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Comment On “Comparison of the V&V10.1 and V&V20 Modeling Error Quantification Procedures for the V&V10.1 Example” 对“V&V10.1实例中V&V10.1与V&V20建模误差量化程序的比较”的评论
IF 0.6 Q3 Mathematics Pub Date : 2022-07-28 DOI: 10.1115/1.4055105
P. Roache
Not Applicable
不适用
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引用次数: 0
Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask 乏核燃料桶分析灵敏度分析
IF 0.6 Q3 Mathematics Pub Date : 2022-07-15 DOI: 10.1115/1.4055013
T. Remedes, S. Ramsey, J. Baciak
Nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies which previously pioneered nuclear engineering are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem, and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the 1D cylindrical monoenergetic neutron diffusion equation using the Forward Sensitivity Analysis Procedure developed by D. Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.
核科学与工程是一个由日益强大的计算工具所主导的计算研究领域。因此,以前作为核工程先驱的分析性研究越来越被视为次要的或不必要的。然而,降低保真度模型的解析解可以提供有关问题的潜在物理的重要信息,并有助于指导计算研究。同样,人们对敏感性分析研究的兴趣也在增加。这些研究通常使用计算工具。然而,提供相关分析模型的补充敏感性研究可以导致对问题的更深入的分析。本文采用D. Cacuci开发的前向灵敏度分析程序对一维圆柱形单能中子扩散方程进行了灵敏度分析。此外,这些结果应用于乏核燃料桶的降低保真度模型,证明了如何通过补充分析灵敏度分析来改进计算分析。
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引用次数: 0
A Methodology for the Efficient Quantification of Parameter and Model Uncertainty 一种有效量化参数和模型不确定性的方法
IF 0.6 Q3 Mathematics Pub Date : 2022-05-18 DOI: 10.1115/1.4054575
R. Feldmann, C. M. Gehb, M. Schäffner, T. Melz
Complex structural systems often entail computationally intensive models that require efficient methods for statistical model calibration due to the high number of required model evaluations. In this paper, we present a BAYESIAN inference-based methodology for efficient statistical model calibration that builds upon the combination of the speed in computation of a low-fidelity model with the accuracy of the computationally intensive high-fidelity model. The proposed two-stage method incorporates the adaptive METROPOLIS algorithm and a GAUSSIAN process (GP)-based adaptive surrogate model as low-fidelity model. In order to account for model uncertainty, we incorporate a GP-based discrepancy function into the model calibration. By calibrating the hyperparameters of the discrepancy function alongside the model parameters, we prevent the results of the model calibration to be biased. The methodology is illustrated by the statistical model calibration of a damping parameter in the modular active spring-damper system, a structural system developed within the collaborative research center SFB 805 at the Technical University of Darmstadt. The reduction of parameter and model uncertainty achieved by application of our methodology is quantified and illustrated by assessing the predictive capability of the mathematical model of the modular active spring-damper system.
复杂的结构系统通常需要计算密集型模型,由于需要大量的模型评估,这些模型需要高效的统计模型校准方法。在本文中,我们提出了一种基于贝叶斯推理的有效统计模型校准方法,该方法建立在低保真度模型的计算速度与计算密集型高保真度模型的精度的结合之上。所提出的两阶段方法结合了自适应METROPOLIS算法和基于高斯过程(GP)的自适应代理模型作为低保真度模型。为了考虑模型的不确定性,我们在模型校准中加入了基于GP的差异函数。通过与模型参数一起校准差异函数的超参数,我们防止了模型校准的结果有偏差。该方法通过模块化主动弹簧阻尼器系统中阻尼参数的统计模型校准来说明,该系统是达姆施塔特工业大学SFB 805合作研究中心开发的一个结构系统。通过评估模块化主动弹簧-阻尼器系统数学模型的预测能力,量化并说明了应用我们的方法所实现的参数和模型不确定性的降低。
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引用次数: 0
Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis 基于时空联合收敛分析的驼鹿/野牛热传导求解方法验证
IF 0.6 Q3 Mathematics Pub Date : 2022-03-29 DOI: 10.1115/1.4054216
A. Toptan, N. Porter, J. Hales, Wen Jiang, B. Spencer, S. Novascone
Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process–called code verification–ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second order accurate finite elements and a variety of time integration schemes. These results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.
