kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2022-19-4-34-41kaz29-569Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESАналитический подход для приложений теории обратных задач к определению теплофизических характеристик грунтаAnalytical approach for inverse problems theory applications towards determination of thermophysical characteristics of soilhttps://orcid.org/0000-0002-5828-7820СиницаА. В.SinitsaA. V.

Синица Артём Витальевич, Кандидат PhD, сениор-лектор

ул. Толе би, 59, 050000, г. Алматы

Sinitsa Artem Vitalievich, PhD Candidate, Senior-lecturer

Tole-bi 59, Almaty 

a.sinitsa@kbtu.kzhttps://orcid.org/0000-0002-2056-495XКапсониА.CapsoniA.

Антонио Капсони, PhD, профессор

площадь Леонардо да Винчи, 32, г. Милан

Antonio Capsoni, PhD, Professor

Piazza Leonardo da Vinci, 32, Milan

 

antonio.capsoni@polimi.itКазахстанско-Британский технический университетКазахстанKazakh-British Technical UniversityKazakhstanПолитехнический университет МиланаИталияPolytechnic University of MilanItaly2022231220221943441Copyright © Синица А.В., Капсони А., 20222022Синица А.В., Капсони А.Sinitsa A.V., Capsoni A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/569

В данной работе представлены аналитические выражения, полученные для исследования определения теплофизических характеристик грунта с применением теории обратных задач. Была рассмотрена экспериментальная схема с точными измерениями и построена математическая модель для рассматриваемого случая. Аналитическое выражение для нестационарного одномерного температурного поля получено с помощью преобразования Лапласа. Дополнительные данные, такие как тепловой поток на входе, получают путем проведения численного моделирования источника тепла с помощью вычислительной модели. Представленное аналитическое выражение для параметра теплопередачи позволяет без потери точности определить тепловые свойства почвы, что крайне важно в сельскохозяйственной сфере. В статье обсуждаются поставленные особенности, учитываемые для методологии обратной задачи, а также этапы вывода аналитического выражения. Аналитическое выражение для предложенной модели представлено как в частотной области, так и в области реального времени с применением прямого и обратного преобразования Лапласа. Измеренные входные данные на выходе дополнительно интерполируются полиномом 8-го порядка и представляются с остатками аппроксимации. Общая цель предлагаемой статьи состоит в том, чтобы изобразить общее представление о методологии аналитического обратного анализа для процедуры определения коэффициентов, используемых для однородной среды.

Current paper presents analytical expressions received for investigation of determination of thermophysical characteristics of soil applying the theory of inverse problems. There was considered experimental design with exact measurements and constructed mathematical model for considered case. The analytical expression for transient one-dimensional temperature field was received by Laplace transform. Additional data, such as the heat flux at inlet domain received by conducting numerical simulation of the heat source via computational model. Presented analytical expression for heat transfer parameter allows to determine the soil thermal property without loss of precision, which is crucial in agricultural field. Paper discusses posed peculiarities considered for the inverse problem methodology along with derivation stages of analytical expression. The analytical expression for proposed model is presented both in the frequency and real time domain by applied direct and inverse Laplace transform. The measured outlet input data is interpolated further by the 8-th order polynomial and presented with approximation residuals.

