Skip to main content

2017 | OriginalPaper | Buchkapitel

An Optimized Reduction Technique via Firefly Algorithm and Gravitational Search Algorithm

verfasst von : Norul Ashikin Norzain, Shafishuhaza Sahlan

Erschienen in: Modeling, Design and Simulation of Systems

Verlag: Springer Singapore

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

To improve effluent quality of a wastewater treatment plant (WWTP), an optimized model order reduction (MOR) for the high order WWTP system is proposed. A high order model may lead to inefficient analysis of the system and can be computationally expensive. Hence, an accurate and suitable reduced order model needs to be obtained. In this research, an optimized MOR algorithm is proposed by the combination of Frequency Domain Gramian based Model Reduction (FDIG) and Singular Perturbation Approximation (SPA). To reduce the high order model to lower order model with minimum reduction error, optimization techniques of Firefly Algorithm (FFA) and Gravitational Search Algorithm (GSA) is applied. To show the effectiveness of the proposed technique, a case study on WWTP is utilized. From the results obtained, the optimized reduced order models obtained is a 9th order system which yield the lowest reduction error while preserving the stability of the original system.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

Literatur
1.
Zurück zum Zitat Schilders, W.: Introduction to model order reduction. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds.) Model Order Reduction: Theory, vol. 13, pp. 3–32. Research Aspects and Applications. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78841-6_1 CrossRef Schilders, W.: Introduction to model order reduction. In: Schilders, W.H.A., van der Vorst, H.A., Rommes, J. (eds.) Model Order Reduction: Theory, vol. 13, pp. 3–32. Research Aspects and Applications. Springer, Heidelberg (2008). doi:10.​1007/​978-3-540-78841-6_​1 CrossRef
2.
Zurück zum Zitat Ishizakiy, T., Sandberg, H., Johansson, K.H., Kashima, K., Imura, J.I., Aihara, K.: Singular perturbation approximation of semistable linear systems. In: Control Conference (ECC), 17 July 2013, European, pp. 4508–4513 (2013) Ishizakiy, T., Sandberg, H., Johansson, K.H., Kashima, K., Imura, J.I., Aihara, K.: Singular perturbation approximation of semistable linear systems. In: Control Conference (ECC), 17 July 2013, European, pp. 4508–4513 (2013)
3.
Zurück zum Zitat Kumar, D., Nagar, S.K.: A new frequency weighted model reduction technique using balanced singular perturbation approximation. In: India Conference (INDICON), 13 December 2013. Annual IEEE, pp. 1–5 (2013) Kumar, D., Nagar, S.K.: A new frequency weighted model reduction technique using balanced singular perturbation approximation. In: India Conference (INDICON), 13 December 2013. Annual IEEE, pp. 1–5 (2013)
4.
Zurück zum Zitat Saragih, R.: Singular perturbation approximation of balanced infinite-dimensional systems. Int. J. Control Autom. 6(5), 409–420 (2013)CrossRef Saragih, R.: Singular perturbation approximation of balanced infinite-dimensional systems. Int. J. Control Autom. 6(5), 409–420 (2013)CrossRef
5.
Zurück zum Zitat Ghafoor, A., Sahlan, S., Sreeram, V.: A new frequency weighted model reduction technique and error bounds. In: 2007 International Conference on Mechatronics and Automation, 5 August 2007, pp. 1962–1967. IEEE (2007) Ghafoor, A., Sahlan, S., Sreeram, V.: A new frequency weighted model reduction technique and error bounds. In: 2007 International Conference on Mechatronics and Automation, 5 August 2007, pp. 1962–1967. IEEE (2007)
6.
Zurück zum Zitat Kumar, D., Nagar, S.: Square-root frequency weighted balanced model reduction via singular perturbation approximation. In: Electrical Engineering Congress (iEECON International), 14 March 2014. IEEE, pp. 1–4 (2014) Kumar, D., Nagar, S.: Square-root frequency weighted balanced model reduction via singular perturbation approximation. In: Electrical Engineering Congress (iEECON International), 14 March 2014. IEEE, pp. 1–4 (2014)
7.
Zurück zum Zitat Enns, D.F.: Model reduction with balanced realizations: an error bound and a frequency weighted generalization. In: The 23rd IEEE Conference on Decision and Control, 12 December 1984. IEEE, pp. 127–132 (1984) Enns, D.F.: Model reduction with balanced realizations: an error bound and a frequency weighted generalization. In: The 23rd IEEE Conference on Decision and Control, 12 December 1984. IEEE, pp. 127–132 (1984)
8.
Zurück zum Zitat Gawronski, W., Juang, J.-N.: Model reduction in limited time and frequency intervals. Int. J. Syst. Sci. 21(2), 349–376 (1990)MathSciNetCrossRefMATH Gawronski, W., Juang, J.-N.: Model reduction in limited time and frequency intervals. Int. J. Syst. Sci. 21(2), 349–376 (1990)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Mulas, M.: Modelling and control of activated sludge processes. University Degli Studi di Cagliari (2006) Mulas, M.: Modelling and control of activated sludge processes. University Degli Studi di Cagliari (2006)
11.
Zurück zum Zitat Halim, F.A.: Empirical Modelling Of Activated Sludge Process Via System Identification. Universiti Teknologi Malaysia, Johor Bahru (2014). Bachelor of Engineering Halim, F.A.: Empirical Modelling Of Activated Sludge Process Via System Identification. Universiti Teknologi Malaysia, Johor Bahru (2014). Bachelor of Engineering
12.
Zurück zum Zitat Eek, R.T.P., Sahlan, S., Wahab, N.A.: Modeling of waste water treatment plant via system id & model reduction technique. In: 2012 IEEE Conference on Control, Systems & Industrial Informatics (ICCSII), 23 September 2012, pp. 131–136 (2012) Eek, R.T.P., Sahlan, S., Wahab, N.A.: Modeling of waste water treatment plant via system id & model reduction technique. In: 2012 IEEE Conference on Control, Systems & Industrial Informatics (ICCSII), 23 September 2012, pp. 131–136 (2012)
13.
Zurück zum Zitat Yang, X.-S.: Firefly algorithm. Nature-inspired metaheuristic algorithms. 20, 79–90 (2008) Yang, X.-S.: Firefly algorithm. Nature-inspired metaheuristic algorithms. 20, 79–90 (2008)
14.
Zurück zum Zitat Yang, X.-S.: Firefly algorithms for multimodal optimization. In: International Symposium on Stochastic Algorithms, pp. 169–178 (2009) Yang, X.-S.: Firefly algorithms for multimodal optimization. In: International Symposium on Stochastic Algorithms, pp. 169–178 (2009)
15.
Zurück zum Zitat Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)CrossRefMATH Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)CrossRefMATH
16.
Zurück zum Zitat Lee, T., Wang, F., Newell, R.: Robust model-order reduction of complex biological processes. J. Process Control 12(7), 807–821 (2002)CrossRef Lee, T., Wang, F., Newell, R.: Robust model-order reduction of complex biological processes. J. Process Control 12(7), 807–821 (2002)CrossRef
Metadaten
Titel
An Optimized Reduction Technique via Firefly Algorithm and Gravitational Search Algorithm
verfasst von
Norul Ashikin Norzain
Shafishuhaza Sahlan
Copyright-Jahr
2017
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-6502-6_63