Bison是一个计算物理代码,使用有限元方法对核燃料的热机械响应进行建模。由于Bison用于为高后果决策提供信息,因此其计算结果的可靠性和预测性很重要。评估模拟工具的可靠性和预测能力的一个重要步骤是验证过程,它量化了离散解中相对于数学模型精确解的数值误差。验证过程中的一个步骤——称为代码验证——确保实现的数值算法是底层数学模型的忠实表示,包括偏微分或积分方程、初始和边界条件以及辅助关系。本文将代码验证过程应用于Bison中的时空热传导问题。在空间和时间上同时细化离散化,以揭示求解的空间和时间分量之间相互作用的数值算法中的任何潜在错误。对于每个验证问题,对于一阶和二阶精确有限元以及各种时间积分方案,都证明了正确的空间和时间精度顺序。这些结果有力地证明了求解时空问题的Bison数值算法可靠地代表了MOOSE中的基本数学模型。所选择的测试问题也可以用于数值求解传导或扩散的其他模拟工具。
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引用次数: 1
Comparison of the V&V10.1 and V&V20 Modeling Error Quantification Procedures for the V&V10.1 Example V&V10.1和V&V20建模误差量化程序的比较
IF 0.6 Q3 Mathematics Pub Date : 2022-02-16 DOI: 10.1115/1.4053881
L. Eça, K. Dowding, D. Moorcroft, U. Ghia
The determination of the transverse tip deflection of an elastic, hollow, tapered, cantilever, box beam under a uniform loading applied over half the length of the beam presented in the V&V10.1 standard is used to compare the application of the validation procedures presented in the V&V10.1 and V&V20 standards. Both procedures aim to estimate the modeling error of the mathematical/computational model used in the simulations taking into account the variability of the modulus of elasticity of the material used in the beam and the rotational flexibility at the clamped end of the beam. The paper discusses the four steps of the two error quantification procedures: 1- characterization of the problem including all the assumptions and approximations made to obtain the experimental and simulation data; 2-selection of the validation variable; 3- determination of the different quantities required by the validation metrics in the two error quantification procedures; 4- outcome of the two validation procedures and its discussion. The paper also discusses the inclusion of experimental, input and numerical uncertainties (assumed or demonstrated to be negligible in V&V10.1) in the two validation approaches. This simple exercise shows that different choices are made in the two alternative approaches, which lead to different ways of characterizing the modeling error. The topics of accuracy requirements and validation comparisons (model acceptance/rejection) for engineering applications are not addressed in this paper.
在超过V&V10.1标准中规定的梁长度一半的均匀载荷下,弹性、空心、锥形、悬臂、箱形梁的横向尖端挠度的测定用于比较V&V10.1和V&V20标准中提出的验证程序的应用。这两个程序都旨在估计模拟中使用的数学/计算模型的建模误差,同时考虑到梁中使用的材料的弹性模量的可变性和梁夹紧端的旋转灵活性。本文讨论了两个误差量化过程的四个步骤:1 .问题的表征,包括为获得实验和仿真数据所做的所有假设和近似;2-验证变量的选择;确定两个误差量化程序中验证指标所需的不同数量;两个验证程序的结果及其讨论。本文还讨论了两种验证方法中包含的实验、输入和数值不确定性(假设或证明在V&V10.1中可以忽略不计)。这个简单的练习表明,在两种可选方法中做出了不同的选择,从而导致表征建模误差的不同方法。本文没有讨论工程应用的精度要求和验证比较(模型接受/拒绝)的主题。
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引用次数: 0
Inferring Extreme Values from Measured Averages Under Deep Uncertainty 从深度不确定性下的测量平均值推断极值
IF 0.6 Q3 Mathematics Pub Date : 2022-01-26 DOI: 10.1115/1.4053411
Y. Ben-Haim
Averages are measured in many circumstances for diagnostic, predictive, or surveillance purposes. Examples include: average stress along a beam, average speed along a section of highway, average alcohol consumption per month, average GDP over a large region, a student's average grade over 4 years of study. However, the average value of a variable reveals nothing about fluctuations of the variable along the path that is averaged. Extremes – stress concentrations, speeding violations, binge drinking, poverty and wealth, intellectual incompetence in particular topics – may be more significant than the average. This paper explores the choice of design variables and performance requirements to achieve robustness against uncertainty when interpreting an average, in face of uncertain fluctuations of the averaged variable. Extremes are not observed, but robustness against those extremes enhances the ability to interpret the observed average in terms of the extremes. The opportuneness from favorable uncertainty is also explored. We examine the design of a cantilever beam with uncertain loads. We derive 4 generic propositions, based on info-gap decision theory, that establish necessary and sufficient conditions for robust or opportune dominance, and for sympathetic relations between robustness to pernicious uncertainty and opportuneness from propitious uncertainty.
