Ідентифікація параметрів дробово-фрактальної моделі фільтраційно-консолідаційної динаміки з використанням штучних нейронних мереж: Fìz.-mat. model. ìnf. tehnol. 2021, 32:52-57

• Date: 2021
• Main Authors: Bohaienko, Vsevolod, Bulavatsky, Volodymy, Gladky, Anatolij
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: фільтраційна консолідація; дробово-фрактальні моделі; ідентифікація параметрів; штучні нейронні мережі
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/159
• Journal Title: Physico-mathematical modeling and informational technologies

Artificial neural networks are applied to solve parameters identification problem for one-dimensional fractional-fractal model of filtration consolidation processes in geo-porous media in the conditions of salt transfer. Based on the indicators of the state of the process in a fixed number of observation points, the values of the orders of fractional derivatives with respect to time and space variables were restored. Testing results based on data sets obtained from noised solutions of the direct problem show the adequacy of fractional derivatives orders restoration with at least 25 observation points and noise levels less than 10%. References Allwright A., Atangana, A. (2018). Fractal advection-dispersion equation for groundwater transport in fractured aquifers with self-similarities. The European Physical Journal Plus, 133(2), 1–14. DOI doi.org/10.1140/epjp/i2018-11885-3 Chen, W. (2006). Time-space fabric underlying anomalous diffusion. Chaos, Soliton. Fract., 28(4), 923–929. DOI doi.org/10.1016/j.chaos.2005.08.199 Cai, W., Chen, W., Wang, F. (2018). Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media. Thermal Science, 22(1), S1-S6. DOI doi.org/10.2298/tsci170630265c Bohaienko, V., Bulavatsky, V. (2020). Fractional-Fractal Modeling of Filtration-Consolidation Processes in Saline Saturated Soils. Fractal and Fractional, 4(4), 59. DOI doi.org/10.3390/fractalfract4040059 Bondarenko, A. N., Bugueva, T. V., Dedok, V. A. (2016). Inverse problems of anomalous diffusion theory: an artificial neural network approach. Journal of Applied and Industrial Mathematics, 10(3), 311-321. Florin, V. A. (1961). Fundamentals of Soil Mechanics. Moscow, USSR: National Technical Information Service. DOI doi.org/10.1134/s1990478916030017 Vlasyuk, A. P., Martynyuk, P. M. (2004). Matematychne modelyuvannya konsolidatsiyi hruntiv v protsesi filtratsiyi solovykh rozchyniv. Rivne: Vyd–vo UDUVHP. Podlubny, I. (1999). Fractional differential equations. New York: Academic Press. Samarskii, A. (2001). The Theory of Difference Schemes. New York: CRC Press.