обратные задачинестационарный теплообменаналитическое решениеэкспериментальные измерениячисленное моделированиегрунтInverse problemstransient heat transferanalytical solutionexperimental measurementsnumerical simulationsoilReferencesNikonorov V.V., Nikonorova D.O., Pikus G.A. Thermophysical properties of the soil massif. Magazine of Civil Engineering. 2019. 92(8). P. 27–35. DOI: 10.18720/MCE.92.2.Nikonorov V.V., Nikonorova D.O., Pikus G.A. Thermophysical properties of the soil massif. Magazine of Civil Engineering. 2019. 92(8). P. 27–35. DOI: 10.18720/MCE.92.2.Murgul V. Investigation of heat losses through ground supported floors of historical buildings. IOP Conference Series: Materials Science and Engineering. 2018. 365. P. 022066. DOI: 10.1088/1757-899X/365/2/022066.Murgul V. Investigation of heat losses through ground supported floors of historical buildings. IOP Conference Series: Materials Science and Engineering. 2018. 365. P. 022066. DOI: 10.1088/1757-899X/365/2/022066.Bushmanova A.V., Barabanshchikov Yu.G., Semenov K.V., Struchkova A.Y., Manovitsky S.S. Thermal cracking resistance in massive foundation slabs in the building period. Magazine of Civil Engineering. 2017. 8. P. 193–200. DOI: 10.18720/MCE.76.17.Bushmanova A.V., Barabanshchikov Yu.G., Semenov K.V., Struchkova A.Y., Manovitsky S.S. Thermal cracking resistance in massive foundation slabs in the building period. Magazine of Civil Engineering. 2017. 8. P. 193–200. DOI: 10.18720/MCE.76.17.Bonivento Bruges J.C., Vieira G., Revelo Orellana D.P., Togo I. Parameter of thermal resistance of bamboo multilayer wall. Magazine of Civil Engineering. 2018. 83(7). P. 92–101. DOI: 10.18720/MCE.83.9.Bonivento Bruges J.C., Vieira G., Revelo Orellana D.P., Togo I. Parameter of thermal resistance of bamboo multilayer wall. Magazine of Civil Engineering. 2018. 83(7). P. 92–101. DOI: 10.18720/MCE.83.9.Buhartsev V.N., Nguyen Tkhay Khoang. Estimation of the soil body stability. Magazine of Civil Engineering. 2012. 35(9). P. 41–48. DOI: 10.5862/MCE.35.6Buhartsev V.N., Nguyen Tkhay Khoang. Estimation of the soil body stability. Magazine of Civil Engineering. 2012. 35(9). P. 41–48. DOI: 10.5862/MCE.35.6Some approximate analytical steady-state solutions for cylindrical fin. Bruvere A. and Buikis A. 2006. Proceedings of 4th IASME/WSEAS International Conference on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT. P. 238–243.Some approximate analytical steady-state solutions for cylindrical fin. Bruvere A. and Buikis A. 2006. Proceedings of 4th IASME/WSEAS International Conference on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT. P. 238–243.Viļums R. Conservative averaging method in mathematical models of heat processes of electric systems. Riga : University of Latvia, 2010. ISBN 978-9934-8180-2-8.Viļums R. Conservative averaging method in mathematical models of heat processes of electric systems. Riga : University of Latvia, 2010. ISBN 978-9934-8180-2-8.Dzung Nguyen Phuong. The dependence of the strength properties of soil on its physical state. Magazine of Civil Engineering. 2012. 35(9). P. 23–28. DOI: 10.5862/MCE.35.3Dzung Nguyen Phuong. The dependence of the strength properties of soil on its physical state. Magazine of Civil Engineering. 2012. 35(9). P. 23–28. DOI: 10.5862/MCE.35.3Utkin V.S. The Calculation of foundation bed reliability by bearing capacity (shift) during operation. Magazine of Civil Engineering. 2014. 45(1). P. 90–100. (rus). DOI: 10.5862/MCE.45.Utkin V.S. The Calculation of foundation bed reliability by bearing capacity (shift) during operation. Magazine of Civil Engineering. 2014. 45(1). P. 90–100. (rus). DOI: 10.5862/MCE.45.Yahya Kooch, Milad Azizi Mehr, Seyed Mohsen Hosseini, Soil biota and fertility along a gradient of forest degradation in a temperate ecosystem, CATENA, Volume 204, 2021, 105428, ISSN 0341-8162. https://doi.org/10.1016/j.catena.2021.105428.Yahya Kooch, Milad Azizi Mehr, Seyed Mohsen Hosseini, Soil biota and fertility along a gradient of forest degradation in a temperate ecosystem, CATENA, Volume 204, 2021, 105428, ISSN 0341-8162. https://doi.org/10.1016/j.catena.2021.105428.Georges Kogge Kome, Roger Kogge Enang, Bernard Palmer Kfuban Yerima, Knowledge and management of soil fertility by farmers in western Cameroon, Geoderma Regional. Vol. 13. 