cpomaemКоррозия: защита материалов и методы исследованийTitle in englishИФХЭ РАН10.61852/2949-3412-2023-1-4-1-37cpomaem-27Research ArticleСтатьиПрогноз скорости подземной коррозии стальных трубопроводов. ОбзорForecast of the rate of underground corrosion of steel pipelines. ReviewГаврюшинаМ. А.GavryushinaM. A.

Москва

119071

Leninsky pr. 31

Moscow

maleeva.corlab@yandex.ruМаршаковА. И.MarshakovA. I.

Москва

119071

Leninsky pr. 31

Moscow

ИгнатенкоВ. Э.IgnatenkoV. E.

Москва

119071

Leninsky pr. 31

Moscow

Институт физической химии и электрохимии им. А.Н. Фрумкина РАНРоссияA.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of SciencesRussian Federation20230401202404137Copyright © Гаврюшина М.А., Маршаков А.И., Игнатенко В.Э., 20242024Гаврюшина М.А., Маршаков А.И., Игнатенко В.Э.Gavryushina M.A., Marshakov A.I., Ignatenko V.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cpmrm.ru/jour/article/view/27

   Задача оценки вероятной скорости коррозии подземных стальных трубопроводов давно стоит перед инженерами и учеными и до сих пор актуальна. В настоящем обзоре рассмотрены факторы, влияющие на процесс образования и развития коррозионных дефектов подземных трубопроводов, и различные методы прогнозирования коррозии трубопроводов. Показаны модели различного типа (детерминистские, вероятностные и созданные с помощью машинного обучения) и проведен анализ критериев их применимости.

   The task of estimating the probable corrosion rate of underground steel pipelines has long been facing engineers and scientists and is still relevant. This review examines the factors influencing the formation and development of corrosion defects of underground pipelines, and various methods for predicting corrosion of pipelines. Models of various types (deterministic, probabilistic and created using machine learning) are shown and the criteria of their applicability are analyzed.

