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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]

The hourly mean wind speed data for Ali Algharbie station locations in south east of Iraq are collected and analyzed over a period of 1 year. The Data are fitted to the Weibull distribution function which is considered as the infrastructure to form a wind atlas for any country obtaining the Weibull distribution is necessary to determine the shape ( k) and scale( c) parameters. There are several methods that can be used to determine these parameters. This paper presents the comparison between two methods, Graphical method and the new method is called Energy Pattern Factor (EPF) method. It is found that the highest value of the shape ( k) and scale (c) in Jun. at the two methods and the lowest value in Oct. at the two methods and this corresponds with the highest (8.597m/s) and lowest (3.265m/s) value of hourly mean wind speed in these months. So the new method shows good agreement compared with the result of the Graphical method therefore, we recommend using this method to calculate the Weibull distribution parameters.

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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]

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]

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]

The two-parameter Weibull probability distribution function is versatile for modelling wind speed frequency distribution and for estimating the energy delivery potential of wind energy systems if its shape and scale parameters, k and c, are correctly determined from wind records. In this study, different methods for determining Weibull k and c from wind speed measurements are reviewed and applied at four sample meteorological stations in Zimbabwe. The appropriateness of each method in modelling the wind data is appraised by its accuracy in predicting the power density using relative deviation and normalised root mean square error. From the methods considered, the graphical method proved to imitate the wind data most closely followed by the standard deviation method. The Rayleigh distribution (k=2 is also generated and compared with the wind speed data. The Weibull parameters were calculated by the graphical method for fourteen stations at which hourly wind speed data was available. These values were then used, with the assistance of appropriate boundary layer models, in the mapping of a wind power density map at 50m hub height for Zimbabwe. [ABSTRACT FROM AUTHOR]

In this study, wind energy potential of Osmaniye was statistically analyzed which based on an h ourly m easured wind s peed d ata in 2013. Today, developing countries like our country especially member states of the European Union have turned to renewable energy sources in order to meet the rapidly growing need for energy. Wind power distribution plays a crucial role in producing electricity from wind power and building wind turbines. The Weibull and Rayleigh Distributions were used to investigate the region's wind energy potential. The preresearch results show that the wind energy potential in Osmaniye is statistically suitable for electricity production. We have collected the data on the 2013 hourlymeasured wind speed from Osmaniye Meteorology Station of the General Directorate of State M eteorology. We have used the 2013 wind speed values of Osmaniye for inquiring the accordance of blowing hours with the Weibull and Rayleigh Distribution function. The adaptation of blowing time of wind speed which was measured for one year in 2013 was investigated at the Weibull and Rayleigh distribution function at Osmaniye region. Graphical and Moment method were used to calculate the parameters of the Weibull and Rayleigh distribution. The shape 'k' and scale parameter 'c' of Graphical method were calculated 1.0046 - 1.7744 (m/s), respectively. The shape 'k' and scale parameter 'c' of Moment method were calculated 1.6394- 2.5391 (m / s), respectively. Consequently, the value obtained by Weibull model, according to the value obtained by Rayleigh model gave better results. [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]

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]

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]

The use of wind as an energy source is becoming popular because of its non-polluting and renewable features. There is an urgent request to develop site-based estimation on wind engineering, which can be used for optimal design of wind turbines and wind farming. The wind speed for Zafarana Project in Suez Gulf, namely Site-3, based on monthly averaged data for 1 year as well as every 10 min for two days, one day in summer season and one day one winter season have been analyzed to estimate the most appropriate method to find Weibull distribution parameters for this site. The investigated methods are the mean wind speed method, the maximum likelihood method, the modified maximum likelihood method, the graphical method and the power density method. These methods results have been compared with the provided data to find their accuracy based on the root mean square errors. From the obtained results, the mean wind speed and the maximum likelihood method are recommended in estimating the wind speed distribution for the studied site in Zafarana wind farm. [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]

In this study, the effectiveness of seven numerical methods is evaluated to determine the shape (K) and scale (C) parameters of Weibull distribution function for the purpose of calculating the wind speed characteristics and wind power density. The selected methods are graphical method (GPM), empirical method of Justus (EMJ), empirical method of Lysen (EML), energy pattern factor method (EPFM), maximum likelihood method (MLM) moment method (MOM) and the proposed. Hybrid method (HM) derived from EPFM and EMJ. The purpose is to identify the most appropriate method for computing the mean wind speed, wind speed standard deviation and wind power density for different costal locations in West Africa. Three costal sites (Lomé, Accra and Cotonou) are selected. The input data was collected, from January 2004 to December 2015 for Lomé site, from January 2009 to December 2015 for Accra site and from January 2009 to December 2012 for Cotonou. The results indicate that the precision of the computed mean wind speed, wind speed standard deviation and wind power density values change when different parameters estimation methods are used. Five of them which are EMJ, EML, EPF, MOM, ML, and HM method present very good accuracy while GPM shows weak ability for all three sites. [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]