2018. P. 43–51, ISSN 2352-0094. https://doi.org/10.1016/j.geodrs.2018.02.001.Georges Kogge Kome, Roger Kogge Enang, Bernard Palmer Kfuban Yerima, Knowledge and management of soil fertility by farmers in western Cameroon, Geoderma Regional. Vol. 13. 2018. P. 43–51, ISSN 2352-0094. https://doi.org/10.1016/j.geodrs.2018.02.001.Yan Gao, Shuyue Dong, Chuang Wang, Yanhong Chen, Wenju Hu, Effect of thermal intensity and initial moisture content on heat and moisture transfer in unsaturated soil, Sustainable Cities and Society. Vol. 55. 2020. 102069. ISSN 2210-6707. https://doi.org/10.1016/j.scs.2020.102069.Yan Gao, Shuyue Dong, Chuang Wang, Yanhong Chen, Wenju Hu, Effect of thermal intensity and initial moisture content on heat and moisture transfer in unsaturated soil, Sustainable Cities and Society. Vol. 55. 2020. 102069. ISSN 2210-6707. https://doi.org/10.1016/j.scs.2020.102069.Incropera F.P. Fundamentals of Heat and Mass Transfer. 6th ed. Hoboken (NJ) : Wiley, 2006. 1024 p.Incropera F.P. Fundamentals of Heat and Mass Transfer. 6th ed. Hoboken (NJ) : Wiley, 2006. 1024 p.Exact Analytical 3D Steady-State Solution for Cylindrical Fin. Piliksere A. and Buiķis A. Puerto de la cruz, Tenerife, Canary Islands, Spain : WSEAS Press, 2007. Proceeding of the 4th WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment. P. 238–243.Exact Analytical 3D Steady-State Solution for Cylindrical Fin. Piliksere A. and Buiķis A. Puerto de la cruz, Tenerife, Canary Islands, Spain : WSEAS Press, 2007. Proceeding of the 4th WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment. P. 238–243.Ali Jahangiri, Samira Mohammadi, Mohammad Akbari, Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach, Physica A: Statistical Mechanics and its Applications. Vol. 525. 2019. P. 13–26. ISSN 0378-4371. https://doi.org/10.1016/j.physa.2019.03.040.Ali Jahangiri, Samira Mohammadi, Mohammad Akbari, Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach, Physica A: Statistical Mechanics and its Applications. Vol. 525. 2019. P. 13–26. ISSN 0378-4371. https://doi.org/10.1016/j.physa.2019.03.040.Alexander Yu. Chebotarev, René Pinnau, An inverse problem for a quasi-static approximate model of radiative heat transfer, Journal of Mathematical Analysis and Applications. Vol. 472. Issue 1. 2019. P. 314–327. ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2018.11.026.Alexander Yu. Chebotarev, René Pinnau, An inverse problem for a quasi-static approximate model of radiative heat transfer, Journal of Mathematical Analysis and Applications. Vol. 472. Issue 1. 2019. P. 314–327. ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2018.11.026.Free convection in a light bulb, application id: 303, created in Comsol Multiphysics 5.6 Comsol application license 5.6.Free convection in a light bulb, application id: 303, created in Comsol Multiphysics 5.6 Comsol application license 5.6.Jackson B.J., Davis J.M. An ergodic approach to Laplace transforms on time scales, Journal of Mathematical Analysis and Applications. Vol. 502. Issue 1. 2021. 125231, ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2021.125231.Jackson B.J., Davis J.M. An ergodic approach to Laplace transforms on time scales, Journal of Mathematical Analysis and Applications. Vol. 502. Issue 1. 2021. 125231, ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2021.125231.Lavrent'ev M.A., Shabat B.V. (1973) Methods of the theory of functions of a complex variable, 4th ed., Rev. and add. M .: Science. Ch. ed. physical-mat. lit. P. 541–550.Lavrent'ev M.A., Shabat B.V. (1973) Methods of the theory of functions of a complex variable, 4th ed., Rev. and add. M .: Science. Ch. ed. physical-mat. lit. P. 541–550.Ali Jahangiri, Samira Mohammadi, Mohammad Akbari, Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach, Physica A: Statistical Mechanics and its Applications. Vol. 525. 2019. P. 13–26/ ISSN 0378-4371. https://doi.org/10.1016/j.physa.2019.03.040.Ali Jahangiri, Samira Mohammadi, Mohammad Akbari, Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach, Physica A: Statistical Mechanics and its Applications. Vol. 525. 2019. P. 13–26/ ISSN 0378-4371. https://doi.org/10.1016/j.physa.2019.03.040.

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