малоуглеродистая стальмоделисостав грунтавероятная скорость коррозииметоды машинного обученияlow–carbon steelmodelssoil compositionprobable corrosion ratemachine learning methodsReferencesI.S. Cole and D. Marney, The science of pipe corrosion: A review of the literature on the corrosion of ferrous metals in soils, Corros. Sci., 2012, 56, 5–16. doi: 10.1016/j.corsci.2011.12.001.I.S. Cole and D. Marney, The science of pipe corrosion: A review of the literature on the corrosion of ferrous metals in soils, Corros. Sci., 2012, 56, 5–16. doi: 10.1016/j.corsci.2011.12.001.L. Arriba-Rodriguez, J. Villanueva-Balsera, F. Ortega-Fernandez and F. Rodriguez-Perez, Methods to Evaluate Corrosion in Buried Steel Structures : A Review, Metals, 2018, 8, no. 5, 334. doi: 10.3390/met8050334.L. Arriba-Rodriguez, J. Villanueva-Balsera, F. Ortega-Fernandez and F. Rodriguez-Perez, Methods to Evaluate Corrosion in Buried Steel Structures : A Review, Metals, 2018, 8, no. 5, 334. doi: 10.3390/met8050334.C. Kim, L. Chen, H. Wang and H. Castaneda, Global and local parameters for characterizing and modeling external corrosion in underground coated steel pipelines : A review of critical factors, Journal of Pipeline Science and Engineering, 2021, 1, no. 1, 17–35. doi: 10.1016/j.jpse.2021.01.010.C. Kim, L. Chen, H. Wang and H. Castaneda, Global and local parameters for characterizing and modeling external corrosion in underground coated steel pipelines : A review of critical factors, Journal of Pipeline Science and Engineering, 2021, 1, no. 1, 17–35. doi: 10.1016/j.jpse.2021.01.010.Н.Д. Томашов, А.Ф. Лунев, В.В. Красноярский, Ю.Н. Михайловский и В.В. Леонов, Полевые испытания коррозионной стойкости стали в грунтах. Труды ИФХ АН СССР. Исследования по коррозии металлов, М.: Изд-во АН СССР, 1960, 226–235.Н.Д. Томашов, А.Ф. Лунев, В.В. Красноярский, Ю.Н. Михайловский и В.В. Леонов, Полевые испытания коррозионной стойкости стали в грунтах. Труды ИФХ АН СССР. Исследования по коррозии металлов, М.: Изд-во АН СССР, 1960, 226–235.И.В. Стрижевский, Подземная коррозия и методы защиты, Москва: Металлургия, 1986, 111 c.И.В. Стрижевский, Подземная коррозия и методы защиты, Москва: Металлургия, 1986, 111 c.A.A. Михайлов, Ю.М. Панченко и Ю.И. Кузнецов, Атмосферная коррозия и защита металлов, Под общей ред. Кузнецова Ю.И., Тамбов: Изд. Першина Р.В., 2016, 555 с.A.A. Михайлов, Ю.М. Панченко и Ю.И. Кузнецов, Атмосферная коррозия и защита металлов, Под общей ред. Кузнецова Ю.И., Тамбов: Изд. Першина Р.В., 2016, 555 с.D. Clover, B. Kinsella, B. Pejcic and R. De Marco, The influence of microstructure on the corrosion rate of various carbon steels, J. Appl. Electrochem., 2005, 35, no 2, 139–149. doi: 10.1007/s10800-004-6207-7.D. Clover, B. Kinsella, B. Pejcic and R. De Marco, The influence of microstructure on the corrosion rate of various carbon steels, J. Appl. Electrochem., 2005, 35, no 2, 139–149. doi: 10.1007/s10800-004-6207-7.Y. Zhu, Y. Xu, M. Wang, X. Wang, G. Liu and Y. Huang, Understanding the influences of temperature and microstructure on localized corrosion of subsea pipeline weldment using an integrated multi-electrode array, Ocean Eng., 2019, 189, 106351. doi: 10.1016/j.oceaneng.2019.106351.Y. Zhu, Y. Xu, M. Wang, X. Wang, G. Liu and Y. Huang, Understanding the influences of temperature and microstructure on localized corrosion of subsea pipeline weldment using an integrated multi-electrode array, Ocean Eng., 2019, 189, 106351. doi: 10.1016/j.oceaneng.2019.106351.А.А. Рыбкина, И.В. Касаткина, Н.А. Гладких, М.А. Петрунин и А.И. Маршаков, Скорости роста локальных коррозионных повреждений трубных сталей в модельных грунтовых электролитах, Коррозия: материалы, защита, 2019, no 3, 1–8. doi: 10.31044/1813-7016-2019-0-3-1-8.А.А. Рыбкина, И.В. Касаткина, Н.А. Гладких, М.А. Петрунин и А.И. Маршаков, Скорости роста локальных коррозионных повреждений трубных сталей в модельных грунтовых электролитах, Коррозия: материалы, защита, 2019, no 3, 1–8. doi: 10.31044/1813-7016-2019-0-3-1-8.Коррозионное растрескивание под напряжением труб магистральных трубопроводов. Атлас, Под общей редакцией А.Б. Аребея и З. Кношински, М.: Наука, 2006, 104 с.Коррозионное растрескивание под напряжением труб магистральных трубопроводов. Атлас, Под общей редакцией А.Б. Аребея и З. Кношински, М.: Наука, 2006, 104 с.А.И. Маршаков, А.А. Рыбкина и Н.П. Чеботарева, Об эффекте аномального растворения металлов: кинетика растворения железа в кислых сернокислых электролитах при катодной поляризации, Защита металлов, 1997, 33, no 6, 590–596.А.И. Маршаков, А.А. Рыбкина и Н.П. Чеботарева, Об эффекте аномального растворения металлов: кинетика растворения железа в кислых сернокислых электролитах при катодной поляризации, Защита металлов, 1997, 33, no 6, 590–596.X. Li, F. Xie, D. Wang, C. Xu, M. Wu, D. Sun and J. Qi, Effect of residual and external stress on corrosion behavior of X80 pipeline steel in sulphate–reducing bacteria environment, Eng. Failure Anal., 2018, 91, 275–290. doi: 10.1016/j.engfailanal.2018.04.016.X. Li, F. Xie, D. Wang, C. Xu, M. Wu, D. Sun and J. Qi, Effect of residual and external stress on corrosion behavior of X80 pipeline steel in sulphate–reducing bacteria environment, Eng. Failure Anal., 2018, 91, 275–290. doi: 10.1016/j.engfailanal.2018.04.016.Т.А. Ненашева, А.И. Маршаков и И.В. Касаткина, Образование локальных очагов коррозии трубной стали под действием циклической знакопеременной поляризации, Коррозия: материалы, защита, 2015, 5, 9–17.Т.А. Ненашева, А.И. Маршаков и И.В. Касаткина, Образование локальных очагов коррозии трубной стали под действием циклической знакопеременной поляризации, Коррозия: материалы, защита, 2015, 5, 9–17.А.И. Маршаков и Т.А. Ненашева, Кинетика активного растворения наводороженной углеродистой стали в сульфидсодержащей среде, имитирующей грунтовый электролит, Коррозия: материалы, защита, 2010, 7, 1–6.А.И. Маршаков и Т.