A Novel Dimension Fusion Based Polynomial Chaos Approach for Mixed Aleatory-Epistemic Uncertainty Quantification of Carbon Nanotube Interconnects

In this paper, a novel PC based approach to model the impact of both aleatory (random) and epistemic (ignorance based) uncertainty on the performance of carbon nanotube (CNT) interconnects is presented. The key feature of this approach is a dimension fusion strategy whereby the aleatory and epistemic uncertainty in a model parameter is collectively represented using a single mixed variable. Thereafter, an approach to extract a set of basis functions that are by definition orthonormal with respect to the arbitrary probability distribution of the mixed variables is proposed. These basis functions are used to generate a reduced dimensional PC metamodel that accurately captures both the epistemic and aleatory uncertainty of the CNT interconnect network. The performance of the reduced PC metamodel relative to a traditional full-blown metamodel is validated using a numerical example.