Skip to main content
SpringerLink
Log in

Comparison of Neural Network and Multilayered Approach to the Problem of Identification of the Creep and Fracture Model of Structural Elements Based on Experimental Data

  • Conference paper
  • First Online:
Modern Information Technology and IT Education (SITITO 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1201))

Abstract

The paper considers the solution of one class of coefficient inverse problems connected with the identification of models describing the process of inelastic deformation of structural elements under creep conditions up to fracture moment. Systems of ordinary differential equations are used to describe the creep process. Some structural materials, such as metals, concrete and composite materials have creep properties at high and moderate temperatures. Wherein, the non-consideration of material creep can lead to significant errors in the structures deformation-strength characteristics determining, that leads to the emergencies. However, creep modeling involves some difficulties. There is no general creep theory describing all or most of the observed phenomena. Dozens of different creep theories have been developed applied to specific narrow classes of problems. Moreover, constitutive equations of each theory contain sets of material constants determined by the results of the experiment. Traditional methods of creep models identification depend both on the type of constitutive equations, and the conditions under which construction works. For identification of creep models parameters, the authors proposed a general unified method, which is based on the technique and principles of neural network modeling. A new multilayered method is developed in addition to using the traditional neural network approximations with activation functions of a special type. In the new approach, the problem is preliminarily discretized using known numerical schemes on a segment with a variable right boundary. The advantages of the proposed approaches compared with the traditional ones are shown by the example of creep model identification for a uniaxial tension of steel 45 cylindrical samples under creep conditions. The reliability of the obtained data is confirmed by a comparison with the experimental data and the results of other authors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Vasilyev, A.N., Kuznetsov, E.B., Leonov, S.S.: Neural network method of identification and analysis of the model of deformation of metal structures under creep conditions. Mod. Inf. Technol. IT-Educ. 11(2), 360–370 (2015). https://elibrary.ru/item.asp?id=26167516. (in Russian)

    Google Scholar 

  2. Yadav, N., Yadav, A., Kumar, M.: An Introduction to Neural Network Methods for Differential Equations. SpringerBriefs in Applied Sciences and Technology. Springer, Dordrecht (2015). https://doi.org/10.1007/978-94-017-9816-7

    Book  MATH  Google Scholar 

  3. Lagaris, I.E., Likas, A., Fotiadis, D.I.: Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9(5), 987–1000 (1998). https://doi.org/10.1109/72.712178

    Article  Google Scholar 

  4. Dissanayake, M.W.M.G., Phan-Thien, N.: Neural-network-based approximations for solving partial differential equations. Commun. Numer. Methods Eng. 10(3), 195–201 (1994). https://doi.org/10.1002/cnm.1640100303

    Article  MATH  Google Scholar 

  5. Fasshauer, G.E.: Solving differential equations with radial basis functions: multilevel methods and smoothing. Adv. Comput. Math. 11(2–3), 139–159 (1999). https://doi.org/10.1023/A:1018919824891

    Article  MathSciNet  MATH  Google Scholar 

  6. Fornberg, B., Larsson, E.: A numerical study of some radial basis function based solution methods for elliptic PDEs. Comput. Math Appl. 46(5–6), 891–902 (2003). https://doi.org/10.1016/S0898-1221(03)90151-9

    Article  MathSciNet  MATH  Google Scholar 

  7. Galperin, E., Pan, Z., Zheng, Q.: Application of global optimization to implicit solution of partial differential equations. Comput. Math Appl. 25(10–11), 119–124 (1993). https://doi.org/10.1016/0898-1221(93)90287-6

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, J., Luo, S., Qi, Y., Huang, Y.: Numerical solution of elliptic partial differential equation using radial basis function neural networks. Neural Netw. 16(5–6), 729–734 (2003). https://doi.org/10.1016/S0893-6080(03)00083-2

    Article  Google Scholar 

  9. Kansa, E.: Multiquadrics – a scattered data approximation scheme with applications to computational fluid dynamics I: surface approximations and partial derivative estimates. Comput. Math Appl. 19(8–9), 127–145 (1990). https://doi.org/10.1016/0898-1221(90)90270-T

    Article  MathSciNet  MATH  Google Scholar 

  10. Kansa, E.: Multiquadrics – a scattered data approximation scheme with applications to computational fluid dynamics II: solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math Appl. 19(8–9), 147–161 (1990). https://doi.org/10.1016/0898-1221(90)90271-K

    Article  MathSciNet  MATH  Google Scholar 

  11. Mai-Duy, N., Tran-Cong, T.: Numerical solution of differential equations using multiquadric radial basis function networks. Neural Netw. 14(2), 185–199 (2001). https://doi.org/10.1016/S0893-6080(00)00095-2