А. Ненашева, Кинетика активного растворения наводороженной углеродистой стали в сульфидсодержащей среде, имитирующей грунтовый электролит, Коррозия: материалы, защита, 2010, 7, 1–6.Y. Perlovich, O. Krymskaya, M. Isaenkova, N. Morozov, I. Ryakhovskikh and T. Esiev, Effect of Layer–by–Layer Texture Inhomogeneity on the Stress Corrosion of Gas Steel Tubes, Materials Science Forum, 2017, 879, 1025–1030. doi: 10.4028/www.scientific.net/MSF.879.1025.Y. Perlovich, O. Krymskaya, M. Isaenkova, N. Morozov, I. Ryakhovskikh and T. Esiev, Effect of Layer–by–Layer Texture Inhomogeneity on the Stress Corrosion of Gas Steel Tubes, Materials Science Forum, 2017, 879, 1025–1030. doi: 10.4028/www.scientific.net/MSF.879.1025.M. Nahal, A. Chateauneuf and Y. Sahraoui, Reliability analysis of irregular zones in pipelines under both effects of corrosion and residual stress, Eng. Failure Anal., 2019, 98, 177–188. doi: 10.1016/j.engfailanal.2019.01.081.M. Nahal, A. Chateauneuf and Y. Sahraoui, Reliability analysis of irregular zones in pipelines under both effects of corrosion and residual stress, Eng. Failure Anal., 2019, 98, 177–188. doi: 10.1016/j.engfailanal.2019.01.081.A. Amirat, A. Mohamed-Chateauneuf and K. Chaoui, Reliability assessment of underground pipelines under the combined effect of active corrosion and residual stress, Int. J. Pressure Vessels Piping., 2006, 83, no 2, 107–117. doi: 10.1016/j.ijpvp.2005.11.004.A. Amirat, A. Mohamed-Chateauneuf and K. Chaoui, Reliability assessment of underground pipelines under the combined effect of active corrosion and residual stress, Int. J. Pressure Vessels Piping., 2006, 83, no 2, 107–117. doi: 10.1016/j.ijpvp.2005.11.004.Н.Д. Томашов и Ю.Н. Михайловский, ДАН СССР, 1956, 110, no 6, 1026.Н.Д. Томашов и Ю.Н. Михайловский, ДАН СССР, 1956, 110, no 6, 1026.A. Rim-Rukeh and J.K. Awatefe, Investigation of soil corrosivity in the corrosion of low carbon steel pipe in soil environment, J. Appl. Sci. Res., 2006, 2, no 8, 466–469.A. Rim-Rukeh and J.K. Awatefe, Investigation of soil corrosivity in the corrosion of low carbon steel pipe in soil environment, J. Appl. Sci. Res., 2006, 2, no 8, 466–469.Z. Ahmad, Principles of Corrosion Engineering and Corrosion Control, Elsevier: Oxford, UK, 2006.Z. Ahmad, Principles of Corrosion Engineering and Corrosion Control, Elsevier: Oxford, UK, 2006.EN 12501-2. Protection of Metallic Materials against Corrosion. CORROSION Likelihood in Soil. Part 2: Low Alloyed and Unalloyed Ferrous Materials; European Standard Store: Pilsen, Czech Republic, 2003.EN 12501-2. Protection of Metallic Materials against Corrosion. CORROSION Likelihood in Soil. Part 2: Low Alloyed and Unalloyed Ferrous Materials; European Standard Store: Pilsen, Czech Republic, 2003.ANSI/AWWA C105. Ductile-Iron Pipe Standard; American Water Works Association, Denver, CO, USA, 2012.ANSI/AWWA C105. Ductile-Iron Pipe Standard; American Water Works Association, Denver, CO, USA, 2012.P.R. Roberge, Handbook of Corrosion Engineering, McGraw-Hill: Columbus, OH, USA, 2000.P.R. Roberge, Handbook of Corrosion Engineering, McGraw-Hill: Columbus, OH, USA, 2000.G. Heim and K.W. Schwen, Corrosion in Aqueous Solutions and Soil. In Handbook of Cathodic Corrosion Protection, 3<sup>rd</sup> ed., Gulf Professional Publishing: Houston, TX, USA, 1997, 139–152.G. Heim and K.W. Schwen, Corrosion in Aqueous Solutions and Soil. In Handbook of Cathodic Corrosion Protection, 3<sup>rd</sup> ed., Gulf Professional Publishing: Houston, TX, USA, 1997, 139–152.DIN 50929 part 3. Probability of corrosion of metallic materials when subject to corrosion from the outside. Buried and underwater pipelines and structural components, German Institute for Standardization: Berlin, Germany, 1985.DIN 50929 part 3. Probability of corrosion of metallic materials when subject to corrosion from the outside. Buried and underwater pipelines and structural components, German Institute for Standardization: Berlin, Germany, 1985.ГОСТ 9.602-2005. Сооружения подземные. Общие требования к защите от коррозии.ГОСТ 9.602-2005. Сооружения подземные. Общие требования к защите от коррозии.ASTM G187-12a. Standard Test Method for Measurement of Soil Resistivity Using the Two-Electrode Soil Box Method, ASTM International: West Conshohocken, PA, USA, 2012.ASTM G187-12a. Standard Test Method for Measurement of Soil Resistivity Using the Two-Electrode Soil Box Method, ASTM International: West Conshohocken, PA, USA, 2012.J.P. Busby, D. Entwisle, P. Hobbs, P. Jackson, N. Johnson, R. Lawley, K. Linley, T. Mayr, R. Palmer, M. Raines, H. Reeves, S. Tucker and J. Zawadska, A GIS for the planning of electrical earthing, Q. J. Eng. Geol. Hydrogeol., 2012, 45, no 3, 379–390. doi: 10.1144/1470-9236/11-023.J.P. Busby, D. Entwisle, P. Hobbs, P. Jackson, N. Johnson, R. Lawley, K. Linley, T. Mayr, R. Palmer, M. Raines, H. Reeves, S. Tucker and J. Zawadska, A GIS for the planning of electrical earthing, Q. J. Eng. Geol. Hydrogeol., 2012, 45, no 3, 379–390. doi: 10.1144/1470-9236/11-023.Н.Д. Томашов, Ю.Н. Михайловский и В.В. Леонов, ЖФХ, 1961, 35 no 4, 736.Н.Д. Томашов, Ю.Н. Михайловский и В.В. Леонов, ЖФХ, 1961, 35 no 4, 736.Ю.Н. Михайловский, П.И. Зубов, В.И. Завражина, С.Ф. Наумова, Е.М. Соколова и В.Б. Серафимович, Исследование кинетики коррозии металлов под полимерными покрытиями, Труды 111 Международного конгресса по коррозии металлов, 1968.Ю.Н. Михайловский, П.И. Зубов, В.И. Завражина, С.Ф. Наумова, Е.М. Соколова и В.Б. Серафимович, Исследование кинетики коррозии металлов под полимерными покрытиями, Труды 111 Международного конгресса по коррозии металлов, 1968.M. Xu, C.N. Catherine Lam, D. Wong and E. Asselin, Evaluation of the cathodic disbondment resistance of pipeline coatings – A review, Prog. Org. Coat., 2020, 146, 105728. doi: 10.1016/j.porgcoat.2020.105728.M. Xu, C.N. Catherine Lam, D. Wong and E. Asselin, Evaluation of the cathodic disbondment resistance of pipeline coatings – A review, Prog. Org. Coat., 2020, 146, 105728. doi: 10.1016/j.porgcoat.2020.105728.F.M. Song, A mathematical model developed to predict the chemistry and corrosion rate in a crevice of variable gap, Electrochim. Acta, 2011, 56, no 19, 6789–6803. doi: 10.1016/j.electacta.2011.05.083.F.M. Song, A mathematical model developed to predict the chemistry and corrosion rate in a crevice of variable gap, Electrochim. Acta, 2011, 56, no 19, 6789–6803. doi: 10.1016/j.electacta.2011.05.083.M. Meyer, X. Campaignolle, F. Coeuille and M.E.R. Shanahan, Impact of aging processes on anticorrosion properties of thick polymer coatings for steel pipelines, Proceedings of the Corrosion/2004 Research Topical Symposium: Corrosion Modeling for Assessing the Condition of Oil and Gas Pipelines, 2004, 93–146.M. Meyer, X. Campaignolle, F. Coeuille and M.E.R. Shanahan, Impact of aging processes on anticorrosion properties of thick polymer coatings for steel pipelines, Proceedings of the Corrosion/2004 