Abstract
Modeling and simulation of MEMS devices is a very complex tasks which involve the electrical, mechanical, fluidic, and thermal domains, and there are still some uncertainties that need to be accounted for during the robust design of MEMS actuators caused by uncertain material and/or geometric parameters. According to these problems, we put forward stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses; the method makes use of polynomial chaos expansions in terms of the random input variables for the matrices of a finite element model of the system and then uses its transformation matrix to reduce the model; the method is independent of the MOR algorithm, so it is seamlessly compatible with MOR method used in popular finite element solvers. The simulation results verify the method is effective in large scale MEMS design process.
Highlights
MEMS are attractive for many applications because of their small size and weight, which allow systems to be miniaturized [1]
The method is solely based on the mathematical properties of the original system and is, formal, robust, and in great part automatic [2, 3]. These properties render the use of mathematical model order reduction more and more popular in the study of MEMS devices
Variations during fabrication lead to uncertain material and/or geometric parameters causing a significant impact on MEMS device performance [4]
Summary
MEMS are attractive for many applications because of their small size and weight, which allow systems to be miniaturized [1]. The method is solely based on the mathematical properties of the original system and is, formal, robust, and in great part automatic [2, 3] These properties render the use of mathematical model order reduction more and more popular in the study of MEMS devices. Several techniques have been developed, for improving convergence, for example, Latin hypercube sampling, [9, 10], the quasi-Monte Carlo (QMC) method, and the Markov chain Monte Carlo method [11] The statistics such as the mean and standard deviation of the required output quantity such as the electrostatic force are generated. Stochastic model order reduction can offer an efficient way for optimization of dynamic problems [15,16,17] This has led to a lot of efforts towards developing MOR algorithms for variational and parametric uncertainty analysis. The computational gain provided by the sparse PC expansions simulation is illustrated in Section 6 by numerical examples
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