Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics
DOI:
https://doi.org/10.1260/175095409788922293Abstract
In the paper the application of uncertainty analysis performed for microelectromechanical resonator is presented. Main objective of undertaken analysis is to assess the propagation of considered uncertainties in the variation of chosen dynamic characteristics of Finite Element model of microresonator. Many different model parameters have been assumed to be uncertain: geometry and material properties. Apart from total uncertainty propagation, sensitivity analysis has been carried out to study separate influences of all input uncertain characteristics. Uncertainty analysis has been performed by means of fuzzy arithmetics in which alpha-cut strategy has been applied to assemble output fuzzy number. Monte Carlo Simulation and Genetic Algorithms have been employed to calculate intervals connected with each alpha-cut of searched fuzzy number. Elaborated model of microresonator has taken into account in a simplified way the presence of surrounding air and constant electrostatic field.
References
Van der Auweraer H., Requirements and opportunities for structural testing in view of hybrid and virtual modeling, Proceedings of the International Conference on Noise and Vibration Engineering ISMA 2002, Leuven, Belgium, September 16-18, 2002, 1687-1702.
Lin R.M., Wang W.J., Structural dynamics of microsystems - current state of research and future directions, Mechanical Systems and Signal Processing, 2006, 20, 1015-1043. https://doi.org/10.1016/j.ymssp.2005.08.013
Liu M., Maute K., Frangopol D.M., Multi-objective design optimization of electrostatically actuated microbeam resonators with and without parameter uncertainty, Reliability Engineering and System Safety, 2007, 92, 1333-1343. https://doi.org/10.1016/j.ress.2006.09.007
Pitchumani M.R., Design of microresonators under uncertainty, Journal of Microelectromechanical Systems, 2005, 14(1), 63-69.
Codreanu I., Martowicz A., Gallina A., Pieczonka L., Uhl T., Study of the effect of process induced uncertainties on the performance of a micro-comb resonator, Proceedings of 4th Conference Mechatronic Systems and Materials 2008 - MSM 2008, Bialystok, Poland, July 14-17, 2008. https://doi.org/10.4028/www.scientific.net/ssp.147-149.716
Martowicz A., Codreanu I., Uhl T., Uncertainty of design parameters and their influence on dynamic properties of MEMS microresonators. Proceedings of 8th. World Congress on Computational Mechanics WCCM8 and 5th. European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2008, Venice, Italy, June 30 - July 5, 2008. https://doi.org/10.7712/100016.2198.7129
Codreanu I., Martowicz A., Uhl T., Influence of uncertain parameters on the performance of a micro-comb resonator. Proceedings of 19th MicroMechanics Europe Workshop - MME 2008, Aachen, Germany, September 28-30, 2008.
Moens D., Vandepitte D., A survey of non-probabilistic uncertainty treatment in finite element analysis, Computer Methods in Applied Mechanics and Engineering, 2005, 194, 1527-1555. https://doi.org/10.1016/j.cma.2004.03.019
Oberkampf W.L., DeLand S.M., Rutherford B.M., Diegert K.V., Alvin K.F., Error and uncertainty in modeling and simulation, Reliability Engineering and System Safety, 2002, 75, 333-357. https://doi.org/10.1016/s0951-8320(01)00120-x
Moens D., Vandepitte D., Non probabilistic approaches for non deterministic FE analysis of imprecisely defined structures. Proceedings of the International Conference on Noise and Vibration Engineering ISMA 2004, Leuven, Belgium, September 20-22, 2004, 3095-3119.
Schueller G.I., A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, 1997, 12(4), 197-321. https://doi.org/10.1016/s0266-8920(97)00003-9
Moore R.E., Interval analysis, Prentice-Hall, Englewood Cliffs, N. J., 1966.
Dubois D., Prade H., Fuzzy sets and systems. Theory and applications, Academic Press, New York, 1980.
Hanss M., Applied fuzzy arithmetic. An introduction with engineering applications, Springer-Verlag, Berlin, 2005.
Hanss M., The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets and Systems, 2002, 130, 277-289. https://doi.org/10.1016/s0165-0114(02)00045-3
Mir S., Charlot B., Courtois B., Extending fault-based testing to micromechanical systems, Journal of Electronic Testing: Theory and Applications, 2000, 16, 279-288. https://doi.org/10.1023/a:1008303717862
Bao M., Analysis and design principles of MEMS devices, Elsevier Science, 2005.
Helton J.C., Davis F.J., Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliability Engineering and System Safety, 2003, 81(1), 23-69. https://doi.org/10.1016/s0951-8320(03)00058-9
Goldberg D.E., Genetic algorithms in search, optimization, and machine learning, Addison-Wesley Publishing Company, Reading, Massachusetts, USA, 1989.
Michalewicz Z., Genetic algorithms + data structures = evolution programs, Springer-Verlag, Berlin, Heidelberg, 1996.
Kleiber M., Antunez H., Hien T.D., Kowalczyk P., Parameter sensitivity in nonlinear mechanics, John Wiley & Sons, Chichester, England, 1997.
Validation and updating of FE models for structural analysis. Theory, practice and applications, Course materials, Dynamic Design Solutions NV, Leuven, Belgium, 2007.
Published
How to Cite
Issue
Section
Copyright (c) 2009 A Martowicz, I Stanciu, T Uhl
This work is licensed under a Creative Commons Attribution 4.0 International License.