Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Stable compact modeling of piezoelectric energy harvester devices

Stable compact modeling of piezoelectric energy harvester devices Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”Design/methodology/approachPiezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. FindingsThis contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.Originality/valueThe stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

Stable compact modeling of piezoelectric energy harvester devices

Download PDF
14 pages

Loading next page...
 
/lp/emerald-publishing/stable-compact-modeling-of-piezoelectric-energy-harvester-devices-8X0yzHtJgh
Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0332-1649
DOI
10.1108/compel-07-2019-0305
Publisher site
See Article on Publisher Site

Abstract

Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”Design/methodology/approachPiezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. FindingsThis contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.Originality/valueThe stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.

Journal

COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing

Published: May 20, 2020

Keywords: Piezoelectricity; Energy harvester; Model order reduction; Finite element method; Coupled systems

References

  • New modelling approach for micro energy harvesting systems based on model order reduction enabling truly system-level simulation
    Aftab, T.; Bechtold, T.; Hohlfeld, D.; Rudnyi, E.B.; Korvink, J.G.
  • Dimension reduction of large-scale second-order dynamical system via a second-order Arnoldi method
    Bai, Z.; Su, Y.
  • A survey of projection-based model reduction methods for parametric dynamical systems
    Benner, P.; Gugercin, S.; Willcox, K.
  • Model reduction by rational interpolation
    Beattie, C.; Gugercin, S.; Benner, P.; Ohlberger, M.; Cohen, A.; Willcox, K.
  • Index-aware model order reduction methods for DAEs
    Banagaaya, N.
  • Model order reduction for differential-algebraic equations: a survey
    Benner, P.; Stykel, T.; Ilchmann, A.; Reis, T.
  • Structure preserving model order reduction of large scale sparse second-order index-1 systems and application to a mechatronics model
    Benner, P.; Saak, J.; Uddin, M.M.
  • Multiphysics modeling and simulation of a dual frequency energy harvester
    Bouhedma, S.; Zheng, Y.H.; Hohlfeld, D.
  • Stability-preserving adaptive model order reduction of DAEs by Krylov-subspace methods
    Castagnotto, A.; Lohmann, B.
  • Generating passive compact models for piezoelectric devices
    Chen, C.C.; Kuo, C.W.; Yang, Y.J.
  • Krylov-subspace methods for reduced-order modeling in circuit simulation
    Freund, R.W.
  • SPRIM: structure-preserving reduced order interconnect macromodeling
    Freund, R.W.
  • Model reduction of descriptor systems by interpolary projection methods
    Gugercin, S.; Stykel, T.; Wyatt, S.
  • Quasi-Schur transformation for the stable compact modeling of piezoelectric energy harvester devices
    Hu, S.Y.; Yuan, C.D.; Bechtold, T.
  • Stable reduced order modeling of piezoelectric energy harvesting modules using implicit Schur complement
    Hu, S.Y.; Yuan, C.D.; Castagnotto, A.; Lohmann, B.; Bouhedma, S.; Hohlfeld, D.; Bechtold, T.
  • Computationally efficient and stable order reduction methods for a large-scale model of MEMS piezoelectric energy harvester
    Kudryavtsev, M.; Rudnyi, E.B.; Korvink, J.G.; Hohlfeld, D.; Bechtold, T.
  • Entwicklung einer simulationsumgebung für die auslegung piezoelectrischer energy harvester
    Kurch, M.
  • MOR for ANSYS
    Rudnyi, E.B.; Bechtold, T.; Schrag, G.; Feng, L.
  • Structure preserving order reduction of large scale second order models
    Salimbahrami, B.
  • A piezoelectric vibration harvester based on clamped-guided beams
    Wang, Z.; Matova, S.; Elfrink, R.; Jambunathan, M.; de Nooijer, C.; van Schaijk, R.; Vullers, R.J.M.
  • Implicit Schur complement for model order reduction of second order piezoelectric energy harvester model
    Yuan, C.D.; Hu, S.Y.; Castagnotto, A.; Lohmann, B.; Bechtold, T.
  • Order reduction of large-scale second-order systems using Krylov subspace methods
    Salimbahrami, B.; Lohmann, B.