Uncertainty Quantification Using Polynomial-Chaos Expansion

In this chapter, we explore uncertainty quantification techniques based on polynomial chaos expansion. We begin by looking at the general MEMS stochastic equation before setting up the stochastic governing system for the tapered piezoelectric energy harvester. We first illustrate the application of polynomial chaos expansion on the general MEMS stochastic equation. We then proceed to apply the PCE on the tapered PEH stochastic equation and apply Galerkin projection on the expanded system for its solution. We present the uncertainty dependency graph of the tapered PEH model that can be used to incrementally propagate the uncertainty model through to the desired node. We use a numerical probability transformation approach to estimate the probability density functions at any of the graph nodes. In the end, we propose to use the stochastic testing-based hierarchical UQ approach developed by Zhang (2014) on the TPEH equivalent circuit model.