Skip to main content
Top

2018 | OriginalPaper | Chapter

Combination of a Particle Swarm Optimization and Nelder–Mead Algorithm in a Diffuser Shape Optimization

Authors : Prokop Moravec, Pavel Rudolf

Published in: Advances in Hydroinformatics

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This work focuses on the optimization of a hydraulic turbine diffuser, which is located behind the runner of the swirl turbine. The present paper extends our work in shape optimization using direct methods (namely Nelder–Mead method) and stochastic methods (namely Particle swarm optimization) coupled with CFD simulations. Both methods have their own advantages and disadvantages. Present work focuses on a combination of particle swarm optimization (at the beginning of the algorithm) and Nelder–Mead algorithm (NMA) (at the end of the algorithm). The diffuser will serve as the test case to demonstrate efficient coupling of the mathematical optimization procedure and CFD simulation. The main goal of this test problem is set to maximize the coefficient of pressure recovery c p, which is the main parameter to judge the proper design of the draft tube. Results obtained with this new method will be discussed and their advantages/disadvantages summarized.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Moravec, P., Hliník, J., & Rudolf, P. (2016). Optimization of hydraulic turbine diffuser. In EFM 2015, Prague, EPJ Web of Conferences (Vol. 114, pp. 1–7). Moravec, P., Hliník, J., & Rudolf, P. (2016). Optimization of hydraulic turbine diffuser. In EFM 2015, Prague, EPJ Web of Conferences (Vol. 114, pp. 1–7).
2.
go back to reference Moravec, P., & Rudolf, P. (2017). Application of a particle swarm optimization for shape optimization in hydraulic machinery. In EFM 2016, Marianske Lazne, EPJ Web of Conferences (Vol. 143, pp. 1–11). Moravec, P., & Rudolf, P. (2017). Application of a particle swarm optimization for shape optimization in hydraulic machinery. In EFM 2016, Marianske Lazne, EPJ Web of Conferences (Vol. 143, pp. 1–11).
3.
go back to reference Hliník, J. (2015). Shape optimization of hydraulic turbine diffuser. Bachelor thesis. In Slovak, Brno. Hliník, J. (2015). Shape optimization of hydraulic turbine diffuser. Bachelor thesis. In Slovak, Brno.
4.
go back to reference Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In The IEEE International Conference on Neural Networks, Perth (Vol. 4, pp. 1942–1948). Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In The IEEE International Conference on Neural Networks, Perth (Vol. 4, pp. 1942–1948).
5.
go back to reference Shi, Y. H., & Eberhart, R. (1998). A modified particle swarm optimizer. In The International Conference on Evolutionary Computation (pp. 69–73). Shi, Y. H., & Eberhart, R. (1998). A modified particle swarm optimizer. In The International Conference on Evolutionary Computation (pp. 69–73).
6.
go back to reference Shi, Y. H., & Eberhart, R. (1998). Parameter selection in particle swarm optimization. In Evolutionary Programming VII: Proceedings of the 7. Annual Conference on Evolutionary programming, San Diego (pp. 591–600). Shi, Y. H., & Eberhart, R. (1998). Parameter selection in particle swarm optimization. In Evolutionary Programming VII: Proceedings of the 7. Annual Conference on Evolutionary programming, San Diego (pp. 591–600).
7.
go back to reference Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In The 1998 IEEE International Conference on Evolutionary Computation Proceedings (pp. 69–73). IEEE World Congress on Computational Intelligence. Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In The 1998 IEEE International Conference on Evolutionary Computation Proceedings (pp. 69–73). IEEE World Congress on Computational Intelligence.
8.
go back to reference Zhan, Z.-H., Zhang, J., Li, Y., & Chung, H. S.-H. (2009). Adaptive particle swarm optimization. The IEEE Transactions on Systems, Man, and Cybernetics, 39, 1362–1381.CrossRef Zhan, Z.-H., Zhang, J., Li, Y., & Chung, H. S.-H. (2009). Adaptive particle swarm optimization. The IEEE Transactions on Systems, Man, and Cybernetics, 39, 1362–1381.CrossRef
