爆炸波问题中偶然不确定度的量化

复杂工程建模与模拟中始终存在不确定度,分析与辨识不确定度的来源及量化不确定度对建模与模拟可信度评估具有重要意义。为此,给出了建模与模拟中误差与不确定度的概念以及不确定度量化的过程,并以爆炸波问题为例说明量化偶然不确定度的过程,得到了爆炸波问题的期望和标准差以及激波位置的概率密度函数,验证了非嵌入多项式混沌方法在复杂非线性系统不确定度量化中的有效性。     

校准条件下的数值模拟不确定度量化方法

当存在众多不确定输入因素时,不确定度的传递分析往往导致对数值模拟不确定度的过高估计.利用校准行为能够消减系统级数值模拟中认知不确定度的客观机制,提出一个综合利用已有系统级试验对比信息和新增建模与模拟传递信息的不确定度量化方法,结合一个虚拟试验的例子对该方法进行展示和验证.     

不确定性边缘表示与提取的认知物理学方法

图像边缘检测是图像处理的一种重要技术, 其中不确定性表示与提取是关键问题之一. 在现有模拟物理学思想的相关方法基础之上, 提出了基于认知物理学的不确定性边缘表示与提取方法. 该方法利用数据场发现图像全局灰度认知, 构建图像灰度值空间到数据场势值空间的映射关系, 从场论的角度建立了可扩展的理论框架、统一了现有相关方法; 另一方面, 构造半升云模型建立云模型确定度的变化幅度与边缘像素表示与提取的内在关联关系, 最终在认知物理学核心理论的支持下实现图像不确定性边缘表示与提取. 所提出的方法时间耗费近似与图像尺寸成线性关系. 定性和定量的实验结果及分析表明, 该方法的分割效果较好, 性能稳定, 具有合理性和有效性. 关键词： 边缘检测 图像分割 云模型 数据场     

一种不确定性捆扎线束电磁耦合效应的广义等效建模方法

线束在实际布线过程中存在空间布局特性,其芯线数目大、空间任意弯曲以及位置不确定等特点给线束耦合干扰的建模与分析带来了挑战.不确定性全线束模型耦合干扰的数值仿真对计算能力提出了更高要求,甚至无法进行有效计算.因此,本文提出了不确定性捆扎弧形线束电磁耦合效应的广义简化建模方法,考虑了捆扎线束内导线相对位置的不确定性.基于高斯分布和样条插值方法,建立了不确定性捆扎线束内导线的位置,根据多导体传输线理论确立了等效线束的几何截面结构参数,通过圆弧和正弦捆扎线束数值算例验证了本文方法的有效性.     

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。     

模板方法消除FY-2辐射计可见杂散光

风云二号辐射计的可见光通道图像受到由折镜进入的一级漏射杂散光的影响,仅仅依靠光机设计已经无法完全消除.为改善图像质量提出采用图像处理方法消除杂散光.在光机建模的基础上,确定出辐射计不同工作状态的直射漏光区域分布,并变换到图像坐标系.通过理论计算确定了单像元信杂比,作为漏光模板能量系数的依据.以卷积的方法来模拟一级杂散光的叠加过程,据此原理处理了正午时刻的卫星图像.结果表明,图像主观视觉效果明显改善,检查处理前后的对比度、熵值和MTF,发现此消杂过程在改善图像质量的同时不会对有用信号产生副作用.     

爆轰模拟不确定度的量化方法

通过对数值模拟不确定度产生机制的理论分析以及对不确定度从考核区到应用区发展趋势的反演,展示数值模拟不确定度量化评估的关键技术.基于工程设计的现实需求和数值模拟中验证与确认的思想,提出数值模拟用于对爆轰系统进行科学预测时不确定度的评估框架,并结合实例对方法进行演示和验证.     

主动中子多重性法估算铀材料质量的不确定性（英文）

近年来,国际社会对核材料保护、控制和衡算日益加强。对不明材料损失量(MUF)的关注逐渐提升。铀材料质量不确定性测量在估算铀材料生产量中扮演重要角色。由于铀材料自发裂变相对较弱,主动中子多重性法被应用于估算铀材料质量。通过拟合对不同系列铀金属壳的数值模拟结果,获得了描述铀材料质量与主动中子多重性特征之间的算法和参数。得到的关系表明,可以通过分析不同重数中子多重性探测结果获得铀部件的质量。对不同探测条件下的模拟结果的定量分析,确定了探测系统设置对铀质量估算的影响,以及认知不确定性和随机不确定在估算过程中传播对质量估算的影响。对不确定度的分析获得了本文模拟采用的探测系统的最佳源强和探测时间窗设置,在此设置下,质量估算的不确定性最小。     

血糖检测中建模方法和温度引入的偶然相关研究

近红外光谱分析技术应用在血糖检测中,需要借助化学计量学方法建立模型来实现对未知样品的定量分析。在模型建立和验证的过程中通常会引入一定程度的偶然相关,从而影响模型的稳健性。采用随机数模拟光谱数据及参考浓度的研究方式,从建模波长数的选择和交互验证方法两方面考察了不同建模方法在建模的过程中存在偶然相关的概率水平,并给出了最佳的建模波长数以及最优的交互验证方法,以降低引入的偶然相关。此外通过离体实验,研究温度对葡萄糖浓度检测的影响并指导如何在实际血糖检测中降低温度引入的偶然相关。     

爆轰流体力学模型敏感度分析与模型确认

验证、确认与不确定度量化(VVUQ)是评估物理模型可信度和量化复杂工程数值模拟结果置信度的系统方法.验证是要回答数值模拟程序是否正确求解了物理模型和程序是否正确实施或给出求解模型的误差、不确定性大小及使用范围,确认是要通过数值结果回答物理模型是否反映了真实客观世界或反映真实客观世界的可信程度.文章围绕爆轰流体力学模型,剖析了模型中不确定性因素,给出了影响模拟结果不确定性的关键因素清单,并对其开展了敏感度分析,确认了模型的适应性.     

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.     

辐射不透明度计算中含温有界原子结构理论的不确定度量化

以交换势的泛函表达式为核心,分析产生原子结构理论不确定度的主要原因,阐述辐射不透明度计算中含温有界原子结构理论不确定度量化的具体步骤,给出能级、矩阵元的不确定度量化计算公式,以及判定理论模型优劣的判据.以汞、金、铁元素为例,通过数值计算,根据对比分析,验证该不确定度量化方法的可行性.     

Spectral stochastic uncertainty quantification in chemical systems

Uncertainty quantification (UQ) in the computational modelling of physical systems is important for scientific investigation, engineering design, and model validation. We have implemented an ‘intrusive’ UQ technique in which (1) model parameters and field variables are modelled as stochastic quantities, and are represented using polynomial chaos (PC) expansions in terms of Hermite polynomial functions of Gaussian random variables, and (2) the deterministic model equations are reformulated using Galerkin projection into a set of equations for the time evolution of the field variable PC mode strengths. The mode strengths relate specific parametric uncertainties to their effects on model outputs. In this work, the intrusive reformulation is applied to homogeneous ignition using a detailed chemistry model through the development of a reformulated pseudospectral chemical source term. We present results analysing the growth of uncertainty during the ignition process. We also discuss numerical issues pertaining to the accurate representation of uncertainty with truncated PC expansions, and ensuing stability of the time integration of the chemical system.     

Multifidelity Model Calibration in Structural Dynamics Using Stochastic Variational Inference on Manifolds

Bayesian techniques for engineering problems, which rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian process based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.     

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either computationally unaffordable or with limited application scope.Accordingly,a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed.The fuzziness propagation in the random reliability,which is the focus of the present study,is performed by the proposed method,in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation.First-Order,Second-Moment(FOSM)method which can be replaced by its counterparts is utilized to calculate the structural random reliability.Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.     

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.     

基于数值模拟的QMU决策体系

裕度及不确定度量化方法（Quantification of Margin and Uncertainty,QMU）能够基于裕度及其不确定度信息对系统是否达到其指标要求进行科学的判断与决策.借助新的数值模拟不确定度量化方法,建立基于数值模拟预测及其不确定度的QMU决策技术体系.结合库存产品可靠性评估的实例,展示该体系的主要思想及其实现过程.     

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.