A neural-network-based method of model reduction for the dynamic simulation ofMEMS

Abstract

This paper proposes a neuro-network-based method for modelreduction that combines the generalized Hebbian algorithm (GHA) with theGalerkin procedure to perform the dynamic simulation and analysis ofnonlinear microelectromechanical systems (MEMS). An unsupervised neuralnetwork is adopted to find the principal eigenvectors of a correlationmatrix of snapshots. It has been shown that the extensive computer resultsof the principal component analysis using the neural network of GHA canextract an empirical basis from numerical or experimental data, which canbe used to convert the original system into a lumped low-order macromodel.The macromodel can be employed to carry out the dynamic simulation of theoriginal system resulting in a dramatic reduction of computation timewhile not losing flexibility and accuracy. Compared with other existingmodel reduction methods for the dynamic simulation of MEMS, the presentmethod does not need to compute the input correlation matrix in advance.It needs only to find very few required basis functions, which can belearned directly from the input data, and this means that the methodpossesses potential advantages when the measured data are large. Themethod is evaluated to simulate the pull-in dynamics of a doubly-clampedmicrobeam subjected to different input voltage spectra of electrostaticactuation. The efficiency and the flexibility of the proposed method areexamined by comparing the results with those of the fully meshedfinite-difference method.