Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.

NUMERICAL SIMULATION OF ORIENTATION DISTRIBUTION FUNCTION OF CYLINDRICAL PARTICLE SUSPENSIONS

The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much. in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.

Resolution Increase and Noise Removal in Particle Size Distribution Measurement with Shifrin Transform

Based on the laser diffraction and Shifrin transform,the measurement method of particle size distribution has been improved extensively.While in real measurements,some noise peaks exist in the inversion data and are easily to be misread as particle distribution peaks.The improved method used a truncation function as a filter is hard to distinguish adjacent peaks.Here,by introducing the bimodal resolution criterion,the filter function is optimized,and to a quasi truncation function with the optimized filter function is studied to achieve optimal bimodal resolution and to remove noise peaks.This new quasi truncation function fits multimode distribution very well.By combining the quasi truncation function with Shifrin transform,noise peaks are removed well and the adjacent peaks are distinguished clearly.Finally,laser diffraction experiments are conducted and the particle size distribution is analyzed by adoping the method.The results show that the quasi truncation function has better bimodal resolution than the truncation function.Generally,by combining the quasi truncation function with the Shifrin transform,in particle size distribution measurements with laser diffraction,the bimodal resolution is greatly increased and the noise is removed well.And the results can restore the original distribution perfectly.Therefore,the new method with combination of the quasi truncation function and the Shifrin transform provides a feasible and effective way to measure the multimode particle size distribution by laser diffraction.

Effects of shear rates on radial distribution of different types of heavy particles in light media

In order to study distribution properties of different types of heavy particles in light media and to link macro-properties of a system with its micro-structures,radial distribution functions(RDF)of partly charged metallic particles in uni-and bi-polar systems at various shear rates were investigated by Brownian dynamics simulation.The results are good in agreement qualitatively or quantitatively compared with ones in non-polar systems and other works.The investigation indicates that dispersibility of the particles in the uni-polar system of high ionic concentrations is the largest.Therefore,it is the most unfavored to grow into clusters for precipitation.The dispersibility in the bi-polar systems is less than that in uni-polar systems,but larger than that in non-polar systems.Furthermore,all the RDFs at the same shear rates in three systems approach a limit,which implies that a threshold value exists.

Pair distribution function analysis: Fundamentals and application to battery materials

Battery materials are of vital importance in powering a elean and sustainable society.Improving their performance relies on a clear and fundamental understanding of their properties,in particular,structural properties.Pair distribution function(PDF) analysis,which takes into account both Bragg scattering and diffuse scattering,can probe structures of both crystalline and amorphous phases in battery materials.This review first introduces the principle of PDF,followed by its application in battery materials.It shows that PDF is an effective tool in studying a series of key scientific topics in battery materials.They range from local ordering,nano-phase quantification,anion redox reaction,to lithium storage mechanism,and so on.

MICROSTRUCTURE OF AGGREGATES IN DISPERSIONS DESCRIBED IN TERMS OF RADIAL DISTRIBUTION FUNCTION

Following a sticky particle model and its computer simulation scheme proposed in the previous papers, the motions of particles in both 2-and 3-dimensional shear flow fields are simulated. At a steady state of clustering process, the radial distribution functions are calculated to precisely describe the microstructure of aggregates in dispersions, and the configuration of particles is displayed,which gives a direct view of microstructure. It is found that (1) the kind of the microstructure transforms from compact clusters to a loose network as the concentration of particles increases; (2) the microstructure is independent of shear rate which only dominates the size of clusters formed at steady state.

Particle swarm optimization algorithm for simultaneous optimal placement and sizing of shunt active power conditioner(APC)and shunt capacitor in harmonic distorted distribution system

Due to development of distribution systems and increase in electricity demand,the use of capacitor banks increases.From the other point of view,nonlinear loads generate and inject considerable harmonic currents into power system.Under this condition if capacitor banks are not properly selected and placed in the power system,they could amplify and propagate these harmonics and deteriorate power quality to unacceptable levels.With attention of disadvantages of passive filters,such as occurring resonance,nowadays the usage of this type of harmonic compensator is restricted.On the other side,one of parallel multi-function compensating devices which are recently used in distribution system to mitigate voltage sag and harmonic distortion,performs power factor correction,and improves the overall power quality as active power conditioner(APC).Therefore,the utilization of APC in harmonic distorted system can affect and change the optimal location and size of shunt capacitor bank under harmonic distortion condition.This paper presents an optimization algorithm for improvement of power quality using simultaneous optimal placement and sizing of APC and shunt capacitor banks in radial distribution networks in the presence of voltage and current harmonics.The algorithm is based on particle swarm optimization(PSO).The objective function includes the cost of power losses,energy losses and those of the capacitor banks and APCs.

Reconstruction of Probability Density Function for Gamma Distribution

The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.