Research Topical Symposium: Corrosion Modeling for Assessing the Condition of Oil and Gas Pipelines, 2004, 93–146.R.R. Fessler, A.J. Markworth and R.N. Parkins, Cathodic Protection Levels under Disbonded Coatings, Corrosion, 1983, 39, no 1, 20–25. doi: 10.5006/1.3580809.R.R. Fessler, A.J. Markworth and R.N. Parkins, Cathodic Protection Levels under Disbonded Coatings, Corrosion, 1983, 39, no 1, 20–25. doi: 10.5006/1.3580809.T.R. Jack, G.V. Boven, M.J. Wilmott, R.L. Sutherby and R.G. Worthingham, Cathodic protection potential penetration under disbonded pipeline coating, Mater. Perform., 1994, 33, no 8, 17–21.T.R. Jack, G.V. Boven, M.J. Wilmott, R.L. Sutherby and R.G. Worthingham, Cathodic protection potential penetration under disbonded pipeline coating, Mater. Perform., 1994, 33, no 8, 17–21.A. Turnbull and A.T. May, Cathodic protection of crevices in BS 4360 50D structural steel in 3.5 % NaCl and in seawater, Mater. Perform., 1983, 22, no 10, 34–38.A. Turnbull and A.T. May, Cathodic protection of crevices in BS 4360 50D structural steel in 3.5 % NaCl and in seawater, Mater. Perform., 1983, 22, no 10, 34–38.J.J. Perdomo and I. Song, Chemical and electrochemical conditions on steel under disbonded coatings: the effect of applied potential, solution resistivity, crevice thickness and holiday size, Corros. Sci., 2000, 42, no 8, 1389–1415. doi: 10.1016/S0010-938X(99)00136-5.J.J. Perdomo and I. Song, Chemical and electrochemical conditions on steel under disbonded coatings: the effect of applied potential, solution resistivity, crevice thickness and holiday size, Corros. Sci., 2000, 42, no 8, 1389–1415. doi: 10.1016/S0010-938X(99)00136-5.M.H. Peterson and T.J. Lennox, A Study of Cathodic Polarization and pH Changes in Metal Crevices, Corrosion, 1973, 29, no 10, 406–412. doi: 10.5006/0010-9312-29.10.406.M.H. Peterson and T.J. Lennox, A Study of Cathodic Polarization and pH Changes in Metal Crevices, Corrosion, 1973, 29, no 10, 406–412. doi: 10.5006/0010-9312-29.10.406.A.C. Toncre and N. Ahmad, Cathodic protection in crevices under disbonded coatings, Mater. Perform., 1980, 19, no 6, 39–43.A.C. Toncre and N. Ahmad, Cathodic protection in crevices under disbonded coatings, Mater. Perform., 1980, 19, no 6, 39–43.M.D. Orton, The effectiveness of cathodic protection under unbonded coatings on pipelines, Mater. Perform., 1985, 24, no 6, 17–20.M.D. Orton, The effectiveness of cathodic protection under unbonded coatings on pipelines, Mater. Perform., 1985, 24, no 6, 17–20.F.M. Song, Predicting the effect of soil seasonal change on stress corrosion cracking susceptibility of buried pipelines at high pH, Corrosion, 2010, 66, no 9, 95004–950014. doi: 10.5006/1.3490309.F.M. Song, Predicting the effect of soil seasonal change on stress corrosion cracking susceptibility of buried pipelines at high pH, Corrosion, 2010, 66, no 9, 95004–950014. doi: 10.5006/1.3490309.F.M. Song, D.W. Kirk, D.E. Cormack and D. Wong, Barrier properties of two field pipeline coatings, Mater. Perform., 2005, 44, no 4, 26–29.F.M. Song, D.W. Kirk, D.E. Cormack and D. Wong, Barrier properties of two field pipeline coatings, Mater. Perform., 2005, 44, no 4, 26–29.F.M. Song, D.W. Kirk, J.W. Graydon and D.E. Cormack, Steel Corrosion under a Disbonded Coating with a Holiday—Part 2: Corrosion Behavior, Corrosion, 2003, 59, no 1, 42–49. doi: 10.5006/1.3277535.F.M. Song, D.W. Kirk, J.W. Graydon and D.E. Cormack, Steel Corrosion under a Disbonded Coating with a Holiday—Part 2: Corrosion Behavior, Corrosion, 2003, 59, no 1, 42–49. doi: 10.5006/1.3277535.F.M. Song, D.A. Jones and D.W. Kirk, Predicting Corrosion and Current Flow within a Disc Crevice on Coated Steels, Corrosion, 2005, 60, no 2, 145–154. doi: 10.5006/1.3278169.F.M. Song, D.A. Jones and D.W. Kirk, Predicting Corrosion and Current Flow within a Disc Crevice on Coated Steels, Corrosion, 2005, 60, no 2, 145–154. doi: 10.5006/1.3278169.F.M. Song and N. Sridhar, A Two-Dimensional Model for Steel Corrosion under a Disbonded Coating Due to Oxygen with or without Cathodic Protection—Part 1: Full Numerical Solution, Corrosion, 2006, 62, no 8, 676. doi: 10.5006/1.3278294.F.M. Song and N. Sridhar, A Two-Dimensional Model for Steel Corrosion under a Disbonded Coating Due to Oxygen with or without Cathodic Protection—Part 1: Full Numerical Solution, Corrosion, 2006, 62, no 8, 676. doi: 10.5006/1.3278294.F.M. Song and N. Sridhar, A Two-Dimensional Model for Steel Corrosion under a Disbonded Coating Due to Oxygen with or without Cathodic Protection—Part 2: Model Simplification for Practical Application, Corrosion, 2006, 62, no 10, 873–882. doi: 10.5006/1.3279897.F.M. Song and N. Sridhar, A Two-Dimensional Model for Steel Corrosion under a Disbonded Coating Due to Oxygen with or without Cathodic Protection—Part 2: Model Simplification for Practical Application, Corrosion, 2006, 62, no 10, 873–882. doi: 10.5006/1.3279897.F.M. Song and N. Sridhar, Modeling pipeline crevice corrosion under a disbonded coating with or without cathodic protection under transient and steady state conditions, Corros. Sci., 2008, 50, no 1, 70–83. doi: 10.1016/j.corsci.2007.05.024.F.M. Song and N. Sridhar, Modeling pipeline crevice corrosion under a disbonded coating with or without cathodic protection under transient and steady state conditions, Corros. Sci., 2008, 50, no 1, 70–83. doi: 10.1016/j.corsci.2007.05.024.F. King, T. Jack, M. Kolar and R. Worthingham, A permeable coating model for predicting the environment at the pipe surface under CP-compatible coatings, The 5<sup>–th</sup> biennial international pipeline conference, IPC 2004: the power of technology, 2004.F. King, T. Jack, M. Kolar and R. Worthingham, A permeable coating model for predicting the environment at the pipe surface under CP-compatible coatings, The 5<sup>–th</sup> biennial international pipeline conference, IPC 2004: the power of technology, 2004.F.M. Song, Simple algorithms for 1D oxygen concentration profile in an occluded region, Corros. Sci., 2008, 50, no 12, 3287–3295. doi: 10.1016/j.corsci.2008.08.039.F.M. Song, Simple algorithms for 1D oxygen concentration profile in an occluded region, Corros. Sci., 2008, 50, no 12, 3287–3295. doi: 10.1016/j.corsci.2008.08.039.F.M. Song, Predicting the chemistry, corrosion potential and corrosion rate in a crevice formed between substrate steel and a disbonded permeable coating with a mouth, Corros. Sci., 