Soft Computing

, Volume 23, Issue 10, pp 3449–3463 | Cite as

Bio-inspired heuristics for layer thickness optimization in multilayer piezoelectric transducer for broadband structures

  • Aneela ZameerEmail author
  • Mohsin Majeed
  • Sikander M. Mirza
  • Muhammad Asif Zahoor Raja
  • Asifullah Khan
  • Nasir M. Mirza
Methodologies and Application


Recently, enhancement of sensitivity of multilayered piezoelectric transducer and reduction in electrical impedance has gained importance due to development of stacked active element designs. This work presents mathematical optimization of layer thicknesses for broadband structures using piezo-composite with ceramic and single crystal as active material for underwater SONAR. The proposed technique employs bio-inspired heuristics-based genetic algorithms by invoking one-dimensional thickness model. Initially, optimization has been performed for monolithic materials in the stack for various acoustic media, and then, the results were validated by comparing with the published data. In the proposed scheme, optimization is carried out for two-phase 1–3 piezo-composite stacks with same active elements for better mechanical output and broadband structure while preserving the minima among first three harmonics under \(-\,3\) and \(-\,6\) dB from the peaks in the frequency spectrum. The results show that the optimized single-crystal-based transducers have higher mechanical output and lower electrical impedance than their counterparts using piezo-ceramic in single- and two-phase materials.

Graphical abstract


Genetic algorithms Piezo-ceramic transducer SONAR Piezo-composites Single crystal Optimization 


Compliance with ethical standards

Conflict of interest

All the authors of the manuscript declared that there are no potential conflicts of interest.


