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HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION 基于维数分解的广义多项式混沌展开的因变量下高维随机设计优化
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023043457
Dongjin Lee, S. Rahman
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引用次数: 3
BAYESIAN CALIBRATION WITH ADAPTIVE MODEL DISCREPANCY 自适应模型误差贝叶斯校正
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023046331
Nicolas Leoni, O. Le Maître, M. G. Rodio, P. Congedo
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引用次数: 0
Sensitivity analysis with correlated inputs: focus on the linear case. 具有相关输入的敏感性分析:关注线性情况。
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023042817
J. Blanchard
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引用次数: 1
Likelihood and depth-based criteria for comparing simulation results with experimental data, in support to validation of numerical simulators 将模拟结果与实验数据进行比较的基于似然和深度的标准,以支持数值模拟器的验证
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023046666
Amandine Marrel, Heloise Velardo, Antoine Bouloré
Within the framework of Best-Estimate-Plus-Uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation must be compared and validated against experimental values, when such data is available. This validation step, as part of the broader Verification, Validation and Uncertainty Quantification process, is required to ensure a reliable use of the simulator for modeling and prediction. This work aims to define quantitative criteria to support this validation for multivariate outputs, while taking into account modeling uncertainties (uncertain input parameters) and experimental uncertainties (measurement uncertainties). For this purpose, different statistical indicators, based on likelihood or statistical depths, are investigated and extended to the multidimensional case. First, the properties of the criteria are studied, either analytically or by simulation, for some specific cases (Gaussian distribution for experimental uncertainties, identical distributions of experiments and simulations, particular discrepancies). Then, some natural extensions to multivariate outputs are proposed, with guidelines for practical use depending on the objectives of the validation (strict/hard or average validation). From this, transformed criteria are proposed to make them more comparable and less sensitive to the dimension of the output. It is shown that these transformations allow for a fairer and more relevant comparison and interpretation of the different criteria. Finally, these criteria are applied to a code dedicated to nuclear material behavior simulation.
在最佳估计加不确定性方法的框架内,与数值模拟器相关的模型参数不确定性评估是安全分析的关键因素。当有实验数据时,必须将模拟的结果(或输出)与实验值进行比较和验证。这个验证步骤,作为更广泛的验证、验证和不确定度量化过程的一部分,是确保模拟器可靠地用于建模和预测所必需的。这项工作旨在定义定量标准,以支持多变量输出的验证,同时考虑到建模不确定性(不确定输入参数)和实验不确定性(测量不确定性)。为此目的,根据可能性或统计深度调查不同的统计指标,并将其扩展到多维情况。首先,对某些特定情况(实验不确定性的高斯分布,实验和模拟的相同分布,特殊差异)的准则性质进行了分析或模拟研究。然后,提出了对多变量输出的一些自然扩展,并根据验证的目标(严格/硬验证或平均验证)提供了实际使用的指导方针。在此基础上,提出了转换后的标准,使它们更具可比性,并且对输出的维度不那么敏感。报告显示,这些转变使得对不同标准的比较和解释更加公平和相关。最后,将这些准则应用于核材料行为模拟程序。
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引用次数: 0
Improving Accuracy and Computational Efficiency of Optimal Design of Experiment via Greedy Backward Approach 利用贪婪倒推法提高实验优化设计的精度和计算效率
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023046204
M. Taghizadeh, D. Xiu, Negin Alemazkoor
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引用次数: 0
CALCULATING PROBABILITY DENSITIES WITH HOMOTOPY, AND APPLICATIONS TO PARTICLE FILTERS 用同伦计算概率密度,并在粒子滤波中的应用
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-04-01 DOI: 10.1615/int.j.uncertaintyquantification.2022038553
Juan Restrepo
We explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution tofind, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution.In the context of stationary distributions that are associated with physical systems the method is an alternative way to estimate an unknown microcanonical ensemble.We make the connection between the homotopy and a dynamics problem explicit. Further, we propose a reformulation of the method that leads to a rejection sampling alternative. We derive the error incurred in computing the target distribution normalization, when sample inversion is not possible.The error in the procedure depends on the errors incurred in sample averaging and the number of stages used in thecomputational implementation of the process. However, we show that it is possible to exchange the number of homotopy stages and the total number of samples needed at each stage in order to enhance the computational efficiency of the implemented algorithm. Estimates of the error as a function of stages and sample averages are derived. These could guide computational efficiency decisions on how the calculation would be mapped to a given computer architecture.Consideration is given to how the procedure can be adapted to Bayesian estimation problems, both stationary and non-stationary. The connection between homotopy sampling and thermodynamic integration is made. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique know
我们探索了一个同伦抽样过程及其推广,它松散地建立在重要抽样的基础上,被称为退火重要抽样。该程序利用已知的概率分布,通过同伦找到目标分布的未知归一化,以及目标分布的样本。在与物理系统相关的平稳分布的背景下,该方法是估计未知微正则系综的另一种方法。我们明确了同伦与动力学问题之间的联系。此外,我们提出了一种导致拒绝抽样替代方法的重新表述。我们推导了在无法进行样本反演时计算目标分布归一化所产生的误差。过程中的误差取决于样本平均产生的误差和过程计算实现中使用的阶段数。然而,我们证明可以交换同伦阶段的数量和每个阶段所需的样本总数,以提高所实现算法的计算效率。给出了误差作为阶段函数和样本平均值的估计。这些可以指导计算效率决策,决定如何将计算映射到给定的计算机体系结构。考虑到如何程序可以适应贝叶斯估计问题,平稳和非平稳。提出了同伦采样与热力学积分之间的联系。重点放在非平稳问题上,特别是序贯估计技术
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引用次数: 0
Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling 基于重要性抽样的相关输入的面向可靠性的敏感性分析中的Shapley效应估计
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-02-25 DOI: 10.1615/int.j.uncertaintyquantification.2022043692
Julien Demange-Chryst, F. Bachoc, J. Morio
Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N-sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.
面向可靠性的敏感性分析旨在通过量化数值模型的每个输入变量对与其故障相关的感兴趣量的影响,将可靠性和敏感性分析相结合。特别是,目标灵敏度分析侧重于故障的发生,更准确地说,旨在确定哪些输入更有可能导致系统故障。Shapley效应是能够处理相关输入变量的量化全局敏感性指数。它们最近已适应目标敏感性分析框架。在本文中,我们研究了两种基于重要性抽样的这些指标的估计方案,当失效概率较小时,这两种方案比现有方案更有效。此外,还提出了对仅根据重要性采样辅助分布分布的i.i.d.输入/输出N样本的情况的扩展。这种扩展允许仅使用根据可靠性分析产生的重要性采样辅助分布分布的数据集来估计Shapley效应,而无需对数值模型进行额外调用。此外,我们还从理论上研究了一些估计量的无偏性以及重要性抽样的好处。我们还提供了数值指南,最后,实际的测试案例表明了所提出方法的实用性。
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引用次数: 2
Stochastic polynomial chaos expansions to emulate stochastic simulators 模拟随机模拟器的随机多项式混沌展开
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-02-07 DOI: 10.1615/Int.J.UncertaintyQuantification.2022042912
X. Zhu, B. Sudret
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated instead. However, due to the random nature of the model response, classical surrogate models cannot be applied directly to the emulation of stochastic simulators. To efficiently represent the probability distribution of the model output for any given input values, we develop a new stochastic surrogate model called stochastic polynomial chaos expansions. To this aim, we introduce a latent variable and an additional noise variable, on top of the well-defined input variables, to reproduce the stochasticity. As a result, for a given set of input parameters, the model output is given by a function of the latent variable with an additive noise, thus a random variable. In this paper, we propose an adaptive algorithm which does not require repeated runs of the simulator for the same input parameters. The performance of the proposed method is compared with the generalized lambda model and a state-of-the-art kernel estimator on two case studies in mathematical finance and epidemiology and on an analytical example whose response distribution is bimodal. The results show that the proposed method is able to accurately represent general response distributions, i.e., not only normal or unimodal ones. In terms of accuracy, it generally outperforms both the generalized lambda model and the kernel density estimator.
