Application of multiplicative dimensional reduction method for uncertainty quantification and sensitivity analysis of MEMS electrostatic actuators

Abstract

The effect of electrostatic actuation allows MEMS devices to have specific physical movements. They have several advantages including low power, low cost, and small size and are used widely in variable capacitors, micro-accelerometers, etc. In this study, we consider a MEMS actuator consisting of a moveable plate and a fixed plate in the presence of an applied electric field. The gap between the two plates can normally be changed by voltage control. It is known that as the gap reduces to two thirds of the original gap, the so-called “pull-in effect” tends to occur, causing the plates to collide (resulting in dielectric breakdown and actuator failure). It is therefore important to predict the onset of the “pull-in effect”. As it is practically impossible to obtain the model parameters precisely, this prediction should account for the presence of uncertainties. Sampling methods such as Monte Carlo and Quasi Monte Carlo are easy to use with the caveat of low accuracy and high computational cost. The other popular method is polynomial chaos. It has high accuracy and low computational cost under smoothness assumption for problems with small number of uncertain parameters. In this study, we consider a two-stage approach to quantify the parametric uncertainty of MEMS electrostatic actuators with a moderate number of causal stochastic factors. In the first stage, a multiplicative dimensional reduction method is used to approximate the variance-based global sensitivity measures in order to simplify the model for the uncertainty quantification stage. The second stage involves the use of the generalized polynomial chaos (gPC) approach to quantify uncertainty of the simplified model from the first stage.