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

This paper proposes a neuro-network-based method for model reduction that c ombines the generalized Hebbian algorithm (GHA) with the Galerkin procedure to perform the dynamic simulation and analysis of nonlinear microelectrome chanical systems (MEMS). An unsupervised neural network is adopted to find the principal eigenvectors of a correlation matrix of snapshots. It has bee n shown that the extensive computer results of the principal component anal ysis using the neural network of GHA can extract an empirical basis from nu merical or experimental data, which can be used to convert the original sys tem into a lumped low-order macromodel, The macromodel can be employed to c arry out the dynamic simulation of the original system resulting in a drama tic reduction of computation time while not losing flexibility and accuracy . Compared with other existing model reduction methods for the dynamic simu lation of MEMS, the present method does not need to compute the input corre lation matrix in advance. It needs only to find very few required basis fun ctions, which can be learned directly from the input data, and this means t hat the method possesses potential advantages when the measured data are la rge. The method is evaluated to simulate the pull-in dynamics of a doubly-c lamped microbeam subjected to different input voltage spectra of electrosta tic actuation. The efficiency and the flexibility of the proposed method ar e examined by comparing the results with those of the fully meshed finite-d ifference method.