Modified Joint Distribution of Wave Heights and Periods

The modified versions of the linear theoretical model of Longuet-Higgins （1983） are derived in this work and also compared with the laboratory experiments carried out in MAR1NTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties ＆these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.

Long-Term Joint Distribution of One-Tenth Large (or Significant) Wave Height with Average Period

In this paper, by using the wave data from a few oceanographic observation stations in the coastal zone of the Yellow Sea, the East China Sea and the South China Sea, the long-term joint distribution of the one-tenth large (or significant) wave height with average period is studied. The statistical data demonstrate that the long- term distribution of the one- tenth wave height or average period fits the log-normal distribution, thus the joint distribution also fits the two-dimensional log-normal distribution. Then the conditional probability distribution of the average period is derived, and the range as well as the mode of the average wave period corresponding to a certain return period of wave height can be calculated easily.

Joint Distribution of Wave Periods and Rate of Change of Wave Surface Elevation

The rate of change of wave surface elevation is of much importance in ocean engineering, especially for the determination of the limitation of wave breaking. This paper gives a kind of joint distribution of wave periods and the rate of change of wave surface elevation by means of calculation of the two-order to four-order moment of the frequency spectrum based on the linear wave theory. For the first time, the distribution density function of wave periods determined by peaks is provided, and the conclusion is drawn that the rate of change of wave surface elevation obeys the Rayleigh distribution.

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme wave height.

RB-DEM Modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

Generative Adversarial Networks with Joint Distribution Moment Matching

Generative adversarial networks(GANs)have shown impressive power in the field of machine learning.Traditional GANs have focused on unsupervised learning tasks.In recent years,conditional GANs that can generate data with labels have been proposed in semi-supervised learning and have achieved better image quality than traditional GANs.Conditional GANs,however,generally only minimize the difference between marginal distributions of real and generated data,neglecting the difference with respect to each class of the data.To address this challenge,we propose the GAN with joint distribution moment matching(JDMM-GAN)for matching the joint distribution based on maximum mean discrepancy,which minimizes the differences of both the marginal and conditional distributions.The learning procedure is iteratively conducted by the stochastic gradient descent and back-propagation.We evaluate JDMM-GAN on several benchmark datasets,including MNIST,CIFAR-10 and the Extended Yale Face.Compared with the state-of-the-art GANs,JDMM-GAN generates more realistic images and achieves the best inception score for CIFAR-10 dataset.

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.

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

Parametric message passing-based relative navigation in joint tactical information distribution system

Relative navigation is a key feature in the joint tactical information distribution system（JTIDS）.A parametric message passing algorithm based on factor graph is proposed to perform relative navigation in JTIDS.First of all,the joint posterior distribution of all the terminals＇ positions is represented by factor graph.Because of the nonlinearity between the positions and time-of-arrival（TOA） measurement,messages cannot be obtained in closed forms by directly using the sum-product algorithm on factor graph.To this end,the Euclidean norm is approximated by Taylor expansion.Then,all the messages on the factor graph can be derived in Gaussian forms,which enables the terminals to transmit means and covariances.Finally,the impact of major error sources on the navigation performance are evaluated by Monte Carlo simulations,e.g.,range measurement noise,priors of position uncertainty and velocity noise.Results show that the proposed algorithm outperforms the extended Kalman filter and cooperative extended Kalman filter in both static and mobile scenarios of the JTIDS.

Research on Coordinated Development and Optimization of Distribution Networks at All Levels in Distributed Power Energy Engineering

The uncertainty of distributed generation energy has dramatically challenged the coordinated development of distribution networks at all levels.This paper focuses on the multi-time-scale regulation model of distributed generation energy under normal conditions.The simulation results of the example verify the self-optimization characteristics and the effectiveness of real-time dispatching of the distribution network control technology at all levels under multiple time scales.

基于分布鲁棒联合机会约束的光储充电站滚动优化调控模型

随着电动汽车的普及和清洁能源装机容量的日益增加,光储充电站展现出广阔的应用前景。针对电动汽车随机接入影响下光储充电站功率难以精准调控的问题,提出基于分布鲁棒联合机会约束(DRJCC)的光储充电站滚动优化调控模型。将基于混合整数规划(MIP)的精确DRJCC模型、基于CVaR-Slim凸松弛的DRJCC模型、基于Bonferroni不等式的DRJCC模型进行对比,通过算例分析验证了所提优化调控模型的有效性。算例分析表明,所提基于CVaR-Slim凸松弛的DRJCC模型能够同时满足更多电动汽车的充电需求。

