Importance measures for imprecise probability distributions and their sparse grid solutions

For the imprecise probability distribution of structural system, the variance based importance measures (IMs) of the inputs are investigated, and three IMs are defined on the conditions of random distribution parameters, interval distribution parameters and the mixture of those two types of distribution parameters. The defined IMs can reflect the influence of the inputs on the output of the structural system with imprecise distribution parameters, respectively. Due to the large computational cost of the variance based IMs, sparse grid method is employed in this work to compute the variance based IMs at each reference point of distribution parameters. For the three imprecise distribution parameter cases, the sparse grid method and the combination of sparse grid method with genetic algorithm are used to compute the defined IMs. Numerical and engineering examples are em-ployed to demonstrate the rationality of the defined IMs and the efficiency of the applied methods.

A new probability distribution model of turbulent irradiance based on Born perturbation theory

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled.Theory reliably describes the behavior in the weak turbulence regime,but theoretical description in the strong and whole turbulence regimes are still controversial.Based on Born perturbation theory,the physical manifestations and correlations of three typical PDF models (Rice-Nakagami,exponential-Bessel and negative-exponential distribution) were theoretically analyzed.It is shown that these models can be derived by separately making circular-Gaussian,strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory,which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications.In addition,a common shortcoming of the three models is that they are all approximations.A new model,called the Maclaurin-spread distribution,is proposed without any approximation except for assuming the correlation coefficient to be zero.So,it is considered that the new model can exactly reflect the Born perturbation theory.Simulated results prove the accuracy of this new model.

An Estimation Method for Kill Probability Based on Random Residence Time Series

Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimation method for kill probability is proposed, which solves the probability of number of residence times satisfied effective shooting in given time. Some expressions and their approximate formulae of kill probability are derived, under known the distribution of residence time series. Theoretical analysis and simulation results show that this method is suitable for evaluating the hit ability of fire system for maneuver targets in random shooting.

考虑分布式风电出力相关性的配电网概率区间潮流计算方法

为了更加准确地模拟分布式风电接入对配电网不确定性潮流分布的影响,提出考虑相关性的配电网概率区间潮流计算方法。将分布式风电出力区间划分成若干个子区间并赋予子区间对应的概率,并构建分布式风电出力的焦元模型;结合仿射算术将基于焦元模型的配电网概率区间潮流模型转化为仿射优化模型,并采用平行四边形模型、凸多边形模型、椭球模型来描述分布式风电出力的相关性,通过坐标变换将相关性模型转换为仿射约束条件,并将其嵌入仿射优化模型中进行联立求解;根据证据理论合成规则得到配电网概率区间潮解的概率边界。2个配电网的算例仿真结果表明,所建模型可以通过最大、最小概率描述潮流解的不确定度,同时椭球模型对相关性的建模比其他2类方法更准确。

Free Probability Theory Based Event Detection for Power Grids Using IoT-enabled Measurements

Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability theory(FPT).Using big data collected from phasor measurement units(PMUs),we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states.The event detection matrix is further described as an information matrix plus a noise matrix,and the essence of event detection is to extract event information from the event detection matrix.By associating the event detection problem with FPT,the empirical spectral distributions(ESDs)related moments of the sample covariance matrix of the information matrix are computed,to distinguish events from“noises”,including normal fluctuations,background noises,and measurement errors.Based on central limit theory(CLT),the alarm threshold is computed using measurements collected in normal states.Additionally,with the aid of sliding window,this paper builds an event detection architecture to reflect power grid state and detect events online.Case studies with simulated data from Anhui,China,and real PMU data from Guangdong,China,verify the effectiveness of the proposed method.Compared with other data-driven methods,the proposed method is more sensitive and has better adaptability to the normal fluctuations,background noises,and measurement errors in real PMU cases.In addition,it does not require large number of training samples as needed in the training-testing paradigm.

Fuzzy stochastic damage mechanics(FSDM) based on fuzzy auto-adaptive control theory

In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

Quantitative Analysis Model and Application of the Hydrocarbon Distribution Threshold

