Abstract
This chapter explores the use of the Duffing nonlinearity and fast dynamics found in microelectromechanical beam oscillators for reservoir computing applications. General properties of MEMS are discussed, and the Duffing microscale beam characteristics are analyzed through analytical models and simulations. The reservoir computer is then constructed around a single such nonlinear oscillator through temporal multiplexing of the input and self-coupling via delayed feedback. The parameters of the resulting physical system are finally adjusted for optimal performance on computing the parity of a binary input stream, as well as on a spoken digit recognition task.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Abdolvand, B. Bahreyni, J. Lee, F. Nabki, Micromachined resonators, a review. Micromachines 7(9), 160 (2016)
A. Agresti, B.A. Coull, Approximate is better than “Exact” for interval estimation of binomial proportions. Am. Stat. 52(2), 119 (1998)
G. Ananthasuresh, Micro and Smart Systems: Technology and Modeling (Wiley, Hoboken, 2012)
D. Antonio, D.H. Zanette, D. Lopez, Frequency stabilization in nonlinear micromechanical oscillators. Nat. Commun. 3(1) (2012)
L. Appeltant, M.C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C.R. Mirasso, I. Fischer, Information processing using a single dynamical node as complex system. Nat. Commun. 2, 468 (2011)
S.I. Arroyo, D.H. Zanette, Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators. Eur. Phys. J. B 89(1) (2016)
A. Bala, I. Ismail, R. Ibrahim, S.M. Sait, Applications of metaheuristics in reservoir computing techniques: a review. IEEE Access 6, 58012–58029 (2018)
M. Bao, Analysis and Design Principles of MEMS Devices, 1st edn. (Elsevier, Amsterdam, 2005). OCLC: 254583926
M. Bao, H. Yang, Squeeze film air damping in MEMS. Sens. Actuators A 136(1), 3–27 (2007)
B. Barazani, G. Dion, A. Idrissi-El Oudrhiri, F. Ghaffari, J. Sylvestre, Micromachined neuro-processing accelerometer. To appear in 27th Canadian congres of Applied Mechanics, vol. 3 (2019)
B. Barazani, G. Dion, J.-F. Morissette, L. Beaudoin, J. Sylvestre, M. Neuroaccelerometer, Integrating sensing and reservoir computing in MEMS. J. Microelectromech. Syst. 29(3), 338–347 (2020)
R.C. Batra, M. Porfiri, D. Spinello, Review of modeling electrostatically actuated microelectromechanical systems. Smart Mater. Struct. 16(6), R23–R31 (2007)
M.J. Brennan, I. Kovacic, A. Carrella, T.P. Waters, On the jump-up and jump-down frequencies of the Duffing oscillator. J. Sound Vib. 318(4–5), 1250–1261 (2008)
D. Brunner, M.C. Soriano, C.R. Mirasso, I. Fischer, Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 1364 (2013)
E. Buks, B. Yurke, Mass detection with a nonlinear nanomechanical resonator. Phys. Rev. E 74(4) (2006)
A. Cammarano, T.L. Hill, S.A. Neild, D.J. Wagg, Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator. Nonlinear Dyn. 77(1), 311–320 (2014)
J.C. Coulombe, M.C.A. York, J. Sylvestre, Computing with networks of nonlinear mechanical oscillators. PLOS ONE 12(6), e0178663 (2017)
M. Dale, S. Stepney, J.F. Miller, M. Trefzer, Reservoir computing in materio: an evaluation of configuration through evolution, in 2016 IEEE Symposium Series on Computational Intelligence (SSCI), December 2016, Athens, Greece (IEEE, 2016), pp. 1–8
G. Dion, S. Mejaouri, J. Sylvestre, Reservoir computing with a single delay-coupled non-linear mechanical oscillator. J. Appl. Phys. 124(15) (2018)