  1. Abo-Hammour Z, Alsmadi O, Momani S, Arqub OA (2013) A genetic algorithm approach for prediction of linear dynamical systems. Math Probl Eng 2013.
  2. Abo-Hammour Z, Arqub OA, Momani S, Shawagfeh N (2014a) Optimization solution of Troesch’s and Bratu’s problems of ordinary type using novel continuous genetic algorithm. Discrete Dyn Nat Soc 2014.
  3. Abo-Hammour Z, Arqub OA, Alsmadi O, Momani S, Alsaedi A (2014b) An optimization algorithm for solving systems of singular boundary value problems. Appl Math Inf Sci 8(6):2809MathSciNetCrossRefGoogle Scholar
  4. Abrar A, Cochran S (2007) Mathematical optimization of multilayer piezoelectric devices with nonuniform layers by simulated annealing. IEEE Trans Ultrason Ferroelectr Freq Control 54:1920–1929CrossRefGoogle Scholar
  5. Abrar A, Zhang D, Su B, Button TW, Kirk KJ, Cochran S (2004) 1–3 connectivity piezoelectric ceramic-polymer composite transducers made with viscous polymer processing for high frequency ultrasound. Ultrasonics 42(1):479–484CrossRefGoogle Scholar
  6. Berlincourt D, Krueger HA, Near C (2000) Properties of Morgan electro ceramic ceramics. In: TP-226.
  7. Chen Y, Zeng Z, Lu J (2017) Neighborhood rough set reduction with fish swarm algorithm. Soft Comput 21:6907. CrossRefGoogle Scholar
  8. Cochran A, Kirk KJ, Franch PM, Abrar A (2011) Multilayer piezoelectric and polymer ultrawideband ultrasonic transducer. US patent 7,876,027Google Scholar
  9. Cochran S, Parker M, Marin-Franch P (2005) Ultrabroadband single crystal composite transducers for underwater ultrasound. In: Ultrasonics symposium, 2005 IEEE. IEEE, pp 231–234Google Scholar
  10. Dey S, Bhattacharyya S, Maulik U (2014) Chaotic map model-based interference employed in quantum-inspired genetic algorithm to determine the optimum gray level image thresholding. In: Global trends in intelligent computing research and development. IGI Global, pp 68–110Google Scholar
  11. Fu B, Hemsel T, Wallaschek J (2006) Piezoelectric transducer design via multiobjective optimization. Ultrasonics 44:e747–e752CrossRefGoogle Scholar
  12. Gao XZ, Ovaska SJ (2002) Genetic algorithm training of Elman neural network in motor fault detection. Neural Comput Appl 11(1):37–44CrossRefzbMATHGoogle Scholar
  13. Hochreiter R, Waldhauser C (2015) Evolving accuracy: a genetic algorithm to improve election night forecasts. Appl Soft Comput 34:606–612CrossRefGoogle Scholar
  14. Jurczuk K, Czajkowski M, Kretowski M (2017) Evolutionary induction of a decision tree for large-scale data: a GPU-based approach. Soft Comput 21:7363. CrossRefGoogle Scholar
  15. Khan JA, Raja MAZ, Rashidi MM, Syam MI, Wazwaz AM (2015a) Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory. Connect Sci 27(04):377–396.
  16. Khan JA, Raja MAZ, Syam MI, Tanoli SAK, Awan SE (2015b) Design and application of nature inspired computing approach for nonlinear stiff oscillatory problems. Neural Comput Appl 26(7):1763–1780CrossRefGoogle Scholar
  17. Liu T, Gao X, Yuan Q (2017) An improved gradient-based NSGA-II algorithm by a new chaotic map model. Soft Comput 21:7235. CrossRefGoogle Scholar
  18. Lommi A, Massa A, Storti E, Trucco A (2002) Sidelobe reduction in sparse linear arrays by genetic algorithms. Microw Opt Technol Lett 32:194–196CrossRefGoogle Scholar
  19. Martin KH, Lindsey BD, Ma J, Lee M, Li S, Foster FS, Jiang X, Dayton PA (2014) Dual-frequency piezoelectric transducers for contrast enhanced ultrasound imaging. Sensors 14(11):20825–20842CrossRefGoogle Scholar
  20. Mattiat OE (2013) Ultrasonic transducer materials. Springer, New YorkGoogle Scholar
  21. McCall J (2005) Genetic algorithms for modelling and optimisation. J Comput Appl Math 184:205–222MathSciNetCrossRefzbMATHGoogle Scholar
  22. Mokrý P (2016) 100 years of piezoelectric materials in acoustics: from a sonar to active metasurfaces. In: Proceedings of meetings on acoustics 22ICA, vol 28, no 1, p 045008Google Scholar
  23. Panda S, Yegireddy NK (2013) Automatic generation control of multi-area power system using multi-objective non-dominated sorting genetic algorithm-II. Int J Electr Power Energy Syst 53:54–63CrossRefGoogle Scholar
  24. Paul PV, Moganarangan N, Kumar SS, Raju R, Vengattaraman T, Dhavachelvan P (2015) Performance analyses over population seeding techniques of the permutation-coded genetic algorithm: an empirical study based on traveling salesman problems. Appl Soft Comput 32:383–402CrossRefGoogle Scholar
  25. Powell DJ, Hayward G, Ting RY (1998) Unidimensional modeling of multi-layered piezoelectric transducer structures. IEEE Trans Ultrason Ferroelectr Freq Control 45:667–677CrossRefGoogle Scholar
  26. Raja MAZ (2014a) Numerical treatment for boundary value problems of pantograph functional differential equation using computational intelligence algorithms. Appl Soft Comput 24:806–821CrossRefGoogle Scholar
  27. Raja MAZ (2014b) Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP. Connect Sci 26(3):195–214. MathSciNetCrossRefGoogle Scholar
  28. Raja MAZ (2014c) Stochastic numerical techniques for solving Troesch’s problem. Inf Sci 279:860–873. CrossRefzbMATHGoogle Scholar
  29. Raja MAZ, Sabir Z, Mehmood N, Al-Aidarous ES, Khan JA (2015a) Design of stochastic solvers based on genetic algorithms for solving nonlinear equations. Neural Comput Appl 26:1–23CrossRefGoogle Scholar
  30. Raja MAZ, Shah FH, Khan AA, Khan NA (2015b) Design of bio-inspired computational intelligence technique for solving steady thin film flow of Johnson–Segalman fluid on vertical cylinder for drainage problem. J Tiawan Inst Chem Eng 60:59–75.
  31. Raja MAZ, Samar R, Alaidarous ES, Shivanian E (2016a) Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids. Appl Math Model.
  32. Raja MA, Zahoor AK, Kiani AS, Zameer A (2016b) Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models. SpringerPlus 5(1):2063CrossRefGoogle Scholar
  33. Rhim, SM, Jung H, Lee K-J (2004) Multilayer PMN-PT single crystal transducer for medical application In: Ultrasonics symposium, 2004 IEEE. IEEE, vol 2, pp 1021–1024Google Scholar
  34. Ru C, Liu X, Sun Y et al (2015) Nanopositioning technologies: fundamentals and applications. Springer, New YorkGoogle Scholar
  35. Ruí z A, Ramos A, Emeterio JS (2004) Estimation of some transducer parameters in a broadband piezoelectric transmitter by using an artificial intelligence technique. Ultrasonics 42:459–463CrossRefGoogle Scholar
  36. Smith WA, Auld B (1991) Modeling 1–3 composite piezoelectrics: thickness-mode oscillations. IEEE Trans Ultrason Ferroelectr Freq Control 38:40–47CrossRefGoogle Scholar
  37. Soloviev AN, Oganesyan PA, Lupeiko TG, Kirillova EV, Chang SH, Yang CD (2016) Modeling of non-uniform polarization for multi-layered piezoelectric transducer for energy harvesting devices. In: Parinov I, Chang SH, Topolov V (eds) Advanced materials. Springer, Cham, pp 651–658Google Scholar
  38. Wu Z, Abrar A, McRobbie G, Gallagher S, Cochran S (2003) Implementation of multilayer ultrasonic transducer structures with optimized non-uniform layer thicknesses. In: 2003 IEEE symposium on ultrasonics. IEEE, pp 1292–1295Google Scholar
  39. Xu Y, Xu D, Qu J, Cheng X, Jiao H, Huang S (2015) Concrete crack damage location based on piezoelectric composite acoustic emission sensor. In: Shen G, Wu Z, Zhang J (eds) Advances in acoustic emission technology. Springer, New York, pp 347–353Google Scholar
  40. Zameer A, Mirza SM, Mirza NM (2014) Core loading pattern optimization of a typical two-loop 300MWe PWR using Simulated Annealing (SA), novel crossover Genetic Algorithms (GA) and hybrid GA (SA) schemes. Ann Nucl Energy 65:122–131CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Aneela Zameer
    • 1
    Email author
  • Mohsin Majeed
    • 2
  • Sikander M. Mirza
    • 3
  • Muhammad Asif Zahoor Raja
    • 4
  • Asifullah Khan
    • 1
  • Nasir M. Mirza
    • 3
  1. 1.Department of Computer and Information SciencesPakistan Institute of Engineering and Applied Sciences (PIEAS)NilorePakistan
  2. 2.Department of Nuclear EngineeringPakistan Institute of Engineering and Applied Sciences (PIEAS)NilorePakistan
  3. 3.Department of Physics and Applied MathematicsPakistan Institute of Engineering and Applied Sciences (PIEAS)NilorePakistan
  4. 4.Department of Electrical EngineeringCOMSATs Institute of Information TechnologyAttockPakistan

Personalised recommendations