Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction(NWP).To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations,hydrometeor control variables are necessary.Common data assimilation systems theoretically require that the probability density functions(PDFs)of analysis,background,and observation errors should satisfy the Gaussian unbiased assumptions.In this study,a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables,which is modified from the Softmax function and renamed as Quasi-Softmax transform.The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform.The spatial distribution,the non-Gaussian nature of the background errors,and the characteristics of the background errors of hydrometeors in each method are studied.Compared to the logarithmic and Softmax transform,the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent.The results of the D′Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods.The Gaussian transform has been added to the control variable transform to estimate the background error covariances.Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method.The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system,and are promising control variables for data assimilation systems.

Continuous-Variable Quantum Network Coding Based on Quantum Discord

Establishing entanglement is an essential task of quantum communication technology.Beyond entanglement,quantum discord,as a measure of quantum correlation,is a necessary prerequisite to the success of entanglement distribution.To realize efficient quantum communication based on quantum discord,in this paper,we consider the practical advantages of continuous variables and propose a feasible continuous-variable quantum network coding scheme based on quantum discord.By means of entanglement distribution by separable states,it can achieve quantum entanglement distribution from sources to targets in a butterfly network.Compared with the representative discrete-variable quantum network coding schemes,the proposed continuous-variable quantum network coding scheme has a higher probability of entanglement distribution and defends against eavesdropping and forgery attacks.Particularly,the deduced relationship indicates that the increase in entanglement is less than or equal to quantum discord.

Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering

By constructing a mcan-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts： a real-valued non-random recurrence equation and the standard Kalman filtering.

变工况下动态卷积域对抗图神经网络故障诊断

针对基于无监督域自适应故障诊断方法忽略了域间数据结构信息、传统域对齐平均最大差异法全局泛化能力差等问题,本文提出一种基于无监督域自适应理论的动态卷积域对抗图神经网络故障诊断模型,分别通过对数据的类别标签、域标签和数据结构信息进行建模。通过分类器和域鉴别器分别建模类别标签和域标签,通过图神经网络将数据结构信息嵌入到实例图节点中,利用高斯Wasserstein距离来度量不同领域的实例图之间的差异。本文对比了不同工况下共14种迁移任务在各模型下故障识别的准确率。实验结果表明:基于动态卷积的域对抗图神经网络模型在变工况下的故障诊断效果均优于其他对比模型,且模型性能稳定。

基于不同变系数和势场的分数系统中二次相位调控厄米-高斯光束动力学

本文基于带有不同变系数和势的分数薛定谔方程,研究了二次相位调制(QPM)下厄米-高斯光束的演化特性.在自由空间中,光束聚焦位置随着正QPM系数的增加或莱维指数的减小而变大.QPM为负时,光束聚焦消失.在余弦调制和QPM共同作用下,光束的传输不再遵循余弦规律振荡,而是表现出一大一小的呼吸结构,其演化周期会随调制频率的增加而降低.引入线性调制时,分裂光束的运动轨迹呈现抛物线状.在线性调制和QPM共同影响下,光束呈现出聚焦或聚焦消失的特性.当考虑幂函数调制和正QPM共同影响时,在莱维指数较小时,光束在一定传输距离内保持不失真的直线传输.当线性势作用时,光束的分裂随着线性系数的增加而逐渐消失,最终呈现周期性演化.在加入QPM后,光束会得到明显放大.另外,光束演化周期与线性系数成反比,横向振幅随着莱维指数的增加而变大.当抛物势和QPM共同作用时,光束会呈现出自动聚焦,散焦效应,聚焦频率会随着莱维指数和抛物系数的增加而变大.这些特性在光学操纵,光学聚焦等领域具有潜在的应用价值.

