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.

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.

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.

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.

A Study of Wind Statistics Through Auto-Regressive and Moving-Average (ARMA) Modeling

Statistical properties of winds near the Taichung Harbour are investigated. The 26 years'incomplete data of wind speeds, measured on an hourly basis, are used as reference. The possibility of imputation using simulated results of the Auto-Regressive (AR), Moving-Average (MA), and/ or Auto-Regressive and Moving-Average (ARMA) models is studied. Predictions of the 25-year extreme wind speeds based upon the augmented data are compared with the original series. Based upon the results, predictions of the 50- and 100-year extreme wind speeds are then made.

The Trend of Changes in Surface Wind in the Indian Ocean, in the Period from 1981 to 2015, Using Reanalysis Data, NCEP/NCAR

Knowing the pattern of surface winds on the seas and oceans and how it changes over time is of great importance. In this research, the monthly surface wind fields on the Indian Ocean have been studied and analyzed for a 35-year period (1981-2015), using NCEP/NCAR data reanalysis. The results show that transition from cold to warm pattern happens in May and that the summer monsoon pattern begins in June and continues until August. The wind speed pattern tends to the winter monsoon from November on. The maximum average wind speed in June is 13 m/s and its minimum is 2 m/s in October. Direction of prevailing winds is the southwest in the summer. The highest wind speed happens in the latitude of 10 - 15 degrees. Analysis of the wind distribution shows that the wind speed of 2 - 5 m/s happens in about 60% of the cases. There is probability of blowing 0.5 - 4 m/s wind for all months;but this probability is higher in the autumn (October and November) than that in the summer (July and August). Probability of the monthly over 5 m/s winds shows a definitely opposite distribution;that is, wind speed in July and August is higher than that in October. A long-term survey on the speed of surface water wind and sea surface temperature shows an opposite changing trend in wind speed and sea surface temperature during a 55-year statistical period. Wind speed reduced, while the sea surface temperature was increasing. The wind speed gradient in the upper levels of atmosphere graph has been increasing;this phenomenon confirms the effects of global warming and ocean warming on the monsoon system patterns in the Indian Ocean. Keywords

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.

Load distributions of some classic DHTs

The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.

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.

Seismic loss assessment of RC high-rise buildings designed according to Eurocode 8

A probabilistic seismic loss assessment of RC high-rise(RCHR)buildings designed according to Eurocode 8 and located in the Southern Euro-Mediterranean zone is presented herein.The loss assessment methodology is based on a comprehensive simulation approach which takes into account ground motion(GM)uncertainty,and the random effects in seismic demand,as well as in predicting the damage states(DSs).The methodology is implemented on three RCHR buildings of 20-story,30-story and 40-story with a core wall structural system.The loss functions described by a cumulative lognormal probability distribution are obtained for two intensity levels for a large set of simulations(NLTHAs)based on 60 GM records with a wide range of magnitude(M),distance to source(R)and different site soil conditions(SS).The losses expressed in percent of building replacement cost for RCHR buildings are obtained.In the estimation of losses,both structural(S)and nonstructural(NS)damage for four DSs are considered.The effect of different GM characteristics(M,R and SS)on the obtained losses are investigated.Finally,the estimated performance of the RCHR buildings are checked to ensure that they fulfill limit state requirements according to Eurocode 8.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals

The study of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using trajectory distances of the reconstructed attractors from solid concentration signals collected from a 76 mm internal diameters and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m2s solids flux. Spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3 together with 70% to 80% humid air was used. Solid concentration data were analyzed using codes prepared in FORTRAN 2008 to get trajectories of the reconstructed attractors and their distances apart. Trajectory distances were found to increase from the centre towards the wall indicating the expansion of the attractor. The probability density function (PDF) of the trajectory distances changes from single peak at the centre to multiple peaked profiles in the wall region. Multiple peaked profiles indicate multifractal flow behaviours. Cumulative distribution functions (CDF) of the trajectory distances changes from single S-shaped at the centre to multiple S-shaped profiles in some locations of the wall region indicating multifractal flow behaviours. The PDF distribution of these distances at the entrance section and in the wall region forms different types of statistical distributions showing differences in gas-solid flow structures in various spatial locations of the wall region and the entrance sections. Most of the distributions at the centre fall under the Gumbel max distribution for all flow development sections of the riser, especially at air velocities of 5.5 m/s and 8 m/s showing uniform flow structures. Further, it was found that increase of the number of the phase space reconstruction embedding dimension increases the trajectory distances between the state vectors leading to the expansion of the attractor.