2012, 55, no 2, 107–115. doi: 10.1016/j.corsci.2011.10.013.F.M. Song, Predicting the chemistry, corrosion potential and corrosion rate in a crevice formed between substrate steel and a disbonded permeable coating with a mouth, Corros. Sci., 2012, 55, no 2, 107–115. doi: 10.1016/j.corsci.2011.10.013.M. Yan, J. Wang, E. Han and W. Ke, Local environment under simulated disbonded coating on steel pipelines in soil solution, Corros. Sci., 2008, 50, no 5, 1331–1339. doi: 10.1016/j.corsci.2008.01.004.M. Yan, J. Wang, E. Han and W. Ke, Local environment under simulated disbonded coating on steel pipelines in soil solution, Corros. Sci., 2008, 50, no 5, 1331–1339. doi: 10.1016/j.corsci.2008.01.004.J.J. Perdomo, M.E. Chabica and I. Song, Chemical and electrochemical conditions on steel under disbonded coatings: the effect of previously corroded surfaces and wet and dry cycles, Corros. Sci., 2001, 43, no 3, 515–532. doi: 10.1016/S0010-938X(00)00103-7.J.J. Perdomo, M.E. Chabica and I. Song, Chemical and electrochemical conditions on steel under disbonded coatings: the effect of previously corroded surfaces and wet and dry cycles, Corros. Sci., 2001, 43, no 3, 515–532. doi: 10.1016/S0010-938X(00)00103-7.Q. Cao, T. Pojtanabuntoeng, M. Esmaily, S. Thomas, M. Brameld, A. Amer and N. Birbilis, A Review of Corrosion under Insulation: A Critical Issue in the Oil and Gas Industry, Metals, 2022, 12, no 4, 561. doi: 10.3390/met12040561.Q. Cao, T. Pojtanabuntoeng, M. Esmaily, S. Thomas, M. Brameld, A. Amer and N. Birbilis, A Review of Corrosion under Insulation: A Critical Issue in the Oil and Gas Industry, Metals, 2022, 12, no 4, 561. doi: 10.3390/met12040561.M.G. Fontana and R.W. Staehle, Advances in Corrosion Science and Technology; Springer Science & Business Media: Berlin, Germany, 2013.M.G. Fontana and R.W. Staehle, Advances in Corrosion Science and Technology; Springer Science & Business Media: Berlin, Germany, 2013.E.M. Gutman, Mechanochemistry of Materials, Cambridge: Cambridge Interscience Publishing, 1998.E.M. Gutman, Mechanochemistry of Materials, Cambridge: Cambridge Interscience Publishing, 1998.L.Y. Xu and Y.F. Cheng, An experimental investigation of corrosion of X100 pipeline steel under uniaxial elastic stress in a near-neutral pH solution, Corros. Sci., 2012, 59, no 6, 103–109. doi: 10.1016/j.corsci.2012.02.022.L.Y. Xu and Y.F. Cheng, An experimental investigation of corrosion of X100 pipeline steel under uniaxial elastic stress in a near-neutral pH solution, Corros. Sci., 2012, 59, no 6, 103–109. doi: 10.1016/j.corsci.2012.02.022.L.Y. Xu and Y.F. Cheng, Development of a finite element model for simulation and prediction of mechano–electrochemical effect of pipeline corrosion, Corros. Sci., 2013, 73, no 8, 150–160. doi: 10.1016/j.corsci.2013.04.004.L.Y. Xu and Y.F. Cheng, Development of a finite element model for simulation and prediction of mechano–electrochemical effect of pipeline corrosion, Corros. Sci., 2013, 73, no 8, 150–160. doi: 10.1016/j.corsci.2013.04.004.L.Y. Xu and Y.F. Cheng, A finite element based model for prediction of corrosion defect growth on pipelines, Int. J. Pressure Vessels Piping, 2017, 153, no 6, 70–79. doi: 10.1016/j.ijpvp.2017.05.002.L.Y. Xu and Y.F. Cheng, A finite element based model for prediction of corrosion defect growth on pipelines, Int. J. Pressure Vessels Piping, 2017, 153, no 6, 70–79. doi: 10.1016/j.ijpvp.2017.05.002.E.M. Gutman, Mechanochemistry of Solid Surfaces, Singapore: World Scientific Publication, 1994.E.M. Gutman, Mechanochemistry of Solid Surfaces, Singapore: World Scientific Publication, 1994.M. Wasim, S. Shoaib, N.M. Mubarak and A.M. Asiri, Factors influencing corrosion of metal pipes in soils, Environ. Chem. Lett., 2018, 16, 861–879. doi: 10.1007/s10311-018-0731-x.M. Wasim, S. Shoaib, N.M. Mubarak and A.M. Asiri, Factors influencing corrosion of metal pipes in soils, Environ. Chem. Lett., 2018, 16, 861–879. doi: 10.1007/s10311-018-0731-x.X.H. Nie, X.G. Li, C.W. Du and Y.F. Cheng, Temperature dependence of the electrochemical corrosion characteristics of carbon steel in a salty soil, J. Appl. Electrochem., 2009, 39, 277–282. doi: 10.1007/s10800-008-9669-1.X.H. Nie, X.G. Li, C.W. Du and Y.F. Cheng, Temperature dependence of the electrochemical corrosion characteristics of carbon steel in a salty soil, J. Appl. Electrochem., 2009, 39, 277–282. doi: 10.1007/s10800-008-9669-1.A.W. Peabody, Peabody’s Control of Pipeline Corrosion, NACE International: Houston, TX, USA, 2001.A.W. Peabody, Peabody’s Control of Pipeline Corrosion, NACE International: Houston, TX, USA, 2001.J. Bhattarai, Study on the corrosive nature of soil towards the buried-structures, Sci. World J., 2013, 11, no 11, 43–47. doi: 10.3126/sw.v11i11.8551J. Bhattarai, Study on the corrosive nature of soil towards the buried-structures, Sci. World J., 2013, 11, no 11, 43–47. doi: 10.3126/sw.v11i11.8551R.L. Starkey and K.M. Wight, Anaerobic Corrosion of Iron in Soil: Soil Science, LWW: Philadelphia, PA, USA, 1946, 62.R.L. Starkey and K.M. Wight, Anaerobic Corrosion of Iron in Soil: Soil Science, LWW: Philadelphia, PA, USA, 1946, 62.L. Veleva, Soils and Corrosion (Chapter 32). In Corrosion Tests and Standards: Application and Interpretation, 2<sup>nd</sup> ed., ASTM International: West Conshohocken, PA, USA, 2005.L. Veleva, Soils and Corrosion (Chapter 32). In Corrosion Tests and Standards: Application and Interpretation, 2<sup>nd</sup> ed., ASTM International: West Conshohocken, PA, USA, 2005.DVGW GW 9:2011. Evaluation of Soils in View of Their Corrosion Behavior towards Buried Pipelines and Vessels of Non–Alloyed Iron Materials; German Technical and Scientific Association for Gas and Water, Bonn, Germany, 2011.DVGW GW 9:2011. Evaluation of Soils in View of Their Corrosion Behavior towards Buried Pipelines and Vessels of Non–Alloyed Iron Materials; German Technical and Scientific Association for Gas and Water, Bonn, Germany, 2011.J. Robinson, Predicting the In–Ground Performance of Galvanized Steel, Mount Townsend Solutions Pty Ltd.: Jesmond, Australia, 2005.J. Robinson, Predicting the In–Ground Performance of Galvanized Steel, Mount Townsend Solutions Pty Ltd.: Jesmond, Australia, 2005.The Design Decision Model for Corrosion Control of Ductile Iron Pipelines, Ductile Iron Pipe Research Association: Birmingham, AL, USA, 2016.The Design Decision Model for Corrosion Control of