Hydrocarbon source rock obviously controls the formation and distribution of hydrocarbon reservoirs. Based on the geological concept of ＂source control theory＂, the concept of a hydrocarbon distribution threshold was put forward. This means the maximum range for hydrocarbon controlled by the source rock conditions to migrate in the hydrocarbon basins. Three quantitative analysis models are proposed on this basis, namely the hydrocarbon accumulation probability, maximum hydrocarbon scale threshold and reserve distribution probability, which respectively refer to the probability of forming a hydrocarbon reservoir, the possible maximum scale of the hydrocarbon reservoir and the percentage of reserve distribution in a certain area within the hydrocarbon distribution threshold. Statistical analysis on 539 hydrocarbon reservoirs discovered in 28 hydrocarbon source kitchens from seven sedimentary basins and sags of eastern China shows the maximum reservoir scale possibly formed in the hydrocarbon basin, hydrocarbon accumulation probability and oil and gas reserve distribution probability are all controlled by the characteristics of the hydrocarbon source rock. Generally, as the distances from the hydrocarbon source rock center and hydrocarbon discharge boundary get longer and the hydrocarbon discharge intensity of hydrocarbon source rock center gets smaller, there will be lower probability of hydrocarbon accumulation. Corresponding quantitative models are established based on single factor statistics and multivariate analysis. Practical application in the Jiyang Depression shows that the prediction from the quantitative analysis model for the hydrocarbon distribution threshold agree well with the actual exploration results, indicating that the quantitative analysis model is likely to be a feasible tool.

Slant Range Distribution Characteristics of Submarine Launch Mobile Mine

With the bias between the predetermined planting location and the fact mine position,slant range of SLMM(submarine launch mobile mine)appears randomly scattered.The normal distribution model of slant range was proposed by the distribution theory of multivariate random variables,and the simplified model based on key parameters was present,and the laws of slant range distribution parameters such as mean and variance were given,which were affected by key parameters.The conclusions ensure that slant range of SLMM can be controlled when laying mines and provide the basis for tactical decision-making.

COOPERATIVE MIMO SPECTRUM SENSING BASED ON RANDOM MATRIX THEORY

Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.

考虑温度和时间双重影响的混凝土蠕变模型构建

为了研究温度对混凝土结构蠕变特性的影响,开展不同温度作用下混凝土三轴蠕变试验,分析了不同温度作用下混凝土结构的轴向蠕变特性。在温度作用下,混凝土的内部损伤与非均匀程度参数有关,建立非均匀程度参数与温度之间的关系;假定混凝土蠕变模型是关于温度和时间的函数,结合上述损伤变量和微元体强度分布概率模型,建立了考虑温度和时间双重影响的混凝土蠕变模型。基于最小二乘法和试验数据对模型的准确性进行验证,并采用西原模型对其优越性作进一步验证。结果表明:不同温度作用下蠕变损伤模型与试验数据的吻合度都较好,且相关性系数在0.95以上,说明了所建立模型的正确性;同时,该模型与试验数据的吻合度要优于西原模型,并且在描述加速蠕变方面具有一定的优越性。该理论模型为地下工程中混凝土支护结构的长期变形预测研究提供理论依据。

考虑需求侧灵活性资源配置的配电网分布鲁棒优化规划方法研究

考虑需求侧灵活性资源(简称“资源”)配置,开展网-荷-储联合规划是提升配电网灵活性以适应新能源出力波动的关键途径。为此提出一种灵活性缺失场景筛选与不确定性分析方法改进相结合的配电网规划研究模型:首先,立足资源视角进行配电网灵活性供需关系建模;其次,基于影子价格理论提出配电网灵活性缺失场景筛选策略,建立筛选指标以描述规划资源、运行约束、场景筛选间闭环关系;然后,将该策略嵌入配电网-多资源两阶段联合规划模型,一阶段考虑投资成本最优,二阶段协调运行及灵活性综合成本期望;将规划模型重构并于改进场景概率驱动型分布鲁棒优化(ISPD-DRO)框架下求解,其优势在于实现了概率优化求解与场景动态更新的有机统一;最后经算例分析验证所提模型在提升决策经济性及配电网灵活性层面的优势。

俗语警句情景下的概率论研究

把概率论里枯燥艰涩的理论知识与丰富多彩的生活实践相结合,理论联系实际,用概率论的基础知识和基本原理去阐释挖掘俗语警句中所蕴涵的人生哲理、科学思想和文化渊源,揭示“数学”、“哲学”与“文化”的关系,进而激发学生学习的兴趣和热情,提高学生学习概率论的效率.

非精确概率下基于证据理论的典型系统可靠性模型

当系统的各个单元的失效概率为不精确概率时,传统的概率方法难以使用,而区间分析法等非概率方法得到的结果则比较粗糙。基于证据理论,建立了非精确概率下串联、并联、串并混联、k-out-of-n等典型系统的可靠性模型,利用信任函数和似然函数、根据证据推理,将单元可靠性中的不确定性传递到顶层系统,从而得出系统失效概率和可靠度的概率分布的上下界。实例分析表明,提出的方法能较好的处理可靠性计算中的不精确信息,且比区间分析法得到的有效信息更多。