耦合变密度地下水流降阶模型与高斯过程的蒙特卡罗模拟

变密度地下水流系统受水力梯度和密度梯度共同驱动,非线性强,数值模型计算量大,尤其在开展不确定性分析时需要的计算成本很高。常规的数据驱动机器学习方法只能对点监测信息进行模拟分析,不能模拟整个地下水流系统。本研究发展了变密度地下水流降阶模型,利用高斯过程模型对降阶模型的数值误差进行修正组成耦合模型。耦合模型既能克服高斯过程只能模拟有限监测点信息的缺陷,又能提高降阶模型对监测点信息的模拟精度。考虑二维剖面变密度地下水流案例,将渗透系数场设定为空间随机变量,采用基于全阶模型(FSMC)、降阶模型(ROMC)和耦合模型(GP-ROMC)3种蒙特卡罗模拟方法进行不确定分析。研究结果表明:(1)ROMC能替代FSMC开展不确定性分析;(2)水头和盐度的平均相对二范误差与降阶模型维度的关系可用指数函数描述(决定性系数R2≥0.99);(3)GP-ROMC对监测点信息的模拟精度比ROMC高,GP-ROMC可有效修正降阶模型误差提高蒙特卡罗模拟的精度。研究成果可为地下水建模、不确定性分析、风险评估及参数反演等工作提供重要技术支撑。

变截面压电悬臂梁能量采集器在高斯白噪声激励下的稳态统计特性研究

环境振动是一种非周期、随机的宽频激励,研究振动能量采集器在环境振动下的能量采集特性具有重要意义。本文采用改进随机平均法,求解了变截面压电梁在高斯白噪声激励下的等效振幅、位移、速度的稳态概率密度函数,位移与速度的联合概率密度函数以及稳态均方输出电压,随后研究了变截面压电梁的能量采集效能。结果表明:负载电阻一定时,截面系数β>0时的变截面压电梁相比β=0时的等截面压电梁有更好的稳态均方输出电压;截面系数β>0时,随着电阻电容乘积的倒数的增加,变截面压电梁的均方电压均呈现逐渐减小的趋势,当电阻电容乘积的倒数值一定时,β值越大,均方电压也越高;随着噪声强度的增加,变截面压电梁的均方电压均呈现逐渐增大的趋势,当噪声强度一定时,β值越大,均方电压也越高。本文研究结果可为变截面压电悬臂梁能量采集系统的设计及应用提供理论依据。

基于GMM-Ada-LASSO模型的高维过程统计质量监控方法

针对高维数据往往不服从正态分布导致统计监控模型识别精度低、监控效率差的问题,文章提出一种基于高斯混合模型的变量选择控制图方法。首先,利用高斯混合模型将高维过程分解成若干个服从正态分布的子分布;然后,运用Adaptive LASSO算法识别潜在异常变量;最后,构建多元EWMA控制图实现高维过程统计质量监控。通过仿真实验,在六种不同情形下对所提方法的监控性能进行测试。结果表明,与传统MEW⁃MA和VS-MEWMA控制图相比,所提监控方法对非正态数据具有较强的稳健性,对高维过程具有良好的监控性能。

铝型材静电粉末喷涂模型的研究与应用

针对实际生产中企业为实现铝型材表面均匀涂层而耗费巨大人力物力的问题,提出了一种适用于生产实际的变高斯分布模型。通过对铝型材静电粉末喷涂影响因素的分析,使用控制变量法进行定点和连续喷涂实验,获得涂层厚度实验数据,基于高斯分布对定点实验数据进行拟合,对于拟合模型存在的远离中心截面偏差问题,采用变峰值宽度的方式对模型进行优化修正,进一步提高了模型与实验数据的拟合程度,在此基础上,通过实验数据分析了静电电压、粉末流量、喷涂速度对膜厚分布的影响,建立了不同参数下静电粉末喷涂涂层的变高斯分布模型。最后进行了喷涂实验,铝型材成品的膜厚分布情况符合模型仿真预测的结果,表明该模型能准确预测不同参数下铝型材的膜厚分布情况,在生产实际中,模型的应用可以为均匀涂层提供可靠的仿真参考和生产指导,有效减少企业调试参数的次数,提高了企业的生产效率。