Ductile Iron Pipelines, Ductile Iron Pipe Research Association: Birmingham, AL, USA, 2016.I.A. Denison and R.B. Darniele, Observations on the behavior of steel corroding under cathodic control in soils, Trans. Electrochem. Soc., 1939, 76, no 1, 199–214.I.A. Denison and R.B. Darniele, Observations on the behavior of steel corroding under cathodic control in soils, Trans. Electrochem. Soc., 1939, 76, no 1, 199–214.G. Doyle, M.V. Seica and M.W.F. Grabinsky, The role of soil in the external corrosion of cast iron water mains in Toronto, Canada, Can. Geotech. J., 2003, 40, 2, 225–236. doi: 10.1139/t02-106.G. Doyle, M.V. Seica and M.W.F. Grabinsky, The role of soil in the external corrosion of cast iron water mains in Toronto, Canada, Can. Geotech. J., 2003, 40, 2, 225–236. doi: 10.1139/t02-106.F. Kajiyama and Y. Koyama, Statistical analyses of field corrosion data for ductile cast iron pipes buried in sandy marine sediments, Corrosion, 1997, 53, no 2, 156–162. doi: 10.5006/1.3280453.F. Kajiyama and Y. Koyama, Statistical analyses of field corrosion data for ductile cast iron pipes buried in sandy marine sediments, Corrosion, 1997, 53, no 2, 156–162. doi: 10.5006/1.3280453.Y. Katano, K. Miyata, H. Shimizu and T. Isogai, Predictive model for pit growth on underground pipes, Corrosion, 2003, 59, no 2, 155–161. doi: 10.5006/1.3277545.Y. Katano, K. Miyata, H. Shimizu and T. Isogai, Predictive model for pit growth on underground pipes, Corrosion, 2003, 59, no 2, 155–161. doi: 10.5006/1.3277545.K.H. Logan, Underground Corrosion, National Bureau of Standards (USA), Washington, DC, 1945.K.H. Logan, Underground Corrosion, National Bureau of Standards (USA), Washington, DC, 1945.M. Romanoff, Underground Corrosion, National Bureau of Standards (USA), NBS Circular 579, Gaithersburg, MD, 1957.M. Romanoff, Underground Corrosion, National Bureau of Standards (USA), NBS Circular 579, Gaithersburg, MD, 1957.R.E. Ricker, Analysis of Pipeline Steel Corrosion Data from NBS (NIST) Studies Conducted between 1922–1940 and Relevance to Pipeline Management, Journal of Research (NIST JRES), 2010, 115, no 5, 373–392. doi: 10.6028/jres.115.026.R.E. Ricker, Analysis of Pipeline Steel Corrosion Data from NBS (NIST) Studies Conducted between 1922–1940 and Relevance to Pipeline Management, Journal of Research (NIST JRES), 2010, 115, no 5, 373–392. doi: 10.6028/jres.115.026.R.F. Stratful, A new test for estimating soil corrosivity based on investigation of metal highway culverts, Corrosion, 1961, 17, no 10, 115–118. doi: 10.5006/0010-9312-17.10.115.R.F. Stratful, A new test for estimating soil corrosivity based on investigation of metal highway culverts, Corrosion, 1961, 17, no 10, 115–118. doi: 10.5006/0010-9312-17.10.115.J.A. Beavers and C.L. Durr, Corrosion of Steel Piling in non-Marine Application, report 408 National Cooperative Highway Research Program, Transportation Research Board, National Academy Press, Washington, D.C., 1998.J.A. Beavers and C.L. Durr, Corrosion of Steel Piling in non-Marine Application, report 408 National Cooperative Highway Research Program, Transportation Research Board, National Academy Press, Washington, D.C., 1998.O.E Picozzi, S.E. Lamb and A.C. Frank, Evaluation of prediction Methods for Pile Corrosion at the Buffalo Skyway, New York State Departament of Transportation, Technical Service Division, Albany, NY, 1993.O.E Picozzi, S.E. Lamb and A.C. Frank, Evaluation of prediction Methods for Pile Corrosion at the Buffalo Skyway, New York State Departament of Transportation, Technical Service Division, Albany, NY, 1993.P. Cazenave and R. Mcnealy, Some consideration in the determination of corrosion growth rates and remaining life from single In–line inspections, 2007.P. Cazenave and R. Mcnealy, Some consideration in the determination of corrosion growth rates and remaining life from single In–line inspections, 2007.F. Caleyo, J.M. Hallen, J.L. Gonzalez and F. Fernandez-Lagos, Reliability-based assessment method assesses corroding pipelines, Oil Gas J., 2003, 101, no 2, 56–61.F. Caleyo, J.M. Hallen, J.L. Gonzalez and F. Fernandez-Lagos, Reliability-based assessment method assesses corroding pipelines, Oil Gas J., 2003, 101, no 2, 56–61.M.M. Din, M.A. Ngadi and N.M. Noor, Improving inspection data quality in pipeline corrosion assessment, International conference on computer engineering and applications, 2009.M.M. Din, M.A. Ngadi and N.M. Noor, Improving inspection data quality in pipeline corrosion assessment, International conference on computer engineering and applications, 2009.A. Valor, F. Caleyo, J.M. Hallen and J.C. Velazquez, Reliability assessment of buried pipelines based on different corrosion rate models, Mexico, Corros. Sci., 2013, 66, no 1, 78–87. doi: 10.1016/j.corsci.2012.09.005.A. Valor, F. Caleyo, J.M. Hallen and J.C. Velazquez, Reliability assessment of buried pipelines based on different corrosion rate models, Mexico, Corros. Sci., 2013, 66, no 1, 78–87. doi: 10.1016/j.corsci.2012.09.005.J.R. Rossum, Prediction of pitting rates in ferrous metals from soil parameters, Journal of American Water Works Association, 1969, 61, no 6, 305–310.J.R. Rossum, Prediction of pitting rates in ferrous metals from soil parameters, Journal of American Water Works Association, 1969, 61, no 6, 305–310.S.F. Mughabghab and T.M. Sullivan, Evaluation of the pitting corrosion of carbon steels and other ferrous metals in soil systems, Waste Management, 1989, 9, no 4, 239–251. doi: 10.1016/0956-053X(89)90408-X.S.F. Mughabghab and T.M. Sullivan, Evaluation of the pitting corrosion of carbon steels and other ferrous metals in soil systems, Waste Management, 1989, 9, no 4, 239–251. doi: 10.1016/0956-053X(89)90408-X.J.M. Race, S.J. Dawson, L. Stanley and S. Kariyawasam, Predicting Corrosion Rates for Onshore Oil and Gas Pipelines, In Proceedings of the 6<sup>th</sup> International Pipeline Conference, Calgary, AB, Canada, 25–29 September 2006, Paper: IPC2006-10261, 385–396. doi: 10.1115/IPC2006-10261.J.M. Race, S.J. Dawson, L. Stanley and S. Kariyawasam, Predicting Corrosion Rates for Onshore Oil and Gas Pipelines, In Proceedings of the 6<sup>th</sup> International Pipeline Conference, Calgary, AB, Canada, 25–29 September 2006, Paper: IPC2006-10261, 385–396. doi: 10.1115/IPC2006-10261.J.C. Velazquez, F. Caleyo, A. Valor and J.M. Hallen, Predictive model for pitting corrosion in buried oil and gas