采煤机牵引部传动系统动态可靠性分析

考虑齿轮的时变啮合刚度、非线性侧隙等因素,根据3自由度齿轮集中质量模型,建立了采煤机牵引部的动力学整体模型,研究变速重载工况下系统的振动响应,获得了牵引部各位置的动态接触应力。考虑随机运动参数、结构参数与材料参数系统等的影响,基于鞍点逼近方法获得了系统功能函数的概率密度函数与概率分布函数,基于顺序统计量理论研究了载荷多次作用下牵引部传动系统的动态可靠性评价问题,计算结果表明:随着系统运转时间的增加,传动系统中齿轮接触应力分布均值增大且标准差减小;动态运转过程中,牵引系统首次运转是较为安全的,系统前期可靠性降低速度较快,后期可靠性递减速度较缓慢。

基于极值理论的中国台风降水分布不确定性分析

以浙江温州站点为例,对5种极值模型模拟台风降水极值累积概率分布的方法进行了详细阐述,并分析不同极值模型的差异;对全国748个气象观测站点的1951—2005年所有台风事件的降水及概率进行了系统分析,结果表明Weibull分布模拟中国台风极值降水整体检验效果最佳;定量探讨了Weibull分布与其他分布模型在台风降水强度-概率分布上的定量差异及采用不同分布模型可能造成的台风降水概率分布不确定性.

地基沉降修正系数的Bayes概率推断

通过分析常规方法在沉降修正系数的选取中具有的定值性和随意性,引入建立在过去信息和现在样本信息之上的Bayes理论,结合某客运专线红黏土路基工程,提出用后验分布得到修正系数的取值范围。实例研究表明,用以往经验综合样本信息,估计修正系数的先验概率在某一区间上服从均匀分布。由现场载荷试验实测沉降量与理论计算沉降量分析所得的修正系数,将现场量测的沉降变形信息与先验信息结合起来,利用Bayes统计理论,由小样本试验数据推算得到修正系数的后验概率服从正态分布。对后验分布所得参数进行区间估计,得到该区域红黏土地基沉降修正系数的取值优化区间为[1.0,1.7],分析了不同荷载作用条件下沉降修正系数的概率分布模型。

变形对土水特征曲线影响规律模拟研究

建立预测土水特征曲线随变形变化规律的模型是研究变形对非饱和土渗透系数影响的基础,它也可为建立考虑水力和力学耦合的非饱和土本构模型奠定基础。以概率论为基础,通过引入孔隙尺寸分布函数,建立了土中的平均孔隙半径与孔隙率之间的函数关系,并以此为基础得到了一个能够模拟孔隙率对土水特征曲线的影响规律的经验模型。通过计算和试验结果的对比分析,验证了这一模型的合理性。

气候概率分布理论及其应用新进展

随着全球变暖加剧,气候变化的研究不断深入,有关气候概率分布理论及其应用研究不但增加了许多新的内涵,而且有了长足的发展。文章从观测资料的分布拟合,气候概率分布的形成机制,气候变化的标志,即气候概率分布的变化、全球气候变化背景下的气候极值分布模式以及气候变量的空间域概率分布模式等方面简要综述了近年来气候概率分布理论及其应用领域的若干新进展。

南水北调西线工程水源区河流与黄河的丰枯遭遇分析

针对目前二维联合分布模型不能同时分析多条河流的丰枯遭遇特性,运用四元Copula连接函数构造了鲜水河、足木足河、绰斯甲河以及黄河上游兰州水文站天然径流系列的四维联合分布,研究了南水北调西线工程水源区河流与受水区黄河上游的丰枯遭遇问题。结果表明,如果不考虑黄河上游兰州水文站丰与水源区河流非全枯的组合,则有利于调水的丰枯遭遇频率为43.8%;如果把兰州水文站丰与水源区河流非全枯的组合考虑进来,有利于调水的丰枯遭遇频率可达77.8%,即调水河流之间能进行补偿调度的概率比较大,这对南水北调西线工程的实施是非常有利的。

基于最大熵原理的浙江毛竹胸径分布及测量不确定度评定

应用最大熵原理构造了测树因子概率分布的统一模型,这样构造的模型具有明确的解析表达式,并能克服常用方法无法解释测树因子服从某种概率分布的真正原因,从而为测树因子统计分布建模提供了一种有效方法。使用1-3阶样本矩、1-4阶样本矩与1-5阶样本矩,用所构建的概率分布统一模型分别对浙江省域毛竹胸径分布分别作了仿真试验,结果表明当采用1-4阶样本矩时,仿真效果最好,而且比通过假设检验的Weibull分布仿真结果理想:(1)图形非常相似,对实测数据都能很好的模拟;(2)最大熵法的离差平方和为0.00018,Weibull分布的为0.00045[1]。由于各种系统与非系统的原因,都会影响测量结果的准确性,对所构建的模型作了不确定度评定,表明结果具有很大的可靠性,测量结果的估计:7.85100,测量结果的标准不确定度:1.82710,置信概率:0.96020。