Memetic Computing

, Volume 10, Issue 2, pp 209–231 | Cite as

Fabrication of a resonant PEMC sensor using hybrid \(\upvarepsilon \)-constraint lexicographical ranking DE-MSBA with Jacobean approximation

  • S. Mohammadrezaei NodehEmail author
  • A. Mozaffari
  • M. Ghaneh
  • F. Bakhtiarinejad
Regular Research Paper


In the current research, a novel algorithm is proposed for the optimal fabrication of a resonant piezoelectric excited millimeter-sized cantilever (PEMC) sensor. PEMC sensor is one of the most well-known types of sensors with a wide range of applications in today’s industry. The proposed design mechanism is general, and can be used for the fabrication of PEMCs for different applications. A physics-based analytical model based on Euler–Bernoulli theory is adopted for performance analysis. A novel hybrid nature-inspired optimizer, called \(\upvarepsilon \)-constraint lexicographical ranking differential evolution mutable smart bee algorithm (\(\upvarepsilon \)lr-DEMSBA), is developed which can effectively search the non-convex and multimodal solution domain. The optimal values of PEMC design parameters are obtained using \(\upvarepsilon \)lr-DEMSBA. To ensure the veracity of the parameters suggested by \(\upvarepsilon \)lr-DEMSBA, a PEMC is fabricated using the suggested optimal values, and some post analysis are carried out. By investigating the relation between the frequency shift of natural frequency and increasing of immersion depth, it is observed that the linear performance zone of optimized PEMC sensor is increased by 2.5 mm which is a favorable property. Also, from numerical viewpoint, it was observed that \(\upvarepsilon \)lr-DEMSBA surpasses different variants of optimization techniques for the current case study.


PEMC sensor design Hybrid nature-inspired algorithms Constraint optimization Mathematical modeling 


