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This study predicted the fatigue life (N) of UHPC incorporated with different volume fractions (Vf = 0.0%, 0.5%, 1.0%, 1.5% and 2.0%) of steel fiber under flexural cyclic loading at various stress levels (S). The Weibull distribution, a twoparameter model, was utilized to estimate the distribution of fatigue life in UHPC. Subsequently, three methods were employed to calculate the parameters: the graphical method, the method of moments, and the method of maximum likelihood. The averaged values of these parameters were then obtained to enhance the accuracy of the estimation. The results are presented in the form of S-N diagrams, which depict the quantitative relationship between stress (S) and fatigue life (N). This relationship was determined using the Wohler equation, the modified Wohler equation, and the power equation. By employing these equations, the flexural fatigue strength of UHPC can be accurately predicted. Subsequently, the fatigue failure probability (Pf) was incorporated to enhance the reliability of the S-N quantitative relation. The fatigue testing results were presented in the form of S-N-Pf curves, which comprehensively reflect the relationship between stress, fatigue life, and failure probability. Furthermore, the mathematical relation of the S-N-Pf curves was derived to predict the fatigue life of UHPC with a given failure probability, providing a more comprehensive and accurate assessment of its fatigue behavior. [ABSTRACT FROM AUTHOR]

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The Weibull algorithm is one of the most accurate tools for forecasting and estimating wind energy potential. Two main parameters of the Weibull algorithm are the 'Weibull shape' and 'Weibull scale' factors. There are six different numerical methods to estimate the two Weibull parameters. These six methods are the empirical method of Justus (method 1), the empirical method of Lysen (method 2), the maximum likelihood method (method 3), the modified maximum likelihood method (method 4), the energy pattern factor method (method 5) and the graphical method (method 6). Many commercial wind energy software programs use the Weibull algorithm, and these six methods are used to calculate the potential wind energy at a given site. However, their accuracy is rarely discussed, particularly regarding wind data height. For this purpose, wind data measured for a long period (six years) at real sites are introduced. The wind data sites are categorized into three levels, i.e., low, medium, and high, based on wind data measurement height. The analysis shows that methods 1 and 2 are the most accurate methods among all six methods at low and medium heights. The number of errors increases with the height of these two methods. Methods 3 and 4 are the most suitable options for larger heights, as these scenarios have minimal error. The present study's findings can be used in various fields, e.g., wind energy forecasting and wind farm planning. [ABSTRACT FROM AUTHOR]

In this study, the graphical method, which is widely used to find the coefficients of the Weibull distribution function (WDF), has been improved by using the moving least squares approximation (MLSA) replace least squares method (LSM). The accuracy of the results obtained by the moving least squares method is shown by two different error analysis tests. In order to implement this method, Osmaniye region, which is rich in wind potential maintenance, has been selected. The root mean square error (RMSE) and mean percentage error (MPE) are used to compare the efficiency of proposed method. In this study, the results of the graphical method developed by the MLSA were compared monthly and yearly with the results obtained according to the least squares method. It was observed that the results of the proposed method in the two error analysis tests were much better. Also, the mean wind speed and average wind power values of the selected region were calculated with the coefficients found by MLSA. These calculated values were compared with actual values. [ABSTRACT FROM AUTHOR]

In recent years, wind energy has become remarkably popular among renewable energy sources due to its low installation costs and easy maintenance. Having high energy potential is of great importance in the selection of regions where wind energy investments will be made. In this study, the wind power potential in Çanakkale Province, located in the northwest of Türkiye, is examined, and the wind speed is estimated using hourly and daily data over a one-year period. The data, including 12 different meteorological parameters, were taken from the Turkish State Meteorological Service. The two-parameter Weibull and Rayleigh distributions, which are the most widely preferred models in wind energy studies, are employed to estimate the wind power potential using hourly wind speed data. The graphical method is implemented to calculate the shape (k) and scale (c) parameters of the Weibull distribution function. Daily average wind speed estimation is performed with artificial neural network–genetic algorithm (ANN-GA) and ANN–particle swarm optimization (ANN-PSO) hybrid approaches. The proposed hybrid ANN-GA and ANN-PSO algorithms provide correlation coefficient values of 0.94839 and 0.94042, respectively, indicating that the predicted and measured wind speed values are notably close. Statistical error indices reveal that the ANN-GA model outperforms the ANN-PSO model. [ABSTRACT FROM AUTHOR]

The accuracy in analysis of wind speed is very critical to assess wind potential at any site. Wind power potential has been estimated using statistical distribution methods at numerous places around the world. The main aim of this article is to analyse wind potential and to compare between metaheuristic optimization algorithms and numerical approaches utilising the wind data at various places in India measured from masts and remote sensing technologies. The Weibull distribution fitness test is calculated using real-time wind data from various locations. The optimal Weibull parameters are estimated using numerical methods such as empirical method of Justus, maximum likelihood method, graphical method, modified maximum likelihood method and Wind Atlas Analysis and Application Program (WAsP). Furthermore, to assess Weibull distribution function for different sites (onshore, nearshore and offshore) in India, the social spider optimization is compared to particle swarm optimization and genetic algorithm. To examine the accuracy of various approaches, further goodness-of-fit method is estimated. The mean power density is maximum for offshore, followed by nearshore and onshore site with 452.32 W/m2, 431.53 W/m2, and 283 W/m2, respectively, at 120 m height. WAsP approach outperforms other numerical approaches used in this work. When compared to the genetic algorithm, the social spider optimization and particle swarm optimization were shown to be more efficient. The suggested method is more accurate than the numerical approaches utilised for wind potential assessment, according to the results. [ABSTRACT FROM AUTHOR]