    Article  MATH  Google Scholar 

  12. Tarkhov, D., Vasilyev, A.: New neural network technique to the numerical solution of mathematical physics problems. I: Simple problems. Opt. Mem. Neural Netw. (Inf. Opt.) 14, 59–72 (2005)

    Google Scholar 

  13. Tarkhov, D., Vasilyev, A.: New neural network technique to the numerical solution of mathematical physics problems. II: Complicated and nonstandard problems. Opt. Mem. Neural Netw. (Inf. Opt.) 14, 97–122 (2005)

    Google Scholar 

  14. Vasilyev, A., Tarkhov, D.: Mathematical models of complex systems on the basis of artificial neural networks. Nonlinear Phenom. Complex Syst. 17(3), 327–335 (2014). https://elibrary.ru/item.asp?id=29102291

    MathSciNet  MATH  Google Scholar 

  15. Budkina, E.M., Kuznetsov, E.B., Lazovskaya, T.V., Leonov, S.S., Tarkhov, D.A., Vasilyev, A.N.: Neural network technique in boundary value problems for ordinary differential equations. In: Cheng, L., Liu, Q., Ronzhin, A. (eds.) ISNN 2016. LNCS, vol. 9719, pp. 277–283. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40663-3_32

    Chapter  Google Scholar 

  16. Lazovskaya, T.V., Tarkhov, D.A., Vasilyev, A.N.: Parametric neural network modeling in engineering. Recent Patents Eng. 11(1), 10–15 (2017). https://doi.org/10.2174/1872212111666161207155157

    Article  Google Scholar 

  17. Li, Z., Mao, X.-Z.: Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy data. Int. J. Numer. Methods Eng. 84(1), 1–26 (2010). https://doi.org/10.1002/nme.2880

    Article  MathSciNet  MATH  Google Scholar 

  18. Gorbachenko, V.I., Lazovskaya, T.V., Tarkhov, D.A., Vasilyev, A.N., Zhukov, M.V.: Neural network technique in some inverse problems of mathematical physics. In: Cheng, L., Liu, Q., Ronzhin, A. (eds.) ISNN 2016. LNCS, vol. 9719, pp. 310–316. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40663-3_36

    Chapter  Google Scholar 

  19. Lozhkina, O., Lozhkin, V., Nevmerzhitsky, N., Tarkhov, D., Vasilyev, A.: Motor transport related harmful PM2.5 and PM10: from on-road measurements to the modeling of air pollution by neural network approach on street and urban level. IOP Conf. Ser. J. Phys. Conf. Ser. 772(1), 012031 (2016). https://doi.org/10.1088/1742-6596/772/1/012031

    Article  Google Scholar 

  20. Kaverzneva, T., Lazovskaya, T., Tarkhov, D., Vasilyev, A.: Neural network modeling of air pollution in tunnels according to indirect measurements. IOP Conf. Ser. J. Phys. Conf. Ser. 772(1), 012035 (2016). https://doi.org/10.1088/1742-6596/772/1/012035

    Article  Google Scholar 

  21. Kainov, N.U., Tarkhov, D.A., Shemyakina, T.A.: Application of neural network modeling to identification and prediction problems in ecology data analysis for metallurgy and welding industry. Nonlinear Phenomena Complex Syst. 17(1), 57–63 (2014). https://elibrary.ru/item.asp?id=29102259

    MathSciNet  MATH  Google Scholar 

  22. Bolgov, I., Kaverzneva, T., Kolesova, S., Lazovskaya, T., Stolyarov, O., Tarkhov, D.: Neural network model of rupture conditions for elastic material sample based on measurements at static loading under different strain rates. IOP Conf. Ser. J. Phys. Conf. Ser. 772(1), 012032 (2016). https://doi.org/10.1088/1742-6596/772/1/012032

    Article  Google Scholar 

  23. Egorchev, M.V., Tiumentsev, Y.: Learning of semi-empirical neural network model of aircraft three-axis rotational motion. Opt. Mem. Neural Netw. (Inf. Opt.) 24(3), 201–208 (2015). https://doi.org/10.3103/S1060992X15030042

    Article  Google Scholar 

  24. Kozlov, D.S., Tiumentsev, Y.: Neural network based semi-empirical models for dynamical systems described by differential-algebraic equations. Opt. Mem. Neural Netw. (Inf. Opt.) 24(4), 279–287 (2015). https://doi.org/10.3103/S1060992X15040049

