Using genetic algorithms for estimating Weibull parameters with application to wind speed
DOI:
https://doi.org/10.11121/ijocta.01.2020.00741Keywords:
Weibull distribution, genetic algorithms, wind speed modeling, parameter estimationAbstract
Renewable energy has become a prominent subject for researchers since fossil fuel reserves have been decreasing and are not promising to meet the energy demand of the future. Wind takes an important place in renewable energy resources and there is extensive research on wind speed modeling. Herein, one of the most commonly used distributions for wind speed modeling is the Weibull distribution with its simplicity and flexibility. Maximum likelihood (ML) method is the most frequently used technique in Weibull parameter estimation. Iterative techniques such as Newton-Raphson (NR) use random initial values to obtain the ML estimators of the parameters of the Weibull distribution. Therefore, the success of the iterative techniques highly depends on the initial value selection. In order to deliver a solution to the initial value problem, genetic algorithm (GA) is considered to obtain the estimators of the model parameters. The ML estimators obtained using the GA and NR techniques are compared with the method of moments (MoM) estimators via Monte Carlo simulation and wind speed applications. The results show that the ML estimators obtained using GA present superiority over MoM and the ML estimators obtained using NR.
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Hou, Y., Peng, Y., Johnson, A.L. & Shi, J. (2012). Empirical analysis of wind power potential at multiple heights for North Dakota wind observation sites. Energy Science and Technology, 4(1), 1-9. DOI:10.3968/j.est.1923847920120401.289
Sohoni, V., Gupta, S. & Nema, R. (2016). A comparative analysis of wind speed probability distributions for wind power assessment of four sites. Turkish Journal of Electrical Engineering & Computer Sciences, 24(6), 4724-4735. DOI:10.3906/elk-1412-207
Turkan, Y.S., Aydogmus, H.Y. & Erdal, H. (2016). The prediction of the wind speed at different heights by machine learning methods. An International Journal of Optimization and Control: Theories & Applications, 6(2), 179-197. DOI:10.11121/ijocta.01.2016.00315
Koca, M.B., Kılıç, M.B. & Şahin, Y. Assessing wind energy potential using finite mixture distributions. Turkish Journal of Electrical Engineering & Computer Sciences, 27(3), 2276-2294. DOI:10.3906/elk-1802-109
Seguro, J.V., & Lambert, T.W. (2000). Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. Journal of Wind Engineering and Industrial Aerodynamics, 85, 75-84. DOI:10.1016/S0167-6105(99)00122-1
Akgül, F.G., Şenoğlu, B., & Arslan, T. (2016). An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240. DOI:10.1016/j.enconman.2016.02.026
Lun, I.Y.F., & Lam, J.C. (2000). A study of Weibull parameters using long-term wind observations. Renewable Energy, 20, 145-153. DOI:10.1016/s0960-1481(99)00103-2
Arslan, T., Bulut, Y.M., & Yavuz, A.A. (2014). Comparative study of numerical methods for determining Weibull parameters for wind speed modeling. Renewable and Sustainable Energy Reviews, 40, 820-825. DOI:10.1016/j.ser/2014.08.009
Safari, B. (2011). Modeling wind speed and wind power distributions in Rwanda. Renewable and Sustainable Energy Reviews, 15, 925-935. DOI:10.1016/j.ser.2010.11.001
Kaplan, Y.A. (2016). The evaluating of wind energy potential of Osmaniye region with using Weibull and Rayleigh distributions. Süleyman Demirel University Journal of Natural and Applied Sciences, 20(1), 62-71. DOI:10.19113/sdufbed.63806
Kollu, R., Rayapudi, S.R., Narasimham, S.V.L., & Pakkurthi, K.M. (2012). Mixture probability distribution functions to model wind speed distributions. International Journal of Energy and Environmental Engineering, 3(27). DOI:10.1186/2251-6832-3-27
Akpınar, E.K., & Akpınar, S. (2004). Determination of the wind energy potential for Maden-Elazig, Turkey. Energy Conversion and Management, 45, 2901-2914. DOI:10.1016/j.enconman.2003.12.016
Teimouri, M., Hoseini, S.M., & Nadarajah, S. (2013). Comparison of estimation methods for the Weibull distribution. Statistics, 47(1), 93-109. DOI:10.1080/02331888.2011.559657
Akdağ, S.A. & Dinler, A. (2009). A new method to estimate Weibull parameters for wind energy applications. Energy Conversion and Management, 50, 1761-1766. DOI:10.1016/j.enconman.2009.03.020
Saleh, H., Abou El-Azm Aly, A. & Abdel-Hady, S. (2012). Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gold, Egypt. Energy, 44, 710-719. DOI:10.1016/j.energy.2012.05.021
Azad. A.K., Rasul, M. G. & Yusaf, T. (2014). Statistical diagnosis of the best Weibull methods for wind power assessment for agricultural applications. Energies, 7, 3056-3085. DOI:10.3390/en7053056
Usta, I., Arik, I., Yenilmez, I. & Kantar, Y.M. (2018). A new estimation approach based on moments for estimating Weibull parameters in wind speed power applications. Energy Conversion and Management, 164, 570-578. DOI:10.1016/j.enconman.2018.03.033
Tu, T.V. & Sano, K. (2013). Genetic algorithm for optimization in adaptive bus signal priority control. An International Journal of Optimization and Control: Theories & Applications, 3(1), 35-43. DOI:10.11121/ijocta.01.2013.00138
Şimşek, B. & Şimşek, E.H. (2017). Assessment and optimization of thermal and fluidity properties of high strength concrete via genetic algorithm. An International Journal of Optimization and Control: Theories & Applications, 7(1), 90-97. DOI:10.11121/ijocta.01.2017.00345
Gençtürk, Y., & Yiğiter, A. (2016). Modelling claim number using a new mixture model: negative binomial gamma distribution. Journal of Statistical Computation and Simulation, 86, 1829-1839. DOI:10.1080/00949655.2015.1085987
Yalçınkaya, A., Şenoğlu, B., & Yolcu, U. (2018). Maximum likelihood estimation for the parameters of skew normal distribution using genetic algorithm. Swarm and Evolutionary Computation, 38, 127-138. DOI:10.1016/j.swevo.2017.07.007
Altunkaynak, B., & Esin, A. (2004). The genetic algorithm method for parameters estimation in nonlinear regression. Gazi University Journal of Science, 17(2), 43-51.
Thomas, G.M., Gerth, R., Velasco, T., & Rabelo, L.C. (1995). Using real-coded genetic algorithms for Weibull parameter estimation. Computers & Industrial Engineering, 29, 377-381. DOI:10.1016/0360-8352(95)00102-7
Henningsen, A., & Toomet, O. (2010). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26, 443-458. DOI: 10.1007/s00180-010-0217-1
Scrucca, L. (2013). GA: A package for genetic algorithms in R. Journal of Statistical Software, 53(4), 1-37. DOI: 10.18637/jss.v053.i04
Massey JR, F.J. (1951). The Kolmogorov-Smirnov test for goodness of fıt. Journal of American Statistical Association, 46, 68-78. DOI:10.1080/01621459.1951.10500769
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