The Adaptive Controlled Stratification Method Applied to the Determination of Extreme Interference Levels in EMC Modeling With Uncertain Input Variables

Abstract

International audienceThis paper deals with electromagnetic compatibility simulations at early design stage of equipment or systems development. In this context, expensive simulations based on rigorous modeling are performed, including numerous uncertain variables. The most important configurations are those associated to extreme values of the observed quantity. In this paper we introduce a variance reduction technique to accelerate the estimation of an extreme quantile of theoutput distribution. The approach is based on using a simple model (at a low computational cost) to identify relevant realizations of uncertain variables in strata partitioning the output space of the model. Applicationof the method is detailed on a rather simple cable system in order to estimate an extreme quantile level ofan interfering current. We show that extreme current values are obtained at a reduced computational costcompared to a standard empirical quantile estimation

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

“…The previous quoted techniques were mainly applied to numerical simulations including various applications: shielding effectiveness [17], scattering and propagation [18] and/or EMC/EMI problems. Other important aspects of statistical developments (especially considering the EMC framework) deal with extreme quantile estimation based on reliability techniques [19]- [22] as well as on the so-called controlled stratification (CS) method [23], [24]. This last technique in particular reduces the variance of estimation of extreme quantiles, which is the purpose of our study.…”

“…A SM for CS needs to be specifically correlated to the true model in terms of probability of reaching extreme values for both SM and the true model, with the same input realizations. In [24], the SM was a physical approximation of the true model. Finding a systematic approach to build an appropriate SM for the CS is an open question in literature.…”

Comparison of Surrogate Models for Extreme Quantile Estimation in the Context of EMC Risk Analysis

“…SMs may also be used in addition to other techniques targeting the output distribution tail, such as controlled stratification (CS) [2], subset simulation [3], importance sampling [4]. The CS has been successfully applied to an EMC case study in [5] but the SM was specific and based on physical knowledge. In fact, CS performances rely on the strong correlation between the SM and the reference model.…”

Combining Kriging and Controlled Stratification to Identify Extreme Levels of Electromagnetic Interference

“…This is possibly a SM as we propose in this paper. Note that CS has been successfully applied to a springmass-damper problem with splines as SM [4] and to an EMC crosstalk problem with a simple model which was not a SM [5].…”