Robust design optimization of electro-thermal microactuator using probabilistic methods

Micromachining of microelectromechanical systems which is similar to other fabrication processes has inherent variation that leads to uncertain dimensional and material properties. Methods for optimization under uncertainty analysis can be used to reduce microdevice sensitivity to these uncertainties in order to create a more robust design, thereby increasing reliability and yield. In this paper, approaches for uncertainty and sensitivity analysis, and robust optimization of an electro-thermal microactuator are applied to take into account the influence of dimensional and material property uncertainties on microactuator tip deflection. These uncertainties include variation of thickness, length and width of cold and hot arms, gap, Young modulus and thermal expansion coefficient. A simple and efficient uncertainty analysis method is performed by creating second-order metamodel through Box-Behnken design and Monte Carlo simulation. Also, the influence of uncertainties has been examined using direct Monte Carlo Simulation method. The results show that the standard deviations of tip deflection generated by these uncertainty analysis methods are very close to each other. Simulation results of tip deflection have been validated by a comparison with experimental results in literature. The analysis is performed at multiple input voltages to estimate uncertainty bands around the deflection curve. Experimental data fall within 95 % confidence boundary obtained by simulation results. Also, the sensitivity analysis results demonstrate that microactuator performance has been affected more by thermal expansion coefficient and microactuator gap uncertainties. Finally, approaches for robust optimization to achieve the optimal designs for microactuator are used. The proposed robust microactuators are less sensitive to uncertainties. For this goal, two methods including Genetic Algorithm and Non-dominated Sorting Genetic Algorithm are employed to find the robust designs for microactuator.