•IW distribution is used to model wind speed data.•MML methodology is used to estimate the distribution parameters.•Efficiencies of the LS, the ML and the MML estimators are compared.•Two stations ...located in north-west part of Turkey are investigated.
Weibull distribution is widely used for modeling the wind speed data in literature. However, in real life, the wind speed data may not always be modeled by using the Weibull distribution. In other words, it may not represent all wind speed characteristic encountered in nature. Therefore, the alternative distributions are used in such cases. In this study, the Inverse Weibull (IW) distribution is used to model the wind speed. First, the modified maximum likelihood (MML) estimators of the parameters of IW distribution are obtained. Then the efficiencies of the MML estimators are compared with the well-known maximum likelihood (ML) and the least squares (LS) estimators via Monte-Carlo simulation study. Simulation results show that the LS estimators are the least efficient among the others. Finally, Weibull and IW distributions are used for modeling the seasonal wind speed data sets obtained from the Turkish State Meteorological Service. It is shown that IW distribution based on the ML and the MML estimates of the parameters provides better modeling than the Weibull distribution based on the corresponding estimates in most of the cases. The suitability of these distributions is compared with respect to root mean square error (RMSE) and coefficient of determination (R2) criteria.
Based on the current EU environmental policy, wind power industry has been growing fast in recent years. Knowledge of wind characteristics helps to define site requirements, choose a proper turbine ...design and estimate profits from the wind energy production.
The paper describes and compares the techniques of available wind energy evaluation using Weibull distributions: two-parameter Weibull probability distribution, and three-parameter Weibull distribution. The two-parameter Weibull distribution is recognized as an appropriate model and the most widely used in the wind industry sector. In some cases, in which the probability of null wind is significant, the Weibull distribution cannot reveal good conformity for the low wind speed. In theory, it seems that the three-parameter Weibull distribution, which takes into account the frequency of null winds, may better represent wind ranges for the low wind speed.
In the paper, the available wind energy is calculated for three different turbine locations. The results show that for the higher probability of the null wind the three-parameter Weibull distribution gives better results comparing to the two-parameter Weibull distribution and can be proposed as an alternative to wind energy estimation technique. Additional analyses confirm the observation.
•Two probability density functions are correlated to the wind measurements.•Two-parameter Weibull distribution is not always adequate to evaluate wind power.•Three-parameter Weibull distribution fits better the sets of wind velocity data.•Two-parameter Weibull distribution can give higher values of energy production.
The accurate assessment of the potential wind energy at a define site is very important from economic point of view, measures cost effectiveness of the project and helps estimating future incomes, ...revenues. Knowledge of wind characteristics also facilitates a proper turbine design selection. There are different techniques for wind energy evaluation. The direct wind speed measurement is the most accurate method to determine wind conditions, but often the different wind speed frequency distributions are proposed. One of the most widely used distribution is Weibull distribution. The two-parameter Weibull distribution is recognized as an appropriate model and the most widely used in the wind industry sector. In some cases, in which the probability of null wind is significant, the Weibull distribution does not reveal good conformity for the low wind speed. In theory, it seems that the three-parameter Weibull distribution, which takes into account the frequency of null winds, may better represent wind ranges with high percentages of null wind speeds and may give better results. In the paper, the review of the literature is carried out on the application of two and three-parameter Weibull distribution in wind energy analyses and also focuses on the comparison of results received from different probability density functions, used in cited papers, with the frequency of 0–2m/s wind speed range in real data. For higher percentages of null wind speeds or the wind speed below 2m/s, the three-parameter Weibull model should have the advantage in relation to two-parameter Weibull distribution, gives more appropriate results and can be proposed as an alternative to wind energy estimation technique.
For the first time, the statistical distribution of Young’s modulus and of strain at break of ultra-high-molecular-weight polyethylene (UHMWPE) gel-cast highly oriented film threads have been ...investigated by employing the Weibull model. These have been produced by the multi-stage hot-zone drawing technique. It has been shown that the results of a large number of mechanical measurements for the two series of UHMWPE film threads drawn to an ultimate draw ratio (
λ
) of 120 from xerogels formed from 1.5% solutions of UHMWPE in decalin or paraffin oil (50 samples in each case) can be satisfactorily described in the framework of the standard Weibull distribution. The values of Weibull modulus and scale factor have been estimated for the two film threads series investigated. It has been found that the scatter in the experimental data depends on the solvent nature and the mechanical characteristic analysed.
