Controlled Stratification Based on Kriging Surrogate Model: An Algorithm for Determining Extreme Quantiles in Electromagnetic Compatibility Risk Analysis

An electromagnetic compatibility failure is a consequence of an applied interference level being in excess of the susceptibility level of the electronic equipment under investigation. Both interference and susceptibility levels depend on various configurations of coupling paths described by sets of unknown or uncertain parameters. It is therefore convenient to describe the applied interference and the susceptibility levels as random variables. As extreme values may have a strong impact on the risk of failure, we focus in this article on the estimation of extreme values of interference level (relevant applied fields, currents or voltages) by means of a restricted set of numerical simulations. The controlled stratification method aims at reducing the variance of estimation of extreme quantile, based on a correlated simple model. We recently highlighted that a kriging surrogate model was a good candidate to provide this simple model. Combined with controlled stratification, we obtained better estimation performances than using a standalone kriging model with the same output sample size. In practice, this sample size is limited due to the excessive simulation time of electromagnetic solvers. In this paper, we propose an original algorithm, which aims at checking whether the sample size is adequate to perform an acceptable estimation or not. We first validate the algorithm using analytical models. Finally, we apply this method to estimate the 99% quantile of the total radiated power of a source located inside an open cavity with 16 uncertain inputs. In that case, the algorithm reduces the number of calls to the initial model to approximately 40% of the budget that is required using a standard Monte Carlo approach. Moreover, it provides almost 4 times more extreme outputs. More remarkably, our proposed algorithm provides guidance for assessing the performance of quantile estimation according to the initially sample size of the design of experiment.