基于λ-PDF和一次二阶矩的不确定性反求方法

为了有效评价测量响应中不确定性对结构参量识别结果的影响,提出一种基于λ概率密度函数(Probability distribution function,PDF)和一次二阶矩的不确定性计算反求方法。采用二次衍生λ-PDF对待识不确定性参量的PDF进行建模。内层通过对参量呈λ-PDF的功能函数采用一次二阶矩法进行正问题求解,得到计算响应的概率分布;外层通过最小化测量响应与计算响应之间的概率分布特征量将不确定性反问题转化为确定性的最优化问题,并用隔代映射遗传算法识别未知参量λ-PDF的参数。本方法不仅有效地实现了结构未知参量PDF的估计,而且与传统基于抽样的统计方法相比,计算效率较高。数值算例和工程应用验证了本方法的可行性和有效性。

偏振微面双向反射分布函数建模与仿真研究

偏振双向反射分布函数(p-BRDF)可以描述物体表面反射光的空间偏振特性,在许多领域得到了应用。基于微面理论,由微面和物体表面的角度关系以及微面上的菲涅耳反射,对任意偏振状态入射光和反射光的电场振动矢量进行分解与合成,得到偏振反射率pjk,将其作为菲涅耳反射项代入Cook-Torrance BRDF模型中,建立偏振微面BRDF模型。在几何光学模型中引入偏振,模型简单且有明确的物理意义。利用粒子群优化算法,结合黄铜表面的面内BRDF实验数据拟合模型中的参数,参数选取的标准均方误差为0.2820~5.7049%,最佳校正决定系数为0.9957。结果表明,偏振微面BRDF模型用于描述偏振反射特性的准确性和可行性。

ATLAS 2.76 TeV单喷注实验数据对CT18NNLO部分子分布函数的影响

通过ePump(error PDF(parton distribution function)updating method package)研究了大型强子对撞机(large hadron collider,LHC)在质心能量√s=2:76TeV时,来自ATLAS(a toroidal LHC apparatus)探测器单喷注的双微分散射截面的实验数据对CT18NNLO(next-to-next-to-leading order)部分子分布函数(PDF)的影响.首先,使用CT18NNLO部分子分布函数计算了单喷注的双微分散射截面,观察到理论预测与实验数据符合得较好;其次,计算了单喷注双微分散射截面的理论预测值与CT18NNLO胶子部分子分布函数的关联余弦cosϕ;最后,使用ePump更新了CT18NNLO部分子分布函数,并研究了实验数据与全局拟合数据间的冲突.通过比较在Q=100GeV时CT18NNLO胶子部分子分布函数和ePump更新的胶子部分子分布函数,发现ATLAS 2.76 TeV单喷注双微分散射截面实验数据在大和小的动量分数区域对CT18NNLO胶子部分子分布函数的约束较小.

考虑小样本不平衡的主动配电网预测辅助鲁棒状态估计

为了解决主动配电网状态估计中数据集的小样本不平衡问题,提出了基于改进少数过采样技术(synthetic minorityoversamplingtechnique,SMOTE)的Prophet和粒子滤波(particlefilter,PF)的主动配电网预测辅助鲁棒状态估计方法(robust forecasting-aided state estimation, FASE),对主动配电网进行状态估计。首先,针对主动配电网小样本不平衡问题,基于主动配电网的数据特征构建哈希函数,提出利用哈希函数对Borderline-SMOTE+Tomek-Links算法进行优化的方法,处理主动配电网数据集。然后,针对主动配电网海量数据量、分布式能源的出力随机变化等特点,将Prophet预测模型用于主动配电网状态估计,提出了一种基于Prophet-PF的鲁棒FASE方法,达到快速、准确地估计主动配电网状态的目的。最后以IEEE 118节点标准配电网和DTU 7k 47实际配电系统为测试系统进行仿真,结果表明所提方法具有较高的精度和鲁棒性,为主动配电网状态估计提供相应参考。

生物氧化预处理过程pH值随机分布控制方法研究

生物氧化预处理过程中氧化槽pH值是影响细菌活性的关键因素之一,而pH值输出形态分布不符合高斯分布,使传统的均值和方差难以描述输出pH值分布,本文提出一种对矿浆输出pH的概率密度函数(PDF)统计信息控制方法。首先,采用B样条逼近矿浆输出pH值的PDF统计信息;其次,针对权值向量之间的关系,利用动态神经网络(DNN)建立控制输入和权值向量之间的非线性动态模型,基于建立pH的PDF统计信息权值模型,设计滑模变结构控制器,通过构造Lyapunov函数进行稳定性分析;最后,实现输出PDF统计信息对目标PDF统计信息的跟踪。仿真结果验证了所提方法的有效性,为生物氧化预处理过程提供了新方法。