Currently, Pakistan is facing severe energy crises and global warming effects. Hence, there is an urgent need to utilize renewable energy generation. In this context, Pakistan possesses massive wind energy potential across the coastal areas. This paper investigates and numerically analyzes coastal areas' wind power density potential. Eight different state-of-the-art numerical methods, namely an (a) empirical method, (b) graphical method, (c) wasp algorithm, (d) energy pattern method, (e) moment method, (f) maximum likelihood method, (g) energy trend method, and (h) least-squares regression method, were analyzed to calculate Weibull parameters. We computed Weibull shape parameters (WSP) and Weibull scale parameters (WCP) for four regions: Jiwani, Gwadar, Pasni, and Ormara in Pakistan. These Weibull parameters from the above-mentioned numerical methods were analyzed and compared to find an optimal numerical method for the coastal areas of Pakistan. Further, the following statistical indicators were used to compare the efficiency of the above numerical methods: (i) analysis of variance ( R 2 ), (ii) chi-square ( X 2 ), and (iii) root mean square error (RMSE). The performance validation showed that the energy trend and graphical method provided weak performance for the observed period for four coastal regions of Pakistan. Further, we observed that Ormara is the best and Jiwani is the worst area for wind power generation using comparative analyses for actual and estimated data of wind power density from four regions of Pakistan. [ABSTRACT FROM AUTHOR]

In this study, the success of the numerical methods and a metaheuristic algorithm in parameter estimation of Weibull distribution, which is frequently used in wind energy applications, are compared. Numerical methods are Justus empirical method, moment method, graphical method, energy pattern factor method (EPM), energy trend method, maximum likelihood estimation method (MLE). The metaheuristic algorithm is manta ray foraging optimization method (MRFO). The wind data used in the study were recorded hourly in the Isparta region in the southwest of Turkey. A graphical user interface design has been made to easily perform the calculations in this study. The success of the methods was tested with four different statistical error analysis methods. According to the results of the analysis, the MRFO method was by far the most successful method. EPM and MLE methods were the most unsuccessful methods. [ABSTRACT FROM AUTHOR]

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 R 2 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. [ABSTRACT FROM AUTHOR]

The accurate selection of the wind speed distributions is crucial for a better utilisation of wind energy. The Weibull distribution is most commonly used distribution and hence its parameters need to be optimized. In this study five numerical methods, namely, maximum likelihood method (MLM), graphical method (GM), empirical method of Justus (EMJ), modified maximum likelihood method (MMLM) and wind atlas analysis and application program (WAsP) and three metaheuristic optimization algorithms, namely, social spider optimization (SSO), particle swarm optimization (PSO) and genetic algorithm (GA) are applied for estimating Weibull distribution parameters at three different locations (onshore—Kayathar, nearshore—Jafrabad and offshore—Gulf of Khambhat (GOK) in India and also comparison of numerical and optimization methods are employed to tune the optimal parameters. The accuracy of the methods was evaluated using three different statistical analysis techniques. As per the results, GOK has the maximum wind power density of 450.2 W/m2 compared to Jafrabad and Kayathar. It was observed that among the five methods used for Weibull parameters estimation, WAsP method presented a better curve fit with the histogram of the wind speed. The results shows that SSO and PSO presents a comparably better performance than GA in the term of accuracy on the basis of closeness to converged solution. [ABSTRACT FROM AUTHOR]

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

Among several methods employed for sizing thickeners available in the literature, the Kynch, Biscaia Jr., Talmadge and Fitch, Roberts, Coe and Clevenger, and Oltmann methods use experimental data from sedimentation curves and graphical approaches. By using the Weibull distribution, it is possible to represent sedimentation curves with algebraic equations, which does not require the use of graphical approaches and provides more accuracy and speed for sizing calculations. In the present work, the main objective is the development of a set of equations for sizing continuous thickeners, for six conventional methods found in the literature, using the Weibull model. A comparative analysis of calculated and literature diameters for each graphical method presented variations between 0.73% and 8.93%. The use of the Weibull model presented the best accuracy for the Biscaia Jr. method, with a 0.73% average absolute error. [ABSTRACT FROM AUTHOR]

• Inspiration on the heterogeneous nature of water adsorption in bentonites. • Noval (continuum) SWRC model considering adsorption and capillarity. • New model contains only 5 parameters, with high efficiency in parameter estimation. • A graphical method was suggested to estimate maximum adsorption capacity. Understanding soil–water retention behavior is a longstanding topic. Water retained in soils can be decomposed into adsorptive and capillary components, controlled by different physicochemical mechanisms. The capillary water retention was frequently discussed in literatures, but the adsorption role was rarely considered, especially for high active clays (e.g., bentonite). In this study, two novel equations for quantifying adsorptive and capillary water retentions are proposed, generating a twofold model to continuously simulate soil–water retention behavior of bentonites. Only 5 parameters, i.e., the maximum adsorption capacity, characteristic adsorptive and capillary suctions, and uniformities of adsorptive and capillary pores, are defined with clear physical meanings. A graphical method was suggested to firstly determine the maximum adsorption capacity, and the remaining parameters are efficiently estimated by non-linear curve fitting. The water retention data for various bentonites, representing a variety of hydration conditions, initial compactness, montmorillonite content and suction range, are used to assess the model performance. The predictions agree well with the measured total, adsorptive and capillary water contents of a Wyoming bentonite, and the fitting curves also match well with test data for other bentonites over the full suction range. Adsorption parameters are distributed within a narrow range, while the characteristic capillary suction is also distributed within a limited range under constant volume condition. The proposed model allows reasonable predictions about the capillary onset and the transition from adsorption to capillarity, revealing obvious superiority by comparison with other hybrid models. This work offers a new pathway to quantitively assess the soil–water retention curve of high active clays. [ABSTRACT FROM AUTHOR]

