Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics

A Martowicz, I Stanciu, T Uhl

Abstract


In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.

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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.
CrossRef

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.
CrossRef

Pitchumani M.R., Design of microresonators under uncertainty, Journal of Microelectromechanical Systems, 2005, 14(1), 63-69.
CrossRef

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.

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.

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.
CrossRef

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.
CrossRef

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.
CrossRef

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.
CrossRef

Mir S., Charlot B., Courtois B., Extending fault-based testing to micromechanical systems, Journal of Electronic Testing: Theory and Applications, 2000, 16, 279-288.
CrossRef

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.
CrossRef

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.




DOI: http://dx.doi.org/10.1260/175095409788922293

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