Hybrid Possibilistic-Probabilistic Approach to Uncertainty Quantification in Electromagnetic Compatibility Models

In this Chapter, possibility theory is briefly presented as a framework to deal with electromagnetic compatibility (EMC) problems characterized by incomplete or lack of knowledge (i.e., epistemic uncertainty) on the variability of some of the involved parameters. Accordingly, such parameters are modeled by fuzzy variables (characterized by possibility distributions), that, in real-case scenarios, usually coexist with random variables (characterized by probability distributions). This is the case of typical test setups for EMC verification, such as the radiated susceptibility case study here presented, where the uncertainty of output quantities strongly depends on some input parameters, whose probability distribution functions are unknown. To overcome this limitation, a hybrid approach is presented to propagate the uncertainty within the model, still retaining the possibilistic and probabilistic nature of the two sets of involved parameters. Two methods to aggregate the obtained random-fuzzy sets are presented and compared versus the results obtained by running fully-probabilistic Monte Carlo (MC) simulations, where all uncertain parameters were assigned known probability distributions.