Estimation of Weibull Distribution Parameters for Wind Speed Characteristics Using Neural Network Algorithm

Harvesting the power coming from the wind provides a green andenvironmentally friendly approach to producing electricity. To facilitate theongoing advancement in wind energy applications, deep knowledge aboutwind regime behavior is essential. Wind speed is typically characterized bya statistical distribution, and the two-parameters Weibull distribution hasshown its ability to represent wind speeds worldwide. Estimation of Weibullparameters, namely scale (c) and shape (k) parameters, is vital to describethe observed wind speeds data accurately. Yet, it is still a challenging task.Several numerical estimation approaches have been used by researchers toobtain c and k. However, utilizing such methods to characterize wind speedsmay lead to unsatisfactory accuracy. Therefore, this study aims to investigatethe performance of the metaheuristic optimization algorithm, Neural NetworkAlgorithm (NNA), in obtaining Weibull parameters and comparing itsperformance with five numerical estimation approaches. In carrying out thestudy, the wind characteristics of three sites in Saudi Arabia, namely HaferAl Batin, Riyadh, and Sharurah, are analyzed. Results exhibit that NNA hashigh accuracy fitting results compared to the numerical estimation methods.The NNA demonstrates its efficiency in optimizing Weibull parameters at allthe considered sites with correlations exceeding 98.54.

Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution

The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

A Statistical Analysis of Wind Speed and Power Density Based on Weibull and Rayleigh Models of Jumla, Nepal

In the present study, wind speed data of Jumla, Nepal have been statistically analyzed. For this purpose, the daily averaged wind speed data for 10 year period (2004-2014: 2012 excluded) provided by Department of Hydrology and Meteorology (DHM) was analyzed to estimate wind power density. Wind speed as high as 18 m/s was recorded at height of 10 m. Annual mean wind speed was ascertained to be decreasing from 7.35 m/s in 2004 to 5.13 m/s in 2014 as a consequence of Global Climate Change. This is a subject of concern looking at government’s plan to harness wind energy. Monthly wind speed plot shows that the fastest wind speed is generally in month of June (Monsoon Season) and slowest in December/January (Winter Season). Results presented Weibull distribution to fit measured probability distribution better than the Rayleigh distribution for whole years in High altitude region of Nepal. Average value of wind power density based on mean and root mean cube seed approaches were 131.31 W/m2/year and 184.93 W/m2/year respectively indicating that Jumla stands in class III. Weibull distribution shows a good approximation for estimation of power density with maximum error of 3.68% when root mean cube speed is taken as reference.

Resource Assessment of Wind Energy Potential of Mokha in Yemen with Weibull Speed

The increasing use of fossil fuels has a significant impact on the environment and ecosystem,which increases the rate of pollution.Given the high potential of renewable energy sources in Yemen and other Arabic countries,and the absence of similar studies in the region.This study aims to examine the potential of wind energy in Mokha region.This was done by analyzing and evaluating wind properties,determining available energy density,calculating wind energy extracted at different altitudes,and then computing the capacity factor for a few wind turbines and determining the best.Weibull speed was verified as the closest to the average actual wind speed using the cube root,as this was verified using 3 criteria for performance analysis methods(R^(2)=0.9984,RMSE=0.0632,COE=1.028).The wind rose scheme was used to determine the appropriate direction for directing the wind turbines,the southerly direction was appropriate,as the winds blow from this direction for 227 days per year,and the average southerly wind velocity is 5.27 m/s at an altitude of 3 m.The turbine selected in this study has a tower height of 100m and a rated power of 3.45 MW.The capacitance factor was calculated for the three classes of wind turbines classified by the International Electrotechnical Commission(IEC)and compared,and the turbine of the first class was approved,and it is suitable for the study site,as it resists storms more than others.The daily and annual capacity of a single,first-class turbine has been assessed to meet the needs of 1,447 housing units in Mokha region.The amount of energy that could be supplied to each dwelling was around 19 kWh per day,which was adequate to power the basic loads in the home.

