Probabilistic Approach to the Solution of Inverse Problems in Civil Engineering

Abstract

A wide range of important problems in civil engineering can be classified as inverse problems. In such problems, the observational data regarding the performance of a system is known, and the characteristics of the system and/or the input are sought. There are two general approaches to the solution of inverse problems: deterministic and probabilistic. Traditionally, inverse problems in civil engineering have been solved using a deterministic approach. In this approach, the objective is to find a specific model of a system that its theoretical response best fits the observed data. Obtaining the best fit solution, however, does not provide any information regarding the effect of data and/or theoretical uncertainties on the obtained solution. In this paper, a general probabilistic approach to the solution of the inverse problems is introduced, which provides uncertainty measures for the obtained solution. Techniques for direct analytical evaluation and numerical approximation of the probabilistic solution using Monte Carlo Markov Chains, with and without neighborhood algorithm approximation, are introduced and explained. The presented concepts and techniques and their application are then illustrated in practical terms using a simple example of a modulus determination experiment.