SpringerLink
Log in

Grey wolf optimizer for parameter identification of an activated sludge process model

  • Application of soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper considers a new meta-heuristic method called Grey Wolf optimizer (GWO). It is inspired by the behavior of grey wolves (Canis lupus) in nature, especially the leadership hierarchy and the hunting mechanism of a pack. This recent optimization method presents an interesting case of study given its promising performance in a variety of engineering fields. We are mainly focusing on the parameter identification problem given its crucial role in systems modeling and control. For this reason, the GWO is investigated to solve this kind of problem for an activated sludge process model used in wastewater treatment. The considered model is a nonlinear hybrid one. It has four unknown parameters to be identified. Simulation results are carried out and compared to other techniques: classical (Nelder–Mead method) and intelligent ones (Genetic Algorithm, Particle Swarm Optimization, Fireflies Algorithm, Cuckoo Search, and Teaching–Learning Based Optimization). The outcome of this comparison shows the satisfactory effectiveness and simplicity of the proposed method versus the others approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability

Data will be made available on reasonable request.

References

  • Ahmed F (2007) Effects of cation addition on the flocculation behaviour of activated sludge at applied constant shear force, Master’s thesis.

  • Anam S, Kumaralalita I (2019) Grey wolf optimizer for parameter estimation of enzymatic reaction in biodiesel synthesis. IOP Conf Ser Mater Sci Eng 546(5):052005

    Article  Google Scholar 

  • Angelova M, Roeva O, Pencheva T (2018) Cuckoo search algorithm for parameter identification of fermentation process model. In: International conference on numerical methods and applications. Springer, 39–47

  • Geleta DK, Manshahia MS, Vasant P, Banik A (2020) Grey wolf optimizer for optimal sizing of hybrid wind and solar renewable energy system. In: Computational intelligence

  • Gomez-Quintero C (2002) Modélisation et estimation robuste pour un procédé boues activées en alternance de phases. Doctoral thesis.

  • Gomez Quintero C, Queinnec I, Babary JP (2000) A reduced nonlinear model of an activated sludge process. IFAC Adv Control Chem Process Pisa Italy 33(10):1001–1006

    Google Scholar 

  • Han F, Mo C, Gao H (2018) An adaptive hybrid differential evolutionary algorithm for the parameter identification of rotating machinery. J Vib Control 24(21):5087–5096

    Google Scholar 

  • Henze M, Gujer W, Mino T, van Loosdrecht MC (2000) Activated sludge models ASM1, ASM2, ASM2d and ASM3. IWA Publishing, London

    Google Scholar 

  • Heemels WPMH, De Schutter B, Lunze J, Lazar M (2010) Stability analysis and controller synthesis for hybrid dynamical systems. Philos Trans R Soc A Math Phys Eng Sci 368(1930):4937–4960

    Article  MathSciNet  MATH  Google Scholar 

  • Jiang W, Shi Y, Zhao W, Wang X (2016) Parameters identification of fluxgate magnetic core adopting the biogeography-based optimization algorithm. Sensors 16(7):979

    Article  Google Scholar 

  • Kamalova A, Navruzov S, Qian D, Lee SG (2019) Multi-robot exploration based on multi-objective grey wolf optimizer. Appl Sci 9(14):2931

    Article  Google Scholar 

  • Khoja I, Ladhari T, Sakly A, M’sahli F (2018a) Parameter identification of an activated sludge wastewater treatment process based on particle swarm optimization method. Math Probl Eng 2018:7823930

    Article  Google Scholar 

  • Khoja I, Ladhari T, M’sahli F, Sakly A (2018b) Cuckoo search approach for parameter identification of an activated sludge process. Comput Intell Neurosci 2018:3476851

    Article  Google Scholar 

  • KumarKumar LSGN, Madichetty S (2017) Pattern search algorithm based automatic online parameter estimation for AGC with effects of wind power. Int J Electr Power Energy Syst 84:135–142

    Article  Google Scholar 

  • Ladhari T, Khoja I, Msahli F, Sakly A (2019) Parameter identification of a reduced nonlinear model for an activated sludge process based on cuckoo search algorithm. Trans Inst Meas Control 41(12):3352–3363

    Article  Google Scholar 

  • Long W, Cai S, Jiao J, Tang M (2020) An efficient and robust grey wolf optimizer algorithm for large-scale numerical optimization. Soft Comput 24(2):997–1026

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Panda M, and Das B (2019) Grey wolf optimizer and its applications: a survey. In Proceedings of the third international conference on microelectronics, computing and communication systems,: 179–194

  • Pandey AH, Pawar RV, Pradhan SS, Sarpotdar DD (2020) Effect of non-continuous aeration on activated sludge process