Wind Speed and Power Density Analysis for Sustainable Energy in Batouri, East Region of Cameroon

This paper develops the modeling of wind speed by Weibull distribution in the intention to evaluate wind energy potential and help for designing small wind energy plant in Batouri in Cameroon. The Weibull distribution model was developed using wind speed data collected from a metrological station at the small Airport of Batouri. Four numerical methods (Moment method, Graphical method, Empirical method and Energy pattern factor method) were used to estimate weibull parameters K and C. The application of these four methods is effective using a sample wind speed data set. With some statistical analysis, a comparison of the accuracy of each method is also performed. The study helps to determine that Energy pattern factor method is the most effective (K = 3.8262 and C = 2.4659).

Extreme Values of Wind Speed over the Kara Sea Based on the ERA5 Dataset

Extreme values of wind speed were studied based on the highly detailed ERA5 dataset covering the central part of the Kara Sea. Cases in which the ice coverage of the cells exceeded 15% were filtered. Our study shows that the wind speed extrema obtained from station observations, as well as from modelling results in the framework of mesoscale models, can be divided into two groups according to their probability distribution laws. One group is specifically designated as black swans, with the other referred to as dragons (or dragon-kings). In this study we determined that the data of ERA5 accurately described the swans, but did not fully reproduce extrema related to the dragons;these extrema were identified only in half of ERA5 grid points. Weibull probability distribution function (PDF) parameters were identified in only a quarter of the pixels. The parameters were connected almost deterministically. This converted the Weibull function into a one-parameter dependence. It was not clear whether this uniqueness was a consequence of the features of the calculation algorithm used in ERA5, or whether it was a consequence of a relatively small area being considered, which had the same wind regime. Extremes of wind speed arise as mesoscale features and are associated with hydrodynamic features of the wind flow. If the flow was non-geostrophic and if its trajectory had a substantial curvature, then the extreme velocities were distributed according to a rule similar to the Weibull law.

Urban Wind Speed Analysis in Global Climate Change Perspective: <i>Karachi as a Case Study</i>

It is now well known that coastal urban local climate has been showing changing pattern due to global climate change. This communication attempts to explore fluctuating pattern of urban average monthly wind speed during past 50 years (1961-2010). It shows peculiar results taking Karachi (24?53'N, 67?00'E), a coastal mega-city of Pakistan, as a case study. Mann-Kendall trend test shows that March, April and October and both summer and winter seasons show positive trends for the average monthly wind speed during the whole study period (1961-2010). For the earlier 25 years data, it has been found that January, March, May, August, November and December and annual wind speed data have shown the negative trends. Only summer season has shown the positive trend for the wind speed. Similarly, for the most recent 25 years data it has been found that January, February, March, April, May, June, October, November and December and annual and both summer and winter wind speed data have shown the positive trends showing some degree of change in wind speed pattern. Probabilistic analysis reveals that average monthly wind speed data sets follow lognormal, logistic, largest extreme value, and Weibull (two-and three-parameters) probability distributions. Change point analysis has also confirmed the change in the pattern of observed average monthly wind speed data near 1992. The analysis performed reveals the effect of global warming on the local urban wind speed which appears to be temporal non-stationary.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

Multi-hazard joint probability distribution model for wind speed,wind direction and rain intensity

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures.However,most existing studies ignored the dependence structure between them,as well as the effect of wind direction.From the dimension of the engineering sector,this paper introduces the vine copula to model the joint probability distribution(JPD)of wind speed,wind direction and rain intensity based on the field data in Yangjiang,China during 1971–2020.First,the profiles of wind and rain in the studied area are statistically analyzed,and the original rainfall amounts are converted into short-term rain intensity.Then,the marginal distributions of individual variables and their pairwise dependence structures are built,followed by the development of the trivariate joint distribution model.The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed,wind direction and rain intensity.Meanwhile,the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction,thus the effect of wind direction cannot be neglected.The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

