A Polymorphic Polynomial Chaos Formulation for Mixed Epistemic-Aleatory Uncertainty Quantification of RF/Microwave Circuits

In RF/microwave circuits, parametric uncertainty can take two forms--epistemic and aleatory uncertainty. Epistemic uncertainty arises from the instrumentation, human, and approximation errors when measuring the value of a circuit parameter. This uncertainty is modeled using variables whose values lie within fixed intervals of support. On the other hand, aleatory uncertainty arises from random fabrication process variations and manufacturing tolerances. This uncertainty is modeled using random variables of known probability density functions. Standard polynomial chaos (PC) metamodels suffer from the aggravated curse of dimensionality when tackling both these forms of uncertainty. To address this issue, in this article, a new polymorphic PC (PPC) formulation is developed for cases where both epistemic and aleatory uncertainty reside in the same circuit parameter. This PPC formulation uses a new type of variable called a polymorphic variable. Polymorphic variables can capture the combined effects of both epistemic and aleatory uncertainty embedded in a circuit parameter, thus leading to a compression in the number of dimensions without any loss in information. This leads to significantly faster training of the PC metamodel as illustrated by multiple numerical examples in this article.