Proper orthogonal decomposition and its applications - Part II: Model reduction for MEMS dynamical analysis

Abstract

Proper orthogonal decomposition (POD) methods are popular tools for data analysis aimed at obtaining low-dimensional approximate descriptions of a high-dimensional process in many engineering fields. The applications of POD methods to model reduction for microelectromechanical systems (MEMS) are reviewed in this paper. In view of the fact that existing POD methods in the model reduction for dynamic simulation of MEMS dealt with only noise-free data, this paper proposes a neural-network-based method that combines robust principal component analysis (PCA) neural network model with Galerkin procedure for dynamic simulation and analysis of non-linear MEMS with noisy data. Simulations are given to show the performance of the proposed method in comparison with the existing method. Compared with the standard PCA neural network model, the robust PCA neural network model has a number of numerical advantages such as the stability and robustness to noise-injected data and the faster convergence of iterations in the training stages than the existing neural network technique. The macro-model generated by using the eigenvectors extracted from the proposed method as basis functions shows its flexibility and efficiency in the representation and simulation of the original non-linear partial differential equations. © 2002 Elsevier Science Ltd. All rights reserved.