A bayesian approach for the determination of pod curves from empirical data merged with simulation results

Abstract : POD curves estimations are based on statistical studies of empirical data obtained from inspection results. In order to achieve statistical significance, requirements are that 60 to 80 mock-ups containing ``realistic'' flaws must be inspected by a set of inspectors. This is a costly and time consuming process and the effort must be done for each NDT configuration which requires POD estimation. One way to achieve cost reduction is to replace some of the required experimental data with numerical simulation results. This idea follows the concept of Model Assisted POD (MAPOD). POD curves are no longer estimated from a fully empirical dataset but rather from a mix of experimental and simulated data. Simulations are performed using physics-based models, whose predictions are validated for the considered application case. In order to make the approach suitable for industrial needs, it is required that uncertainties introduced in the process thru the merging of simulation and experimental data are assessed. In this paper, a statistical method based on Bayesian updating is proposed, which mixes numerical simulations and information brought by the measurements. A practical implementation of the approach to a high frequency eddy current inspection for fatigue cracks is presented.