基于爬坡方向状态划分的MCMC风电功率序列建模方法

由于电网弃风或者灵活性资源不足往往发生在风电大量发电时,故提高风电时间序列模型对大出力状态的建模-抽样精度,有助于后续的电网灵活性资源相关研究。在传统马尔科夫链蒙特卡洛(MCMC)法和持续与波动蒙特卡罗(PV-MC)法基础上,提出一种考虑爬坡方向状态划分的改进方法,以更准确地描述风电出力连续爬坡至大出力状态的过程。该方法以累积分布概率而不是以功率大小均匀划分状态区间,使各个状态区间的样本分布更均匀,提高了风电时间序列模型对大出力状态的建模-抽样精度。通过算例比较所提方法、MCMC法及PV-MC法生成风电功率序列与历史数据的分布特性和统计特性指标,结果表明,所提方法的拟合度较好,且能够有效解决MCMC法和PV-MC法高出力、样本偏少的问题。

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。

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。

蒙特卡洛模拟法在计算风场超越概率发电量中的应用

[目的]风场不确定性给风场发电量带来呈概率的分布,对不确定性因素进行科学并客观地评估是计算风场超越概率发电量的重要前提。目前行业普遍采用折减系数的办法来预估发电量,达到控制风险的目的,或者对不确定性因素按概率取值计算,以评估风场的超越概率发电量。针对这种简单的折减或者忽视不确定因素的本质计算风场超越概率发电量的做法,文章旨在提出一种既遵循不确定因素的本质还能科学地计算风场超越概率发电量计算方法。[方法]文章采用蒙特卡洛模拟法构建不确定性因素的正态概率分布模型,对不确定性进行模拟,并得出统计结果。通过借助风速-发电量敏感因子,确定风场发电量的不确定性程度,最终计算风场超越概率发电量。[结果]蒙特卡洛进行多次随机模拟结果是服从正态分布的具体函数。文章举例模拟了不确定性因素标准差分别为平均值的12.0%、14.0%、16.0%3种情况的结果,特定置信区间95%风速不确定性程度的分布范围分别为7.08%~8.56%、6.97%~8.71%、6.88%~8.84%,发电量总不确定性程度分布范围分别为13.36%~15.92%、13.17%~16.18%、13.01%~16.41%,超越概率发电量分布范围分别为96.06~101.52 GWh、95.50~101.92 GWh、95.01~102.26 GWh。[结论]采用超越概率发电量作为评估风场投资风险依据,有助于在正确、可靠的基础上进行决策,运用蒙特卡洛模拟方法体现了科学性和高效性,得到的结果具有统计意义。

基于机组与测风塔数据的机舱风速传递函数关系建模方法比对研究

基于某风电场机组SCADA数据和测风塔实测数据构建机舱风速传递函数(NTF)。选择线性方法(标准方法、VR、VS、SS)、由风速分布特点衍生的曲线方法(WBL)、时间矩阵方法(MTS),共计三类方法,6种函数模型,探究不同函数模型的拟合效果,并将拟合后的结果数据与激光雷达实测数据进行对比验证,同时与国际电工委员会(IEC)提出的方法进行比对。验算结果表明:线性分析模型中,相比于IEC标准推荐的函数模型,VR、SS函数模型从总体数据出发,考虑到风速散点图中的偏离点,其拟合效果会较为优异;对于WBL模型,基于风速风特性角度,其函数分布特点能够涵盖住样本散点图中的偏离数据点。因此在实际工程项目中,可考虑优先应用WBL模型进行仿真计算,线性模型中推荐VR、SS函数模型。

风电功率波动特性的概率分布研究

波动性是风电功率的固有特性，如何定量地描述风电功率的波动性尚缺乏有效方法。基于大量实测数据的分析，发现可以采用带移位因子与伸缩系数的t分布（flocation-scale）描述风电功率波动特性的概率分布。分析表明：风电功率的min级分量约占风电场装机容量的2％～5％：多个风电场输出叠加在一起后可以有效减小min级分量的比例：风机类型对风电波动特性的影响很小，而风电场当前风电出力则对风电波动特性几乎无影响。带移位因子与伸缩系数的t分布还适合于描述风电场相邻时间间隔平均功率变化的概率分布，时间间隔加长后，由于风速相关性减弱，相邻时段平均功率的波动特性增强。