A nonstationary covariance function model for spatial uncertainties in electrostatically actuated microsystems

Abstract

This paper presents a data-driven method of estimating stochastic models that describe spatial uncertainties. Relating these uncertainties to the spatial statistics literature, we describe a general framework that can handle heterogeneous random processes by providing a parameterization for the nonstationary covariance function in terms of a transformation function and then estimating the unknown hyperparameters from data using Bayesian inference. The transformation function is specified as a displacement that transforms the coordinate space to a deformed configuration in which the covariance between points can be represented by a stationary model. This approach is then used to model spatial uncertainties in microelectromechanical actuators, where the ground plate is assumed to have a spatially varying profile. We estimate the stochastic model corresponding to the random surface using synthetic profilometric data that simulate multiple experimental measurements of ground plate surface roughness.We then demonstrate the effect of the uncertainty on the displacement of the actuator as well as on other parameters, such as the pull-in voltage. We show that the nonstationarity is essential when performing uncertainty quantification in electrostatic microactuators.