Skip to main content
SpringerLink
Log in

Inverse problem analysis for nondestructive evaluation of structural characteristics of multilayered foundations

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

This article has been updated

Abstract

The evaluation of the parameters of multilayered foundations (pavements, runway strips, etc.) plays an important role in ensuring the safe movement of vehicles. An approach of model construction for estimating the mechanical and geometric parameters of such foundations based on the solutions of inverse problems for multilayered elastic packets is proposed. As input data for such problems the measured displacements (or velocities) of certain points on the package surface are used. The proposed approach is based on informational-probabilistic paradigm for inverse problem analysis, whose task is to obtain a posteriori probability density in the space of unknown parameters. The essence of the approach is the block-parametric approximation of the a priori probability density and likelihood function in the spaces of parameters and model data of the problem. The method allows estimating the parameters of the a priori distribution of unknown variable parameters, identifying and excluding outliers of the measured data from the created model, and constructing a posteriori estimation of the unknown parameters’ probability density with acceptable resolution. Proposed method can be used to create a new generation of equipment intended for nondestructive monitoring and estimating of the condition of pavements, runways and foundations of artificial structures. The appropriate software for such high-speed scanning devices that allow on-the-fly display of the diagnosed layered foundation parameters can be developed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Change history

  • 13 January 2021

    Journal abbreviated title on top of the page has been corrected to “Arch Appl Mech”

References

  1. Nikolaides, A.: Highway Engineering Materials and Control of Quality. CRC Press, Taylor & Francis Group, Pavements (2014)

    Google Scholar 

  2. Berkovic, G., Shafir, E.: Optical methods for distance and displacement measurements. Adv. Opt. Photonics 4, 441–471 (2012)

    Article  Google Scholar 

  3. Ullidtz, P.: Pavement Analysis. Elsevier, Amsterdam (1987)

    Google Scholar 

  4. Flintsch, G., Katicha, S., Bryce, J., Ferne, B., Nell, S., Diefenderfer, B.: Assessment of Continuous Pavement Deflection Measuring Technologies. SHRP 2 Report S2-R06F-RW-1. TRB, National Academy of Sciences, Washington, DC (2013)

    Book  Google Scholar 

  5. Morosiuk, G., Riley, M., Odoki, J.B.: Modelling Road Deterioration and Works Effects. Version 2, HDM-4. The Highway Development and Managemen Series, vol. 6. World Road Association, Paris (2004)

    Google Scholar 

  6. Zhang, Y., Roesler, J.R., Huang, Z.: A method for evaluating CRCP performance based on edge-loaded FWD test. Mater. Struct. 53, 46 (2020). https://doi.org/10.1617/s11527-020-01481-0

    Article  Google Scholar 

  7. Park, S., Park, H.M., Hwang, J.: Application of genetic algorithm and finite element method for backcalculating layer moduli of flexible pavements. KSCE J. Civ. Eng. 14, 183–190 (2010). https://doi.org/10.1007/s12205-010-0183-8

    Article  Google Scholar 

  8. Ji, Richard, Siddiki, Nayyarzia, Nantung, Tommy, Kim, Daehyeon: Evaluation of resilient modulus of subgrade and base materials in Indiana and its implementation in MEPDG. TheScientificWorldJournal 2014, 1–14 (2014)

    Google Scholar 

  9. Saltan, M., Terzi, S., Küçüksille, E.U.: Backcalculation of pavement layer moduli and Poisson’s ratio using data mining. Expert Syst. Appl. 38, 3 (2011)

    Article  Google Scholar 

  10. Xiaohui, R., Wanji, C., Zhen, W.: A C0-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations. Arch. Appl. Mech. 82, 391–406 (2012). https://doi.org/10.1007/s00419-011-0563-7

    Article  MATH  Google Scholar 

  11. Liu, Jie, Li, Kun: Sparse identification of time-space coupled distributed dynamic load. Mech. Syst. Signal Process. (2021). https://doi.org/10.1016/j.ymssp.2020.107177

    Article  Google Scholar 

  12. Tam, J.H.: Identification of elastic properties utilizing non-destructive vibrational evaluation methods with emphasis on definition of objective functions: a review. Struct. Multidisc. Optim. 61, 1677–1710 (2020). https://doi.org/10.1007/s00158-019-02433-1

    Article  MathSciNet  Google Scholar 

  13. Saltan, M., Terzi, S.: Backcalculation of pavement layer thickness and moduli using adaptive neuro-fuzzy inference system. In: Gopalakrishnan, K., Ceylan, H., Attoh-Okine, N.O. (eds.) Intelligent and Soft Computing in Infrastructure Systems Engineering. Studies in Computational Intelligence, p 259. Springer, Berlin (2009)

