A data-driven stochastic collocation approach for uncertainty quantification in MEMS

Nitin Agarwal, N. R. Aluru

Research output: Contribution to journalArticlepeer-review


This work presents a data-driven stochastic collocation approach to include the effect of uncertain design parameters during complex multi-physics simulation of Micro-ElectroMechanical Systems (MEMS). The proposed framework comprises of two key steps: first, probabilistic characterization of the input uncertain parameters based on available experimental information, and second, propagation of these uncertainties through the predictive model to relevant quantities of interest. The uncertain input parameters are modeled as independent random variables, for which the distributions are estimated based on available experimental observations, using a nonparametric diffusion-mixing-based estimator, Botev (Nonparametric density esti-mation via diffusion mixing. Technical Report, 2007). The diffusion-based estimator derives from the analogy between the kernel density estimation (KDE) procedure and the heat dissipation equation and constructs density estimates that are smooth and asymptotically consistent. The diffusion model allows for the incorporation of the prior density and leads to an improved density estimate, in comparison with the standard KDE approach, as demonstrated through several numerical examples. Following the characterization step, the uncertainties are propagated to the output variables using the stochastic collocation approach, based on sparse grid interpolation, Smolyak (Soviet Math. Dokl. 1963; 4:240-243). The developed framework is used to study the effect of variations in Young's modulus, induced as a result of variations in manufacturing process parameters or heterogeneous measurements on the performance of a MEMS switch.

Original languageEnglish (US)
Pages (from-to)575-597
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - Jul 30 2010


  • Diffusion estimator
  • Nonparametric density estimation
  • Polysilicon young's modulus
  • Smolyak algorithm
  • Sparse grids
  • Stochastic collocation
  • Uncertainty quantification

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics
  • Numerical Analysis


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