10.
go back to reference Shi, Y. H., & Eberhart, R. (1999). Empirical study of particle swarm optimization (pp. 1945–1950). IEEE. Shi, Y. H., & Eberhart, R. (1999). Empirical study of particle swarm optimization (pp. 1945–1950). IEEE.
11.
go back to reference Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7, 308–313. Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7, 308–313.
12.
go back to reference Machalová, J., & Netuka, H. (2013). Numerické metody nepodmíněné optimalizace. 1. vyd. Olomouc: Univerzita Palackého v Olomouci, 2013, 142s. ISBN 978-80-244-3403-2. Machalová, J., & Netuka, H. (2013). Numerické metody nepodmíněné optimalizace. 1. vyd. Olomouc: Univerzita Palackého v Olomouci, 2013, 142s. ISBN 978-80-244-3403-2.
13.
go back to reference Fan, S.-K. S., Liang, Y.-C., & Zahara, E. (2006). A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search. Computers & Industrial Engineering, 50(4), 401–425.CrossRef Fan, S.-K. S., Liang, Y.-C., & Zahara, E. (2006). A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search. Computers & Industrial Engineering, 50(4), 401–425.CrossRef
14.
go back to reference Zahara, E., & Hu, C.-H. (2008). Solving constrained optimization problems with hybrid particle swarm optimization. Engineering Optimization, 40(11), 1031–1049.MathSciNetCrossRef Zahara, E., & Hu, C.-H. (2008). Solving constrained optimization problems with hybrid particle swarm optimization. Engineering Optimization, 40(11), 1031–1049.MathSciNetCrossRef
15.
go back to reference Zahara, E., & Kao, Y.-T. (2009). Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Systems with Applications, 36(2), 3880–3886.CrossRef Zahara, E., & Kao, Y.-T. (2009). Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Systems with Applications, 36(2), 3880–3886.CrossRef
16.
go back to reference Liu, A., & Yang, M. -T. (2012). A new hybrid nelder-mead particle swarm optimization for coordination optimization of directional overcurrent relays. Mathematical Problems in Engineering, 2012. Liu, A., & Yang, M. -T. (2012). A new hybrid nelder-mead particle swarm optimization for coordination optimization of directional overcurrent relays. Mathematical Problems in Engineering, 2012.
17.
go back to reference Liao, S. -H., Hsieh, J. -G., Chang, J. -Y., & Lin, C. -T. (2014). Training neural networks via simplified hybrid algorithm mixing Nelder–Mead and particle swarm optimization methods. Soft Computing, 19(3), 679–689. Liao, S. -H., Hsieh, J. -G., Chang, J. -Y., & Lin, C. -T. (2014). Training neural networks via simplified hybrid algorithm mixing Nelder–Mead and particle swarm optimization methods. Soft Computing, 19(3), 679–689.
18.
go back to reference Vakil Baghmisheh, M. T., Peimani, M., Sadeghi, M. H., Ettefagh, M. M., & Tabrizi, A. F. (2012). A hybrid particle swarm–Nelder–Mead optimization method for crack detection in cantilever beam. Applied Soft Computing Journal, 12(8), 2217–2226. Vakil Baghmisheh, M. T., Peimani, M., Sadeghi, M. H., Ettefagh, M. M., & Tabrizi, A. F. (2012). A hybrid particle swarm–Nelder–Mead optimization method for crack detection in cantilever beam. Applied Soft Computing Journal, 12(8), 2217–2226.
19.
go back to reference Hu, X., & Eberhart, R. (2002). Adaptive particle swarm optimization: Detection and response to dynamic systems. In Evolutionary Computation, 2002. CEC ’02. Proceedings of the 2002 Congress on Honolulu (pp. 1666–1670). Hu, X., & Eberhart, R. (2002). Adaptive particle swarm optimization: Detection and response to dynamic systems. In Evolutionary Computation, 2002. CEC ’02. Proceedings of the 2002 Congress on Honolulu (pp. 1666–1670).
21.
go back to reference Rudolf, P. (2004). Study of the shear layers for swirl draft tube optimization. PhD thesis. In Czech, Brno. Rudolf, P. (2004). Study of the shear layers for swirl draft tube optimization. PhD thesis. In Czech, Brno.
Metadata
Title
Combination of a Particle Swarm Optimization and Nelder–Mead Algorithm in a Diffuser Shape Optimization
Authors
Prokop Moravec
Pavel Rudolf
Copyright Year
2018
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-7218-5_70