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

Abstract

This paper proposes a neuro-network-based method for model reduction that combines the generalized Hebbian algorithm (GHA) with the Galerkin procedure to perform the dynamic simulation and analysis of nonlinear microelectromechanical systems (MEMS). An unsupervised neural network is adopted to find the principal eigenvectors of a correlation matrix of snapshots. It has been shown that the extensive computer results of the principal component analysis using the neural network of GHA can extract an empirical basis from numerical or experimental data, which can be used to convert the original system into a lumped low-order macromodel. The macromodel can be employed to carry out the dynamic simulation of the original system resulting in a dramatic reduction of computation time while not losing flexibility and accuracy. Compared with other existing model reduction methods for the dynamic simulation of MEMS, the present method does not need to compute the input correlation matrix in advance. It needs only to find very few required basis functions, which can be learned directly from the input data, and this means that the method possesses potential advantages when the measured data are large. The method is evaluated to simulate the pull-in dynamics of a doubly-clamped microbeam subjected to different input voltage spectra of electrostatic actuation. The efficiency and the flexibility of the proposed method are examined by comparing the results with those of the fully meshed finite-difference method.

Proper Orthogonal Decomposition and Its Applications – Part Ii: Model Reduction for Mems Dynamical Analysis

“…Then, in general, these snapshots are used to generate the eigenvectors from the application of the POD methods. The validity and suitability of the eigenvectors obtained using the GHA model as proper shape functions have been demonstrated in reference [11]. The eigenvectors given by the GHA and those obtained by the KLD are examined and compared.…”

“…However, computational prototyping using full models to simulate non-linear PDE are usually computationally very intensive and time consuming, making them di$cult to use when a large number of simulations are needed. It has been demonstrated that a Galerkin procedure employing the eigenvectors obtained from the GHA neural network can convert the dynamic non-linear system to a model with a small number of degrees of freedom, while capturing most of the accuracy and #exibility of the original system e$ciently [11]. The principal components are the most important linear features of the random observation vectors.…”

“…In order to compare the simulation results in this paper with those obtained from reference [11] using the GHA model we adopt the adaptive choice for I employed in reference [11], where I can be calculated iteratively by…”

“…In recent years, several approaches of model reduction for dynamic simulations of MEMS have been presented [9}20], including lumped-parameter techniques, linear modal analysis techniques and Arnoldi-based model reduction approaches, etc., which are reviewed in references [10,11]. More recently, three POD methods including the singular value decomposition (SVD), the Karhunen}Loe`ve decomposition (KLD), and the principal component analysis (PCA) using neural networks have been proposed to handle the model reduction for MEMS respectively [10}13].…”

Macromodels of Micro-Electro-Mechanical Systems (MEMS)

“…Generalized Hebbian algorithm (GHA) is an Artificial Neural Network (ANN) approach of performing Principal Component Analysis (PCA) on a set of data and can be also used as a learning procedure for the approximation of PDE solutions by the expression (5) [10] . The modal approach to MEMS macromodeling is illustrated by sensor device ( fig.7), which is described by coupling a 1-D elastic beam equation with electrostatic force and 2-D compressible isothermal squeeze-film Reynold's equation [11].…”