Reducing the Statistical Complexity of EMC Testing: Improvements for Radiated Experiments Using Stochastic Collocation and Bootstrap Methods

The assessment of statistics and confidence intervals is deeply linked with electromagnetic compatibility (EMC) and electromagnetic interferences (EMI) issues. Indeed, the evaluation of margins and risks are inherent to EMC/EMI: many standards and/or guidelines require the accurate prediction of mean, standard deviation and/or extreme quantities of interest (voltages, currents, E-/H-fields, S-parameters, impedances ...). It is well known that EMC/EMI testing configurations (both considering the devices under test and setups) are, by essence, complex to handle: for instance regarding the increase of frequency bandwidth and the coexistence of multi-physics/multi-scales issues. Although EMC/EMI studies are governed by the management of margins, taking into account the stochastic nature both of inputs and outputs remains a serious bottleneck. This is mostly due to stochastic (identification and characterization of random parameters, number of random variables.) and deterministic (computing and/or measuring costs at design and/or qualification steps) considerations. In order to tackle this problem, many stochastic techniques have been explored by different international groups during the past decade. Among these, this communication will be devoted to the introduction of reduced order models (inputs) and the application of bootstrapping (outputs). The advocated models will be discussed regarding pre- and post-inferences, and they will be applied to numerical and experimental radiated EMC tests; frequency- and time-domain experiments will demonstrate the accuracy and efficiency of these methods comparatively to brute force Monte Carlo approaches for electromagnetic field-to-wire coupling configurations.