898","DOI":"10.11591\/eei.v9i3.1727","article-title":"Application of phase-metric compensation method for geoelectric control of near-surface geodynamic processes","volume":"9","author":"Kuzichkin","year":"2020","journal-title":"Bull. Electr. Eng. Inform."},{"key":"ref_26","first-page":"6858","article-title":"Application of phase-metric measuring system for geodynamic control of karst processes","volume":"12","author":"Kuzichkin","year":"2017","journal-title":"J. Eng. Appl. Sci."},{"key":"ref_27","first-page":"463","article-title":"The phase-metric method of isolating the information component in the distributed processing of geoelectric signals in geoecological monitoring systems","volume":"12","author":"Kuzichkin","year":"2020","journal-title":"J. Adv. Res. Dyn. Control Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kuzichkin, O., Dorofeev, N., Grecheneva, A., Bykov, A., and Romanov, R. (July, January 29). The use of vertical electrical sounding by the method of two components for allocation of an initial phase of a landslide. Proceedings of the SGEM2017 Conference, Albena, Bulgaria.","DOI":"10.5593\/sgem2017\/51\/S20.134"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"218","DOI":"10.29042\/2020-10-5-218-224","article-title":"Railway Traffic Monitoring System by Seismic Methods","volume":"10","author":"Kovalenko","year":"2020","journal-title":"Helix"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.jhydrol.2019.05.082","article-title":"Incipient karst formation in carbonate rocks: Influence of fracture network topology","volume":"575","author":"Aliouache","year":"2019","journal-title":"J. Hydrol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"109700","DOI":"10.1016\/j.measurement.2021.109700","article-title":"Measurement and prediction of tunnelling-induced ground settlement in karst region by using expanding deep learning method","volume":"183","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/B978-0-12-811685-2.00011-4","article-title":"Environmental Geophysics","volume":"Volume 2","author":"Eppelbaum","year":"2019","journal-title":"Computational Geophysics, Geophysical Potential Fields"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"126508","DOI":"10.1016\/j.jhydrol.2021.126508","article-title":"Karst modelling challenge 1: Results of hydrological modelling","volume":"600","author":"Jeannin","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"104036","DOI":"10.1016\/j.advwatres.2021.104036","article-title":"The role of aperture heterogeneity in incipient karst evolution in natural fracture networks: Insights from numerical simulations","volume":"156","author":"Wang","year":"2021","journal-title":"Adv. Water Resour."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Soloviev, V. (2018, January 1\u20133). Fintech Ecosystem in Russia. Proceedings of the 2018 11th International Conference; Management of Large-Scale System Development, MLSD, Moscow, Russia.","DOI":"10.1109\/MLSD.2018.8551808"},{"key":"ref_36","unstructured":"Sebyakin, A., Soloviev, V., and Zolotaryuk, A. Proceedings of the 16th International Conference on Information: iConference 2021: Diversity, Divergence, Dialogue, Beijing, China, 17\u201331 March 2021, Springer."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Gataullin, T.M., Gataullin, S.T., and Ivanova, K.V. (2020, January 19\u201320). Modeling an Electronic Auction. Proceedings of the Institute of Scientific Communications Conference: ISC 2020: \u201cSmart Technologies\u201d for Society, State and Economy, Volgograd, Russia.","DOI":"10.1007\/978-3-030-59126-7_122"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Gataullin, T.M., and Gataullin, S.T. (2018, January 1\u20133). Best Economic Approaches under Conditions of Uncertainty. Proceedings of the 2018 Eleventh International Conference \u201cManagement of large-scale system development\u201d (MLSD), Moscow, Russia.","DOI":"10.1109\/MLSD.2018.8551800"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Dogadina, E.P., Smirnov, M.V., Osipov, A.V., and Suvorov, S.V. (2021). Evaluation of the forms of education of high school students using a hybrid model based on various optimization methods and a neural network. Informatics, 8.","DOI":"10.3390\/informatics8030046"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tatarintsev, M., Korchagin, S., Nikitin, P., Gorokhova, R., Bystrenina, I., and Serdechnyy, D. (2021). Analysis of the forecast price as a factor of sustainable development of agriculture. Agronomy, 11.","DOI":"10.3390\/agronomy11061235"}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/9\/24\/3164\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:43:42Z","timestamp":1760168622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/9\/24\/3164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,8]]},"references-count":40,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["math9243164"],"URL":"https:\/\/doi.org\/10.3390\/math9243164","relation":{},"ISSN":["2227-7390"],"issn-type":[{"value":"2227-7390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,8]]}}}