pipelines, Corrosion, 2009, 65, no 5, 332–342. doi: 10.5006/1.3319138.J.C. Velazquez, F. Caleyo, A. Valor and J.M. Hallen, Predictive model for pitting corrosion in buried oil and gas pipelines, Corrosion, 2009, 65, no 5, 332–342. doi: 10.5006/1.3319138.J.C. Velazquez, F. Caleyo, A. Valor and J.M. Hallen, Technical note: Field Study – Pitting Corrosion of Underground Pipelines Related to Local Soil and Pipe Characteristics, Corrosion, 2010, 66, no 1, 1–5. doi: 10.5006/1.3318290.J.C. Velazquez, F. Caleyo, A. Valor and J.M. Hallen, Technical note: Field Study – Pitting Corrosion of Underground Pipelines Related to Local Soil and Pipe Characteristics, Corrosion, 2010, 66, no 1, 1–5. doi: 10.5006/1.3318290.J.L. Alamilla, M.A. Espinosa-Medina and E. Sosa, Modelling steel corrosion damage in soil environment, Corros. Sci., 2009, 51, no 11, 2628–2638. doi: 10.1016/j.corsci.2009.06.052.J.L. Alamilla, M.A. Espinosa-Medina and E. Sosa, Modelling steel corrosion damage in soil environment, Corros. Sci., 2009, 51, no 11, 2628–2638. doi: 10.1016/j.corsci.2009.06.052.J. Du, J. Zheng, Y. Liang, N. Xu, Q. Liao, B. Wang and H. Zhang, Deeppipe: Theory-guided prediction method based automatic machine learning for maximum pitting corrosion depth of oil and gas pipeline, Chem. Eng. Sci., 2023, 278, 118927. doi: 10.1016/j.ces.2023.118927.J. Du, J. Zheng, Y. Liang, N. Xu, Q. Liao, B. Wang and H. Zhang, Deeppipe: Theory-guided prediction method based automatic machine learning for maximum pitting corrosion depth of oil and gas pipeline, Chem. Eng. Sci., 2023, 278, 118927. doi: 10.1016/j.ces.2023.118927.H.R. Vanaei, A. Eslami and A. Egbewande, A review on pipeline corrosion, in-line inspection (ILI), and corrosion growth rate models, International Journal of Pressure Vessels and Piping, 2017, 149, 43–54. doi: 10.1016/j.ijpvp.2016.11.007.H.R. Vanaei, A. Eslami and A. Egbewande, A review on pipeline corrosion, in-line inspection (ILI), and corrosion growth rate models, International Journal of Pressure Vessels and Piping, 2017, 149, 43–54. doi: 10.1016/j.ijpvp.2016.11.007.J.L. Alamilla, E. Sosa, Stochastic modelling of corrosion damage propagation in active sites from field inspection data, Corros. Sci., 2008, 50, no 7, 1811–1819. doi: 10.1016/j.corsci.2008.03.005.J.L. Alamilla, E. Sosa, Stochastic modelling of corrosion damage propagation in active sites from field inspection data, Corros. Sci., 2008, 50, no 7, 1811–1819. doi: 10.1016/j.corsci.2008.03.005.F. Caleyo, J.C. Velazquez, A. Valor and J.M. Hallen, Probability distribution of pitting corrosion depth and rate in underground pipelines: a Monte Carlo study, Corros. Sci., 2009, 51, no 9, 1925–1934. doi: 10.1016/j.corsci.2009.05.019.F. Caleyo, J.C. Velazquez, A. Valor and J.M. Hallen, Probability distribution of pitting corrosion depth and rate in underground pipelines: a Monte Carlo study, Corros. Sci., 2009, 51, no 9, 1925–1934. doi: 10.1016/j.corsci.2009.05.019.J. D. Whiteside II, A practical application of Monte Carlo simulation in forecasting, AACE International Transactions EST.04.1, 2008.J. D. Whiteside II, A practical application of Monte Carlo simulation in forecasting, AACE International Transactions EST.04.1, 2008.J.A. Kiefner and K.M.K. Kiefner, Calculation of corrosion rate using Monte Carlo simulation, NACE corrosion conference, 2007.J.A. Kiefner and K.M.K. Kiefner, Calculation of corrosion rate using Monte Carlo simulation, NACE corrosion conference, 2007.ANSI/NACE Standard RP0502-2002, Pipeline external corrosion direct assessment methodology, NACE, Houston, Texas, 2002.ANSI/NACE Standard RP0502-2002, Pipeline external corrosion direct assessment methodology, NACE, Houston, Texas, 2002.С.А. Тимашев, А.В. Бушинская, М.Г. Малюкова и Л.В. Полуян, Целостность и безопасность трубопроводных систем, НИЦ «НиР БСМ» УрО РАН, 2013, 349–392.С.А. Тимашев, А.В. Бушинская, М.Г. Малюкова и Л.В. Полуян, Целостность и безопасность трубопроводных систем, НИЦ «НиР БСМ» УрО РАН, 2013, 349–392.S.A. Timashev, M.G. Malyukova, L.V. Poluian and A.V. Bushiskaya, Markov description of corrosion defects growth and its application to reliability based inspection and maintenance of pipelines, in: Proc. 7th ASME Int. Pipeline Conf. IPC2008, Calgary, Canada, Paper IPC2008-64546, 2008, September 26–29.S.A. Timashev, M.G. Malyukova, L.V. Poluian and A.V. Bushiskaya, Markov description of corrosion defects growth and its application to reliability based inspection and maintenance of pipelines, in: Proc. 7th ASME Int. Pipeline Conf. IPC2008, Calgary, Canada, Paper IPC2008-64546, 2008, September 26–29.F. Caleyo, J.C. Velazquez, A. Valor and J.M. Hallen, Markov chain modelling of pitting corrosion in underground pipelines, Corros. Sci., 2009, 51, 2197–2207. doi: 10.1016/j.corsci.2009.06.014.F. Caleyo, J.C. Velazquez, A. Valor and J.M. Hallen, Markov chain modelling of pitting corrosion in underground pipelines, Corros. Sci., 2009, 51, 2197–2207. doi: 10.1016/j.corsci.2009.06.014.H. Hong, Inspection and maintenance planning of pipeline under external corrosion considering generation of new defects, Structural Safety, 1999, 21, no 3, 203–222. doi: 10.1016/S0167-4730(99)00016-8.H. Hong, Inspection and maintenance planning of pipeline under external corrosion considering generation of new defects, Structural Safety, 1999, 21, no 3, 203–222. doi: 10.1016/S0167-4730(99)00016-8.H. Wang, A. Yajima and H. Castaned, A stochastic defect growth model for reliability assessment of corroded underground pipelines, Process Saf. Environ. Prot., 2019, 123, 179–189. doi: 10.1016/j.psep.2019.01.005H. Wang, A. Yajima and H. Castaned, A stochastic defect growth model for reliability assessment of corroded underground pipelines, Process Saf. Environ. Prot., 2019, 123, 179–189. doi: 10.1016/j.psep.2019.01.005W. Xiang, W. Zhou, A Nonparametric Bayesian Network Model for Predicting Corrosion Depth on Buried Pipelines, Corrosion, 2020, 76, no 3, 235–247. doi: 10.5006/3421.W. Xiang, W. Zhou, A Nonparametric Bayesian Network Model for Predicting Corrosion Depth on Buried Pipelines, Corrosion, 2020, 76, no 3, 235–247. doi: 10.5006/3421.N. Balekelayi and S. Tesfamariam, External corrosion pitting depth prediction using Bayesian spectral analysis on bare oil and gas pipelines, Int. J. Pressure Vessels Piping, 2020, 188, article: 104224. doi: 10.1016/j.ijpvp.2020.104224.N. Balekelayi and S. Tesfamariam, External corrosion pitting depth prediction using Bayesian spectral analysis on bare oil and gas pipelines, Int. J. Pressure Vessels Piping, 2020, 188, article: 104224. doi: 10.1016/j.ijpvp.2020.104224.