计及多重不确定性的规模化电动汽车接入配电网调度方法

规模日益增长的电动汽车和可再生能源带来的不确定性给配电网的安全运营带来了严峻挑战。为综合考虑多重不确定性、平衡运营成本与系统可靠性,首先,提出一种基于分布鲁棒联合机会约束的电动汽车-配电网充放电调度模型。该模型将节点电压、支路功率、备用需求等通过联合机会约束建模,可以直观地管理系统整体的可靠性。然后,为求解该模型,基于最优Bonferroni近似方法将联合机会约束问题转化为混合整数二次规划模型,其中,风险等级也被视为决策变量。随后,在不同电力系统上验证了所提模型的有效性和可扩展性。结果表明,所提模型克服了经典的随机优化和鲁棒优化存在的问题,能够有效平衡成本和可靠性,计算效率高、可扩展性好,较Bonferroni近似方法降低约6.5%的成本。

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

考虑内–外生双重不确定性的风储系统联合规划方法

风电场配置储能设备提供了良好的并网特性,但传统风储联合规划中,仅考虑不受决策结果影响的外生不确定性,受决策影响的内生不确定性被忽视,无法给出兼具经济性和鲁棒性的规划方案。为此,首先从不确定优化理论的角度梳理风储联合规划的模型演化路径,给出对应优化模型的拓扑表示。引入随机过程中的鞅理论,针对不确定性的外生与内生问题进行严格数学定义加以区分,并采用散度对风储联合规划中的内生与外生不确定性进行数学建模,同时设计参考分布修正过程使内生不确定性的参考分布逼近真实分布。构建改进分布鲁棒优化模型,设计对应的求解流程。最后,以改进IEEE 30节点系统和中国蒙西某区域电网验证所提模型的有效性和通用性,分析储能配置与内生不确定性间的相互影响,为该类规划问题提供先验信息支撑。

考虑不确定性物理边界的灵活爬坡备用分布鲁棒经济调度

面对新能源不确定性的影响,需要充分挖掘电力系统的灵活调节能力。为此,提出了一种基于数据驱动分布鲁棒机会约束的灵活爬坡备用经济调度模型。考虑新能源不确定性功率波动的物理边界,利用Wasserstein距离构建模糊集,从而建立更加准确的不确定性模型。采用联合机会约束控制第二阶段安全越限风险,在保证安全鲁棒性的同时,避免过于保守的决策结果。基于仿射决策规则和条件风险价值理论,将两阶段分布鲁棒问题近似为线性模型,从而实现高效求解。以改进的IEEE 9节点系统为算例验证所提方法的有效性,探究了训练样本量对结果的影响,并将所提方法与鲁棒优化方法和随机优化方法进行对比。

考虑光伏不确定性和时序相关性的分布鲁棒光储协同优化配置方法

随着“碳达峰,碳中和”双碳目标的提出,大量强随机性的光伏将接入配电网,提高光伏的消纳能力和降低弃光率成为了新的挑战。此外,储能系统在平抑光伏随机波动性有重要作用。针对光伏接入配电网的消纳能力评估问题,考虑光伏出力的不确定性和时序相关性,提出一种以光伏有效消纳能力为目标的光储协同分布鲁棒优化配置方法,并将光伏电站和储能装置的选址和定容同时作为决策变量。首先以历史数据驱动统计出考虑时序相关性的光伏出力的参考联合概率分布,基于Jensen-Shannon散度距离构建模糊集合,并采用二阶锥等技术将模型转化为混合整数凸规划模型以加速求解,然后通过列与约束生成(CCG)算法求解光储联合配置方案。最后,以某个实际180节点配电网为算例进行仿真计算,验证了所提方法的有效性。

Diversity of beetle species and functional traits along gradients of deadwood suggests weak environmental filtering

Background: Gradients in local environmental characteristics may favour the abundance of species with particular traits, while other species decline, or favour species with different traits at the same time, without an increase in average species abundances. Therefore, we asked: do variations in species and traits differ along gradients of deadwood variables? Do species abundance and trait occurrence change with species richness within or between functional groups? Thus, we analysed the beetle assemblages of five forest sites located in Italy, along the Apennines mountains.Methods: From 2012 to 2018 we sampled beetles and five deadwood types in 193 plots to characterise the deadwood gradient: standing dead trees, snags, dead downed trees, coarse woody debris, and stumps. We modelled beetle species relative abundances and trophic traits occurrences against the deadwood variables using joint species distribution models.Results: Out of 462 species, only 77 showed significant responses to at least one deadwood type, with a weak mean response across species. Trophic groups showed mostly negative responses to deadwood variables. Species abundance increased with species richness among sites only for phytophagous and saproxylophagous. Trait occurrence did not increase with species richness among sites, except for phytophagous and saproxylophagous.However, trait occurrence changed significantly with species richness of several trophic groups within some sites.We found that increases in species richness do not result in decreases in species abundance of a given trophic group, but rather null or positive relationships were found suggesting low interspecific competition.Conclusions: Our findings suggest that in Mediterranean mountain forests there is still room for increasing the level of naturalness, at least for what concerns deadwood management. On one side, our findings suggest that competition for deadwood substrates is still low, on the other side they indicate that increasing deadwood volume and types to improve overall beetle richness may increase also beetle abundances.

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.