This study analyzes the wind speed characteristics, compares the six different methods (graphical, method of moment, wind energy pattern factor, empirical method of Justus and Lysen, and maximum likelihood method) of estimating Weibull parameters and calculates wind power density using daily mean wind speed data collected, at a height of 2 m, over a period of seven and eight years for Jumla and Okhaldhunga, respectively. Wind data were estimated at a height of 50 m to calculate average wind speed, Weibull parameters, and wind power density. Based on the results, Jumla has an average monthly maximum wind speed of 9.78 m/s in June and minimum wind speed of 6.71 m/s in December, whereas Okhaldhunga has an average monthly maximum wind speed of 10.95 m/s in April and minimum wind speed of 4.52 m/s in October. Jumla has an average annual wind speed of 8.11 m/s while Okhaldhunga has an average annual wind speed of 6.89 m/s. The accuracy of estimation methods was statistically tested using root mean square error and coefficient of determination. The empirical method of Justus and Lysen was found to be the best performing while the graphical method performed the poorest. By using the best method, an average wind power density has been estimated as 336.07 W/m 2 and 326.73 W/m 2 for Jumla and Okhaldhunga, respectively, indicating that both locations belong to wind power class III and have a moderate potential for wind energy harvesting. [ABSTRACT FROM AUTHOR]

In this paper, the distribution network reconfiguration with simultaneous capacitor switching, in the presence of wind generators, by Simulated Annealing is presented. IEEE 69 bus network is analyzed which has 69 nodes including the slack one and 73 branches, all of which can commutate. Following assumptions are made: load in nodes is changed according to Gauss distribution and wind generator power with Weibull one, every hour, then there are two wind generators of 200 kW maximum power each (10% of total, nominal active power load) and they can be allocated to any node but the slack one. The same is valid for the capacitor banks regarding allocation. This switching logic is unrealistic. On its basis more realistic one was issued with fixed nodes for allocation of wind generators and capacitor banks (the most frequently visited nodes), by Monte Carlo graphical method. Input power factor is to be greater than 0.85 which is not fulfilled with commencing configuration (from the start) so that allocation of capacitor banks is mandatory. Another constraint is that the network should not be overcompensated. Four realistic scenarios are investigated. In the first one only network with wind generators is analyzed and the rest are dedicated to all possible combinations of the regulation. The programme is automated indicating the price of configuration, generated banks, input data (active and reactive load, power and location of wind generators) and savings which change on an hourly basis. The wind generators are uniformly distributed in accordance with nodes (for the less realistic scenario) and generate only active power complying with Weibull distribution. The graphical results are presented for a 1008-h operation (operation in one thousand and eight hours, every hour different) and the analysis is done for a thousand and eight-hour work. The presented method shows that considerable savings can be achieved by simultaneous application of reconfiguration method and capacitor switching with already allocated wind generators. [ABSTRACT FROM AUTHOR]

Accurate estimation of wind speed distributions is a challenging task in wind power planning and operation. The selection of convenient functions for describing wind speed distribution is a crucial requisite. In this paper, remarkable bi-parameter Weibull function is presented to estimate the wind energy potential. Weibull parameters based on different six estimation methods, namely graphical, method of moment, energy pattern factor, mean standard deviation, power density methods, and genetic algorithm are evaluated. Besides, the goodness of fit of the estimation methods is investigated via mean absolute error, root mean square error, normalized mean absolute error, Chi-square error, and regression coefficient. To plainly identify the best matching estimation method, Net Fitness test is also presented. Catalca in the Marmara region in Istanbul, Republic of Turkey, is selected to be the underlying site. The experimental results show the effectiveness of the estimation methods in modeling wind distribution but with relatively small differences in terms of performance. However, the genetic algorithm and energy pattern factor accomplish the best and worst matching estimation methods, respectively. [ABSTRACT FROM AUTHOR]

In this study, we propose two estimators called the 3-step modified maximum likelihood (MML) and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators. [ABSTRACT FROM AUTHOR]

To establish Weibull distribution patterns for outdoor wind speed (WS) over an extended time period and determine wind conditions for building energy-efficient design, this study collected daily WS data from 381 cities spanning all thermal design zones in China. Weibull distribution shape and scale parameters were estimated using three methods: Maximum Likelihood Estimation (MLE), Graphical Method (GM), and Method of Moments (MM). A comprehensive goodness-of-fit assessment of these methods revealed that GM and MLM exhibited superior performance, making them suitable for determining Weibull parameters in the summer, winter, and the entire year. Through a rigorous examination and evaluation of the shape and scale parameters within each subzone across the summer, winter, and the entire year periods, the study identified the Rayleigh distribution as the typical pattern for low WS in building energy-efficient design. The determined Weibull distribution patterns can serve as fundamental information for wind inlet in assessing climate potential, WS in Outdoor Climate Design Conditions, and wind information in Typical Meteorological Year. • A comparative analysis was conducted using daily wind speed data from 381 stations using three estimation methods. • Weibull parameter ranges for the summer, winter, and annual were determined and analysed across all subzones. • A consistent Rayleigh distribution pattern was found in all seasons. • The distribution patterns can be used to determine wind conditions in building energy-efficient design. [ABSTRACT FROM AUTHOR]