    Article  Google Scholar 

  25. Gorbachenko, V.I., Zhukov, M.V.: Solving boundary value problems of mathematical physics using radial basis function networks. Comput. Math. Math. Phys. 57(1), 145–155 (2017). https://doi.org/10.1134/S0965542517010079

    Article  MathSciNet  MATH  Google Scholar 

  26. Rabotnov, Y.: Creep Problems in Structural Members. North-Holland Publishing Company, Amsterdam/London (1969)

    MATH  Google Scholar 

  27. Gorev, B.V., Zakharova, T.E., Klopotov, I.D.: On description of creep and fracture of the materials with non-monotonic variation of deformation-strength properties. Phys. Mesomech. J. 5(2), 17–22 (2002). https://elibrary.ru/item.asp?id=12912517. (in Russian)

    Google Scholar 

  28. Gorev, B.V., Lyubashevskaya, I.V., Panamarev, V.A., Iyavoynen, S.V.: Description of creep and fracture of modern construction materials using kinetic equations in energy form. J. Appl. Mech. Tech. Phys. 55(6), 1020–1030 (2014). https://doi.org/10.1134/S0021894414060145

    Article  Google Scholar 

  29. Polak, E.: Computational Methods in Optimization: A Unified Approach. Academic Press, New York (1971)

    Google Scholar 

  30. Lazovskaya, T., Tarkhov, D.: Multilayer neural network models based on grid methods. IOP Conf. Ser. Mater. Sci. Eng. 158(1), 012061 (2016). https://doi.org/10.1088/1757-899X/158/1/012061

    Article  Google Scholar 

  31. Lazovskaya, T., Tarkhov, D., Vasilyev, A.: Multi-layer solution of heat equation. In: Kryzhanovsky, B., Dunin-Barkowski, W., Redko, V. (eds.) NEUROINFORMATICS 2017. SCI, vol. 736, pp. 17–22. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66604-4_3

    Chapter  Google Scholar 

  32. Vasilyev, A.N., Tarkhov, D.A., Tereshin, V.A., Berminova, M.S., Galyautdinova, A.R.: Semi-empirical neural network model of real thread sagging. In: Kryzhanovsky, B., Dunin-Barkowski, W., Redko, V. (eds.) NEUROINFORMATICS 2017. SCI, vol. 736, pp. 138–144. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66604-4_21

    Chapter  Google Scholar 

  33. Zulkarnay, I.U., Kaverzneva, T.T., Tarkhov, D.A., Tereshin, V.A., Vinokhodov, T.V., Kapitsin, D.R.: A two-layer semi-empirical model of nonlinear bending of the cantilevered beam. IOP Conf. Ser. J. Phys. Conf. Ser. 1044, 012005 (2018). https://doi.org/10.1088/1742-6596/1044/1/012005

    Article  Google Scholar 

  34. Bortkovskaya, M.R., et al.: Modeling of the membrane bending with multilayer semi-empirical models based on experimental data. In: CEUR Workshop Proceedings. Proceedings of the II International Scientific Conference “Convergent Cognitive Information Technologies” (Convergent 2017), vol. 2064, pp. 150–156. MSU, Moscow (2017). http://ceur-ws.org/Vol-2064/paper18.pdf

Download references

Acknowledgments

The article was prepared on the basis of scientific research carried out with the financial support of the Russian Science Foundation grant (project No. 18-19-00474).

Author information

Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, Politekhnicheskaya Str. 29, 195251, St. Petersburg, Russia

    Alexander Vasilyev & Dmitry Tarkhov

  2. Moscow Aviation Institute (National Research University), Volokolamskoe shosse 4, 125993, Moscow, Russia

    Evgenii Kuznetsov & Sergey Leonov

Authors
  1. Alexander Vasilyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evgenii Kuznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey Leonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dmitry Tarkhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Vasilyev .

Editor information

Editors and Affiliations

  1. Moscow State University, Moscow, Russia

    Vladimir Sukhomlin

  2. Moscow State University, Moscow, Russia

    Elena Zubareva

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Vasilyev, A., Kuznetsov, E., Leonov, S., Tarkhov, D. (2020). Comparison of Neural Network and Multilayered Approach to the Problem of Identification of the Creep and Fracture Model of Structural Elements Based on Experimental Data. In: Sukhomlin, V., Zubareva, E. (eds) Modern Information Technology and IT Education. SITITO 2018. Communications in Computer and Information Science, vol 1201. Springer, Cham. https://doi.org/10.1007/978-3-030-46895-8_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-46895-8_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-46894-1

  • Online ISBN: 978-3-030-46895-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation