Probabilistic Inversion: A New Approach to Inversion Problems in Pavement and Geomechanical Engineering
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.
- 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
- 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
- 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
- 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
- Bhat, U.N., Miller, G.K.: Elements of Applies Stochastic Processes. John Willey & Sons Inc., Hoboken (2002)Google Scholar
- Menke, W.: Geophysical Data Analysis: Discrete Inverse Theory. Academic Press Inc., Orlando (1984)Google Scholar
- 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
- Reddy, S.: Improved Impulse Response Testing - Theoretical and Practical Validations. M.S. Thesis, The University of Texas at El Paso (1992)Google Scholar
- Santamarina, J.C., Fratta, D.: Introduction to Discrete Signals and Inverse Problems in Civil Engineering. ASCE Press, Reston (1998)Google Scholar
- Sansalone, M.: Impact-Echo: The Complete Story. ACI Structural Journal 94(6), 777–786 (1997)Google Scholar