Green hydrogen is becoming increasingly popular, with academics, institutions, and governments concentrating on its development, efficiency improvement, and cost reduction. The objective of the Ministry of Petroleum, Mines, and Energy is to achieve a 35% proportion of renewable energy in the overall energy composition by the year 2030, followed by a 50% commitment by 2050. This goal will be achieved through the implementation of feed-in tariffs and the integration of independent power generators. The present study focused on the economic feasibility of green hydrogen and its production process utilizing renewable energy resources on the northern coast of Mauritania. The current investigation also explored the wind potential along the northern coast of Mauritania, spanning over 600 km between Nouakchott and Nouadhibou. Wind data from masts, Lidar stations, and satellites at 10 and 80 m heights from 2022 to 2023 were used to assess wind characteristics and evaluate five turbine types for local conditions. A comprehensive techno-economic analysis was carried out at five specific sites, encompassing the measures of levelized cost of electricity (LCOE) and levelized cost of green hydrogen (LCOGH), as well as sensitivity analysis and economic performance indicators. The results showed an annual average wind speed of 7.6 m/s in Nouakchott to 9.8 m/s in Nouadhibou at 80 m. The GOLDWIND 3.0 MW model showed the highest capacity factor of 50.81% due to its low cut-in speed of 2.5 m/s and its rated wind speed of 10.5 to 11 m/s. The NORDEX 4 MW model forecasted an annual production of 21.97 GWh in Nouadhibou and 19.23 GWh in Boulanoir, with the LCOE ranging from USD 5.69 to 6.51 cents/kWh, below the local electricity tariff, and an LCOGH of USD 1.85 to 2.11 US/kg H2. Multiple economic indicators confirmed the feasibility of wind energy and green hydrogen projects in assessed sites. These results boosted the confidence of the techno-economic model, highlighting the resilience of future investments in these sustainable energy infrastructures. Mauritania's north coast has potential for wind energy, aiding green hydrogen production for energy goals. [ABSTRACT FROM AUTHOR]

The Weibull probability distribution indicates the probability of a specific wind speed and must be calculated before wind turbine installation. The Weibull distribution is affected by shape and scale parameters, which are driven in various ways. Many studies have conducted research to determine a more reliable method among various Weibull parameter estimation methods. However, since these studies showed different results, studies on determining the higher reliable Weibull parameter estimation methods continues. In this study, we analyzed 10 years of data collected at the same location and height level in Maldo island(from 2010 to 2019) and Saemangeum seawall (from 2011 to 2012), the Republic of Korea. While former studies tried to rank the Weibull distribution methods based on the statistical analyses, in this study, we compared the Weibull parameters using twelve methods and identified the highest reliable and efficient methods for deriving the Weibull probability distribution by using the new approach comparing the variance of RMSE, R2, and χ2, which give a comprehensive insight about the level and fluctuations errors. These twelve methods are Alternative maximum likelihood method, Equivalent energy method, Empirical method of Justus, Empirical method of Lysen, Energy pattern factor method, Graphical method, Modified energy pattern factor method, Maximum likelihood method, Moment method, Modified maximum likelihood method, Power density method, Standard deviation method. The results showed while Empirical method of Justus, Empirical method of Lysen, Moment method, and Standard deviation method had the best accuracies in prediction of wind speed distribution, some methods such as Graphical method, Alternative maximum likelihood method, Equivalent energy method, and Energy pattern factor method had the worst prediction of wind speed distribution based on all variance of statistical methods for both regions.

Natural fibers derived from plants were gaining favor as a viable alternative to synthetic materials. However, searching for sustainable raw materials with superior qualities is cumbersome because most natural fibers are limited to specific geographical areas. Himalayacalamus falconeri (HF) is a fast-growing plant that is abundant in the hills of Uttarakhand, India. This study is aimed at extracting fibers from the stem of Himalayacalamus falconeri (HF) culms, and investigate their properties by XRD analysis, TGA analysis, AFM analysis, and single-fiber tensile test. The extracted HF fiber was alkali-treated to enhance its mechanical properties. It was observed that the alkali treatment on HF fibers increased the cellulose content by 6%, and density by 4% compared with untreated fiber. Furthermore, the removal of amorphous components from the fiber surface resulted in a decrease in diameter from 103.95 to 94.4 μm. In addition, the alkali treatment on HF fiber enhanced the material's crystallinity index (from 58.92 to 67.79%), tensile strength (from 132 to 196.5 MPa), thermal stability (from 250 to 258 °C), and surface roughness (from 23.478 to 37 nm). The experimental findings confirmed that HF fiber is a suitable replacement material for synthetic reinforcement materials in lightweight polymer composites. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian estimators for the Inverse Weibull Distribution (IWD) scale parameter are derived when the shape parameter of distribution is known. The Bayesian estimators for the parameter are obtained by using the Gamma prior under the different types of loss functions such as square error loss function (Self), Entropy loss function (Elf), Precautionary loss function (Plf), Linear exponential loss function (Linexlf) and nonlinear exponential loss function (Nlinexlf). A classical maximum likelihood estimator (mle) for the parameter is also derived. To compare the efficiency of the parameter estimation methods, a simulation study is carried out. The comparison is based on mean square error. [ABSTRACT FROM AUTHOR]

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution. [ABSTRACT FROM AUTHOR]

Slovakia currently has a relatively large unused potential in the area of electricity production from solar radiation and wind as renewable sources. The conversion of the wind's mechanical energy into electrical energy depends, among other things, on the wind speed and its turbulence. Perhaps the most widely used probability distribution for a wind speed model is the Weibull distribution. In the article, we deal with the comparison of seven methods for estimating the parameters of this distribution - maximum likelihood method, method of moments, empirical method, empirical method of Lysen, power density method, least squares method and weighted least squares method - on wind speed records from the city of Nitra for the period of 2005-2021. The vicinity of this city is one of the places identified as a suitable location for the installation of wind turbines. The performance of individual estimation methods is evaluated based on the indicators - the coefficient of determination R² and the root mean square error RMSE. Based on these values, the most accurate method is the weighted least squares method, although all other methods achieved similarly good results. [ABSTRACT FROM AUTHOR]