Graphical abstract
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Highly porous ceramic scaffolds have been fabricated from a 70% SiO2–30% CaO glass powder using stereolithography and the lost-mould process combined with gel-casting. After sintering at 1200°C the ...glass crystallised to a structure of wollastonite and pseudowollastonite grains in a glassy matrix with a bulk porosity of 1.3%. All scaffolds had a simple cubic strut structure with an internal porosity of approximately 42% and internal pore dimensions in the range 300–600μm. The mean crushing strength of the scaffolds is in the range 10–25MPa with the largest pore sizes showing the weakest strengths. The variability of scaffold strengths has been characterised using Weibull statistics and each set of scaffolds showed a Weibull modulus of m≈3 independent of pore size. The equivalent strength of the struts within the porous ceramics was estimated to be in the range 40–80MPa using the models of the Gibson and Ashby. These strengths were found to scale with specimen size consistent with the Weibull modulus obtained from compression tests. Using a Weibull analysis, these strengths are shown to be in accordance with the strength of 3-point bend specimens of the bulk glass material fabricated using identical methods. The strength and Weibull modulus of these scaffolds are comparable to those reported for other porous ceramic scaffold materials of similar porosity made by different fabrication routes.
•Long-term wind measurements at five typical weather stations in Hong Kong are analyzed.•Wind characteristics and wind energy potential over typical terrain conditions are statistically assessed.•The ...measured wind speed data fit well with the Weibull distribution function.•Annual, seasonal and monthly variations of the Weibull parameters are presented.•Hilltops and offshore islands are identified as promising sites for wind energy development in Hong Kong.
The harvesting of renewable energy sources has become increasingly important to take account of the gradual decline of fossil fuel reserves and the environment degradation associated with the use of fossil fuels. Wind energy, as one of the most well-known renewable energy sources, has been extensively harnessed across the world. Nevertheless, the wind energy exploitation in Hong Kong is still rare.
Based on 6-year wind data recorded at five meteorological stations with different terrain conditions, this study presents a statistical analysis of the wind characteristics and wind energy potential at typical sites in Hong Kong by the assistance of Weibull distribution model. The variations of mean wind speed, as well as Weibull parameters, were highlighted on various timescales. Among all the sites, the annual Weibull scale parameter varied from 2.85m/s to 10.19m/s, and the range of the annual shape parameter was 1.65–1.99. The highest Weibull scale parameter was observed at a hilltop, whilst the lowest was found at an urban site. The monthly variation of wind power density was presented and discussed for each site. Hilltops and offshore islands demonstrated prominently greater wind power density than urban areas. It was thus indicated that hilltops and offshore islands are the most promising locations for wind energy exploitation in Hong Kong.
•Thespesia populnea fibers treated at 5% NaOH for 60 min gives optimal results.•Cellulose crystallinity of treated fibers increases from 48.17%–67.52%.•Optimally treated fibers are thermally stable ...up to 341.82 °C.•The consistency of tensile test results is validated with Weibull distribution model.•SEM & AFM analysis reveals that fiber surface turns rough after alkali treatment.
Natural fibers are emerging as best alternatives for synthetic materials in selective applications. These fibers may not have the required properties in its raw form and hence needs some alterations in its characteristics. Likely, this article reports enhancement in surface and structural properties of Thespesia populnea bark fiber treated with NaOH under various concentration and soaking period. Fibers treated with 5% NaOH for 60 min yields noteworthy mechanical strength (678.41 ± 48.91 MPa) owing to its relatively high cellulose fraction (76.42%). Fourier transform infrared spectra endorses the removal of non-cellulosic compounds and X-ray diffraction studies reveals 13.6% growth in the size of cellulose crystals on optimally treated fibers. Weibull distribution model statistically interprets the reliability of acquired tensile test results. Finally, microscopic examinations with scanning electron microscopy and atomic force microscopy explore that fiber surface turns rough after alkali treatment and makes it appropriate for reinforcement in polymer matrices.
Exponentiated additive Weibull distribution Ahmad, Abd EL-Baset A.; Ghazal, M.G.M.