球磨法制备芡实超微粉及其理化功能性质分析

芡实淀粉属小颗粒淀粉,且以超聚合的复粒形式存在。为了解超微粉碎对淀粉复粒结构及其中功效组分溶出的影响,文中采用球磨法制备超微芡实粉,分析了不同球磨参数对芡实粉理化功能性质的影响。研究显示,芡实粉的适宜球磨参数为:转速200 r/min,m(用料量)∶m(研磨球)=1∶30,研磨球直径4 mm,研磨时间30 min。与对照相比,所得超微芡实粉中超细粉末(粒径0~1μm)占比达到85.04%,其中总黄酮溶出量增加不显著,但总酚溶出量有明显增加(P≤0.05)。所得超微芡实粉吸水性和吸油性显著提高,分别达到3.88、2.46 g/g,分别增加了3.26、1.34倍。X-衍射图谱和扫描电子显微镜照片显示,超微芡实粉中淀粉的复粒结构发生碎裂,淀粉颗粒完整性及其晶体结构也被严重破坏,印证了超微芡实粉理化功能性质改变的内在原因。研究结果表明,球磨处理不仅改善了芡实粉的理化功能性质,也有利于其中功效组分的溶出。

新能源接入下配电网电能损耗控制方法研究

考虑新能源接入电网后发电方式不匹配而导致电能损耗较大的问题,提出了一种电能损耗控制方法。依据配电网网损计算结果,分析在新能源接入时影响电能意外损耗的相关因素;获取配电网电能损耗最佳控制目标函数,制定控制约束条件,构建配电网的电能损耗最佳控制模型;利用粒子群算法求解控制模型,获取电能损耗最佳控制值,实现配电网在新能源发电接入下的电能损耗控制。实验结果表明,使用该方法开展电能损耗控制时,可以将输电线路首端有功功率和无功功率的损耗控制在期待范围内。

基于改进粒子群算法的输电线路舞动断线概率预测研究

【目的】为了解决冰风暴灾害下输电线路舞动断线问题,提出了基于改进粒子群算法的输电线路舞动断线概率预测模型。【方法】首先,采用改进粒子群算法确定输电线路在冰风暴灾害下风荷载与冰荷载的广义极值分布参数;其次,根据输电线路舞动的起舞风速和覆冰密度求取舞动情况下线路冰荷载和风荷载的极值分布。【结果】在此基础上,基于二元t-Copula连接函数计算线路舞动时风荷载和冰荷载的联合概率分布,实现了线路舞动断线的概率预测。【结论】结合湖南冬季输电线路舞动断线的历史数据,验证了改进粒子群算法的优越性和该模型的准确性,为输电线路舞动预报和指导线路提前部署防舞动措施提供了依据。

考虑风险测度的交直流柔性配电网协调优化调度方法

由于现行方法在交直流柔性配电网协调优化调度中应用效果不佳,不仅配电网线路容量越限率较高,而且线损率也比较高,无法达到预期的调度效果,为此本文提出了考虑风险测度的交直流柔性配电网协调优化调度方法。采用综合分析法对配电网进行运行风险测度,以风险最小为目标建立优化目标函数,通过设定约束条件来约束配电网潮流和有功功率,利用粒子群算法对目标函数进行求解,确定并执行最优协调调度策略,以此来完成考虑风险测度的交直流柔性配电网协调优化调度。经实验证明,本文所设计的方法应用之后,交直流柔性配电网线路容量越限率与线损率均低于1%,其具有良好的调度效果,其在交直流柔性配电网协调优化调度方面具有良好的应用前景。

Shape control on probability density function in stochastic systems

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

磨浆过程输出纤维长度随机分布预测PDF控制

磨浆过程作为制浆和造纸工业最为重要的生产环节之一,其输出纤维长度随机分布(Fiber length stochastic distribution,FLSD)形状直接决定着后续造纸过程的能耗和纸品质量.针对传统的均值和方差难以描述输出FLSD特征,即具有非高斯分布特性,本文提出一种磨浆过程输出FLSD的预测概率密度函数(Probability density function,PDF)控制方法.首先,采用径向基函数(Radical basis function,RBF)神经网络逼近输出FLSD的PDF,在采用迭代学习方法完成基函数参数整定基础上对相应权值向量进行估计.其次,针对权值之间存在强耦合特点,利用随机权神经网络(Random vector functional-networks,RVFLNs)建立表征输入变量和权值之间关系的预测模型.最后,基于建立的输出FLSD模型设计预测PDF控制器,最终实现对期望输出PDF的跟踪控制.基于工业数据实验验证了所提方法的有效性,为磨浆过程优化运行和控制提供理论依据.

Hypoexponential Distribution with Different Parameters

The Hypoexponential distribution is the distribution of the sum of n ≥ 2 independent Exponential random variables. This distribution is used in moduling multiple exponential stages in series. This distribution can be used in many domains of application. In this paper we consider the case of n exponential Random Variable having distinct parameters. Using convolution, some properties ofLaplacetransform and the moment generating function, we analyse this case and give new properties and identities. Moreover, we shall study particular cases when are arithmetic and geometric.