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens, namely four-point bending as well as three-point bending tests with different span lengths. Flaw strength is provided by the elemental stress operating on the critical flaw at the fracture of a test specimen. Fracture-inducing flaws and their locations are identified using fractography. A single population of pores was found to dominate the fracture. The construction of diagrams of p-quantile vs. elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. The Weibull distributions of strengths are then compared to the normal reference distributions. The parameters of the Weibull cumulative probability distributions are estimated using maximum likelihood and moment methods. The cumulative distributions of flexural strengths for the different bending tests are predicted from the flaw strength density function using the elemental strength model, and from the cumulative distribution of flexural strength using the Weibull function. Flaw strength distributions that include the weaker flaws that are potentially present in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed regarding the pertinence of an intrinsically representative flaw strength distribution, considering failure predictions. Finally, the influence of the characteristics of fracture-inducing flaw populations expressed in terms of flaw strength interval, size, dispersion, heterogeneity, and reproducibility with volume change is examined. [ABSTRACT FROM AUTHOR]

Wind energy represents a clean, abundant and cost-effective power source, fostering job growth and environmental mitigation. Although wind energy harnesses several gigawatts today, its availability hinges on diverse factors, with geographical location standing out. Commercial turbines, with varying capacity ranges, saturate the market. Locating site-specific suitability and matching the appropriate turbine to meet specific requirements are of paramount importance. This study aims to assess the feasibility of wind energy in Surat, Gujarat, India and select an optimal small commercial turbine for residential use. The research involves Rayleigh and Weibull probability distribution functions based on yearlong velocity data. These distributions are fitted with actual data, revealing the most probable velocity (v mf = 3 m/s) and velocity at maximum power (v pmax = 5 m/s). The power availability of the site has been assessed as 42.6 W/m2 using both graphical and analytical methods. Several commercial turbines have been shortlisted based on on-site power criteria and their specifications are evaluated against site power availability. A comparative analysis culminates in identifying the most suitable turbine for the location. The best suitable turbine for the site with an annual energy yield of 8 MW has been suggested amongst selected turbines for small-scale residential applications. [ABSTRACT FROM AUTHOR]

This study predicted the fatigue life (N) of UHPC incorporated with different volume fractions (Vf = 0.0%, 0.5%, 1.0%, 1.5% and 2.0%) of steel fiber under flexural cyclic loading at various stress levels (S). The Weibull distribution, a two-parameter model, was utilized to estimate the distribution of fatigue life in UHPC. Subsequently, three methods were employed to calculate the parameters: the graphical method, the method of moments, and the method of maximum likelihood. The averaged values of these parameters were then obtained to enhance the accuracy of the estimation. The results are presented in the form of S-N diagrams, which depict the quantitative relationship between stress (S) and fatigue life (N). This relationship was determined using the Wohler equation, the modified Wohler equation, and the power equation. By employing these equations, the flexural fatigue strength of UHPC can be accurately predicted. Subsequently, the fatigue failure probability (Pf) was incorporated to enhance the reliability of the S-N quantitative relation. The fatigue testing results were presented in the form of S-N-Pf curves, which comprehensively reflect the relationship between stress, fatigue life, and failure probability. Furthermore, the mathematical relation of the S-N-Pf curves was derived to predict the fatigue life of UHPC with a given failure probability, providing a more comprehensive and accurate assessment of its fatigue behavior.

The two-parameter Weibull probability density function (PDF) is widely utilized by different researchers and engineers to fit wind speed data for statistical analysis and modeling. The characterization of wind resources in the frequency and probability domain is necessary to estimate the power output potential of new wind energy projects. Considering that exist a variety of Weibull equations evidenced in the literature review, this article evaluates 11 different methods to calculate the shape and scale parameters of the Weibull PDF. In this sense, it was written an algorithm within a Matlab function that solves the 11 methods for calculating the Weibull PDF parameters. Wind speed data extracted from the ERA5 database was used as input data for applying the proposed algorithm, and statistical parameters such as the Root Mean Square Error (RMSE), the Relative Root Mean Square Error (RRMSE), and chi-square test (X²) we utilized for assessing the performance of each one of the 11 methods for modeling the wind distribution. The statistical results pointed that the numerical iteration methods (e.g. maximum likelihood method) showed better results than parameterized equations such as the Graphical Method, hence, this research recommends the implicit methods for determining Weibull PDF parameters of wind speed data. [ABSTRACT FROM AUTHOR]

Currently, Pakistan is facing severe energy crises and global warming effects. Hence, there is an urgent need to utilize renewable energy generation. In this context, Pakistan possesses massive wind energy potential across the coastal areas. This paper investigates and numerically analyzes coastal areas’ wind power density potential. Eight different state-of-the-art numerical methods, namely an (a) empirical method, (b) graphical method, (c) wasp algorithm, (d) energy pattern method, (e) moment method, (f) maximum likelihood method, (g) energy trend method, and (h) least-squares regression method, were analyzed to calculate Weibull parameters. We computed Weibull shape parameters (WSP) and Weibull scale parameters (WCP) for four regions: Jiwani, Gwadar, Pasni, and Ormara in Pakistan. These Weibull parameters from the above-mentioned numerical methods were analyzed and compared to find an optimal numerical method for the coastal areas of Pakistan. Further, the following statistical indicators were used to compare the efficiency of the above numerical methods: (i) analysis of variance (R2), (ii) chi-square (X2), and (iii) root mean square error (RMSE). The performance validation showed that the energy trend and graphical method provided weak performance for the observed period for four coastal regions of Pakistan. Further, we observed that Ormara is the best and Jiwani is the worst area for wind power generation using comparative analyses for actual and estimated data of wind power density from four regions of Pakistan.

