Bayesian Framework Combination of Simulated and Experimental Data for Improved Estimation of Probability of Detection Curves

The uncertainties in non-destructive evaluation (NDE) inspections have over the years been represented using ‘probability of detection’ or ‘POD’ curves. Determination of POD capabilities of NDE methods for different flaw types is often an experimentation and personnel intensive operation. Analytical or numerical simulations can provide convenient prior estimates, but integrating simulation results with experimental data is a challenge. Here we aim to develop a framework for integrating the results from simulation and experiment using the Bayesian approach where the data from the simulations are taken as a prior knowledge. In order to find the parameter estimate that best describes the experimental data, the likelihood function has to be maximized. The simulation results are combined with the maximum likelihood estimates of the experimental data, to give us the posterior (updated) knowledge of the parameters. POD curves are obtained for the posterior distribution and compared with those from the experiment and the simulation.