平均值在许多情况下都是为了诊断、预测或监测目的而测量的。示例包括:横梁上的平均应力、高速公路上的平均速度、每月平均饮酒量、大区域的平均GDP、学生4年学习的平均成绩。然而,变量的平均值没有显示出变量沿着平均路径的波动。极端情况——压力集中、超速驾驶、酗酒、贫困和财富、在特定话题上的智力无能——可能比平均水平更重要。本文探讨了在解释平均值时,面对平均变量的不确定波动,设计变量和性能要求的选择,以实现对不确定性的鲁棒性。没有观测到极值,但对这些极值的鲁棒性增强了根据极值解释观测到的平均值的能力。还探讨了有利的不确定性带来的时机。我们研究了具有不确定载荷的悬臂梁的设计。基于信息间隙决策理论,我们导出了4个一般命题,这些命题为鲁棒或适时优势以及对有害不确定性的鲁棒性和对有利不确定性的适时性之间的同情关系建立了必要和充分的条件。
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引用次数: 1
Estimating Discretization Error with Preset Orders of Accuracy and Fractional Refinement Ratios 预估离散化误差的精度和分数精化比
IF 0.6 Q3 Mathematics Pub Date : 2022-01-01 DOI: 10.1115/1.4056491
S. C. Y. Lo
Solution verification is crucial for establishing the reliability of simulations. A central challenge is to estimate the discretization error accurately and reliably. Many approaches to this estimation are based on the observed order of accuracy; however, it may fail when the numerical solutions lie outside the asymptotic range. Here we propose a grid refinement method which adopts constant orders given by the user, called the Prescribed Orders Expansion Method (POEM). Through an iterative procedure, the user is guaranteed to obtain the dominant orders of the discretization error. The user can also compare the corresponding terms to quantify the degree of asymptotic convergence of the numerical solutions. These features ensure that the estimation of the discretization error is accurate and reliable. Moreover, the implementation of POEM is the same for any dimensions and refinement paths. We demonstrate these capabilities using some advection and diffusion problems and standard refinement paths. The computational cost of using POEM is lower if the refinement ratio is larger; however, the number of shared grid points where POEM applies also decreases, causing greater uncertainty in the global estimates of the discretization error. We find that the proportion of shared grid points is maximized when the refinement ratios are in a certain form of fractions. Furthermore, we develop the Method of Interpolating Differences between Approximate Solutions (MIDAS) for creating shared grid points in the domain. These approaches allow users of POEM to obtain a global estimate of the discretization error of lower uncertainty at a reduced computational cost.
解的验证是建立仿真可靠性的关键。一个核心的挑战是准确可靠地估计离散误差。这种估计的许多方法都是基于观察到的精度顺序;然而,当数值解超出渐近范围时,它可能失效。本文提出了一种采用用户给出的常数阶数的网格细化方法,称为规定阶数展开法(POEM)。通过迭代过程,保证用户得到离散误差的主导阶。用户还可以比较相应的项来量化数值解的渐近收敛程度。这些特点保证了离散化误差估计的准确性和可靠性。此外,对于任何维度和细化路径,POEM的实现都是相同的。我们使用一些平流和扩散问题以及标准细化路径来演示这些功能。细化比越大,使用POEM的计算成本越低;然而,应用POEM的共享网格点的数量也会减少,这在离散化误差的全局估计中造成了更大的不确定性。我们发现,当细化比例为一定的分数形式时,共享网格点的比例最大。此外,我们开发了近似解之间的插值差异方法(MIDAS),用于在域中创建共享网格点。这些方法使POEM的用户能够以较少的计算成本获得较低不确定性的离散化误差的全局估计。
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引用次数: 0
Verification of a Specialized Hydrodynamic Simulation Code for Modeling Deflagration and Detonation of High Explosives 高烈度炸药爆燃爆轰模拟专用水动力模拟程序的验证
IF 0.6 Q3 Mathematics Pub Date : 2021-12-21 DOI: 10.1115/1.4053340
Stephen A. Andrews, T. Aslam
A specialized hydrodynamic simulation code has been developed to simulate one-dimensional unsteady problems involving the detonation and deflagration of high explosives. To model all the relevant physical processes in these problems, a code is required to simulate compressible hydrodynamics, unsteady thermal conduction and chemical reactions with complex rate laws. Several verification exercises are presented which test the implementation of these capabilities. The code also requires models for physics processes such as equations of state and conductivity for pure materials and mixtures as well as rate laws for chemical reactions. Additional verification tests are required to ensure these models are implemented correctly. Though this code is limited in the types of problems it can simulate, its computationally efficient formulation allow it to be used in calibration studies for reactive burn models for high explosives.
一个专门的水动力模拟程序已经开发出来,用于模拟涉及高烈性炸药爆轰和爆燃的一维非定常问题。为了模拟这些问题中所有相关的物理过程,需要一个程序来模拟具有复杂速率定律的可压缩流体力学、非定常热传导和化学反应。提出了几个验证练习,以测试这些能力的执行情况。该规范还需要物理过程的模型,如纯材料和混合物的状态方程和电导率方程,以及化学反应的速率定律。需要额外的验证测试来确保这些模型被正确地实现。虽然这个程序在模拟的问题类型上受到限制,但其计算效率高的公式允许它用于高能炸药反应性燃烧模型的校准研究。
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引用次数: 4
Uncertainty Quantification of Time-Dependent Quantities in a System with Adjustable Level of Smoothness 平滑度可调系统中时变量的不确定性量化
IF 0.6 Q3 Mathematics Pub Date : 2021-12-06 DOI: 10.1115/1.4053161
Marks Legkovskis, P. Thomas, M. Auinger
We summarise the results of a computational study involved with Uncertainty Quantification (UQ) in a benchmark turbulent burner flame simulation. UQ analysis of this simulation enables one to analyse the convergence performance of one of the most widely-used uncertainty propagation techniques, Polynomial Chaos Expansion (PCE) at varying levels of system smoothness. This is possible because in the burner flame simulations, the smoothness of the time-dependent temperature, which is the study's QoI is found to evolve with the flame development state. This analysis is deemed important as it is known that PCE cannot accurately surrogate non-smooth QoIs and thus perform convergent UQ. While this restriction is known and gets accounted for, there is no understanding whether there is a quantifiable scaling relationship between the PCE's convergence metrics and the level of QoI's smoothness. It is found that the level of QoI-smoothness can be quantified by its standard deviation allowing to observe the effect of QoI's level of smoothness on the PCE's convergence performance. It is found that for our flow scenario, there exists a power-law relationship between a comparative parameter, defined to measure the PCE's convergence performance relative to Monte Carlo sampling, and the QoI's standard deviation, which allows us to make a more weighted decision on the choice of the uncertainty propagation technique.
我们总结了在基准湍流燃烧器火焰模拟中涉及不确定性量化(UQ)的计算研究结果。该仿真的UQ分析使人们能够分析最广泛使用的不确定性传播技术之一,多项式混沌展开(PCE)在不同系统平滑水平下的收敛性能。这是可能的,因为在燃烧器火焰模拟中,发现随时间变化的温度的平滑度,即研究的qi,随着火焰的发展状态而变化。这种分析被认为是重要的,因为众所周知,PCE不能准确地代替非平滑的qi,从而执行收敛的UQ。虽然这一限制是已知的,并得到了解释,但PCE的收敛指标和qi的平滑水平之间是否存在可量化的缩放关系,我们不得而知。研究发现,qi平滑程度可以通过其标准差来量化,从而可以观察到qi平滑程度对PCE收敛性能的影响。研究发现,在我们的流场景中,用于衡量PCE相对于蒙特卡罗采样的收敛性能的比较参数与qi的标准差之间存在幂律关系,这使得我们可以在不确定性传播技术的选择上做出更加权的决策。
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引用次数: 0
Developing Uncertainty Quantification Strategies in Electromagnetic Problems Involving Highly Resonant Cavities 在涉及高谐振腔的电磁问题中发展不确定性量化策略
IF 0.6 Q3 Mathematics Pub Date : 2021-12-01 DOI: 10.1115/1.4051906
S. Campione, J. A. Stephens, Nevin Martin, Aubrey Eckert, L. Warne, Gabriel Huerta, R. Pfeiffer, Adam Jones
High-quality factor resonant cavities are challenging structures to model in electromagnetics owing to their large sensitivity to minute parameter changes. Therefore, uncertainty quantification (UQ) strategies are pivotal to understanding key parameters affecting the cavity response. We discuss here some of these strategies focusing on shielding effectiveness (SE) properties of a canonical slotted cylindrical cavity that will be used to develop credibility evidence in support of predictions made using computational simulations for this application.
由于高质量因子谐振腔对微小的参数变化具有很大的敏感性,因此在电磁学中建模具有挑战性。因此,不确定度量化(UQ)策略对于理解影响空腔响应的关键参数至关重要。我们在这里讨论了一些这些策略,重点是典型开槽圆柱腔的屏蔽效率(SE)特性,这些策略将用于开发可信的证据,以支持使用该应用的计算模拟所做的预测。
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引用次数: 0
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Journal of Verification, Validation and Uncertainty Quantification
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