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The demand for electrical energy is increasing every day, which is one of the critical challenges facing the world today. Hence, the necessity of turning to clean renewable energy sources that are not harmful to the environment as an alternative to the traditional generation based on fossil fuels has become more important than ever before. Wind power is one of the renewable sources that provides a clean solution to generate electricity. In this context, the Kingdom of Saudi Arabia announces renewable energy projects to generate 9 GW from wind in 2032. Hence, the aim of this paper is to investigate the most suitable method of Weibull parameter estimation in order to predict wind characteristics and employ it for wind energy assessment in the Qassim region located in the center of the country. In this study, wind data is collected from NASA's forecasts of global energy resources for 2010–2015 based on their availability at altitudes of 10m and 50m and analyzed by using six different methods for Weibull parameter estimation: the graphical method (GM), standard deviation method (SDM), energy pattern factor method (EPF), moment method (MM), alternative maximum likelihood method (AMLM), and novel energy pattern factor method (NEPF). The efficiency of each method is tested by calculating the root mean square error (RMSE) and the relative wind power density error (RPDE). The comparison shows that the most appropriate method for estimating wind power density in the country is the Moment Method (MM), with the lowest RPDE ratio equal to 0.2018%. It has been found that the wind power density in the Qassim region falls into the class 1 category, as it is less than 100 W/m2 at a height of 10m and less than 200 W/m2at an altitude of 50m. The results show the region is only suitable for small off-grid projects. Doi: 10.28991/ESJ-2023-07-06-024 Full Text: PDF

The present analysis examines extensive and consistent data from automotive production and service to assess reliability and predict failures in the case of an engine control device. It is based on statistical evaluation of production and lead times to determine vehicle sales. Mileages are integrated to establish the age of the vehicle fleet over time and to predict the censored data. Failure and censored times are merged in a multiple censored data and combined by the Kaplan-Meier estimator for survivals. The Weibull distribution is used as parametric reliability model and its parameters identified to assure precision in predictions (>95%). An average time to failure >80 years and a slightly increasing failure rate ensure a low risk. The study is based on real-world data from various sources, acknowledging that the data are not homogeneous, and it offers a comprehensive roadmap for processing this diverse raw data and evolving it into sophisticated predictive models. Furthermore, it provides insights from various perspectives, including those of the Original Equipment Manufacturer, Car Manufacturer, and Users. [ABSTRACT FROM AUTHOR]

An investigation was carried out to analyze the flexural fatigue performance of pavement quality concrete (PQC) of M40 and M50 grades, made with conventional materials out of which river sand (RS) was replaced by copper slag (CS) by varying concentrations to the extent of 100% by volume. Experiments were conducted in the laboratory to determine the 90-day flexural strength of PQC samples (100×100×500 mm) under four-point loading. Based on respective flexural strength, repeated loads were applied for the conduct of flexural fatigue tests of PQC specimens at stress levels of 0.7, 0.8, and 0.9, each at 1 Hz frequency. In terms of fatigue life distributions, the flexural fatigue performance of several PQC mixtures has been evaluated. Three methods were used to estimate various parameters for the Weibull distribution. It is observed that the fatigue life distribution of both M40 and M50 grade PQC mixes made with CS can be modeled by a two-parameter Weibull distribution with a correlation coefficient of more than 0.95. The estimation of fatigue life of PQC mixes has also been done at different failure probabilities. The 90-day flexural strength of PQC mixes (both grades) with CS replacing RS, increased compared with conventional PQC. Further, X-ray diffraction (XRD) analysis and scanning electron microscope (SEM) images of PQC mixes confirmed the homogeneity of the concrete. The fatigue performance was also enhanced with CS replacing RS. The goodness-of-fit test also indicated that the present model is valid at the 5% significance level for PQC (both grades) made with CS. [ABSTRACT FROM AUTHOR]

In this study, wind characteristics and electricity generation potential from wind energy were investigated in the Bitlis‐Rahva region in eastern Turkey. Ten‐minute wind data from the Bitlis meteorological station were used in the study. The determination of the wind speed (WS) distribution was carried out using the WindPRO program together with the Weibull and Rayleigh distributions. R2, RMSE, and χ2 goodness‐of‐fit tests were used to measure the accuracy of the velocity distribution process. A digital elevation model of the power generation site was created to evaluate wind data and predict turbine performance. Wind power generation performance was evaluated using five different wind turbines (WTs). A power curve model was developed for the WTs to determine the capacity for energy generation. According to the error tests, it has been determined that the results obtained with the WindPRO program can represent the observed wind data most accurately. The results from the WindPRO program analysis showed an average annual WS of 3.26 m/s and a power density of 49.77 W/m2. Increasing height was found to increase WS and power density. The prevailing wind direction was found to be South‐Southwest with a frequency value of 27.5%. The largest capacity factor was obtained from the WT with the largest rotor diameter and rated power. Out of all the WTs examined, the turbine with the largest rated power and rotor diameter produced the greatest amount of energy. According to the capacity factor values calculated for the selected WTs, the region is not considered efficient for wind energy investments. However, as WS and power density increase with increasing altitude, it is thought that different higher parts of the region may be more efficient in terms of wind energy utilization. [ABSTRACT FROM AUTHOR]

