Climate Dynamics

, Volume 46, Issue 5–6, pp 1893–1907 | Cite as

RETRACTED ARTICLE: Application of extreme learning machine for estimation of wind speed distribution

  • Shahaboddin ShamshirbandEmail author
  • Kasra Mohammadi
  • Chong Wen Tong
  • Dalibor Petković
  • Emilio Porcu
  • Ali Mostafaeipour
  • Sudheer Ch
  • Ahmad Sedaghat


The knowledge of the probabilistic wind speed distribution is of particular significance in reliable evaluation of the wind energy potential and effective adoption of site specific wind turbines. Among all proposed probability density functions, the two-parameter Weibull function has been extensively endorsed and utilized to model wind speeds and express wind speed distribution in various locations. In this research work, extreme learning machine (ELM) is employed to compute the shape (k) and scale (c) factors of Weibull distribution function. The developed ELM model is trained and tested based upon two widely successful methods used to estimate k and c parameters. The efficiency and accuracy of ELM is compared against support vector machine, artificial neural network and genetic programming for estimating the same Weibull parameters. The survey results reveal that applying ELM approach is eventuated in attaining further precision for estimation of both Weibull parameters compared to other methods evaluated. Mean absolute percentage error, mean absolute bias error and root mean square error for k are 8.4600 %, 0.1783 and 0.2371, while for c are 0.2143 %, 0.0118 and 0.0192 m/s, respectively. In conclusion, it is conclusively found that application of ELM is particularly promising as an alternative method to estimate Weibull k and c factors.


Wind speed distribution Weibull function Extreme learning machine (ELM) Shape factor Scale factor 



The authors would like to thank the University of Malaya for the research grants allocated (UMRG RP015C-13AET and High Impact Research Grant, HIR-D000006-16001). Special appreciation is also credited to the Malaysian Ministry of Education, MOE for the Fundamental Research Grant Scheme (FP053-2013B). The authors would like to thank the Bright Spark Unit of University of Malaya for the financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Shahaboddin Shamshirband
    • 1
    Email author
  • Kasra Mohammadi
    • 2
  • Chong Wen Tong
    • 3
  • Dalibor Petković
    • 3
  • Emilio Porcu
    • 4
  • Ali Mostafaeipour
    • 5
  • Sudheer Ch
    • 6
  • Ahmad Sedaghat
    • 7
  1. 1.Department of Computer System and Technology, Faculty of Computer Science and Information TechnologyUniversity of MalayaKuala lumpurMalaysia
  2. 2.Faculty of Mechanical EngineeringUniversity of KashanKashanIran
  3. 3.Department of Mechanical Engineering, Faculty of Engineering University of MalayaKuala LumpurMalaysia
  4. 4.Technical University Federico Santa MariaValparaísoChile
  5. 5.Industrial Engineering DepartmentYazd UniversityYazdIran
  6. 6.Department of Civil and Environmental EngineeringITM UniversityGurugaonIndia
  7. 7.Department of Mechanical Engineering, School of EngineeringAustralian College of KuwaitSafatKuwait

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