  1. 1.
    Azimi M, Mozaffari A (2015) Heat transfer analysis of unsteady graphene oxide nanofluid flow using a fuzzy identifier evolved by genetically encoded mutable smart bee algorithm. Eng Sci Technol Int J 18(1):106–123CrossRefGoogle Scholar
  2. 2.
    Basak S, Raman A, Garimella SV (2005) Dynamic response optimization of piezoelectrically excited thin resonant beams. J Vib Acoust 127(1):18–27CrossRefGoogle Scholar
  3. 3.
    Boudjiet MT, Bertrand J, Mathieu F, Nicu L, Mazenq L, Leichle T, Heinrich SM, Pellet C, Dufour I (2015) Geometry optimization of uncoated silicon microcantilever-based gas density sensors. Sens Actuators B Chem 208:600–607CrossRefGoogle Scholar
  4. 4.
    Campbell GA, Mutharasan R (2006) Piezoelectric-excited millimeter-sized cantilever (PEMC) sensors detect Bacillus anthracis at 300 spores/mL. Biosens Bioelectron 21(9):1684–1692CrossRefGoogle Scholar
  5. 5.
    Campbell GA, Mutharasan R (2005) Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever. Sens Actuators A 122(2):326–334CrossRefGoogle Scholar
  6. 6.
    Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31CrossRefGoogle Scholar
  7. 7.
    Fathi A, Mozaffari A (2014) Vector optimization of laser solid freeform fabrication system using a hierarchical mutable smart bee-fuzzy inference system and hybrid NSGA-II/self-organizing map. J Intell Manuf 25(4):775–795CrossRefGoogle Scholar
  8. 8.
    Haddad OB, Afshar A, Marino MA (2006) Honey-bees mating (HBMO) algorithm: a new heuristic approach for water resources optimization. Water Resour Manag 20(5):661–680CrossRefGoogle Scholar
  9. 9.
    Ghaneh M (2014) Design and fabrication of piezoelectric excited millimeter cantilever sensors: Structural optimization to increase sensor sensitivity. M.Sc. thesis, Amirkabir University of TechnologyGoogle Scholar
  10. 10.
    Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42:21–57CrossRefGoogle Scholar
  11. 11.
    Marinaki M, Marinakis Y, Stavroulakis GE (2011) Vibrational control of beams with piezoelectric sensors and actuators using particle swarm optimization. Expert Syst Appl 38(6):6872–6883CrossRefGoogle Scholar
  12. 12.
    Maroufi M, Zihajehzadeh S, Shamshirsaz M, Rezaie AH (2010) Effect of mechanical properties variation of polysilicon on microcantilever mass sensor sensitivity. In IEEE symposium on design test integration and packaging of MEMS/MOEMS (DTIP), pp 144–147Google Scholar
  13. 13.
    Maroufi M, Shamshirsaz M (2012) Dynamic behavior of resonant piezoelectric cantilever as liquid level detection sensor. Microsystem technologies 18(11):1779–1789Google Scholar
  14. 14.
    Maroufi M, Shamshirsaz M (2015) Resonant behavior study of PZT sensor partially immersed in liquid using PSO method: modeling and experiment. Analog Integr Circ Sig Process 82:583–597CrossRefGoogle Scholar
  15. 15.
    Maute M, Raible S, Prins FE, Kern DP, Weimar U, Göpel W (1999) Fabrication and application of polymer coated cantilevers as gas sensors. Microelectron Eng 46(1):439–442CrossRefGoogle Scholar
  16. 16.
    Mezura-Montes E, Coello Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm and Evol Comput 1(4):173–194CrossRefGoogle Scholar
  17. 17.
    Mohammadrezaei Noudeh S (2014) Fatigue life prediction of structures using electro-mechanical impedance method. M.Sc. Thesis, Amirkabir University of TechnologyGoogle Scholar
  18. 18.
    Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174Google Scholar
  19. 19.
    Mozaffari A, Azimi M, Gorji-Bandpy M (2014) Ensemble mutable smart bee algorithm and a robust neural identifier for optimal design of a large scale power system. J Comput Sci 5(2):206–223CrossRefGoogle Scholar
  20. 20.
    Neri F, Tirronen V (2009) Scale factor local search in differential evolution. Memet Comput 1(2):153–171CrossRefGoogle Scholar
  21. 21.
    Neri F, Cotta C, Moscato P (2012) Handbook of memetic algorithms. In: Studies in computational intelligence, vol 379. Springer, BerlinGoogle Scholar
  22. 22.
    Rao SS (2009) Engineering optimization: theory and practice. Wiley, New YorkCrossRefGoogle Scholar
  23. 23.
    Takahama T, Sakai S (2006) Constrained optimization by the \(\upvarepsilon \) constrained differential evolution and with gradient-based mutation and feasible elites. In: IEEE congress on evolutionary computation, Vancouver, pp 308–315Google Scholar
  24. 24.
    Teodorovic D, Luccic P, Markovic G, Dell Orco M (2006) Bee colony optimization: principles and applications. In: 8th seminar on neural network applications in electrical engineering, Belgrade, pp 151–156Google Scholar
  25. 25.
    Upadrashta D, Yang Y (2015) Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction. Smart Mater Struct 24(4), Article ID: 045042Google Scholar
  26. 26.
    Waggoner PS, Craighead HG (2007) Micro and nanomechanical sensors for environmental, chemical, and biological detection. Lab Chip 7(10):1238–1255CrossRefGoogle Scholar
  27. 27.
    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  28. 28.
    Yang XS (2008) Nature-inspired metaheuristic algorithm. Luniver Press, BeckingtonGoogle Scholar
  29. 29.
    Yi W, Li X, Gao L, Zhou Y, Huang J (2016) \(\upvarepsilon \) constraint differential evolution with pre-estimated comparison using gradient-based approximation for constrained problems. Expert Syst Appl 44:37–49CrossRefGoogle Scholar
  30. 30.
    Zhou W, Khaliq A, Tang Y, Ji H, Selmic RR (2005) Simulation and design of piezoelectric microcantilever chemical sensors. Sens Actuators A 125(1):69–75CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • S. Mohammadrezaei Nodeh
    • 1
    Email author
  • A. Mozaffari
    • 2
  • M. Ghaneh
    • 3
  • F. Bakhtiarinejad
    • 3
  1. 1.Department of Mechanical EngineeringBabol Noshirvani University of TechnologyBabolIran
  2. 2.Department of Statistics and Actuarial SciencesUniversity of WaterlooWaterlooCanada
  3. 3.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations