基于D S理论的中子测试数据统计

 针对由于样本数量、测量误差和动态特性等因素，致使采用概率统计方法来对中子发生器的中子测试数据进行统计存在许多局限性和不合理性，讨论了D-S理论中的基本分配、信任函数、上下概率等概念，利用该理论对中子发生器的中子测量数据进行处理统计，最终得到中子产额在一定置信区间内概率分布上、下限值和平均中子产额。与传统的概率统计方法相比，该统计方法能适用于非精确性数据，且不受样本大小的限制。     

舰船辐射噪声贝叶斯方法反演浅海底层结构及地声参数EI北大核心CSCD

针对以舰船辐射噪声为参考声源的浅海海底分层结构及地声参数反演问题,研究了一种基于贝叶斯理论的浅海多层海底地声参数反演方法。反演中以舰船辐射噪声的线谱成分为研究对象,进而采用非线性贝叶斯反演方法反演浅海底层结构、层中声速、声速衰减和密度,并对反演结果的不确定性进行分析。反演结果的最大后验概率估计值和边缘概率分布分别通过拨正模拟退火算法和Metropolis-Hastings采样法在各参数先验区间内计算获得,并根据贝叶斯信息准则确定最佳海底分层结构。海上实验表明:根据该方法反演获得海底分层结构及地声参数,计算得到的声压场与实测舰船辐射噪声传播损失误差不超过10%,反演结果能够准确表征实验海区海底特征。反演结果不确定性分析表明:海底纵波声速、横波声速以及密度的不确定性更小,对声压场变化更加敏感,反演结果更有效、准确。     

ICF用磁性玻璃靶丸悬浮磁场的确定及材料制备初步研究

 根据靶丸悬浮原理,推导出ICF用磁性靶丸在悬浮磁场中受力的函数关系式,从而得到了靶丸悬浮的理论模型。通过实验和理论相结合的方法,得出当靶丸中磁性材料掺入质量百分比由1%增加到6%时,靶丸的磁场强度由0.09 mT增加到0.44 mT,而对应的外界悬浮磁场由0.93 mT减小到0.23 mT。     

激光聚变靶设计中参数不确定性指标的线性近似法

激光聚变的点火对实验、器件、制靶及诊断等各方面的控制能力都有很高的要求。随着实验逐步趋近点火设计, 实验的精密化要求也逐步提高。精密化实验要求靶设计不仅给出激光能量、靶尺寸、气压等参数, 还需要给出这些关键参数的不确定性指标要求。因此, 获得这些不确定性指标也成为靶设计的主要内容之一。针对如何在实验设计中更为方便有效地获得参数的不确定性指标问题, 通过理论结合数值模拟研究给出了一种基于线性近似的方法。这一方法综合考虑各种关键参数变化对实验结果的影响, 平衡器件、制靶等对各种参数的控制能力, 来获得参数的不确定性指标。以一个气体靶设计为例, 通过数值模拟来展示这种方法的使用。结果表明, 这一方法可以在显著降低工作量的情况下有效地获得实验设计的参数不确定性指标。     

基于双经纬仪和弹孔屏的天幕立靶密集度现场校准方法

射击密集度是评定速射武器射击效果的重要参数,而天幕立靶测试系统广泛用于速射武器的密集度测量。但是由于天幕立靶受到运输、反复安装和搬移、外场环境温度变化、长时间使用等因素影响,导致密集度测量误差变大。针对天幕立靶密集度现场校准问题,提出了一种基于双经纬仪和高精度弹孔屏配合的校准方法。该方法利用双经纬仪交会测量弹孔屏上的弹孔坐标,根据所测量的弹孔坐标利用密集度公式计算密集度参数,并与天幕立靶所测得的密集度参数进行对比,完成现场校准。开展实弹射击,并对基于双经纬仪配合弹孔屏方法测量所得的密集度进行不确定度评估,结果表明:该方法测量所得的密集度不确定度为1.6 mm,可用于天幕立靶密集度的现场校准。     

根据非线性贝叶斯理论的界面波频散曲线反演

通过时频分析法从海底环境噪声数据中提取界面波频散曲线,进而采用非线性贝叶斯反演方法估算海底沉积物厚度、剪切波速度、压缩波速度和密度等参数及其不确定性。参数的最大后验概率(MAP)估计值和边缘概率分布分别通过自适应单纯形模拟退火法和Metropolis-Hastings采样法在各参数先验区间内搜索获得,采用贝叶斯信息准则(BIC)从不同参数化模型中选择最优模型。界面波频散曲线反演结果表明:满足实测数据的最优海底模型结构为3层均匀分布剪切波速度剖面结构,海底深度的反演精度在800m以内,比起压缩波速度和密度,剪切波速度的不确定性更小,对界面波频散曲线更敏感。      

X射线法测量的ICF靶丸参数的图像分析

 在ICF靶丸参数测量中，采用接触X射线显微辐射照相法获得靶核的X射线吸收底片图像，将该底片放置于显微镜下并用CCD获得了数字化图像。基于该数字化图像信息，编写了一套完整的计算机算法来计算靶参数。采用辐向平均法标定出靶中心，采用图像强度函数对半径的二阶微分来确定出靶层分界位置，计算精度约为0.2pixels。     

基于模糊理论的土体渗流固结参数识别

基于模糊数学理论,根据埋置在土体内部的超孔隙水压力观测数据,建立了土体固结参数模糊识别数值方法.根据观测点的超孔隙水压力观测数据的统计特性,得到观测数据的隶属度函数.基于待识别土体渗流固结参数的先验信息即约束条件,建立了模糊约束的隶属度函数,进而得到模糊化的目标函数.以信息论方法为基础,研究了观测信息的随机不确定性和荷载的随机不确定性对参数识别结果的影响.研究表明,基于信息论的模糊参数识别方法所得到的参数识别结果同样具有随机不确定性.     

用于光幕测试的时刻信息提取方法研究

从理论上分析了弹尖、弹底、幕中、弹中触发方式和广义相关算法这五种时刻信息提取方法,建立了弹丸穿过光幕的几何计算模型。结合工程实现中的问题如光幕厚度、厚度的一致性、放大电路一致性以及电路噪声,分析比较了不同方法对这些参数的敏感性,采用理论模拟信号在MATLAB上进行了仿真。结果表明,采用幕中、弹中触发和广义相关算法,可以精确提取时刻信息,而不受这些参数的影响。从理论上阐述了光幕厚度与测试精度的关系,其结果可以指导光幕靶和天幕靶的工程设计。     

地声参数及传播损失不确定性估计与建模

地声参数的不确定性对水声传播具有重要的影响。通过贝叶斯理论建立水声环境不确定性推理模型,理论推导了地声参数的似然函数以及地声参数和传播损失的后验概率密度,并采用MCMC(Markov Chain Monte Carlo)进行了仿真计算,给出了地声参数的二维后验联合概率密度和一维边缘概率密度,在此基础上对传播损失的不确定性进行了估计,得到了传播损失80%的可信区间。仿真和实验结果表明,该方法适用于地声参数反演和不确定性估计,并能获取因地声参数不确定性导致的传播损失不确定性估计。     

基于QMU的高空电磁脉冲下电气电子设备易损性评估方法

高空电磁脉冲（HEMP）可能造成广域基础设施的故障或损毁,考虑到经济原因,需要科学合理地评估其中关键电气电子设备在HEMP辐照下的易损性。将不确定性量化与设备效应评估相结合,总结出基于裕量与不确定性量化（QMU）的电气电子设备易损性评估方法及其工作流程,包括:筛选设备关键参数,通常为耦合通道电流、电压的范数;通过HEMP环境及其与设备耦合的数值仿真及不确定性量化,得到HEMP下设备关键参数的概率分布,作为设备的威胁水平;对工作状态下设备进行HEMP效应试验,通过统计推断得到设备效应阈值概率分布,作为设备在威胁下的强度;计算威胁水平与设备强度间的距离,量化设备关键参数的裕量及其不确定性,评估HEMP下的设备易损性。基于QMU的电气电子设备易损性评估方法还可为后续防护设计提供基础数据和评估方法。     

认知不确定二维声场的响应特性数值分析

针对声学参数存在认知不确定性的问题,为实现认知不确定声场声压响应的预测。提出了解决二维认知不确定声场的有限元法(Evidence Theory-based Finite Element Method,ETFEM),引入证据理论,采用焦元和基本可信度的概念来描述认知不确定参数,基于摄动法的区间分析技术,推导了认知不确定声场声压响应的标准差、期望求解公式。为验证本文方法的可行性。以认知不确定参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,对比离散随机变量得到认知不确定参数的声场分析结果和相应的随机声场所得分析结果,研究表明:该方法能够有效的处理认知不确定参数下的二维声场,为工程问题中噪声预测提供可靠的分析模型。      

Numerical approach for quantification of epistemic uncertainty

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty, little attention has been given to the quantification of epistemic uncertainty. In this paper, we propose a numerical framework for quantification of epistemic uncertainty. The proposed methodology does not require any probabilistic information on uncertain input parameters. The method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability. To quantify the epistemic uncertainty, we solve an encapsulation problem, which is a solution to the original governing equations defined on the estimated range of the input variables. We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty. In the case where probability distributions of the epistemic variables become known a posteriori, we can use the information to post-process the solution and evaluate solution statistics. Convergence results are also established for such cases, along with strategies for dealing with mixed aleatory and epistemic uncertainty. Several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology.     

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.     

Amplitude phase-space model for quantum mechanics

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.     

Empirical Frequentist Coverage of Deep Learning Uncertainty Quantification Procedures

Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model’s uncertainty is evaluated using point-prediction metrics, such as the negative log-likelihood (NLL), expected calibration error (ECE) or the Brier score on held-out data. Marginal coverage of prediction intervals or sets, a well-known concept in the statistical literature, is an intuitive alternative to these metrics but has yet to be systematically studied for many popular uncertainty quantification techniques for deep learning models. With marginal coverage and the complementary notion of the width of a prediction interval, downstream users of deployed machine learning models can better understand uncertainty quantification both on a global dataset level and on a per-sample basis. In this study, we provide the first large-scale evaluation of the empirical frequentist coverage properties of well-known uncertainty quantification techniques on a suite of regression and classification tasks. We find that, in general, some methods do achieve desirable coverage properties on in distribution samples, but that coverage is not maintained on out-of-distribution data. Our results demonstrate the failings of current uncertainty quantification techniques as dataset shift increases and reinforce coverage as an important metric in developing models for real-world applications.     

Belief Entropy Tree and Random Forest: Learning from Data with Continuous Attributes and Evidential Labels

As well-known machine learning methods, decision trees are widely applied in classification and recognition areas. In this paper, with the uncertainty of labels handled by belief functions, a new decision tree method based on belief entropy is proposed and then extended to random forest. With the Gaussian mixture model, this tree method is able to deal with continuous attribute values directly, without pretreatment of discretization. Specifically, the tree method adopts belief entropy, a kind of uncertainty measurement based on the basic belief assignment, as a new attribute selection tool. To improve the classification performance, we constructed a random forest based on the basic trees and discuss different prediction combination strategies. Some numerical experiments on UCI machine learning data set were conducted, which indicate the good classification accuracy of the proposed method in different situations, especially on data with huge uncertainty.     

Numerical analysis of the 2D acoustic field with epistemic uncertainty

Aiming at the problem that the epistemic uncertain parameters exist in an acoustic field,an evidence theory-based finite element method(ETFEM) is proposed by introducing the evidence theory,in which the focal element and basic probability assignment(BPA) are used to describe the epistemic uncertainty.In order to reduce the computational cost,the interval analysis technique based on perturbation method is adopted to acquire the approximate sound pressure response bounds for each focal element.The corresponding formulations of intervals of expectation and standard deviation of the sound pressure response with epistemic uncertainty are deduced.The sound pressure response of a 2D acoustic tube and a 2D car acoustic cavity with epistemic uncertain parameters are analyzed by the proposed method.The proposed method is verified through the comparison of the analysis results of random acoustic field with that of epistemic uncertain acoustic field.Numerical analysis results show that the proposed method can analyze the 2D acoustic field with epistemic uncertainty effectively,and has good prospect of engineering application.     

基于多项式混沌方法的场线耦合响应不确定度量化

在传输线场线耦合的计算中,由于辐射场可能从不同方向入射,入射方位角和入射仰角会在一定范围内变化,可以将其看作不确定变量,因此传输线的响应也呈现出不确定性。针对输入参数服从非典型分布的情况,应用多项式混沌方法对传输线场线耦合频域响应进行不确定度量化。结合入射方位角和仰角的物理意义,给出其服从的分布类型并构建相应的正交多项式基底,并对该模型的传输线方程进行多项式混沌展开。最后结合含两个不确定参数的传输线场线耦合算例,给出远端电流响应的统计信息,对比蒙特卡罗方法,验证了该方法的正确性和高效性。     

基于统计学模型的真空绝缘堆闪络概率计算分析

对比了几种不同类型的过电压因子下绝缘堆闪络概率的特点, 考虑了多层均压及圆周渡越时间后得到的闪络概率更能反映绝缘堆耐压水平;简化计算统计学经验公式中矩阵可保持绝缘堆闪络概率计算值准确性并减少过电压因子的静电场计算次数。分析在固定间隙距离下绝缘环个数与电压峰值及电场强度峰值的关系, 计算结果表明:存在最优绝缘环个数承受最高电压峰值与电场强度, 承受最大工作场强的绝缘环个数下, 工作电压幅值已降低很多。在选择绝缘环个数时应综合考虑, 该计算方法可应用于工程绝缘结构设计中合理选取绝缘环个数。