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]

Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to study the probability distribution of flexural fatigue life of self-compacting rubberised concrete (SCRC), the flexural fatigue tests were carried out on 100 × 100 × 400 mm size beam specimens at different stress levels. The test results show that the probability distributions of fatigue life of SCRC can be approximately modelled by two-parameter Weibull distribution, and their fitting correlation coefficients are over 0.9. The shape parameter and scale parameter (two parameters of Weibull distribution) were estimated by different methods, namely the graphical method, the method of moments and the method of maximum likelihood estimates respectively, and it has been showed that the variability of fatigue life distribution of SCRC is higher when compared to plain concrete. The Pf – S – N curve (failure probability Pf, stress level S and fatigue life N) has been generated from the fatigue test data to predict the failure probability and corresponding stress level of the two-million cycle fatigue strength of SCRC. It has been proved that the fatigue performance of SCRC is better than that of the plain concrete by the S – N curve. And the fatigue failure process of SCRC was analyzed by acoustic emission (AE), showing obvious three-stage characteristic with the time. [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]

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]

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.

On Jeju Island, South Korea, an investigation was conducted to determine the best method for estimating Weibull parameters. Six methods commonly used in many fields of the wind energy industry were reviewed: the empirical, moment, graphical, energy pattern factor, maximum likelihood, and modified maximum likelihood methods. In order to improve the reliability of a research result, five-year actual wind speed data taken from nine sites with various topographical conditions were used for the estimation. Furthermore, the effect of various topographical conditions on the accuracy of the methods was analyzed and 10 bin interval types were applied to determine the most appropriate bin interval based on their performances. Weibull distributions that were estimated using these methods were compared with the observed wind speed distribution. Then the accuracy of each method was evaluated using four accuracy tests. The results showed that of the six methods, the moment method had the best performance regardless of topographical conditions, while the graphical method performed the worst. Additionally, topographical conditions did not affect the accuracy ranking of the methods for estimating theWeibull parameters, while an increase of terrain complexity resulted in an increase of discrepancy between the estimated Weibull distribution and the frequency of the observed wind speed data. In addition, the choice in bin interval greatly affected the accuracy of the graphical method while it did not depend on the accuracy of the modified maximum likelihood method. [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.

Purpose The purpose of this study is to select the most accurate and the most efficient method in estimating Weibull parameters at Agadir region in Morocco.Design/methodology/approach In this paper, Weibull distribution is used to model the wind speed in hourly time series format. Since several methods are used to adjust the Weibull distribution to the measured data, in reporting and analyzing the easiest and the most effective method, seven methods have been investigated, namely, the graphical method (GM), the maximum likelihood method (MLM), the empirical method of Justus (EMJ), the empirical method of Lysen (EML), the energy pattern factor method (EPFM), Mabchour’s method (MMab) and the method of moments (MM).Findings According to the statistical analysis tools (the coefficient of determination, root mean square error and chi-square test), it was found that for five months, the MLM presents more efficiency, and for four months, EMJ is ranked first and it is ranked second for February. To select only one method, the selected methods (MLM and EMJ) were compared by calculating the error in estimating the power density using Weibull distribution adjusted by those methods. The average error was found to be −0.51 and −4.56 per cent for MLM and EMJ, respectively.Originality/value This investigation is the first of its kind for the studied region. To estimate the available wind power at Agadir in Morocco, investors can directly use MLM to determine the Weibull parameters at this site. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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 paper presents results of an investigation carried out to study the fatigue life distribution of plain and steel fiber reinforced concrete with different fiber volume fractions and aspect ratios for various levels of the applied fatigue stress. An extensive experimental investigation was planned in which 210 flexural fatigue tests and 84 complementary static flexural tests were conducted on prismatic plain concrete and fibrous concrete specimens of 100×100×500 mm size under three point loading in an MTS closed loop testing machine. Two types of crimped-type flat steel fibers with 25×2.0×0.6 mm and 50×2.0×0.6 mm, corresponding to fiber aspect ratios of 20 and 40, respectively, were used at each of the fiber volume fractions of 0, 1.0, 1.5, and 2.0%. It has been observed that the probabilistic distribution of fatigue life can be approximately modeled using the two-parameter Weibull distribution with statistical correlation coefficient exceeding 0.90. The shape parameter of the Weibull distribution for the fatigue life of concrete is different for different stress levels and fiber aspect ratios. The present study indicates that the probabilistic distribution of fatigue life of concrete depends on the level of applied fatigue stress, fiber volume fraction, and the aspect ratio of fibers. The graphical method, the method of moments, and the method of maximum likelihood estimation have been used to obtain the distribution parameters of the Weibull distribution. These three methods are shown to yield similar values of distribution parameters for the present fatigue data. [ABSTRACT FROM AUTHOR]