基于水代谢和水循环理论的石羊河流域水资源承载力评价

基于水代谢和水循环理论,构建了包含输入、消耗、活力、调节、输出5个子系统的水资源承载力评价指标体系,采用最小二乘法组合网络层次分析法和熵权法确定权重,基于可变模糊集模型综合评价了石羊河流域2011—2020年水资源承载力,耦合高斯混合回归模型和3种可解释性机器学习方法量化了各评价指标对承载力的影响,从全局和局部尺度探究了其与水资源承载力的关系。结果表明:2011—2020年流域水资源承载力总体呈波动向好态势,但仍处于濒临超载的状态,评分值由2011年的3.79增长到2013年的4.18,之后下降到2020年的3.23;高斯混合回归模型能够较好地处理高维、小样本的水资源承载力指标数据;单位面积农业灌溉用水量、污水处理回用率、生态环境用水率、水资源开发利用率、产水模数和地下水开采率是该流域水资源承载力的主要影响因素;从全局看,水资源承载力与主要影响因素呈非线性关系,并随其非单调变化,从局部看,2011—2015年主要影响因素多表现为对水资源承载力的抑制作用,2016—2020年逐步转为促进作用;流域水资源承载力虽有提高,但仍需加强水资源开发利用管理,降低地下水开采率。

可变光阑对高斯光束衍射特性分析

可变光阑作为常见的光学器件,广泛应用于光束整形和空间滤波.根据可变光阑的工作原理可知,其通光孔是多边弧形而非圆形,这导致当光束经可变光阑衍射时,近场会出现齿状光斑.本文对可变光阑的近场衍射图像进行了实验测量,并且采用Matlab对多边弧形的衍射特性进行了理论仿真,理论仿真结果与实验观测结果一致.

梯度折射率介质对复变量sinh-Gaussian光束传输的影响

为了研究梯度折射率介质对复变量双曲正弦高斯光束的传输影响,利用广义惠更斯-菲涅耳衍射积分法推导出了复变量双曲正弦高斯光束在梯度折射率介质中的传输场,运用空间二阶矩的定义解出了光斑尺寸及其变化率的表达式,并进行了数值模拟分析。结果表明,光斑尺寸及其变化率随传输距离的增加呈周期性变化,周期由折射率系数决定;随光束参量的改变,光斑位置不变,周期性不变,但是光斑尺寸的振荡幅度要发生改变;通过调整这些参量,可以改变光斑尺寸及其位置。此项研究对大功率半导体激光器等方面的开发应用有帮助。

基于GMM的幅度相位联合编码CVQKD安全性分析

为了提高离散调制连续变量量子密钥分发协议性能,采用幅度相移键控(APSK)联合调制格式方法,在接收端采用高斯混合模型分类算法识别量子态来提升系统的性能。将密钥传输系统分为状态学习和状态预测两个阶段,在状态学习阶段基于高斯混合模型的分类器对已知类别的量子态进行训练,学习不同类别量子态的幅度相位分布情况;在状态预测阶段则采用最小欧氏距离计算出待测量子态属于每个类别的后验概率,从而判定待测量子态的类别,并通过参数估计、反向协调和保密增强生成最终密钥。结果表明,在反向协调和集体攻击下128-APSK离散调制连续变量量子密钥分发协议能够有效生成安全密钥,当安全码率为10-6 bit/symbol时,传输距离可接近60 km。该研究为进一步提高离散调制连续变量量子密钥分发协议的系统性能提供了参考。

基于强度折减采样与高斯过程回归的空间变异土坡自适应可靠度分析

土体参数空间变异性对土坡稳定性的影响已受到岩土工程界的广泛关注,繁冗的计算量是空间变异土坡可靠度分析面临的瓶颈问题。基于强度折减采样(SRS)和高斯过程回归(GPR)模型,提出一种适用于高维空间的空间变异土坡自适应可靠度分析方法(SRS-GPR)。首先采用Karhunen-Loève展开法将空间变异土体强度参数离散为高维随机变量,随后根据SRS生成土坡临界样本点,接着通过GPR构建土体参数随机场与边坡安全系数之间的高维非线性函数关系,并基于主动学习策略自动搜寻最优训练样本点,迭代更新GPR模型。在此基础上,结合GPR模型和蒙特卡洛模拟进行边坡可靠度分析。最后,通过两个典型算例验证所提方法的准确性、高效性、鲁棒性和适用性。结果表明:所提方法可有效识别靠近极限状态面附近的最优样本点,使得迭代更新的GPR模型在该区域的预测精度逐渐提高。此外,所提方法不受随机变量维度的影响,可直接在高维参数空间应用,且对边坡稳定性模型的调用次数较少,在计算效率方面具有显著优势。