Reliability engineering & system safety,
January 2020, 2020-01-00, 20200101, Volume:
193
Journal Article
Peer reviewed
•We propose a new distribution called exponentiated additive Weibull distribution.•It is very flexible for modeling the bathtub-shaped hazard rate data.•Many properties of the exponentiated additive ...Weibull distribution are discussed.•It provides a better fit for modeling real data sets than its sub-models.•The new distribution is applicable to reliability data analysis.
Additive Weibull distribution combining two Weibull distributions was proposed by Xie and Lai 1. In this paper, we propose a generalization of this distribution which is called exponentiated additive Weibull distribution. It includes a set of exponentiated distributions such as modified generalized linear failure rate, exponentiated Weibull and exponentiated exponential distributions in addition to some widely well known distributions such as additive Weibull, modified Weibull distributions, among others. It represents a flexible model for reliability analysis such as reliability engineering, firmware reliability, decision-making reliability, and cost analysis. Some statistical properties of the new distribution are presented. The estimation of five parameters by maximum likelihood is studied and the observed information matrix is computed. Finally, three real data sets are used to compare the proposed distribution to five of its sub-models. The results showed that the new distribution provides a better fit than its sub-models.
The statistical characteristics of wind speed data recorded at nine buoys, located in Ionian and Aegean Sea (Eastern Mediterranean) are analyzed in this paper, in order to present a more accurate ...method for estimation of wind speed characteristics, according to the suitability of the probability distribution functions (pdf). This article has focussed on wind regimes that present nearly zero percentages of null wind speeds. The selected distributions for examination are the typical two-parameter Weibull wind speed distribution (W-pdf) and the two-component mixture Weibull distribution (WW-pdf), involving five parameters (two shape parameters, two scale parameters, and one proportionality parameter).
Suitable software, based on the maximum likelihood method, is used in order to estimate the aforementioned two-parameters of the typical W-pdf and the five parameters of the mixed WW-pdf. The suitability of the aforementioned distributions is judged from the coefficient of determination (
R
2) and the fit standard error (
RMSE) tests, which had been carried out between each one of the theoretical distributions and the corresponding experimental cumulative frequencies of the nine selected sites. From these tests it is clear that, in most cases (six experimental stations - having either unimodal or bimodal frequency distributions), mixed-Weibull distribution provides the highest degree of fit. In the other three cases, the mixing weight
p of the two-component mixed Weibull density function equals to zero (
p
=
0), so the mixed-Weibull distribution is been transformed to the typical Simple-Weibull distribution.
Hence, the general conclusion is that the aforementioned mixture of two Weibull distributions is more suitable for the description of such wind conditions and could offer less relative errors in determining the annual mean wind power density.
•Offshore wind characteristics and wind energy potential in Hong Kong are assessed.•The Weibull distribution model gives an adequate representation of the actual wind data.•The yearly, seasonal, ...monthly and diurnal variations of various wind characteristics are investigated.•The southeastern waters are identified as the most promising site for offshore wind farm development in Hong Kong.
It has been globally recognized that the harvesting of renewable energy is of considerable importance for the achievement of sustainable development. As for Hong Kong, one of the most densely populated cities, the shortage of indigenous fossil sources has inevitably resulted in excessive dependence on external energy sources. Nevertheless, in consideration of the reduction of fossil fuel reserves, as well as the impact on the environment of fossil fuel uses, the exploration of usable renewable energy sources becomes increasingly important for Hong Kong‘s long-term development. Based on 6-year wind observations from three meteorological stations at three islands in Hong Kong, this study provides a statistical assessment of the wind characteristics and wind energy potential at offshore locations surrounding Hong Kong. The Weibull distribution function was applied to estimate the Weibull parameters which can be used to facilitate the evaluation of offshore wind energy potential. The variation of the mean wind speed, the Weibull parameters and the wind power density were established under various timescales. Significant yearly, seasonal and monthly variations of the Weibull parameters were observed, while the diurnal variation was relatively small. The veracity of the Weibull distribution model to represent offshore wind data was examined, and it was shown that the Weibull model gave an adequate description of the frequencies of actual wind data. Finally, the total wind power capacities at the three potential offshore wind farm locations were derived, which indicated that the Southeastern waters are the most promising locations for offshore wind farm development in Hong Kong.
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