Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

Matthias G.R. Faes; Marcos A. Valdebenito; David Moens; Michael Beer

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Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

机译：操作员标准理论作为传播混合不确定性的有效工具并计算不精确概率

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This paper presents a highly efficient and effective approach to bound the responses and probability of failure of linear systems where the model parameters are subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities or hybrid uncertainties. Typically, such computations involve solving a nested double loop problem, where the propagation of the aleatory uncertainty has to be performed for each realisation of the epistemic uncertainty. Apart from near-trivial cases, such computation is intractable without resorting to surrogate modeling schemes. In this paper, a method is presented to break this double loop by virtue of the operator norm theorem. Indeed, in case linear models are considered and under the restriction that the model definition cannot be subject to aleatory uncertainty, the paper shows that the computational efficiency, quantified by the required number of model evaluations, of propagating these parametric uncertainties can be improved by several orders of magnitude. Two case studies involving a finite element model of a clamped plate and a six-story building are included to illustrate the application of the developed technique, as well as its computational merit in comparison to existing double-loop approaches.

机译：本文提出了一种高效且有效的方法，以绑定模型参数的线性系统失败的响应和概率，其中经历了认知和杀菌性不确定性的组合。这些组合可以采用不精确的概率或混合不确定性的形式。通常，这种计算涉及解决嵌套的双回路问题，其中必须对每个认知不确定性的每个实现来执行杀菌不确定性的传播。除了近乎琐碎的情况外，这种计算是棘手的，不诉诸代理建模方案。在本文中，提出了一种通过操作员规范定理来打破这种双循环。实际上，如果考虑线性模型，在模型定义不能受到蜕膜不确定性的限制下，纸张表明，通过多个模型评估的计算效率，通过所需的模型评估量量化可以得到几个数量级。包括两个涉及夹板和六层建筑物的有限元模型的案例研究，以说明所开发技术的应用，以及与现有的双回路方法相比的计算优点。

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来源
《Mechanical systems and signal processing》 |2021年第5期|107482.1-107482.17|共17页
作者
Matthias G.R. Faes; Marcos A. Valdebenito; David Moens; Michael Beer;
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作者单位

KU Leuven Department of Mechanical Engineering Technology campus De Nayer Jan De Nayerlaan 5 St.-Katelijne-Waver Belgium Institute for Risk and Reliability Leibniz Universitaet Hannover Callinstr. 34 30167 Hannover Germany;

Universidad Tecnica Federico Santa Maria Dept. de Obras Civiles Av. Espana 1680 Valparaiso Chile;

KU Leuven Department of Mechanical Engineering Technology campus De Nayer Jan De Nayerlaan 5 St.-Katelijne-Waver Belgium;

Institute for Risk and Reliability Leibniz Universitaet Hannover Callinstr. 34 30167 Hannover Germany Institute for Risk and Uncertainty and School of Engineering University of Liverpool Peach Street Liverpool L69 7ZF UK International Joint Research Center for Engineering Reliability and Stochastic Mechanics Tongji University 1239 Siping Road Shanghai 200092 PR China;

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正文语种 eng
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Uncertainty Quantification; Imprecise probabilities; Operator norm theorem; Linear models; Decoupling;

机译：不确定性量化;不精确的概率;操作员规范定理;线性模型;去耦;

Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

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