The crashworthiness capability of laterally loaded glass/epoxy (GFRE) tubular components containing halloysite nanotubes (HNTs) was explored in this article. GFRE components filled with 0, 1, 2, 3, and 4 weight percent (wt.%) of HNTs were created using wet-wrapping by hand lay-up technique. For the laterally loaded tubes, the crushing load and the energy absorption versus displacement responses were presented. In addition, distortion histories were tracked. The crashworthiness analysis was carried out by evaluating different indicators, i.e., initial crush load (P ip) , average crush load ( P avg ), crush load efficiency (CFE), energy absorption (U), and specific absorbed energy (SEA). Two parameters of the Weibull distribution were employed to assess the experimental findings statistically. In addition, mathematical regression models were built to predict the energy absorption indicators. Experimental results demonstrated that an unfilled tube demonstrated the largest CFE of 1.84, while the maximum P ip was demonstrated by a tube filled with 2 wt.% of HNTs with a value of 3.70 kN. Additionally, the tube filled with 4 wt.% of HNTs represents the extremes P avg , U, and SEA with values of 4.26 kN, 128.82 J, and 3.84 J/g, respectively. Due to their improved crashworthiness characteristics, GFRE filled with 4 wt.% of HNTs is suitable for use as a crashworthy device in automobiles. [ABSTRACT FROM AUTHOR]

Weibull distribution is widely used in engineering because of its flexibility to take on many different shapes. For different application fields, people put forward different estimation methods, including grey estimation method. The purpose of this paper is to improve the existing grey estimation method of Weibull distribution as its some serious shortcomings. Firstly, a grey three-parameter Weibull model is proposed in a discrete form. Then, by means of the grey Weibull model, a two-stage hybrid method for estimating the three-parameter Weibull distribution is proposed, which is composed of the linear and nonlinear least square principles. To demonstrate the feasibility of the proposed grey Weibull model, a simulation study was conducted and compared the results with the modified MLE method, and a comparison study on the frequency analysis of four breakdown data sets of epoxy resins is also carried out. Moreover, as a practical application, Weibull model based on the grey estimation approach is applied to the frequency analysis of monthly wind speed of Hohhot in 2018, and compared with a series of existing estimation methods. Results show that the proposed grey Weibull estimation improves the existing grey estimation and can be well applied to the frequency analysis of Weibull data. [ABSTRACT FROM AUTHOR]

To assess wind energy potential in Northern Morocco, a validated approach based on the two-parameter Weibull distribution is employed, utilizing wind direction and speed data. Over a span of two years, from January 2019 to December 2020, measurements taken every 10 min are collected. This study is centered on a comprehensive and statistical analysis of electricity generated from a wind farm situated in the Tetouan region in Morocco. This wind farm boasts a total capacity of 120 MW, comprising 40 wind turbines, each with a 3 MW capacity, strategically positioned along the ridge. Among the available techniques for estimating Weibull distribution parameters, the maximum likelihood method (MLM) is chosen due to its statistical robustness and exceptional precision, especially for large sample sizes. Throughout the two-year period, monthly wind speed measurements fluctuated between 2.1 m/s and 9.1 m/s. To enhance accuracy, monthly and annual theoretical power densities were recalculated using the Weibull parameters and compared with actual measurements. This has enabled the detection of production disparities and the mitigation of forecast errors throughout the entire wind farm. In conclusion, over the two-year production period, turbines WTG 30 and WTG 33 displayed the most significant shortcomings, primarily attributed to orientation issues within the "Yaw system". [ABSTRACT FROM AUTHOR]

Statistical distributions are used to model wind speed, and the twoparameters Weibull distribution has proven its effectiveness at characterizing wind speed. Accurate estimation of Weibull parameters, the scale (c) and shape (k), is crucial in describing the actual wind speed data and evaluating the wind energy potential. Therefore, this study compares the most common conventional numerical (CN) estimation methods and the recent intelligent optimization algorithms (IOA) to show how precise estimation of c and k affects the wind energy resource assessments. In addition, this study conducts technical and economic feasibility studies for five sites in the northern part of Saudi Arabia, namely Aljouf, Rafha, Tabuk, Turaif, and Yanbo. Results exhibit that IOAs have better performance in attaining optimal Weibull parameters and provided an adequate description of the observed wind speed data. Also, with six wind turbine technologies rating between 1 and 3MW, the technical and economic assessment results reveal that the CN methods tend to overestimate the energy output and underestimate the cost of energy ($/kWh) compared to the assessments by IOAs. The energy cost analyses show that Turaif is the windiest site, with an electricity cost of $0.016906/kWh. The highest wind energy output is obtained with the wind turbine having a rated power of 2.5 MW at all considered sites with electricity costs not exceeding $0.02739/kWh. Finally, the outcomes of this study exhibit the potential of wind energy in Saudi Arabia, and its environmental goals can be acquired by harvesting wind energy. [ABSTRACT FROM AUTHOR]

In this study, a centrally loaded round panel test was used to investigate the flexural fatigue behavior of steel fibre reinforced concrete (SFRC) considering three influencing factors, such as stress level, steel fiber type and steel fibre content. The results show that the fatigue life of all specimens at different stress levels followed the two-parameter Weibull distribution with a statistical correlation coefficient greater than 0.90. The predicted double logarithmic fatigue equations were also developed, which enables designers to predict fatigue life according to the required reliability and stress level in actual engineering. Due to the geometrical characteristics of hooked-end steel fibres, the SFRC specimens with 3D and 5D hooked-end steel fibres exhibited higher compressive strength, flexural toughness and flexural fatigue performance, showing more effective macrocracks control and higher energy absorption capacity. In addition, a developed analytical model for hooked-end fibers shows that the peak pull-out load of the 5D fiber is 30% higher than that of the 3D fiber, taking into account snubbing and matrix spalling effects. This finding results in the SFRC-5D specimens having the best flexural fatigue performance. [ABSTRACT FROM AUTHOR]