Poisson-Gumbel Model for Wind Speed Threshold Estimation of Maximum Wind Speed

Poisson-Gumbel joint distribution model uses maximum wind speed corresponding to multiple typhoons to construct sample sequence.Thresholds are usually used to filter sample sequences to make them more consistent with Poisson distribution.However,few studies have discussed the threshold setting and its impact on Poisson-Gumbel joint distribution model.In this study,a sample sequence based on the data of Qinzhou meteorological station from 2005 to 2018 were constructed.We set 0%,5%,10%,20%and 30%gradient thresholds.Then,we analyzed the influence of threshold change on the calculation results of maximum wind speed in different return periods.The results showed that:(1)When the threshold increases,the maximum wind speed of each return period will decrease gradually.This indicates that the length of the sample series may have a positive effect on the return period wind speed calculation in Gumbel and Poisson-Gumbel methods.Although the augment of the threshold increases the average value of the maximum wind speed of the sample sequence,it shortens the length of the sample sequence,resulting in a lower calculated value of the maximum wind speed.However,this deviation is not large.Taking the common 10%threshold as an example,the maximum wind speed calculation deviation in the 50 a return period is about 1.9%;(2)Theoretically,the threshold is set to make the sample sequence more consistent with Poisson distribution,but this example showed that the effect is worth further discussion.Although the overall trend showed that the increase of the threshold can makeχ2 decrease,the correlation coefficient of linear fitting was only 0.182.Taking Qinzhou meteorological station data as an example,theχ2 of 20%threshold was as high as 6.35,meaning that the selected sample sequence was not ideal.

Analysis of the Probability Model of Wind Load on the Offshore Wind Turbine

According to the actual measurement data, probability models of horizontal wind load were obtained based on wind velocity statistic and power spectral density function of fluctuating wind velocity through stochastic sampling and using spectrum analysis method. Through the comparison of two models, probability models of horizontal wind load based on probability models of fluctuating wind velocity were obtained by revising the mean and variance of fluctuating wind velocity. Results show that the variance takes lower value when the power spectral density function of fluctuating wind velocity is used to obtain the probability model of horizontal wind load. The quadratic term of fluctuating wind velocity takes a small contribution value in total wind load with almost no contribution to the model of horizontal wind load. It is convenient for practical engineering to obtain the models of horizontal wind load by using probability models of fluctuating wind velocity.

一种相关Weibull杂波背景中的目标检测方法

为提高雷达在非高斯杂波背景下的检测性能,基于球不变随机过程模型和似然比检测准则,给出了一种相关W e ibu ll分布杂波背景中目标的检测方法。首先从理论上导出了基于球不变随机过程的W e ibu ll分布模型,然后在似然比意义下给出了W e ibu ll分布杂波背景下的检验统计量。

基于三参数Weibull分布的安徽省年最大风速均一性检验

以安徽省56个国家级气象站1980-2018年年最大风速序列为研究对象,采用基于三参数Weibull分布的变点检验方法对年最大风速序列均一性进行检验,以郎溪站数据为例,给出了检验和分析的具体过程,最后将该方法检验结果与PMFT法、SNHT法检验结果进行了对比分析。结果表明:56个站点的年最大风速序列均通过Weibull分布检验,而通过正态分布检验的年最大风速序列只有45个,表明年最大风速序列更符合Weibull分布;Weibull法检测出的18个非均一点中有15个得到印证,检验准确率为83.3%,PMFT法检测出的4个非均一点均由迁站造成,检验准确率为100%,SNHT检测出的20个非均一点中有15个得到印证,检验准确率为75%。造成序列非均一的主要原因是台站迁移、仪器换型、仪器高度调整和探测环境变化等;综合比较发现,PMFT法对年最大风速序列非均一点的敏感程度不如Weibull和SNHT,而SNHT法对待检序列要求较高,且检验准确率不及Weibull法,表明Weibull方法在年最大风速序列的均一性检验中更具有优势。

