MEMS stochastic model order reduction method based on polynomial chaos expansion

Abstract

devices have some form of nonlinearity, either geometric nonlinearity due to large amplitude deflections or intrinsic nonlinearities due to governing equations, Multi-energy domain coupling effect of MEMS can hardly be described perfectly, because in a micron-scale or even in a Nanoscale working room, physical quantities of energy among the different domains interact with each other (Mounier 2012). Modeling and simulation is at the basis of the prediction of the device behavior and optimization of its performance. Modeling of MEMS devices is a very complex task. Their behavior involves multiple coupled energy domains. The electrical and the mechanical domains are the main ones, but also the fluidic and thermal domain may be of interest (Gong 2013). In addition, the devices have most of the time a three dimensional and geometrically complex structure. As a consequence, MEMS modelling is always a trade-off between accuracy and computational complexity (Binion and Chen 2010). An accurate device model can be achieved using the so called physical modelling. The partial differential equation governing the device behavior can be discretized on the device domain. The resulting system of ordinary differential equations gives a representation of the device. Several commercial tools are already available for device physical modelling and simulation, which make use of different discretization and solution techniques (Senturia 1998). However, proceeding this way, the afore-mentioned complexity factors lead to device physical models with a large number of degrees of freedom: 10-100 thousands of equations to solve represent a standard problem. The complexity of the simulation analysis adds to the complexity of the model. MEMS characterization often requires computationally expensive analysis such as transient analysis. Moreover, the derived models are often nonlinear. The primary source of nonlinearity is the electrostatic force, which couples the electrical and mechanical energy domains.Abstract Modeling and simulation of MEMS devices is a very complex task which involve the electrical, mechanical, fluidic and thermal domains, and there are still some uncertainties need to be accounted because of uncertain material and/or geometric parameters factors. According to these problems, we put forward to stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses, the method firstly process model order reduction by Structure Preserving Reduced-order Interconnect Macro Modeling method, then makes use of polynomial chaos expansions in terms of the random input and output variables for the matrices of a finite element model of the system; at last we give the expected values and standard deviations computing method to MEMS stochastic model. The simulation results verify the method is effective in large scale MEMS design process.

An Optimal Radial Basis Function Neural Network Enhanced Adaptive Robust Kalman Filter for GNSS/INS Integrated Systems in Complex Urban Areas

“…Even if the observation is reliable, it still requires more accurate dynamic model for both INS and GPS errors, since it is usually difficult to set a certain stochastic model for each inertial sensor that works efficiently in all environments [ 28 ]. In a low-cost GNSS/MINS integrated system, inertial sensor also includes gross error due to unmeasurable external disturbances and high dynamics which against stochastic model, and may be harmful for state prediction vector and its covariance [ 6 ].…”