The utilization of cellulosic fibers is becoming increasingly widespread worldwide as promising raw material in polymer composite reinforcement. However, and despite the multiple advantages of cellulosic fibers like the lower density, cheap cost and biodegradability, their use is limited due to hydrophilic character which reduces their affinity with hydrophobic matrices. A natural fiber treatment, whether chemical or physical, is advised to address this issue. The purpose of this study is to characterize the Ampelodesmos mauritanicus plant (AM) fibers extracted by the chemical method (2% NaOH for 48 h) and treated (chemically and physically). We carried out acetylation, mercerization and microwaves modification of the AM plant fibers to reduce their hydrophilic character. The influence of chemical and physical treatments on the structure and morphology of AM plant fibers was characterized by analytical techniques as per International Standard. X-ray diffraction confirmed that the AM fibers have a good crystallinity index (52.4%). Microwave physical treatment at 550 W increased their density from 1.00 to 1.55 g/cm3, their Young's modulus and tensile strength from 11.0 to 18.6 GPa and from 155 to 290 MPa, respectively, giving the highest values. It is followed by chemical treatments: first with acetic anhydride (C4H6O3) for 4 h and then with 3% NaOH also for 4 h. It should be observed that the data have a very considerable dispersion that calls for statistical analysis (method of Weibull with two and three parameters was utilized). [ABSTRACT FROM AUTHOR]

The evaluation of reanalysis and analysis data (estimated data) against in-situ measured data is essential to find uncertainties before its use for wind resource assessment. The performance evaluation of four different generations reanalysis datasets (NCEP-CFSR, NCEP-DOE, NCEP-NCAR and JRA-55) and two analysis datasets (NCEP-FNL and NCEP-GFS) was done against measured data for six sites using statistical analysis. A comparison of monthly mean time-series, Weibull probability distribution function and wind rose diagram of measured and estimated data was performed. The MBE and RMSE for wind speed range from −2.18 to 2.01 m/s and 1.34 to 3.00 m/s respectively; whereas MBE and RMSE for wind direction range from −34.34° to 13.90° and 40.58° to 71.28° respectively for six sites using all datasets. NCEP-CFSR data show promising results for most of the sites with the lowest errors and better correlation coefficients. NCEP-CFSR data being the new generation reanalysis having higher spatial resolution show better results compared to other reanalyses and analyses. The reanalysis and analysis wind data can be used as alternative to measured data to assess wind energy potential. [ABSTRACT FROM AUTHOR]

This paper presents an optimisation model for cost optimisation of maintenance at an offshore wind farm (OWF). The model is created for OWF project developers to optimise strategic resources to meet their maintenance demand. The model takes into account various maintenance categories on a full range of wind turbine components; the failure rate associated with each component is dependent on wind speed in order to consider weather uncertainty. Weibull distribution is used to predict the probability of wind speed occurring during a given period based on available historical data. The performance of the proposed optimisation model has been validated using reference cases and a UK OWF in operation. Various optimal solutions are investigated for the problems with increased and decreased mean turbine failure rates as a sensitivity test of the model. [ABSTRACT FROM AUTHOR]

Holistic, quality, and sustainability-based inventory policy for perishable items may prove to be a game-changer amid great concern over the carbon footprint and global economic crises. In this paper, first-in-first-out (FIFO) and last-in-first-out (LIFO) dispatching policies have been used to examine the effect of quality on fresh products' sales mind the sustainability concern. The quality of these products worsens with age. Its deterioration rate follows two parameters, Weibull distribution, as it gives better flexibility for various items subjected to deterioration and demonstrates fitness for a range of shape and scale parameters. An adequate preservation effort such as controlled atmosphere (CA) storage and modified atmosphere packaging (MAP) techniques must be applied during storage and handling to maintain such products' quality. Consumers' purchasing behavior and curiosity towards quality and selling price drive these products' demand variability. The demand has been considered a function of quality and unit selling price of the item. The effect of inflation viz. time value of money has also been taken into account, affecting Authoritarian governments' norms on carbon emission control in taxation have also been considered essential for modern sustainable inventory policies. The present models determine the unit price and lot size for the maximum average profit of the system. The behaviors of models have been investigated using a comprehensive sensitivity analysis that offers important operative implications. It has been found that the first-in-first-out model is more profitable as compared to the last-in-first-out model, the price is very rigid, and little flexibility in price drastically decreases the profit. Backlogging has no impact on the selling price of products and order quantity but reduces the average yield because of carbon emission taxation. [ABSTRACT FROM AUTHOR]

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve the likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real dataset are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation. [ABSTRACT FROM AUTHOR]

An effort has been made to enhance the flexural fatigue lives of self compacting concrete (SCC) in which half of the natural aggregates (NA) were substituted with recycled concrete aggregates (RCA) by means of blended cements. Blended SCC mixes containing either silica fume (SF) or metakaolin (MK) along with cement, and fly ash (FA) was also adopted. Fatigue lives have been evaluated as mean value, design value life and theoretical value. The Weibull distribution parameters were utilized for the valuation of mean and design values of fatigue lives for different considered mixes. It has been observed that adding RCA in SCC causes degradation in the fatigue lives, which can be enhanced by adopting the blended mixture comprising of SF or MK, cement and FA. Both SF and MK established a promising result in improving fatigue lives. Still, the blend of MK in SCC contributed most effectively in enhancing the fatigue life of SCC comprising RCA. [ABSTRACT FROM AUTHOR]