Uncertainty quantification of MEMS using a data-dependent adaptive stochastic collocation method

Aravind Alwan, N. R. Aluru

Research output: Contribution to journalArticlepeer-review


This paper presents a unified framework for uncertainty quantification (UQ) in microelectromechanical systems (MEMS). The goal is to model uncertainties in the input parameters of micromechanical devices and to quantify their effect on the final performance of the device. We consider different electromechanical actuators that operate using a combination of electrostatic and electrothermal modes of actuation, for which high-fidelity numerical models have been developed. We use a data-driven framework to generate stochastic models based on experimentally observed uncertainties in geometric and material parameters. Since we are primarily interested in quantifying the statistics of the output parameters of interest, we develop an adaptive refinement strategy to efficiently propagate the uncertainty through the device model, in order to obtain quantities like the mean and the variance of the stochastic solution with minimal computational effort. We demonstrate the efficacy of this framework by performing UQ in some examples of electrostatic and electrothermomechanical microactuators. We also validate the method by comparing our results with experimentally determined uncertainties in an electrostatic microswitch. We show how our framework results in the accurate computation of uncertainties in micromechanical systems with lower computational effort.

Original languageEnglish (US)
Pages (from-to)3169-3182
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Issue number45-46
StatePublished - Oct 15 2011


  • Adaptive analysis
  • Hybrid electrothermomechanical (ETM) actuation
  • Microelectromechanical systems (MEMS)
  • Stochastic collocation
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy


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