Wind speed is a key factor for assessing the wind energy potential of a region. Therefore, determining the best statistical distribution for modeling wind speed data is crucial for effective resource assessment and optimized energy production. The Weibull distribution is widely used for this purpose; however, it may not always provide the most adequate fit. In this study, Kumaraswamy–Weibull (KumW) distribution is used to model wind speed data as a more flexible alternative to Weibull distribution. In estimating the parameters of the KumW distribution, maximum likelihood (ML) methodology is employed. The resulting likelihood equations are not solvable explicitly because they involve nonlinear functions of unknown parameters. In order to obtain the ML estimates of the KumW parameters, this study utilizes three popular metaheuristic algorithms, the genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE), which have emerged as effective alternatives to the traditional numerical methods for solving computationally challenging optimization problems. One of the key challenges in using metaheuristic algorithms is the proper determination of an effective search space. In the literature, search spaces are often chosen arbitrarily, which may lead to reduced accuracy. As a novel contribution, we propose a new search space based on the bootstrap confidence intervals of the unknown KumW parameters for GA, PSO, and DE algorithms. The performances of the estimators obtained using GA, PSO, and DE based on proposed search space are compared with the corresponding estimators based on fixed search space in terms of bias, mean squares error (MSE), and deficiency (Def) criteria via an extensive Monte Carlo simulation study. Finally, the annual and seasonal wind speed data obtained from two stations located in the northern part of the Edremit Gulf, Turkey are modeled using the KumW distribution to demonstrate the practical utility of the proposed search space. The fitting performance of KumW is compared with that of the well-known and widely used Weibull distribution with respect to the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination ($ R^2 $), the Akaike information (AIC) and Kolmogorov–Smirnov (KS) criteria. Moreover, the power density error (PDE) criterion is utilized to evaluate the capability of KumW distribution in estimating wind power.
Citation: Adil Kılıç, Gamze Güven, Özge Gürer, Birdal Şenoğlu. Modeling wind speed using Kumaraswamy–Weibull distribution via improved metaheuristic optimization algorithms: The Edremit Gulf, Turkey[J]. Electronic Research Archive, 2026, 34(11): 7962-7999. doi: 10.3934/era.2026341
Wind speed is a key factor for assessing the wind energy potential of a region. Therefore, determining the best statistical distribution for modeling wind speed data is crucial for effective resource assessment and optimized energy production. The Weibull distribution is widely used for this purpose; however, it may not always provide the most adequate fit. In this study, Kumaraswamy–Weibull (KumW) distribution is used to model wind speed data as a more flexible alternative to Weibull distribution. In estimating the parameters of the KumW distribution, maximum likelihood (ML) methodology is employed. The resulting likelihood equations are not solvable explicitly because they involve nonlinear functions of unknown parameters. In order to obtain the ML estimates of the KumW parameters, this study utilizes three popular metaheuristic algorithms, the genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE), which have emerged as effective alternatives to the traditional numerical methods for solving computationally challenging optimization problems. One of the key challenges in using metaheuristic algorithms is the proper determination of an effective search space. In the literature, search spaces are often chosen arbitrarily, which may lead to reduced accuracy. As a novel contribution, we propose a new search space based on the bootstrap confidence intervals of the unknown KumW parameters for GA, PSO, and DE algorithms. The performances of the estimators obtained using GA, PSO, and DE based on proposed search space are compared with the corresponding estimators based on fixed search space in terms of bias, mean squares error (MSE), and deficiency (Def) criteria via an extensive Monte Carlo simulation study. Finally, the annual and seasonal wind speed data obtained from two stations located in the northern part of the Edremit Gulf, Turkey are modeled using the KumW distribution to demonstrate the practical utility of the proposed search space. The fitting performance of KumW is compared with that of the well-known and widely used Weibull distribution with respect to the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination ($ R^2 $), the Akaike information (AIC) and Kolmogorov–Smirnov (KS) criteria. Moreover, the power density error (PDE) criterion is utilized to evaluate the capability of KumW distribution in estimating wind power.
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Adil Kılıç, Gamze Güven, Özge Gürer, Birdal Şenoğlu. Modeling wind speed using Kumaraswamy–Weibull distribution via improved metaheuristic optimization algorithms: The Edremit Gulf, Turkey[J]. Electronic Research Archive, 2026, 34(11): 7962-7999. doi: 10.3934/era.2026341
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