G. Duffing, Erzwungene Schwingungen bei veranderlicher Eigenfrequenz und ihre technische Bedeutung. Brunswick (1918)
F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, All-optical reservoir computing. Opt. Express 20(20), 22783 (2012)
K.L. Ekinci, M.L. Roukes, Nanoelectromechanical systems. Rev. Sci. Instrum. 76(6) (2005)
A.A. Ferreira, T.B. Ludermir, Genetic algorithm for reservoir computing optimization, in 2009 International Joint Conference on Neural Networks, June 2009, Atlanta, Ga, USA (IEEE, 2009), pp. 811–815
A.A. Ferreira, T.B. Ludermir, Comparing evolutionary methods for reservoir computing pre-training, in The 2011 International Joint Conference on Neural Networks, July 2011, San Jose, CA, USA (IEEE, 2011), pp. 283–290
J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 2002). OCLC: 51506830
C. Gui, R. Legtenberg, M. Elwenspoek, J.H. Fluitman, Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure. J. Micromech. Microeng. 5(2), 183–185 (1995)
A.C. Harrie, Tilmans and Rob Legtenberg, Electrostatically driven vacuum-encapsulated polysilicon resonators: Part II. Theory and performance. Sens. Actuators A: Phys. 45(1), 67–84 (1994)
A. Husain, J. Hone, H.W.Ch. Postma, X.M.H. Huang, T. Drake, M. Barbic, A. Scherer, M.L. Roukes, Nanowire-based very-high-frequency electromechanical resonator. Appl. Phys. Lett. 83(6), 1240–1242 (2003)
B. Huval, T. Wang, S. Tandon, J. Kiske, W. Song, J. Pazhayampallil, M. Andriluka, P. Rajpurkar, T. Migimatsu, R. Cheng-Yue, F. Mujica, A. Coates, A.Y. Ng, An empirical evaluation of deep learning on highway driving, April 2015 (2015), arXiv:1504.01716 [cs]
H. Jaeger, The echo state approach to analysing and training recurrent neural networks-with an erratum note. GMD Technical Report 148(34), 13, German National Research Center for Information Technology, Bonn, Germany (2001)
H. Jaeger, A tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and the “echo state network” approach (2002), p. 46
H. Jaeger, H. Haas, Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304(5667), 78–80 (2004)
Md. Jubayer Alam Rabin, Md. Safayet Hossain, Md. Solaiman Ahsan, Md. Abu Shahab Mollah, Md. Tawabur Rahman, Sensitivity learning oriented nonmonotonic multi reservoir echo state network for short-term load forecasting, in 2013 International Conference on Informatics, Electronics and Vision (ICIEV), May 2013, Dhaka, Bangladesh (IEEE, 2013), pp. 1–6
T. Kalmar-Nagy, B. Balachandran, Forced harmonic vibration of a duffing oscillator with linear viscous damping, in The Duffing Equation, ed. by I. Kovacic, M.J. Brennan (John Wiley & Sons, Ltd., Chichester, 2011), pp. 139–174
F. Khoshnoud, C.W. de Silva, Recent advances in MEMS sensor technology-mechanical applications. IEEE Instrum. Meas. Mag. 15(2), 14–24 (2012)
Y. Lai, J. McDonald, M. Kujath, T. Hubbard, Force, deflection and power measurements of toggled microthermal actuators. J. Micromech. Microeng. 14(1), 49–56 (2004)
L. Larger, M.C. Soriano, D. Brunner, L. Appeltant, J.M. Gutierrez, L. Pesquera, C.R. Mirasso, I. Fischer, Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing. Opt. Express 20(3), 3241 (2012)
L. Larger, A. Baylon-Fuentes, R. Martinenghi, V.S. Udaltsov, Y.K. Chembo, M. Jacquot, High-speed photonic reservoir computing using a time-delay-based architecture: million words per second classification. Phys. Rev. X 7(1) (2017)
Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521(7553), 436–444 (2015)
J.E.-Y. Lee, Y. Zhu, A.A. Seshia, A bulk acoustic mode single-crystal silicon microresonator with a high-quality factor. J. Micromech. Microeng. 18(6) (2008)
D.A. Lieberman, Learning: Behavior and Cognition, 2nd edn. (Thomson Brooks/Cole Publishing Co., Belmont, CA, US, 1993)
R. Lifshitz, M.C. Cross, Nonlinear dynamics of nanomechanical resonators, in Nonlinear Dynamics of Nanosystems, ed. by G. Radons, B. Rumpf, H.G. Schuster (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2010), pp. 221–266
H. Lin Wang, X.-Y.A. Huanling, H. Liu, Effective electricity energy consumption forecasting using echo state network improved by differential evolution algorithm. Energy 153, 801–815 (2018)
C. Liu, Foundations of MEMS (Pearson Prentice Hall, Upper Saddle River, 2006)
R.F. Lyon, A computational model of filtering, detection, and compression in the cochlea 7, 1282–1285 (1982)
M. Madou, Fundamentals of Microfabrication (CRC Press, Boca Raton, 1997)
P. Malatkar, A.H. Nayfeh, Calculation of the jump frequencies in the response of S.D.O.F. Non-linear systems. J. Sound Vib. 254(5), 1005–1011 (2002)
R. Martinenghi, S. Rybalko, M. Jacquot, Y.K. Chembo, L. Larger, Photonic nonlinear transient computing with multiple-delay wavelength dynamics. Phys. Rev. Lett. 108(24) (2012)
A. Matthiessen, C. Vogt, On the influence of temperature on the electric conducting-power of alloys. Philos. Trans. R. Soc. Lond. 167–200 (1864)
K. Naeli, O. Brand, Dimensional considerations in achieving large quality factors for resonant silicon cantilevers in air. J. Appl. Phys. 105(1) (2009)
A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (Wiley, 1995)
Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, Optoelectronic reservoir computing. Sci. Rep. 2(1) (2012)
X. Pitkow, S. Liu, D.E. Angelaki, G.C. DeAngelis, A. Pouget, How can single sensory neurons predict behavior? Neuron 87(2), 411–423 (2015)
H.W.Ch. Postma, I. Kozinsky, A. Husain, M.L. Roukes, Dynamic range of nanotube- and nanowire-based electromechanical systems. Appl. Phys. Lett. 86(22) (2005)
M. Rigamonti, P. Baraldi, E. Zio, I. Roychoudhury, K. Goebel, S. Poll, Ensemble of optimized echo state networks for remaining useful life prediction. Neurocomputing 281, 121–138 (2018)
S.B. Salah, I. Fliss, M. Tagina, Echo state network and particle swarm optimization for prognostics of a complex system, in 2017 IEEE/ACS 14th International Conference on Computer Systems and Applications (AICCSA), October 2017, Hammamet (IEEE, 2017), pp. 1027–1034
J.A. Sanders, F. Verhulst, J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, 2nd edn., Applied Mathematical Sciences (Springer, New York, 2007)
A.T. Sergio, T.B. Ludermir, PSO for reservoir computing optimization, in Artificial Neural Networks and Machine Learning - ICANN 2012, vol. 7552, ed. by D. Hutchison, T. Kanade, J. Kittler, J.M. Kleinberg, F. Mattern, J.C. Mitchell, M. Naor, O. Nierstrasz, C. Pandu Rangan, B. Steffen, M. Sudan, D. Terzopoulos, D. Tygar, M.Y. Vardi, G. Weikum, A.E.P. Villa, W. Duch, P. Erdi, F. Masulli, G. Palm (Springer, Berlin, 2012), pp. 685–692
M.C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. van der Sande, Delay-based reservoir computing: noise effects in a combined analog and digital implementation. IEEE Trans. Neural Netw. Learn. Syst. 26(2), 388–393 (2015)