在不确定性量化的背景下,计算模型需要反复评估。这项任务对于昂贵的数值模型来说是棘手的。对于随机模拟器来说,这样的问题更加严重,因为随机模拟器的输出是给定输入参数集的随机变量。为了减轻计算负担,通常会构建和评估代理模型。然而,由于模型响应的随机性,经典的代理模型不能直接应用于随机模拟器的仿真。为了有效地表示任何给定输入值的模型输出的概率分布,我们开发了一种新的随机代理模型,称为随机多项式混沌展开。为此,我们在定义良好的输入变量之上引入了一个潜在变量和一个额外的噪声变量,以再现随机性。结果,对于给定的一组输入参数,模型输出由具有加性噪声的潜在变量的函数给出,因此是随机变量。在本文中,我们提出了一种自适应算法,该算法不需要对相同的输入参数重复运行模拟器。在数学金融和流行病学的两个案例研究中,以及在一个响应分布为双峰的分析示例中,将所提出的方法的性能与广义lambda模型和最先进的核估计器进行了比较。结果表明,所提出的方法能够准确地表示一般的响应分布,即不仅是正态分布或单峰分布。在精度方面,它通常优于广义lambda模型和核密度估计器。
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引用次数: 4
Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification 控制变分多项式混沌:高保真度不确定性量化的采样和代理的最佳融合
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-01-26 DOI: 10.1615/int.j.uncertaintyquantification.2022043638
Hang Yang, Y. Fujii, K. W. Wang, A. Gorodetsky
We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems such as automotive propulsion systems. Our approach is to build upon ideas from multifidelity uncertainty quantification to leverage the benefits of both sampling and surrogate modeling, while mitigating their downsides. In particular, the surrogate model is selected to exploit problem structure, such as smoothness, and offers a highly correlated information source to the original nonlinear dynamical system. We utilize an intrusive generalized Polynomial Chaos surrogate because it avoids any statistical errors in its construction and provides analytic estimates of output statistics. We then leverage a Monte Carlo-based Control Variate technique to correct the bias caused by the surrogate approximation error. The primary theoretical contribution of this work is the analysis and solution of an estimator design strategy that optimally balances the computational effort needed to adapt a surrogate compared with sampling the original expensive nonlinear system. While previous works have similarly combined surrogates and sampling, to our best knowledge this work is the first to provide rigorous analysis of estimator design. We deploy our approach on multiple examples stemming from the simulation of mechanical automotive propulsion system models. We show that the estimator is able to achieve orders of magnitude reduction in mean squared error of statistics estimation in some cases under comparable costs of purely sampling or purely surrogate approaches.
为了减少非线性动力系统不确定性量化的计算费用,提出了一种混合采样-代理方法。我们的动机是在复杂的机械系统,如汽车推进系统中实现快速的不确定性量化。我们的方法是建立在多保真度不确定性量化的思想基础上,利用采样和代理建模的优点,同时减轻它们的缺点。特别地,选择代理模型来开发问题的结构,如平滑性,并为原始非线性动力系统提供高度相关的信息源。我们使用侵入式广义多项式混沌代理,因为它避免了其构造中的任何统计误差,并提供了输出统计量的分析估计。然后,我们利用基于蒙特卡罗的控制变量技术来纠正由代理近似误差引起的偏差。这项工作的主要理论贡献是分析和解决了一种估计器设计策略,该策略与对原始昂贵的非线性系统进行采样相比,最优地平衡了适应代理所需的计算工作量。虽然以前的工作类似地结合了代理和抽样,但据我们所知,这项工作是第一次提供对估计器设计的严格分析。我们将我们的方法应用于来自机械汽车推进系统模型仿真的多个示例。我们表明,在纯抽样或纯代理方法的可比成本下,在某些情况下,估计器能够实现统计估计的均方误差的数量级降低。
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引用次数: 3
CONTROL VARIATES WITH A DIMENSION REDUCED BAYESIAN MONTE CARLO SAMPLER 控制变量与降维贝叶斯蒙特卡罗采样器
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2022035744
Xin Cai, Junda Xiong, Hongqiao Wang, Jinglai Jinglai
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引用次数: 0
期刊
International Journal for Uncertainty Quantification
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