Solution-Verified Reliability Analysis and Design of Compliant Micro-Electro-Mechanical Systems

Abstract

An important component of verification and validation of computational models is solution verification, which focuses on the convergence of the desired solution quantities as one refines the spatial and temporal discretizations and iterative controls. Uncertainty analyses often treat solution verification as a separate issue, hopefully through the use of a priori grid convergence studies and selection of models with acceptable discretization errors. In this paper, a tighter connection between solution verification and uncertainty quantification is investigated. In particular, error estimation techniques, using global norm and quantity of interest error estimators, are applied to the nonlinear structural analysis of microelectromechanical systems (MEMS). Two primary approaches for uncertainty quantification are then developed: an error-corrected approach, in which simulation results are directly corrected for discretization errors, and an error-controlled approach, in which estimators are used to drive adaptive h-refinement of mesh discretizations. The former requires quantity of interest error estimates that are quantitatively accurate, whereas the latter can employ any estimator that is qualitatively accurate. Combinations of these error-corrected and error-controlled approaches are also explored. Each of these techniques treats solution verification and uncertainty analysis as a coupled problem, recognizing that the simulation errors may be influenced by, for example, conditions present in the tails of input probability distributions. The most effective and affordable of these approaches are carried forward in probabilistic design studies for robust and reliable operation of a bistable MEMS device. Computational results show that on-line and parameter-adaptive solution verification can lead to uncertainty quantification and design under uncertainty studies that are more accurate, efficient, reliable, and convenient.