Genetic Algorithm and ANN for Estimation of SPIV of Micro Beams

In this paper, the static pull-in instability (SPIV) of beam-type micro-electromechanical systems is theoretically investigated. Herein, modified strain gradient theory in conjunction with Euler–Bernoulli beam theory have been used for mathematical modeling of the size dependent instability of the micro beams. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two common beam-type systems including double-clamped and clamped-free cantilever have been investigated. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps and size effect, we identify the static pull-in instability voltage. Back propagation artificial neural network (ANN) with three functions have been used for modelling the static pull-in instability voltage of micro beam. Effect of the size dependency on the pull-in performance has been discussed for both micro-structures. The network has four inputs of length, width, gap and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. The number of nodes in the hidden layer, learning ratio and momentum term are optimized using genetic algorithms (GAs). Numerical data, employed for training the network and capabilities of the model in predicting the pull-in instability behaviour has been verified. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the back propagation neural network has the average error of ۶.۳۶% in predicting pull-in voltage of cantilever micro-beam. Resultant low relative error value of the ANN model indicates the usability of the BPN in this area.

Keywords:

Artificial Neural Networks , Euler-Bernoulli , genetic algorithms , Nonlinear micro-beam , Modified couple stress theory , Static pull-in instability