连续与离散变量协同分析的非平稳非高斯工业过程异常检测

工业过程数据涵盖离散和连续变量,它们之间内在的统计分布特性是揭示系统运行状况的关键.然而,现有的监测模型多聚焦于高斯假设下的连续过程变量,忽略了离散变量、连续变量的多模分布特性以及数据中的噪声、离群点对模型的影响,难以精准反映数据的真实分布特性,对非高斯、非平稳过程的异常检测效果欠佳.因此,本文提出一种鲁棒的工业过程异常检测方法——连续和离散变量协同分析的变分贝叶斯混合判别方法(Continuous and Discrete Variables-Concurrent Analysis-based Variational Bayesian Mixture Discriminant,CDVCA-VBMD).通过构建基于变分贝叶斯推断的面向连续变量的混合学生分布模型与面向离散多变量的混合多项分布模型,有效解决过程变量非高斯分布特性难以有效提取的问题,实现了过程变量复杂相关性的高效处理与分析;同时,在过程监测中引入了持续学习的理念,确保对非平稳时变工业过程异常的有效检测.以数值仿真系统和田纳西·伊斯曼过程为例,进行了大量验证性和对比性实验.结果表明,CDVCA-VBMD能准确估计非平稳工业过程多变量的混合多模分布特性,并对数据中的噪声和离群点具有较强的鲁棒性,从而实现工业异常的准确检测,为非高斯复杂工业过程的长期、鲁棒监测提供了有力支持.

Deterministic quantum key distribution based on Gaussian-modulated EPR correlations

This paper proposes a deterministic quantum key distribution scheme based on Gaussian-modulated continuous variable EPR correlations. This scheme can implement fast and efficient key distribution. The security is guaranteed by continuous variable EPR entanglement correlations produced by nondegenerate optical parametric amplifier. For general beam splitter eavesdropping strategy, the secret information rate ΔI = I（α, β）-I（α, ε） is calculated in view of Shannon information theory. Finally the security analysis is presented.

Sparse Additive Gaussian Process with Soft Interactions

This paper presents a novel variable selection method in additive nonparametric regression model. This work is motivated by the need to select the number of nonparametric components and number of variables within each nonparametric component. The proposed method uses a combination of hard and soft shrinkages to separately control the number of additive components and the variables within each component. An efficient algorithm is developed to select the importance of variables and estimate the interaction network. Excellent performance is obtained in simulated and real data examples.

Elegant Ince-Gaussian beams in a quadratic-index medium

Elegant Ince-Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince-Gaussian beams and they display better symmetry between the ]nce-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince Gaussian beams are discussed.

Risk quantification in grade variability of gold deposits using sequential Gaussian simulation

Risk quantification in grade is critical for mine design and planning.Grade uncertainty is assessed using multiple grade realizations,from geostatistical conditional simulations,which are effective to evaluate local or global uncertainty by honouring spatial correlation structures.The sequential Gaussian conditional simulation was used to assess uncertainty of grade estimates and illustrate simulated models in Sivas gold deposit,Turkey.In situ variability and risk quantification of the gold grade were assessed by probabilistic approach based on the sequential Gaussian simulations to yield a series of conditional maps characterized by equally probable spatial distribution of the gold grade for the study area.The simulation results were validated by a number of tests such as descriptive statistics,histogram,variogram and contour map reproductions.The case study demonstrates the efficiency of the method in assessing risk associated with geological and engineering variable such as the gold grade variability and distribution.The simulated models can be incorporated into exploration,exploitation and scheduling of the gold deposit.

Generation of Non-Gaussian Wide-Sense Stationary Random Processes with Desired PSDs and PDFs

This paper describes a new method to generate discrete signals with arbitrary power spectral density (PSD) and first order probability density function (PDF) without any limitation on PDFs and PSDs. The first approximation has been achieved by using a nonlinear transform function. At the second stage the desired PDF was approximated by a number of symmetric PDFs with defined variance. Each one provides a part of energy from total signal with different ratios of remained desired PSD. These symmetric PDFs defined by sinusoidal components with random amplitude, frequency and phase variables. Both analytic results and examples are included. The proposed scheme has been proved to be useful in simulations involving non-Gaussian processes with specific PSDs and PDFs.