Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

Reliability Analysis of a Small Pneumatic Cylinder Life

2011 ◽  
Vol 110-116 ◽  
pp. 4240-4245
Author(s):  
Jun Zhao Zhang ◽  
Cong Ling Wang ◽  
Xue Fa Fang
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Distribution Model ◽  
Pneumatic Cylinder ◽  
Life Test ◽  
Life Distribution ◽  
Median Rank ◽  
Distribution Parameters

The reliability of the pneumatic cylinder was investigated by routine life test. The results show that the failures of the pneumatic cylinder can be described as a Weibull distribution and fatigue fracture of the aluminum end cap and the head of install bolt is the major failure for the pneumatic cylinder. The pneumatic cylinder life distribution parameters were estimated by the median rank method in combination with maximum likelihood method. The distribution model for the reliability of the pneumatic cylinder was also proposed here.

Summary on Wind Speed Distribution and its Parameter Estimation

2014 ◽  
Vol 986-987 ◽  
pp. 689-693 ◽  
Author(s):  
Hui Li ◽  
Fang Zhang
Keyword(s):  
Parameter Estimation ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Wind Farms ◽  
Rayleigh Distribution ◽  
Speed Distribution ◽  
Wind Speed Distribution ◽  
Log Normal ◽  
Log Normal Distribution

The main objective of this paper is to review some models of medium-and-long-term wind speed distribution in wind farms, for example Gamma distribution, Log-normal distribution, Weibull distribution, Rayleigh distribution and Burr distribution. On the base of the Weibull distribution, some kinds of parameter estimation approaches are introduced. Meanwhile, the advantages and the disadvantages of various algorithms are analyzed and compared. The prospects of this research are put forward at the end of this paper.

scholarly journals Weibull Wind-Speed Distribution Parameters Derived from a Combination of Wind-Lidar and Tall-Mast Measurements Over Land, Coastal and Marine Sites

2015 ◽  
Vol 159 (2) ◽  
pp. 329-348 ◽  
Author(s):  
Sven-Erik Gryning ◽  
Rogier Floors ◽  
Alfredo Peña ◽  
Ekaterina Batchvarova ◽  
Burghard Brümmer
Keyword(s):  
Wind Speed ◽  
Speed Distribution ◽  
Wind Speed Distribution ◽  
Distribution Parameters ◽  
Wind Lidar

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

Wind speed distribution modeling for wind power estimation: Case of Agadir in Morocco

2018 ◽  
Vol 43 (2) ◽  
pp. 190-200 ◽  
Author(s):  
Ijjou Tizgui ◽  
Fatima El Guezar ◽  
Hassane Bouzahir ◽  
Brahim Benaid
Keyword(s):  
Wind Speed ◽  
Wind Energy ◽  
Weibull Distribution ◽  
Wind Power ◽  
Goodness Of Fit ◽  
Statistical Tests ◽  
A Priori ◽  
Speed Distribution ◽  
Distribution Modeling ◽  
Wind Speed Distribution

To estimate a wind turbine output, optimize its dimensioning, and predict the economic profitability and risks of a wind energy project, wind speed distribution modeling is crucial. Many researchers use directly Weibull distribution basing on a priori acceptance. However, Weibull does not fit some wind speed regimes. The goal of this work is to model the wind speed distribution at Agadir. For that, we compare the accuracy of four distributions (Weibull, Rayleigh, Gamma, and lognormal) which have given good results in this yield. The goodness-of-fit tests are applied to select the effective distribution. The obtained results explain that Weibull distribution is fitting the histogram of observations better than the other distributions. The analysis deals with comparing the error in estimating the annual wind power density using the examined distributions. It was found that Weibull distribution presents minimum error. Thus, wind energy assessors in Agadir can use directly Weibull distribution basing on a scientific decision made via statistical tests. Moreover, assessors worldwide can use the followed methodology to model their wind speed measurements.

Zero-truncated Poisson-Lindley distribution

2021 ◽  
pp. 40-50
Author(s):  
Afida Nurul Hilma ◽  
Dian Lestari ◽  
Sindy Devila
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Count Distribution ◽  
Distribution Parameters ◽  
Counting Distribution ◽  
Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

Sign in / Sign up

Export Citation Format

Share Document