J.B. Starr, Squeeze-film damping in solid-state accelerometers, in IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop (1990), pp. 44–47
J. Sylvestre, G. Dion, B. Barazani, Provisional US patent application 62/780,589 (2018)
Y. Tadokoro, H. Tanaka, M.I. Dykman, Driven nonlinear nanomechanical resonators as digital signal detectors. Sci. Rep. 8(1) (2018)
B. Tang, Mj. Brennan, V. Lopes, S. da Silva, R. Ramlan, Using nonlinear jumps to estimate cubic stiffness nonlinearity: an experimental study. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 230(19), 3575–3581 (2016)
Theory Reference for the Mechanical APDL and Mechanical Applications (2017)
H.A.C. Tilmans, M. Elwenspoek, J.H.J. Fluitman, Micro resonant force gauges. Sens. Actuators A: Phys. 30(1), 35–53 (1992)
J. Torrejon, M. Riou, F.A. Araujo, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M.D. Stiles, J. Grollier, Neuromorphic computing with nanoscale spintronic oscillators. Nature 547(7664), 428–431 (2017)
J.T.M. van Beek, G.J.A.M. Verheijden, G.E.J. Koops, K.L. Phan, C. van der Avoort, J. van Wingerden, D. Ernur Badaroglu, J.J.M. Bontemps, Scalable 1.1 GHz fundamental mode piezo-resistive silicon MEMS resonator, in 2007 IEEE International Electron Devices Meeting, December 2007, Washington, DC (IEEE, 2007), pp. 411–414
W.M. Van Spengen, R. Puers, I. De Wolf, On the physics of stiction and its impact on the reliability of microstructures. J. Adhes. Sci. Technol. 17(4), 563–582 (2003)
S.S. Verbridge, J.M. Parpia, R.B. Reichenbach, L.M. Bellan, H.G. Craighead, High quality factor resonance at room temperature with nanostrings under high tensile stress. J. Appl. Phys. 99(12), 124304 (2006)
D. Verstraeten, B. Schrauwen, D. Stroobandt, Isolated word recognition using a liquid state machine, in Proceedings of the 13th European Symposium on Artificial Neural Networks (ESANN) (2005), pp. 435–440
D. Witt, R. Kellogg, M. Snyder, J. Dunn, Windows into human health through wearables data analytics. Curr. Opin. Biomed. Eng. (2019)
K. Worden, On jump frequencies in the response of the duffing oscillator. J. Sound Vib. (1996)
N. Yazdi, F. Ayazi, K. Najafi, Micromachined inertial sensors. Proc. IEEE 86(8), 20 (1998)
M.I. Younis, MEMS Linear and Nonlinear Statics and Dynamics, vol. 20, Microsystems (Springer, New York, 2010). OCLC: ocn495781913
S. Zaitsev, O. Shtempluck, E. Buks, O. Gottlieb, Nonlinear damping in a micromechanical oscillator. Nonlinear Dyn. 67(1), 859–883 (2012)
Y. Zhang, Y. Yu, D. Liu, The application of modified ESN in chaotic time series prediction, in 2013 25th Chinese Control and Decision Conference (CCDC), May 2013, Guiyang, China (IEEE, 2013), pp. 2213–2218
H. Zhou, Y. Wang, K. Xing, Modeling of McKibben pneumatic artificial muscles using optimized echo state networks, in 2010 8th World Congress on Intelligent Control and Automation, July 2010, Jinan, China (IEEE, 2010), pp. 1723–1728
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Dion, G., Oudrhiri, A.IE., Barazani, B., Tessier-Poirier, A., Sylvestre, J. (2021). Reservoir Computing in MEMS. In: Nakajima, K., Fischer, I. (eds) Reservoir Computing. Natural Computing Series. Springer, Singapore. https://doi.org/10.1007/978-981-13-1687-6_9
Download citation
DOI: https://doi.org/10.1007/978-981-13-1687-6_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1686-9
Online ISBN: 978-981-13-1687-6
eBook Packages: Computer ScienceComputer Science (R0)