    Google Scholar 

  14. Saric, A., Pozder, M.: Artificial neural networks application in the backcalculation process of flexible pavement layers elasticity modulus. In: Hadžikadić, M., Avdaković, S. (eds.) Advanced Technologies, Systems, and Applications II. IAT 2017. Lecture Notes in Networks and Systems, p 28. Springer, Berlin (2018)

    Google Scholar 

  15. Sadr, M.H., Astaraki, S., Salehi, S.: Improving the neural network method for finite element model updating using homogenous distribution of design points. Arch. Appl. Mech. 77, 795–807 (2007). https://doi.org/10.1007/s00419-007-0129-x

    Article  MATH  Google Scholar 

  16. Hadidi, R., Gucunski, N.: Probabilistic inversion: a new approach to inversion problems in pavement and geomechanical engineering. In: Gopalakrishnan, K., Ceylan, H., Attoh-Okine, N.O. (eds.) Intelligent and Soft Computing in Infrastructure Systems Engineering Studies in Computational Intelligence, p 259. Springer, Berlin (2009)

    Google Scholar 

  17. Ghasemi, P., Aslani, M., Rollins, D.K., et al.: Principal component analysis-based predictive modeling and optimization of permanent deformation in asphalt pavement: elimination of correlated inputs and extrapolation in modeling. Struct. Multidisc. Optim. 59, 1335–1353 (2019). https://doi.org/10.1007/s00158-018-2133-x

    Article  Google Scholar 

  18. Das, A.: Analysis of Pavement Structures. CRC Press, Taylor & Francis Group (2015)

    Google Scholar 

  19. Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Wiley, New York (1977)

    MATH  Google Scholar 

  20. Backus, G., Gilbert, F.: Uniqueness in the inversion of inaccurate gross Earth data. Philos. Trans. R. Soc. London 266, 123–192 (1970)

    Article  MathSciNet  Google Scholar 

  21. Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM, Society for Industrial and Applied Mathematics, Philadelphia (2005)

    Book  Google Scholar 

  22. Tarantola, A., Valette, B.: Generalized nonlinear inverse problems solved using the least-squares criterion. Rev. Geophys. Space Phys. 20(2), 219–232 (1982)

    Article  MathSciNet  Google Scholar 

  23. Stefansky, W.: Rejecting outliers in factorial designs. Technometrics 14(2), 469–479 (1972)

    Article  Google Scholar 

  24. Ivakhnenko, A.G.: The Group Method of Data Handling – a Rival of the Method of Stochastic Approximation. Soviet Automatic Control 13(3), 43–55 (1968)

    MathSciNet  Google Scholar 

  25. Grasa, A.A.: Econometric Model Selection. Springer, Netherlands (1989)

    Book  Google Scholar 

  26. Trofimov, A.V., Petrova, Y.V.: Multigrid iterative grid generation algorithms for layered elastic and elasto-plastic foundations’ problems. Dnipro Syst. Technol. 54(2), 69–80 (2015)

    Google Scholar 

  27. Trofimov, A.V.: Multigrid iterative algorithms for layered elastic and elasto-plastic foundations with curvilinear boundaries’ boundary-value problems. Dnipro Syst. Technol. 55(1), 119–137 (2016)

    Google Scholar 

  28. Liua, J., Menga, X., Xub, C., Zhangc, D., Jianga, C.: Forward and inverse structural uncertainty propagations under stochastic variables with arbitrary probability distributions. Comput. Methods Appl. Mech. Eng. 342, 287–320 (2018). https://doi.org/10.1016/j.cma.2018.07.035

    Article  MathSciNet  Google Scholar 

  29. Xianghua, M., Liu, J., Cao, L., et al.: A general frame for uncertainty propagation under multimodally distributed random variables. Comput. Methods Appl. Mech. Eng. (2020). https://doi.org/10.1016/j.cma.2020.113109

    Article  MathSciNet  MATH  Google Scholar 

  30. Rosenbluth, M.N.: Genesis of the Monte Carlo Algorithm for Statistical Mechanics. AIP Conf. Proc. 690, 22–30 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Transportation Systems and Technologies, Ukrainian University of Customs and Finance, Volodymyra Vernadskoho Str., 2/4, Dnipro, 49000, Ukraine

    Alexander Vladimirovich Trofimov

Authors
  1. Alexander Vladimirovich Trofimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Vladimirovich Trofimov.

Ethics declarations

Conflict of interest

There is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trofimov, A.V. Inverse problem analysis for nondestructive evaluation of structural characteristics of multilayered foundations. Arch Appl Mech 91, 1773–1792 (2021). https://doi.org/10.1007/s00419-020-01854-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01854-5

Keywords

Search

Navigation