С.Н. Яшин, Н.И. Яшина, Е.В. Кошелев и А.А. Иванов, Метаэвристические алгоритмы в управлении инновациями : Монография, Нижний Новгород: ООО “Печатная Мастерская Радонеж”, 2023, 200 с.С.Н. Яшин, Н.И. Яшина, Е.В. Кошелев и А.А. Иванов, Метаэвристические алгоритмы в управлении инновациями : Монография, Нижний Новгород: ООО “Печатная Мастерская Радонеж”, 2023, 200 с.M. El A. Ben Seghier, B. Keshtegar, K.F. Tee, T. Zayed, R. Abbassi and N.T. Trung, Prediction of maximum pitting corrosion depth in oil and gas pipelines, Eng. Failure Anal., 2020, 112, article: 104505. doi: 10.1016/j.engfailanal.2020.104505.M. El A. Ben Seghier, B. Keshtegar, K.F. Tee, T. Zayed, R. Abbassi and N.T. Trung, Prediction of maximum pitting corrosion depth in oil and gas pipelines, Eng. Failure Anal., 2020, 112, article: 104505. doi: 10.1016/j.engfailanal.2020.104505.R. Eberhart and J. Kennedy, Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, 4, IEEE, 1995, 1942–1948. doi: 10.1109/ICNN.1995.488968.R. Eberhart and J. Kennedy, Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, 4, IEEE, 1995, 1942–1948. doi: 10.1109/ICNN.1995.488968.R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, IEEE, 1995, 39–43. doi: 10.1109/MHS.1995.494215.R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, IEEE, 1995, 39–43. doi: 10.1109/MHS.1995.494215.M. Kumar, M. Husian, N. Upreti and D. Gupta, Genetic algorithm : review and application, International Journal of Information Technology and Knowledge Management, 2010, 2, 451–454. doi: 10.2139/ssrn.3529843.M. Kumar, M. Husian, N. Upreti and D. Gupta, Genetic algorithm : review and application, International Journal of Information Technology and Knowledge Management, 2010, 2, 451–454. doi: 10.2139/ssrn.3529843.X. Yang, Firefly algorithm, stochastic test functions and design optimization, International Journal of Bio–Inspired Computation, 2010, 2, no 2, 78–84. doi: 10.1504/IJBIC.2010.032124.X. Yang, Firefly algorithm, stochastic test functions and design optimization, International Journal of Bio–Inspired Computation, 2010, 2, no 2, 78–84. doi: 10.1504/IJBIC.2010.032124.M.El A. Ben Seghier, B. Keshtegar, M. Taleb-Berrouane, R. Abbassi and N. Trung, Advanced intelligence frameworks for predicting maximum pitting corrosion depth in oil and gas pipelines, Process Saf. Environ. Prot., 2021, 147, 818–833. doi: 10.1016/j.psep.2021.01.008.M.El A. Ben Seghier, B. Keshtegar, M. Taleb-Berrouane, R. Abbassi and N. Trung, Advanced intelligence frameworks for predicting maximum pitting corrosion depth in oil and gas pipelines, Process Saf. Environ. Prot., 2021, 147, 818–833. doi: 10.1016/j.psep.2021.01.008.M. Despotovic, V. Nedic, D. Despotovic and S. Cvetanovic, Review and statistical analysis of different global solar radiation sunshine models, Renewable Sustainable Energy Rev., 2015, 52, 1869–1880. doi: 10.1016/j.rser.2015.08.035.M. Despotovic, V. Nedic, D. Despotovic and S. Cvetanovic, Review and statistical analysis of different global solar radiation sunshine models, Renewable Sustainable Energy Rev., 2015, 52, 1869–1880. doi: 10.1016/j.rser.2015.08.035.B. Akhlaghi, H. Mesghali, M. Ehteshami, J. Mohammadpour, F. Salehi and R. Abbassi, Predictive deep learning for pitting corrosion modeling in buried transmission pipelines, Process Saf. Environ. Prot., 2023, 174, 320–327. doi: 10.1016/j.psep.2023.04.010.B. Akhlaghi, H. Mesghali, M. Ehteshami, J. Mohammadpour, F. Salehi and R. Abbassi, Predictive deep learning for pitting corrosion modeling in buried transmission pipelines, Process Saf. Environ. Prot., 2023, 174, 320–327. doi: 10.1016/j.psep.2023.04.010.J. Du, J. Zheng, Y. Liang, N. Xu, Q. Liao, B. Wang and H. Zhang, Deeppipe: Theory-guided prediction method based automatic machine learning for maximum pitting corrosion depth of oil and gas pipeline, Chem. Eng. Sci., 2023, 278, article: 118927, doi: 10.1016/j.ces.2023.118927.J. Du, J. Zheng, Y. Liang, N. Xu, Q. Liao, B. Wang and H. Zhang, Deeppipe: Theory-guided prediction method based automatic machine learning for maximum pitting corrosion depth of oil and gas pipeline, Chem. Eng. Sci., 2023, 278, article: 118927, doi: 10.1016/j.ces.2023.118927.O. Husson, B. Husson, A. Brunet, D. Babre, K. Alary, J.–P. Sarthou, H. Charpentier, M. Durand, J. Benada and M. Henry, Practical improvements in soil redox potential (Eh) measurement for characterisation of soil properties. Application for comparison of conventional and conservation agriculture cropping systems, Anal. Chim. Acta, 2016, 906, 98–109. doi: 10.1016/j.aca.2015.11.052.O. Husson, B. Husson, A. Brunet, D. Babre, K. Alary, J.–P. Sarthou, H. Charpentier, M. Durand, J. Benada and M. Henry, Practical improvements in soil redox potential (Eh) measurement for characterisation of soil properties. Application for comparison of conventional and conservation agriculture cropping systems, Anal. Chim. Acta, 2016, 906, 98–109. doi: 10.1016/j.aca.2015.11.052.L.B.B. de Melo, B.M. Silva, D.S. Peixoto, T.P.A. Chiarini, G.C. de Oliveira, N. Curi, Effect of compaction on the relationship between electrical resistivity and soil water content in Oxisol, Soil Tillage Res., 2021, 208, article: 104876. doi: 10.1016/j.still.2020.104876.L.B.B. de Melo, B.M. Silva, D.S. Peixoto, T.P.A. Chiarini, G.C. de Oliveira, N. Curi, Effect of compaction on the relationship between electrical resistivity and soil water content in Oxisol, Soil Tillage Res., 2021, 208, article: 104876. doi: 10.1016/j.still.2020.104876.A.W. Al–Kayssi, Use of water retention data and soil physical quality index S to quantify hard-setting and degree of soil compactness indices of gypsiferous soils, Soil Tillage Res., 2021, 206, article: 104805. doi: 10.1016/j.still.2020.104805.A.W. Al–Kayssi, Use of water retention data and soil physical quality index S to quantify hard-setting and degree of soil compactness indices of gypsiferous soils, Soil Tillage Res., 2021, 206, article: 104805. doi: 10.1016/j.still.2020.104805.Н.К. Верещагин, Е.В. Щепин, Информация, кодирование и предсказание, М.: ФМОП, МЦНМО, 2012, 238 с.Н.К. Верещагин, Е.В. Щепин, Информация, кодирование и предсказание, М.: ФМОП, МЦНМО, 2012, 238 с.

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