基于Nakagami分布的风速概率分布拟合研究

准确拟合风速概率分布对估算潜在风场所蕴含的风能具有重要作用。引入二参数Nakagami分布对美国西部涵盖沿海、海岛和内陆的八个站点风速数据进行拟合,并对比瑞丽分布、伽马分布、威布尔分布、对数正态分布、广义极值分布以及JohnsonSB分布,使用决定系数、均方根误差、误差平方和以及Kolmogorov-Smirnov四个拟合指标进行校验。与参数较少的瑞丽分布、伽马分布、对数正态分布以及威布尔分布精度进行比较,Nakagami分布在八个站点的四个拟合指标均值中取得最优的拟合精度。与三参数的广义极值分布以及四参数JohnsonSB分布进行拟合对比,Nakagami分布在四个站点获得最优精度。根据风速数据的统计结果,当站点的平均风速低于3 m/s时,Nakagami比其它分布获得了更高的拟合精度。综合考虑Nakagami简便的计算及较高的拟合精度,其在拟合风速概率分布领域更具优势。

矩函数在风速Weibull分布参数估计中的应用

服从Weibull分布的随机变量的各阶矩仍然服从Weibull分布，根据这一统计学性质，采用矩函数法估计WeibuU分布参数。分别基于风速原点矩和风速中心矩对风速的Weibull分布参数k、c进行了估计，并给出了参数估计公式。根据所提方法解出风速概率分布后，可以根据Weibull分布计算风能特征指标。以河西某风电场为算例．分别以所提方法、均值和方差估计法对其进行Weibull分布参数估计和风能特征指标计算．同时给出了直接由风速数据统计出的各项特征指标进行对比，结果表明所提方法计算结果的整体误差较小．精度明显高于均值和方差估计法。

高速铁路无砟轨道混凝土疲劳性能试验研究

结合无砟轨道混凝土荷载状态,通过Weibull分布函数探讨了混凝土疲劳性能与疲劳试验参数间的联系。从结果看:混凝土疲劳性能在弯曲疲劳加载时有更显著变化,且疲劳荷载下无砟轨道更易出现疲劳破坏;混凝土疲劳寿命在越高加载频率下有越大离散程度,在5—15 Hz范围内,加载频率对混凝土疲劳寿命的影响较小;混凝土疲劳寿命在0.6应力水平时有最小离散程度;混凝土疲劳寿命和离散程度在等幅正弦波加载时较小。综合试验效率、结果精度、加载幅值等考虑,建议以“弯曲疲劳、等幅正弦波、f=20 Hz、S=0.6、λ=0.1”作为无砟轨道混凝土疲劳试验制度。

基于三种不同分布函数的西藏东部地区极大风速估算研究

基于西藏东部地区9个站点40~67 a的长期观测数据(最早自1953年起)与61个站点2014年后的短期观测数据,利用三种不同概率密度分布函数,估算西藏东部地区极大风速并研究其时空分布情况。结果表明:长期来看,西藏东部地区位于西风带与季风共同影响区域,主要以西北风(频率达27%)为主,99%的样本风速不超过9.0 m/s,风速超过15.0 m/s的仅占万分之1.6;对实测极大风速分别进行极值Ⅰ型、极值Ⅱ型和极值Ⅲ型分布函数拟合,发现不同时期数据拟合后的参数无显著差异;利用最小二乘法进行检验订正,可使估算的极大风速的平均绝对偏差和均方根误差大幅降低,观测数据时间序列越长整体估算效果越好;基于极值Ⅱ型函数估算的西藏东部地区极大风速分布能更好地表征该地区实际极大风速的空间分布,极大风速变化范围为13.2~30.9 m/s。

基于风速Weibull分布的电力系统备用容量优化模型

为了解决风电功率的随机波动和预测精度不高对风电并网的影响,引入风速Weibull概率分布函数和风功率概率分布函数,建立了基于风速概率分布的长期经济调度模型。该模型考虑长期调度和风电功率概率分布,在计算备用时不需考虑风电功率的时序性,这样使得模型得到了简化。最后通过算例仿真,讨论了该模型对系统备用容量和风电场成本的影响,同时验证了该模型的可行性。