The variations in impact strength of self-compacting concrete reinforced with recycled Carbon Fibre Reinforced Polymer (CFRP) Pieces were examined using Weibull reliability analysis. For this purpose, the experimental results of an earlier research were investigated statistically using the two parameter Weibull distribution. The shape and scale parameter of Weibull distribution function was determined from five statistical methods namely Least-Squares (LS) regression of Y on X, Least-Squares (LS) regression of X on Y, Empirical Method (EM), Energy Factor Pattern Method (EPM) and Graphical Method (GM). The Weibull parameters were used to describe the impact strengths (number of blows required to cause first crack and failure) in terms of reliability. Further, regression equations were developed between the impact strength and reliability of self-compacting concrete reinforced with recycled CFRP Pieces. In order to validate the developed linear regression equations, six reliable statistical indicators namely Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Deviation (MAD), Integral Absolute Error (IAE), Relative Root Mean Square Error (RRMSE) and Relative Percentage Error (RPE) have been used. Results suggested that the LS- X on Y, EM and EPM are more effective to estimate the Weibull parameters. The developed linear regressions equations which were validated by six statistical indicators show a good fit and higher accuracy. [ABSTRACT FROM AUTHOR]

Graphical techniques are recommended for critical applications because they allow for visual analysis and helpful understanding of the results, also for non-statisticians. However, 'graphical' estimation methods are often criticized because they are less efficient with respect to 'analytical' methods. This paper proposes a new general graphical method that leads to the best linear unbiased estimators of location-scale distribution parameters. Therefore, the reputation of graphical methods is raised and their strategic use is encouraged. An applicative example analyzes the earthquake magnitudes registered during the serious 1983-1984 bradyseismic crisis in Campi Flegrei, Italy. This graphical analysis will certainly work as a strategic reference picture to which the data, arising from the further bradyseismic crises expected in the next future, can be compared. [ABSTRACT FROM AUTHOR]

To install a wind energy conversion system to a region, the wind speed characteristics of that region must be identified. The two-parameter Weibull distribution is highly efficient in modeling wind speed characteristics. In this study, the wind speed data of 32 cities in three different regions of Turkey have been comparatively analysed to estimate Weibull distribution function parameters by the use of three wellknown methods (Graphical Method (GM), Maximum Likelihood Method (MLM), Justus Moment Method (JMM)) and three new parameter estimation methods (Energy Pattern Factor Method (EPFM), Wind Energy Intensification Method (WEIM), Power Density Method (PD)) which have been proposed in recent years. Three years of hourly wind speed data of the specified regions have been used. The performance metrics of these analyses have been compared using Wind Energy Error (WEE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). The results have shown that while the PD method has high model performance, the JMM is closely competitive with the MLM. Besides, the wind energy densities that were estimated by using actual data have been compared with the resulting Weibull distribution. It has been clear that the method that has the closest estimation to the actual values is the PD method. [ABSTRACT FROM AUTHOR]

The influence of three values of inoculation of the alternative culture of Bioyogur on the lactic acid fermentation kinetics during the incubation stage and on the acidity, flavor and texture development of a fermented milk from whole buffalo milk with an 8% sugar was studied. Defined the level of inoculation of the culture and that of flavoring by applying the Friedman test, the fermented milk was characterized in its compositional, sensory, microbiological and cell viability indicators of the probiotic. The shelf-life was determined by the graphical method using the Weibull distribution. It was concluded the possibility of obtaining from buffalo milk, 2.5% of Bioyogur 8% sugar, 0.15% orange emulsion, a product with adequate compositional, sensory and microbiological characteristics. The shelf life of the product packed in 400 mL polypropylene pots and stored at 4 °C was 18 days. The L acidophilus count was higher than the therapeutic minimum considered for probiotic products. [ABSTRACT FROM AUTHOR]