Probabilistic Inversion: A New Approach to Inversion Problems in Pavement and Geomechanical Engineering

  • Rambod Hadidi
  • Nenad Gucunski
Part of the Studies in Computational Intelligence book series (SCI, volume 259)


A wide range of important problems in pavement and geomechnical engineering can be classified as inverse problems. In such problems, the observational data related to the performance of a system is known, and the characteristics of the system that generated the observed data are sought. There are two general approaches to the solution of inverse problems: deterministic and probabilistic. Traditionally, inverse problems in pavement and geomechanical engineering have been solved using a deterministic approach, where the objective is to find a model of the system for which its theoretical response best fits the observed data. In this approach, it is implicitly assumed that the uncertainties in the problem, such as data and modeling uncertainties, are negligible, and the “best fit” model is the solution of the problem. However, this assumption is not valid in some applications, and these uncertainties can have significant effects on the obtained results. In this chapter, a general probabilistic approach to the solution of the inverse problems is introduced. The approach offers the framework required to obtain uncertainty measures for the solution. To provide the necessary background of the approach, few essential concepts are introduced and then the probabilistic solution is formulated in general terms using these concepts. Monte Carlo Markov Chains (MCMC) and its integration with Neighborhood Algorithm (NA), a recently developed global optimization and approximation algorithm, are introduced as computational tools for evaluation of the probabilistic solution. Finally, the presented concepts and computational tools are used to solve inverse problems in Falling Weight Deflectometer (FWD) backcalculation and seismic waveform inversion for shallow subsurface characterization. For each application, the probabilistic formulation is presented, solutions defined, and advantages of the probabilistic approach illustrated and discussed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bush III, A.J., Baladi, G.Y. (eds.) American Society for Testing and Material (ASTM), Nondestructive testing of pavement and Backcalculation of moduli., ASTM Special Technical Publication 1026, ASTM, Philadelphia (1989)Google Scholar
  2. Von Quintus, H.L., Bush III, A.J., Baladi, G.Y. (eds.): ASTM, Nondestructive testing of pavement and Backcalculation of moduli, vol. 2. Special Technical Publication 1198, ASTM, Philadelphia (1994)Google Scholar
  3. Tayabji, S.D., Lukanen, E.O. (eds.): ASTM, Nondestructive testing of pavement and Backcalculation of moduli, vol. 3. ASTM Special Technical Publication 1375, West Conshohocken (2000)Google Scholar
  4. Al-Khoury, R., Scarpas, A., Kasbergen, C., Blaauwendraad, J.: Spectral Element Technique for Efficient Parameter Identification of Layered Media: Part I: Forward Model. International Journal of Solids and Structures 38(9), 1605–1623 (2001)MATHCrossRefGoogle Scholar
  5. Bentsen, R.A., Nazarian, S., Harrison, A.: Reliability of Seven Nondestructive Pavement Testing Devices. In: Bush III, A.J., Baladi, G.Y. (eds.) Nondestructive testing of pavement and Backcalculation of moduli. ASTM Special Technical Publication 1198, ASTM, Philadelphia (1989)Google Scholar
  6. Bhat, U.N., Miller, G.K.: Elements of Applies Stochastic Processes. John Willey & Sons Inc., Hoboken (2002)Google Scholar
  7. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman & Hall/CRC, Boca Raton (2004)MATHGoogle Scholar
  8. Hadidi, R., Gucunski, N.: A Probabilistic Approach to the Solution of Inverse Problems in Civil Engineering. ASCE Journal of Computing in Civil Engineering 22(6), 338–347 (2008)CrossRefGoogle Scholar
  9. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)MATHCrossRefGoogle Scholar
  10. Menke, W.: Geophysical Data Analysis: Discrete Inverse Theory. Academic Press Inc., Orlando (1984)Google Scholar
  11. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by last computing machines. J. Chem. Phys. 21, 1087–1092 (1953)CrossRefGoogle Scholar
  12. Mosegaard, K., Tarantola, A.: Monte Carlo Sampling of Solution to Inverse Problems. Journal of Geophysical Research 100(B7), 12431–12447 (1995)CrossRefGoogle Scholar
  13. Nazarian, S.: In situ determination of elastic moduli of soil deposits and pavement systems by spectral analysis of surface waves method. PhD thesis, Univ. of Texas at Austin, Texas (1984)Google Scholar
  14. Park, C.B., Miller, R.D., Xia, J.: Multichannel Analysis of Surface Waves. Geophysics 64(3), 800–808 (1999)CrossRefGoogle Scholar
  15. Parker, R.L.: Geophysical Inverse Theory. Princeton University Press, Princeton (1994)MATHGoogle Scholar
  16. Reddy, S.: Improved Impulse Response Testing - Theoretical and Practical Validations. M.S. Thesis, The University of Texas at El Paso (1992)Google Scholar
  17. Sambridge, M.: Geophysical Inversion with Neighborhood Algorithm – I. Searching the Parameter Space. Geophysical Journal International 138, 479–494 (1999a)CrossRefGoogle Scholar
  18. Sambridge, M.: Geophysical Inversion with Neighborhood Algorithm – II. Appraising the Ensemble. Geophysical Journal International 138, 727–746 (1999b)CrossRefGoogle Scholar
  19. Santamarina, J.C., Fratta, D.: Introduction to Discrete Signals and Inverse Problems in Civil Engineering. ASCE Press, Reston (1998)Google Scholar
  20. Sansalone, M.: Impact-Echo: The Complete Story. ACI Structural Journal 94(6), 777–786 (1997)Google Scholar
  21. Tarantola, A.: Inverse Problem Theory. SIAM, Philadelphia (2005)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rambod Hadidi
    • 1
  • Nenad Gucunski
    • 2
  1. 1.MACTEC Engineering and Consulting, Inc.Senior EngineerSan Francisco
  2. 2.Professor, Department of Civil and Environmental EngineeringRutgers UniversityPiscataway

Personalised recommendations