采用多随机变量超分位数方法的机组碳捕集率优化决策

碳捕集机组的效益与电价、碳排放权价格密切相关,在售电损失费用、碳排放权交易费用和燃料费用为目标函数的机组碳捕集率优化模型中,同时考虑电价与碳排放权价格的随机性,提出并推导了多随机变量超分位数方法,将机组碳捕集率优化模型变为机组碳捕集率随机函数型的优化模型,便于利用工具箱求解。对比分析了不考虑电价和碳排放权价格波动,仅考虑碳排放权价格波动以及考虑电价与碳排放权价格波动的机组碳捕集率优化模型的3种计算结果。算例仿真结果表明,同时考虑两价格的随机性,增加了系统碳捕集率调节的灵活性,积极响应了电力市场和碳交易市场机制,降低了碳捕集系统的综合运行成本。

基于多随机变量的人致荷载模拟方法

传统的人致荷载求解是基于单随机变量模拟,假定人群中任意两人跳动滞后时间近似服从正态分布,并利用单个人致荷载的标准化时程曲线和数值随机抽样求响应的方法,根据不同跳动类型来求出人群动荷载降低系数。然而,行人步频和人体自重两个随机变量,也会对人群动荷载降低系数产生显著影响,所以传统的单随机变量模拟方法存在明显不足。本文提出了基于多随机变量的人致荷载模拟方法。将人群中任意两人跳动滞后时间、人群跳动频率和人体自重等均视为随机变量参数,分别利用其统计特性,采用拉丁超立方抽样方法,运用MATLAB编程分析了不同随机变量个数和组合模式下的人群动荷载降低系数,并研究其随人群数目和跳动类型的变化规律。结果显示,考虑两个或三个随机变量求出的人群动荷载降低系数基本大于单变量模拟的结果,即传统的单变量模拟方法偏于不安全。最后,通过对比研究,并综合考虑设计安全性,给出了不同随机变量组合的控制范围。本文结论可为相关研究和设计作参考。

HDMR在多维随机变量结构全局灵敏度分析的应用

针对多随机变量作用的框架结构体系,采用构造近似模型替代传统的大规模计算任务,并获取结构体系的全局灵敏度信息进行分析。结果表明,HDMR可以在一定样本的条件下准确构造近似模型并获取灵敏度信息,对结构优化与安全评估具有重要意义。

考虑电价碳价随机性及其相关性的发电商投标决策

电价、碳价在外界因素的影响下具有某种相依关系,因此需要在发电商投标模型中考虑电价、碳价的随机性及其相关性对其决策的影响。本文将低于发电商预期收益部分的期望值定义为风险,采用多随机变量的条件风险方法对其进行度量,建立了考虑电价碳价随机性及其相关性影响的发电商投标决策模型,利用线性变换方法对相关性随机变量进行抽样并求解条件风险值。对电价碳价相关性、碳价成本、碳价随机性和不同风险度量方法对发电商投资决策风险的影响进行了仿真对比,结果表明考虑电价和碳价随机性及其相关性影响的投标模型更符合发电商提高收益降低风险的要求,采用条件风险方法更能准确刻画投标风险。

考虑电价碳价及风功率不确定性的风—火虚拟电厂运行优化策略

风电出力、电价、碳价的波动将影响虚拟电厂净收益,而碳捕集机组具有较大出力调整速率,将其与出力随机的风电聚合为虚拟电厂,可平抑风电并网波动。因此,为寻求风—火虚拟电厂运行优化策略,计及风电出力、电价、碳价三者随机性,以碳捕集机组燃料费用和碳排放权费用、风电成本和碳排放权费用以及虚拟电厂售电损失费用之和最小为目标函数,构建虚拟电厂碳捕集率决策模型,采用多随机变量超分位数方法将该模型转变为条件风险决策模型。分别对不考虑风电出力、电价、碳价三者随机性、仅计及电碳价格随机性、以及计及三者随机性的虚拟电厂碳捕集率决策模型进行算例仿真。结果表明,当计及三者随机性时,通过及时调节碳捕集水平,可降低捕集能耗,有效应对风电波动,更符合实际电力市场和碳市场运行机制。

基于主成分分析的风电场等值方法的研究

针对系统中含有多随机变量的问题,提出了采用主成分分析对多电源提取有效的主成分来进行等值,结合REI等值对网络进行化简的方法。算例分析中运用了主成分分析方法进行了多台风力发电机的主成分提取,将提出的主成分看成虚拟的等效风力发电机来替换原有的多台风电机组,实现了有效的简化替换,降低了系统分析的复杂性。

Reliability analysis of structure with random parameters based on multivariate power polynomial expansion

A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method （ FORM） and second-order reliabilitymethod （ SORM）, te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.

Some Necessary and Sufficient Condition of Multivariate Random Variable Satisfy Normal Distribution

In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.

Some Practical Issues Related to Univariate Regression Analysis Prior to Multivariate Regression Analysis in Randomized Controlled Clinical Trials

Often many variables have to be analyzed for their importance in terms of significant contribution and predictability in medical research. One of the possible analytical tools may be the Multiple Linear Regression Analysis. However, research papers usually report both univariate and multivariate regression analyses of the data. The biostatistician sometimes faces practical difficulties while selecting the independent variables for logical inclusion in the multivariate analysis. The selection criteria for inclusion of a variable in the multivariate regression is that the variable at the univariate level should have a regression coefficient with p 〈 0.20. However, there is a chance that an independent variable with p 〉 0.20 at univariate regression may become significant in the multivariate regression analysis and vice versa, provided the above criteria is not strictly adhered to. We undertook both univariate and multivariate linear regression analyses on data from two multi-centric clinical trials. We recommend that there is no need to restrict the p value of 〈= 0.20. Because of high speed computer and availability of statistical software, the desired results could be achieved by considering all relevant independent variables in multivariate regression analysis.

The Law of the Iterated Logarithm for Independent Random Variables with Multidimensional Parameters and Its Application

For a set of i.i.d.r.v. indexed by positive integer d-dimensional lattice points, and for some general normalizing sequence, we determine necessary and sufficient conditions for the law of iterated logarithm. As its application, we give conditions for the existence of moments of the supremum of normed partial sums.

Information theory in nonlinear error growth dynamics and its application to predictability:Taking the Lorenz system as an example

In nonlinear error growth dynamics,the initial error cannot be accurately determined,and the forecast error,which is also uncertain,can be considered to be a random variable.Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution.This paper effectively combines statistical information theory and nonlinear error growth dynamics,and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics.Entropy based on nonlinear error can be divided into time entropy and space entropy,which are used to estimate the predictabilities of the whole dynamical system and each of its variables.This is not only applicable for investigating the dependence between any two variables of a multivariable system,but also for measuring the influence of each variable on the predictability of the whole system.Taking the Lorenz system as an example,the entropy of nonlinear error is applied to estimate predictability.The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system.The results show that when moving around two chaotic attractors or near the edge of system space,a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit.The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective,especially for estimation of predictability of the whole system.This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.

Asymptotics of the variance of the number of real roots of random trigonometric polynomials

Let an, n≥ 1 be a sequence of independent standard normal random variables. Consider the randomtrigonometric polynomial Tn（θ）=∑^n_i=1 aj cos（j θ）, 0≤θ≤π and let Nn be the number of real roots of Tn（θ）in （0, 2π）. In this paper it is proved that limn→∞ Var（Nn）/n=co,where 0 〈 co〈 ∞.