Merging of Experimental and Simulated Data Sets with a Bayesian Technique in the Context of POD Curves Determination

摘要

POD curves are usually described using a parametric model which relates the probability to detect a specific defect to one of its geometrical characteristics, usually its size. The parameters of the model are estimated following a statistical procedure applied to a set of inspection results which are obtained thru dedicated experimental campaigns. Statistical significance requires that 60 to 80 mock-ups containing realistic flaws are fabricated and inspected by several inspectors. This costly and time consuming process must be done for each NDT procedure for which a measure of NDT reliability is required. Consequently, cost and time reduction of POD trials is currently a major issue. 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 presentation, a statistical method based on Bayesian updating is proposed, which mixes numerical simulations and information brought by the measurements. Traditionally, POD curves are assessed using Maximum Likelihood Estimation methods using either hit/miss or signal response data. This article only deals with hit/miss data. Following Berens article, the POD is modelled by a log-logistics function. Hit/miss data is treated as a Bernoulli's variable and Bayesian updating is performed on the POD model to assess the posterior distributions of the POD parameters assuming non-informative prior distributions on them. Finally, Monte Carlo simulations are run to assess the confidence band POD. A practical implementation of the approach to a high frequency eddy current inspection for fatigue cracks is presented.