  • Prasad R, Mehta U, Kothari K, Cirrincione M, Mohammadi A (2019) Supercapacitor parameter identification using grey wolf optimization and its comparison to conventional trust region reflection optimization. In: 2019 International Aegean conference on electrical machines and power electronics (ACEMP) & 2019 international conference on optimization of electrical and electronic equipment (OPTIM). IEEE, 563–569

  • Puangdownreong D, Hlungnamtip S, Thammarat C, Nawikavatan A (2017) Application of flower pollination algorithm to parameter identification of DC motor model. In: International electrical engineering congress (iEECON). IEEE, 1–4

  • Queinnec I, Gomez-Quintero C (2009) Reduced modeling and state observation of an activated sludge process. Biotechnol Prog 25(3):654–666

    Article  Google Scholar 

  • Robandi I (2017) Photovoltaic parameter estimation using grey wolf optimization. In 2017 3rd international conference on control, automation and robotics (ICCAR),: 593–597

  • Roeva O (2017) Application of artificial bee colony algorithm for model parameter identification. In Innovative computing, optimization and its applications. Springer, 285–303

  • Shafaati M, Mojallali H (2014) IIR system identification using improved harmony search algorithm with chaos. AUT J Electr Eng 46(1):37–47

    Google Scholar 

  • Shayeteh F, Moghaddam RK (2018) Parameter identification of hyperchaotic Chen–Lee system using firefly algorithm. J Soft Comput Appl 2018(1):1–12

    Google Scholar 

  • Song X, Tang L, Zhao S, Zhang X, Li L, Huang J, Cai W (2015) Grey wolf optimizer for parameter estimation in surface waves. Soil Dyn Earthq Eng 75:147–157

    Article  Google Scholar 

  • Suriavel Rao RS, Malathi PJSC (2019) A novel PTS: grey wolf optimizer-based PAPR reduction technique in OFDM scheme for high-speed wireless applications. Soft Comput 23(8):2701–2712

    Article  Google Scholar 

  • Tavakolpour-Saleh A, Sangdani MH (2018) Parameters identification of an experimental vision-based target tracker robot using genetic algorithm. Int J Eng 31(3):480–486

    Google Scholar 

  • Tian X, Yan J, Yang Y, **ao C, Zhou Q (2019) Parameter identification of a nonlinear model using an improved version of simulated annealing. Int J Distrib Sens Netw 15(2):1550147719832788

    Article  Google Scholar 

  • Vinod A (2019) Estimation of parameters for one diode solar PV cell using grey wolf optimizer to obtain exact VI characteristics. J Eng Res 7(1):1–19

    Google Scholar 

  • Yang K, Yu K, Wang H (2020) A hybrid method of multi-objective particle swarm optimization and k-means clustering and its application to modal parameter estimation in the time–frequency domain. J Vib Control 26(9–10):769–778

    Article  MathSciNet  Google Scholar 

  • Yuan Y, Mu X, Shao X, Ren J, Zhao Y, Wang Z (2022a) Optimization of an auto drum fashioned brake using the elite opposition-based learning and chaotic k-best gravitational search strategy based grey wolf optimizer algorithm. Appl Soft Comput 123:108947

    Article  Google Scholar 

  • Yuan Y, Ren J, Wang S, Wang Z, Mu X, Zhao W (2022b) Alpine skiing optimization: a new bio-inspired optimization algorithm. Adv Eng Softw 170:103158

    Article  Google Scholar 

  • Xu Y, Gao Z, Zhu X (2017) Parameter identification of simplified engineering model for PV array based on shuffled frog lea** algorithm. In: 20th international conference on electrical machines and systems (ICEMS). IEEE, 1–6

  • Zebua O, Ginarsa IM, Nrartha IMA (2020) GWO-based estimation of input-output parameters of thermal power plants. TELKOMNIKA Telecommun Comput Electron Control 18(4):2235–2244

    Google Scholar 

Download references

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

  1. Laboratory of Automatic, Electrical Systems and Environment (LAESE), The National Engineering School of Monastir (ENIM), University of Monastir, Av. Ibn El Jazzar Skanes, 5019, Monastir, Tunisia

    Intissar Khoja, Nesrine Majdoub, Taoufik Ladhari, Faouzi M’Sahli & Anis Sakly

Authors
  1. Intissar Khoja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nesrine Majdoub
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Taoufik Ladhari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Faouzi M’Sahli
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anis Sakly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Intissar Khoja.

Ethics declarations

Conflict of interest

Author Intissar KHOJA declares that she has no conflict of interest. Author Nesrine MAJDOUB declares that she has no conflict of interest. Author Taoufik LADHARI declares that he has no conflict of interest. Author Faouzi M’SAHLI declares that he has no conflict of interest. Author Anis SAKLY declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khoja, I., Majdoub, N., Ladhari, T. et al. Grey wolf optimizer for parameter identification of an activated sludge process model. Soft Comput 27, 15293–15304 (2023). https://doi.org/10.1007/s00500-023-07952-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-07952-0

Keywords

Search

Navigation